[David Cooper (OP)]

Mod edit: Topic split off Can you measure the one way speed of light without synchronised clocks?
https://www.thenakedscientists.com/forum/index.php?topic=82170

Imagine lots of clocks being made immediately after the big bang which are then separated from each other by the expansion of space, leaving us with a universe full of clocks rather than galaxies, but all spread out through space evenly. We could take any pair of these clocks and accelerate them towards each other with equal force, and when they meet up they would both agree about what the time is. But that would only apply if the clocks were all at rest in the expanding space. What happens if they were all moving through space at high speed in the same direction? Well, in some cases when you bring two of these clocks together, you’ll be accelerating one and decelerating the other, so they will not agree on the time when they meet up. If those clocks existed, this would provide us with a means to pin down the absolute speeds of motion of the clocks, and once we have those, measuring the one-way speed of light relative to a host of different types of apparatus (and knowing that you're getting the correct answer) becomes trivial..

(We can’t go back to the big bang to place lots of clocks there to do that experiment for real, but space is still expanding, and it’s doing that here. This means that we should be able to carry out essentially the same experiment right here and now, as I set out recently elsewhere.)

If you’re having difficulty understanding why the clocks in some cases would have to go out of sync when you bring them together, this must happen in order to conform to the rules of the twins paradox. Imagine that when the clocks are created right back at the time of the big bang, they all send out watches in two opposite directions. Set A of these watches are all moving in the same direction as each other and at the same speed, while set B of watches were sent out at the same speed but in the opposite direction. Let’s suppose that the clocks are stationary and the watches are moving. If a set A watch meets a set B watch, they will agree with each other about the time, but if any watch meets a clock, the time on the watch will lag behind the time on the clock due to its speed of movement through space. How can I prove that? Well, in a case where a set-A watch passes a clock, then passes a set-B watch later on, and then the set-B watch passes the clock later still, we have the twins paradox experiment being carried out by those three timers. We could have scenarios where the clocks and set-A watches are both ticking at the same rate (which means the clocks aren’t at rest), but the set-B watches would have to be ticking slower than that in order to produce the required result for the twins paradox. Once you understand the necessity for that to happen, you should then be able to see that when clocks/watches pass each other, the amount by which they disagree on the time provides information about their absolute speeds of motion through space. Relativity is cracked wide open by this.

[jeffreyH]

David, you really have cracked the art of unnecessarily complicating an issue.

[Halc]

Imagine lots of clocks being made immediately after the big bang which are then separated from each other by the expansion of space …
If those clocks existed, this would provide us with a means to pin down the absolute speeds of motion of the clocks, and once we have those, measuring the one-way speed of light relative to a host of different types of apparatus (and knowing that you're getting the correct answer) becomes trivial..

There are such clocks (you can look at the apparent ages of the galaxies in various directions with similar redshift).  This cosmological frame is well known as is our motion relative to it (known as peculiar motion). But the frame isn’t inertial except locally, so the usual operations one can perform with objects in inertial frames don’t work. In particular, the peculiar velocity an object will degrade over time, barring external forces pushing it along. Newton’s laws  of motion don’t apply to such a frame. An illustration of this below.

Imagine that when the clocks are created right back at the time of the big bang, they all send out watches in two opposite directions. Set A of these watches are all moving in the same direction as each other and at the same speed, while set B of watches were sent out at the same speed but in the opposite direction.

There is no space at the big bang, so no concept of speed. The watches will just be right by some other clock going in the same direction, and thus none of them will have any peculiar velocity.
So let’s change it just a tiny bit and wait one second.  All the clocks are created at the big bang, and one second later, they all send out watches in random opposite directions, all synced at one second. Say they are ejected at half light speed, and let’s keep it simple and say expansion is flat: no acceleration or deceleration. In reality, there was significant slowing of exansion at the one-second time.
So there’s our reference clock X1, and a second clock X2 receding from X1 at half light speed. X1 now ejects a pair of watches, one of which is chasing X2.  The two are relatively stationary (their proper separation over time remains fixed) and 150,000 km apart, but X2 (all the X clocks) have zero peculiar velocity, which all the watches have a peculiar velocity of 0.5c.  But the watch and X2 will remain forever 150,000 km apart, so an hour later, the watch is already almost stationary.  This is what I mean by its speed (relative to the cosmological frame) degrading over time.  So any object today with significant peculiar velocity has to have been accelerated somewhat recently. Nothing can have retained high speed from long ago. So yes, you could have a universe of clocks all going north at some stupid high speed, but only by waiting until recently and then accelerating them.  This of course would violate conservation of momentum, so the cosmological frame is actually easily determined simply by noting the average momentum of the stuff all around us. The larger the radius of space you include in that average, the more accurate the measurement. Go all the way to the radius of the visible universe and the measurement is accurate down to a few km/sec.

If a set A watch meets a set B watch, they will agree with each other about the time, but if any watch meets a clock, the time on the watch will lag behind the time on the clock due to its speed of movement through space. How can I prove that?

If the watches were ejected at time zero, there would be no meeting of anything. Any watch in the presence of a clock has always been in its presence.  If they were ejected say one second after the big bang, then yes, they’d meet clocks but the time difference will be off by less than a second. It was moving at a significant speed for such a very short time and had no real time to accumulate any serious dilation.

Well, in a case where a set-A watch passes a clock, then passes a set-B watch later on, and then the set-B watch passes the clock later still, we have the twins paradox experiment being carried out by those three timers.

That analysis works if the watches were delay ejected. It doesn’t work if they were immediately ejected since they would never cross paths with a clock. All the watches would have zero peculiar velocity and would not meet anything that hasn’t always been in its presence.

[David Cooper (OP)]

Yes, per RoS, a rigid rotating cylinder will be twisted relative to a frame in which it has linear motion along its axis of rotation, which is not immediately intuitive.

I should add that if you're travelling with it you won't be able to measure the twisting due to Doppler-shift on the light coming from the two ends, and the atoms in the shaft are "fooled" in the same way with their forces applying to the ones around them, still "thinking" that they're the same distance away from their neighbours regardless of the amount or lack of twist.

There is no space at the big bang, so no concept of speed. The watches will just be right by some other clock going in the same direction, and thus none of them will have any peculiar velocity.
So let’s change it just a tiny bit and wait one second.

At the start of an earlier paragraph I said "Imagine lots of clocks being made immediately after the big bang". That word "after" indicates a delay before the clock creation that could be as little as a second, but we could give it a year or more to put some space between all the clocks: if our set A and B watches are sent out at relativistic speed it's sufficient for the clocks to be created early on. We could also just have trillions of clocks created at that moment and sent off in random directions at random speeds. Some of them can later be classed as set A watches, set B watches and set C (clocks). If we keep that universe sufficiently empty, the clocks will soon be far enough apart for their gravitational pull on each other to be irrelevant, so they won't be pulled off course and won't clump together.

This is what I mean by its speed (relative to the cosmological frame) degrading over time. ... Nothing can have retained high speed from long ago.

Well, if that second statement was correct, you'd have identified another way of pinning down absolute speed in an expanding universe because all the clocks would automatically slow down until they're at rest. You would eventually reach a point where the clocks are so spread out that none of them can pass each other any more as they aren't able to close the gaps faster than the spaces between them are expanding, but you've missed something important: they still have their initial speeds of motion through space, and if we go back to an earlier time when they are still able to pass each other, set A watches will continue to pass set B watches at the same relative speed as they did early on: that speed through space does not degrade. The result is that we can continue to have an A, B and C clock carry out a twins paradox experiment at any time up until clocks can no longer meet, and those twins paradox experiments can be of very short duration.

So any object today with significant peculiar velocity has to have been accelerated somewhat recently. Nothing can have retained high speed from long ago.

This too makes it clear that you've miscalculated: for all those ancient speeds to have been lost while the clocks are still able to pass each other, they would have to have slowed to a lower absolute speed, all homing in on being at rest. That won't actually happen, but if it did you would have found another way to pin down absolute speeds. In reality the speeds are maintained and the differences in the times on passing clocks reveals their absolute speeds (or one component of them - you still need it for another two dimensions before you have the correct figure for it, but you'd get that from cases of clocks passing each other in other directions).

If they were ejected say one second after the big bang, then yes, they’d meet clocks but the time difference will be off by less than a second. It was moving at a significant speed for such a very short time and had no real time to accumulate any serious dilation.

After 14 billion years there would still be watches passing clocks at the same relative speed as was happening when the universe was two seconds old, (assuming no collisions or slowing from dust, though in this thought experiment we can use infinitesimally small clocks and we can create and set them moving apart after a year after the big bang.) With set A watches moving at 0.866c relative to the clocks, and set B watches doing the same in the opposite direction and with those relative speeds always being maintained at moments where they're passing each other, we will have clocks registering 14 billion years passing while the watches passing them have only counted up 7 billion years if the clocks are at rest in space. If we have set A watches at rest instead, then they will have registered 14 billion years passing when they pass clocks that have at that moment registered 7 billion years passing, and when set  A watches pass set B watches with the As registering 14 billion years, the Bs will only have registered 2 billion years passing. If you look at our universe today it should be obvious that watches moving at 0.866c today would still be passing clocks here if enough were created at the start for them to be sufficiently well distributed, and they would not have lost any of that relative speed to the expansion of space.

But suppose I'm wrong. Light loses energy to expansion and gets red shifted - it doesn't slow down, but it loses energy. Does matter lose energy in the same way or does it slow down. You can't red shift matter by spreading it out as it will continue to pull back to its preferred length in a way that light doesn't do, but how could it slow down by being stretched if it keeps pulling back to the original length? If it's at rest and is stretched, it will pull back together without changing its speed, so it can't be losing energy to the expansion. That means the expansion has to do work. Well, that's a nice spinoff issue to explore.

For now though, let's just think down a path where there is slowing of objects caused by expansion. (I don't think there will be, but I can't rule out the possibility, so lets work to the premise that there is such slowing.) The watches would all slow down closer to being at rest, allowing us to pin absolute speeds down to a reduced range just by doing that, but set A or B or both would also have spent a considerable amount of their past moving at high relativistic speed, leading to them recording a lot less time passing than the clocks. They may be passing the clocks slowly after 14 billion years, but their timings could still differ by millions of years (or tens or hundreds of millions of years) rather than billions, but even in the worst case scenario that would still reveal extremely precise information about their absolute speeds, so the method would work regardless. What we need to do now is carry out an equivalent experiment in a region of expanding space today, and I've already shown how that could be done. (If there is no local expansion, then there would need to be plate boundaries between galaxies where the expansion happens, and while that used to be what physicists thought was happening, they later ruled it out and currently believe that the expansion is happening smoothly everywhere [though not necessarily uniformly].)

[Halc]

Well, if that second statement was correct, you'd have identified another way of pinning down absolute speed in an expanding universe because all the clocks would automatically slow down until they're at rest.

The physics community calls it peculiar velocity. If it makes you happy to call it absolute speed, go for it. It is very much a preferred coordinate system since any pair of observers anywhere can find it without communication. Yes, all the galaxies have nearly zero peculiar velocity, with what they have being due to recent accelerations towards nearby masses, not due to anything imparted near the time of the big bang.
There are several ways to pin it down, but CMB isotropy has always been the simplest.

we could give it a year or more to put some space between all the clocks

A year is fine

You would eventually reach a point where the clocks are so spread out that none of them can pass each other any more as they aren't able to close the gaps faster than the spaces between them are expanding

With the exception of the addition of dark energy, any objects decreasing their proper separation will forever continue to decrease their proper separation. Expansion cannot reverse that. If expansion is outpacing peculiar motion, then it always was from the moment of last proper acceleration.
Dark energy is the exception to this, but I thought we were considering a reasonably simple case of flat expansion neither accelerating nor decelerating.

but you've missed something important: they still have their initial speeds of motion through space, and if we go back to an earlier time when they are still able to pass each other, set A watches will continue to pass set B watches at the same relative speed as they did early on

No they don’t. Their peculiar velocities drop quickly, as I’ve pointed out in prior posts.
Suppose comoving (‘stationary’) primary clocks P, Q,R, situated such that their proper separation increases at a rate of 1.094 light seconds per second. Q is our observer. 1.094c is not a velocity as measured in an inertial coordinate system. It is a recession rate between two ‘stationary’ objects.
At T=1 year, P and R each launch at Q at 0.8c an A and B clock respectively. These two clocks get to Q after 13.8 billion years, are stationary to an absurd number of digits, and are slow by 8 months. The majority of the dilation takes place in the first year or two after being fired off. After that, their peculiar velocities have dropped to a point where time dilation fades away.
Figuring that out requires some interesting coordinate changes from comoving coordinates to inertial coordinates.

for all those ancient speeds to have been lost while the clocks are still able to pass each other, they would have to have slowed to a lower absolute speed, all homing in on being at rest.

I perhaps cannot convince you of this, but your mistake seems to be applying Newtons laws of inertial motion to a non inertial coordinate system. How do you defend this assertion?

With set A watches moving at 0.866c relative to the clocks, and set B watches doing the same in the opposite direction and with those relative speeds always being maintained ...

But those speeds are maintained only in Minkowski physics, not in the expanding metric.

But suppose I'm wrong. Light loses energy to expansion and gets red shifted - it doesn't slow down, but it loses energy.

Light only loses energy relative to the cosmological (or 'comoving') frame, not in an inertial one. Non-inertial frames play by different rules. In some non-inertial frames, moving things increase in speed. Light might stop, turn around, and go back the way it came.

About 2 3/4 BLY away there’s a galaxy receding from us at 0.2c (inertial coordinates). I fire a rock at it at 0.2c. At what point is it going to accelerate and actually begin to catch up to that galaxy?  It will never catch up to it, and that galaxy is ‘stationary’ (cosmological coordinates). Saying that it not only will, but will pass by it at 0.2c, is a violation of the inertial laws of motion.

I had trouble looking for a reference discussing this. Did find this one where somebody asks “I've read that the momentum of particles declines due to the universe's expansion. " but I wish he’d show where he read that. The reply confirms it and goes into the math which is over my head.
https://physics.stackexchange.com/questions/221231/in-what-manner-does-momentum-of-a-particle-with-mass-decrease-due-to-spatial-exp

[David Cooper (OP)]

The physics community calls it peculiar velocity. If it makes you happy to call it absolute speed, go for it.

For the content of the universe to slow to that peculiar velocity or absolute speed automatically rejects STR. If the sets A, B and C all end up at rest relative to each other, some have lost more speed than others, and the ones that have lost the most speed will have clocks with the least time recorded on them. The difference would show, and they'd all end up practically at rest too.

but you've missed something important: they still have their initial speeds of motion through space, and if we go back to an earlier time when they are still able to pass each other, set A watches will continue to pass set B watches at the same relative speed as they did early on

No they don’t. Their peculiar velocities drop quickly, as I’ve pointed out in prior posts.

I see it now. If I roll a ball along an expanding track where the track expands at a particular point - let's make it telescopic - the ball runs up to the place where the expansion occurs and it's going at a certain rate relative to the track, then it moves onto the part that's coming out from inside and it's now moving at a lower speed relative to the part of the track it's gone onto, so its speed relative to that has gone down. So, if that's the mechanism, then with an expanding track all balls rolling along it will end up at rest relative to the local track. So, the content of expanding space (ignoring radiation) will end up close to being at rest, and that means that when a particle in a particle accelerator is made to move at 0.99c relative to us, it really is moving close to the speed of light and there is no possibility that we are the ones moving at close to the speed of light while that particle is at rest.

The problem here is that this already rules out STR. For STR to be viable, that slowing down of material until it's all close to being at rest simply could not happen. The set A and set B watches have slowed down and ended up at rest relative to the clocks, or alternatively, if the set A watches were stationary to begin with, then the clocks and set B watches have slowed down instead with the set B watches slowing most. In these two rival cases, there would be different timing differences which would tell you which ones were closest to being at rest initially. They might now be essentially at rest and no longer passing each other, but you could still find out what the timing differences are by comparing different timers near to each other.

for all those ancient speeds to have been lost while the clocks are still able to pass each other, they would have to have slowed to a lower absolute speed, all homing in on being at rest.

I perhaps cannot convince you of this, but your mistake seems to be applying Newtons laws of inertial motion to a non inertial coordinate system. How do you defend this assertion?

I didn't think that matter would slow down in expanding space, but I win both ways because if it does, it still reveals that there are absolute speeds, so it never bothered me whether they slow down or not - I'm happy with it either way, and now it looks as if they do slow down, which is absolutely fine with me. Going back to the telescopic track, a ball sitting on the track and not running along it will remain at rest relative to the track. A ball running along the track will slow down and end up almost at rest too. With matter in expanding space doing the same thing, that puts almost all of it almost at rest, apart from the small amount being jetted out of quasars and the like at relativistic speed.

I'm quite happy now to go accept that things slow down in expanding space - you've helped resolve that for me. The experiment reveals absolute speed by reducing the speed of stuff closer and closer to absolute rest in the local space fabric, so we still reveal absolute speeds approximately, and with the timers in the thought experiment we could narrow it down further by looking at which clocks have recorded the most time passing, because those are the ones closest to being completely stationary as the started out that way.

So, we have a theoretical method for pinning down absolute speed regardless, and it shows them in two different ways: the timing differences and the slowing of most matter to rest. The next step is to exploit the ongoing expansion of space to measure its local expansion rate, and, if it is expanding here, to use that to pin down the absolute speed of the measuring apparatus and then use the result to measure the one-way speed of light relative to the apparatus.

By putting two clocks a certain distance apart and allowing space to expand between them, but in this case we aren't moving the clocks relative to each other, so we don't need to care about their speed through space being reduced by by the expansion. If they're both at rest to begin with, they remain at rest at the end. If they're both moving at high speed to the left to begin with, they're still both moving at high speed to the left when it ends, and if they've lost a tiny amount of that, it doesn't matter: they will both lose exactly the same amount as each other through that process. If the clocks are at rest in space, they will retain their synchronisation (which was originally set by having a comoving observer sene out a signal from half way between them - their signals at the end of the experiment will reach the central observer simultaneously). If the clocks are moving to the left at high speed, they both have to send a signal an extra distance across the added space between them back to the observer at the midpoint between them, and that signal crosses that extra distance in opposite directions with one taking longer to do so than the other, leading to them not reaching the observer simultaneously. That allows their absolute speed to be measured, and if it comes out as non-zero, we can then use that information to measure a one-way speed of light relative to the clocks which is not c. If it doesn't come out as non-zero, then either there is no local expansion or the apparatus was at rest, in which case we can redo the experiment after accelerating the apparatus to a different speed, at which point we will either prove that there is no local expansion (though we'd have to do this in multiple directions to be sure of that), or we would then be able to measure a non-zero one-way speed of light relative to the apparatus with it moving at its new speed.

[Halc]

I see it now. If I roll a ball along an expanding track where the track expands at a particular point - let's make it telescopic - the ball runs up to the place where the expansion occurs and it's going at a certain rate relative to the track, then it moves onto the part that's coming out from inside and it's now moving at a lower speed relative to the part of the track it's gone onto, so its speed relative to that has gone down.

I find no fault with that analogy.  The number of places where the telescoping occurs can be one place with a big speed difference or a bunch of little gradients. The limit as the discreet gradients approaches being continuous is the same as the coarse case.

So, if that's the mechanism, then with an expanding track all balls rolling along it will end up at rest relative to the local track.

Arbitrarily close to being at rest, but never completely at rest, else the history of the object would not be able to be extrapolated by its current state. You do say ‘close to’ in your post, so you get this point.

So, the content of expanding space (ignoring radiation) will end up close to being at rest, and that means that when a particle in a particle accelerator is made to move at 0.99c relative to us, it really is moving close to the speed of light and there is no possibility that we are the ones moving at close to the speed of light while that particle is at rest.

If speed is measured relative to the cosmological frame, then yes. I assume you mean this, but without that being explicit, the statement is ambiguous.

The problem here is that this already rules out STR. For STR to be viable, that slowing down of material until it's all close to being at rest simply could not happen.

STR makes no mention of a cosmological frame or peculiar velocity, and you know this. Relative to any inertial coordinate system in Minkowski spacetime, an object, in the absence of force, will maintain its velocity indefinitely. The cosmological frame is not inertial and so Newton’s laws of inertial don’t particularly apply to it, much in the same way they don’t apply to a host of assorted varieties of non-inertial coordinate systems. And our simplified example with gravity and dark energy removed is in fact Minkowskian. The real universe has those two things, making it not Minkowskian except locally.

The set A and set B watches have slowed down and ended up at rest relative to the clocks

Nearly at rest...

or alternatively, if the set A watches were stationary to begin with, then the clocks and set B watches have slowed down instead with the set B watches slowing most. In these two rival cases, there would be different timing differences which would tell you which ones were closest to being at rest initially.

Agree, the unaccelerated clocks will always show more time than the accelerated ones. Just not much.

They might now be essentially at rest and no longer passing each other, but you could still find out what the timing differences are by comparing different timers near to each other.

My example had 8 months difference after all 3 clocks met after 13 billion years. Even less if they’re ejected before the one year mark. The longer you wait to eject them, the longer they take to slow down. The experiment you describe at the end of your post would take many millions of years, when the thing it is trying to detect is already known and readily measured.

I win both ways

Ah, It’s a win/lose thing with you. I kinda suspected. Science isn't about winning. It's about making useful predictions. What useful prediction does your philosophy make?

Yes, there is an objective non-inertial coordinate system that can be determined by multiple parties arbitrarily separated, without communication. I cannot think of another coordinate system with this property. All objects tend to come to rest in this frame, which makes it an excellent candidate for an absolute frame. This has been known since Hubble’s time. You’re just now getting on that bandwagon? I thought you hung with the nLET crowd...

I feel that an absolute coordinate system should in addition order all spacetime events, and should assign absolute times to those events, not relative times.  The cosmological frame falls short on both of those, but it seems to be the preferred candidate for an absolute frame regardless.
It fails to order all events (such as those inside black holes), and times are relative to Earth time, which would not be agreed upon by said non-communicating distant observer.

it still reveals that there are absolute speeds

One could measure time relative to a clock at the average gravitational potential (which isn’t constant over time), but then some clocks would be dilated faster, not slower. Without an absolute clock, there are not absolute speeds.

I feel I am on shaky ground on that one. The lack of an objective clock is a problem, but we know c to an amazing number of digits, and so in theory time is just m/c. Of course, we define the meter based on our clock, so that’s a circular definition of time. Jury is out I think.

apart from the small amount being jetted out of quasars and the like at relativistic speed.

There are no quasars anymore, so stuff accelerated by them has since slowed, but there still are things being accelerated to absolutely stupid speeds. They found some object that was regularly firing off bullets the mass of Jupiter at nearly light speed.

So, we have a theoretical method for pinning down absolute speed regardless

We have a much more practical method than a mere thought experiment. Look at the web. Our peculiar velocity is around 390 km/sec, much slower than it was when the T-rex was around.

[David Cooper (OP)]

STR makes no mention of a cosmological frame or peculiar velocity, and you know this

The point is though that STR is not compatible with this universe. There are clearly absolute speeds because things are slowing down until they're practically at rest, so STR cannot even apply locally. It denies the very idea of there being such a thing as at rest.

Agree, the unaccelerated clocks will always show more time than the accelerated ones. Just not much.

If the clocks were moving and one set of the watches were then decelerated when they were sent out, those decelerated watches will be the ones with the most time displayed on them, but you would call them accelerated. Their timings would reveal what actually happened to them.

My example had 8 months difference after all 3 clocks met after 13 billion years. Even less if they’re ejected before the one year mark. The longer you wait to eject them, the longer they take to slow down.

It's a thought experiment in which we could add a scientist who reads the times on the clocks without having to wait billions of years. The results would show up within seconds of the clocks and watches being created and sent out because some of them would be ticking half as often as others, and it would take a long time for that difference to reduce.

The experiment you describe at the end of your post would take many millions of years, when the thing it is trying to detect is already known and readily measured.

It wouldn't take anything like that long to do the experiment. A month would be sufficient to measure the difference.

Ah, It’s a win/lose thing with you. I kinda suspected. Science isn't about winning. It's about making useful predictions. What useful prediction does your philosophy make?

It's about winning an argument. The point is that this universe clearly has to have absolute speeds of motion in it, whereas STR denies them. You want to have STR in this universe, but you can't logically have that. And then you misuse the word philosophy by implying that your position isn't philosophical while mine is. Science is very much philosophy, but the relevant distinction here is between good philosophy and bad philosophy, and when it tolerates contradictions it becomes the latter. I have described an experiment that could be carried out in the real universe in the not-too-distant future which could pin down the absolute speed of motion of the apparatus and lead to correct measurement of the one-way speed of light relative to it, and you think that has nothing to do with useful predictions while you continue to back a disproved theory. Two sets of the same apparatus being set up and run in the exact same manner but producing different results due to their different absolute speeds of travel is something that LET predicts but STR does not predict. That is really big.

This has been known since Hubble’s time. You’re just now getting on that bandwagon?

Clearly that is not the case, because STR is still being backed by everyone in physics and they're refusing to accept that it's been blown out of the water. Soon they'll all be playing the same game, making out that they always knew STR was wrong and never intended anyone to think it applied to the real universe, but just look back at the history of abuse of people who've objected to STR here and everywhere else by boorish thugs insisting that STR is right and that the objectors are crackpots. That's where the scandal is, quite apart from systematically miseducating the public in a manner that's totally unethical.

It fails to order all events (such as those inside black holes), and times are relative to Earth time, which would not be agreed upon by said non-communicating distant observer.

That distant observer would simply convert between the two times and adjust for minor accelerations, so it's not an issue. But the events in black holes fit with it perfectly: you simply use a theory that makes incorrect predictions about what's going on inside black holes, and that's what creates problems for you as you imagine that stopped clocks continue to tick and that their proper time never runs slow.

One could measure time relative to a clock at the average gravitational potential (which isn’t constant over time), but then some clocks would be dilated faster, not slower. Without an absolute clock, there are not absolute speeds.

Without an absolute clock, the universe would fall apart through event-meshing failures in an instant. But absolute speeds could be pinned down in the way I spelt out even without caring about absolute time as it's sufficient to compare those absolute speeds with light in the local space and express it as a proportion of c.

So, we have a theoretical method for pinning down absolute speed regardless

We have a much more practical method than a mere thought experiment.

It isn't just a thought experiment: it could be carried out for real, and within this century.

Look at the web. Our peculiar velocity is around 390 km/sec, much slower than it was when the T-rex was around.

What's stopping you from just admitting that STR is a disproved theory (in that it's incompatible with this universe)? You're almost there now.

[Halc]

The point is though that STR is not compatible with this universe.

STR covers the special case of Minkkowskian spacetime. With the exception of physical singularities, the universe is Minkowskian only locally, and the theory does not assert otherwise. The universe as a whole is not covered under ‘locally’, so one has to use the general theory, not the special case one. STR never claims to cover the general case, and yet you never seem to rag on GR which does. Is your case so pathetic that the only way you can bring it down is suggest out that the universe as a whole obviously has gravity in it when STR asserts that it does not? Drop an apple on your head. That's am empirical result that STR doesn't predict. You've won, and without all this needless complication.

STR in fact makes no metaphysical assumptions or conclusions, and all your arguments seem to be based on metaphysical assumptions, not empirical ones.
So if you with to continue foaming on about STR being wrong, be a little explicit about what observations you think it predicts and what actually will be observed. Our little thought experiment has gravity and dark energy removed, so it is actually Minkowskian as a whole. STR would cover such a simplified universe, so we can refer to that example if you wish. But the real universe has gravity and such, making GR the applicable theory.

It's a thought experiment in which we could add a scientist who reads the times on the clocks without having to wait billions of years. The results would show up within seconds of the clocks and watches being created and sent out because some of them would be ticking half as often as others, and it would take a long time for that difference to reduce.

The scientist can only read the clocks once when they pass by him. And the accelerated ones will be behind, exactly as STR predicts.

It's about winning an argument.

Then suggest an empirical test in a universe without gravity and such that STR predicts incorrectly. Can’t do that? Then you haven’t won. Asserting that STR denies some metaphysical concept (absolute motion) is just a strawman since it isn’t a metaphysical theory.

Science is very much philosophy, but the relevant distinction here is between good philosophy and bad philosophy, and when it tolerates contradictions it becomes the latter.

But STR doesn’t make any philosophical assertions. It’s all empirical. So it cannot be self contradictory on the philosophical front. It has to be empirical. Anything beyond that, and everything you push, is metaphysical, and thus just an interpretation of relativity, not a contradiction of it. I’m not saying your interpretation is wrong, so there is no ‘winning’ in it for me. I’m just saying that your interpretation cannot pony up a since empirical difference.


Concerning inconsistencies with your interpretation in the real universe (not the thought-experiment one with no gravity in it):

It fails to order all events (such as those inside black holes)

But the events in black holes fit with it perfectly: you simply use a theory that makes incorrect predictions about what's going on inside black holes, and that's what creates problems for you as you imagine that stopped clocks continue to tick and that their proper time never runs slow.

So you’re asserting physics is locally measurably different at different potentials? You’d notice time slowing? Seriously? How about at speed then?  If I move at .99c, will I notice everything moving slow? Just wondering where you stand on this.

Times are relative to Earth time, which would not be agreed upon by said non-communicating distant observer. One could measure time relative to a clock at the average gravitational potential (which isn’t constant over time), but then some clocks would be dilated faster, not slower. Without an absolute clock, there are not absolute speeds.

That distant observer would simply convert between the two times and adjust for minor accelerations, so it's not an issue.

You misunderstand. I’m talking about time as measured by clocks at Earth potential and a different potential (neither at zero potential) of the distant observer. Both are stationary relative to the comoving coordinate system. We’re both measuring the ‘absolute’ speed of some mutually visible object, and getting different numbers because our clocks (neither of which has ever accelerated) tick at different rates. Clearly speed is relative if we’re getting different answers. Where’s the absolute clock that measures the time it takes the object to go distance X?

Without an absolute clock, the universe would fall apart through event-meshing failures in an instant.

I would just have said that absolute speeds are meaningless without such a clock, but if you want the universe to fall apart due to your assertions, who am I to argue?

express it as a proportion of c.

Light doesn’t move at c in your absolute universe. It only moves at c at zero potential. This has been demonstrated. Relativity would say that it empirically moves at c ‘here’, using local rulers and clocks, but at least one of those is wrong in your interpretation.

[David Cooper (OP)]

STR covers the special case of Minkkowskian spacetime. With the exception of physical singularities, the universe is Minkowskian only locally, and the theory does not assert otherwise.

The whole point though is that it doesn't even apply locally in an expanding universe because an expanding universe forces there to be absolute speeds of motion at every locality, including any in which there is no expansion. So STR is gone and needs a replacement. LET continues to fit the facts though, so which is the better of the two theories? We have made progress by eliminating STR from the inquiry.

STR never claims to cover the general case, and yet you never seem to rag on GR which does. Is your case so pathetic that the only way you can bring it down is suggest out that the universe as a whole obviously has gravity in it when STR asserts that it does not?

Pathetic? Showing that STR doesn't work in this universe is the very opposite of pathetic. It's clinging to STR after it's been shown not to fit this universe that would be pathetic. In science you make progress by looking to see what can be ruled out and then you look at the ramifications. The time dimension has gone too, replaced by absolute time, so what does that do for GTR? But that's a discussion for another thread.

STR in fact makes no metaphysical assumptions or conclusions, and all your arguments seem to be based on metaphysical assumptions, not empirical ones.

You've got that entirely the wrong way round. STR's is supposedly just it's two postulates, but they're so ambiguous that they also describe LET if you interpret them in a the way that doesn't result in contradictions. That's why STR's additional dogma is so important for distinguishing it from LET (while Einstein and others were absolutely clear that it is not LET): STR it denies the existence of absolute time and absolute speeds of motion, and in doing so it is making metaphysical assumptions and conclusions.

So if you with to continue foaming on about STR being wrong, be a little explicit about what observations you think it predicts and what actually will be observed. Our little thought experiment has gravity and dark energy removed, so it is actually Minkowskian as a whole. STR would cover such a simplified universe, so we can refer to that example if you wish. But the real universe has gravity and such, making GR the applicable theory.

Who is foaming? A person defending broken theories or a person who has shown them to be broken? Our little thought experiment shows that in an expanding universe it would be possible to measure absolute speeds if you create clocks early on, send them out in different directions and then compare their times to see how they've ticked at different rates. That clearly would work if it had been done. Something like it can still be done now though: we don't need to go back to the big bang to do an experiment like it because any part of space that's expanding today will provide the same kind of opportunity, and that works in a universe with or without gravity in it. At a single locality, we can see that the same apparatus moving through that place at different speeds but otherwise set up identically from the point of view of the observer travelling with it must produce different results that would reveal a different absolute speeds of motion for the two sets of apparatus if that space is expanding. That's a radical breakthrough, and making radical breakthroughs of that kind is not foaming. Foaming is reserved for the people who resist the big advances when they're made.

The scientist can only read the clocks once when they pass by him. And the accelerated ones will be behind, exactly as STR predicts.

Are you sure? We have a clock and a watch sitting near each other which the scientist look at and travel to and fro between them to confirm what they're doing: one of them has registered millions of years less time passing than the other, and other scientists looking at clocks and watches throughout the universe are finding the same thing and sending their findings to each other. The ones that were moving fast early on have slowed to a near halt now, but they still lag behind with their timings. As for which were accelerated, we can have the watches send out miniwatches in the same way and have set D of miniwatches accelerated until they are at rest with the clocks. When you compare the clocks with the watches, which ones are behind with their times and were accelerated. Let's say that the watches are behind with their timings because they were accelerated. When you compare that set of watches with one set of miniwatches though, which ones are behind with their times and were accelerated? STR can't handle that precisely because both these cases can happen in the same system, and if in the first case you have the watches recording less time than the clocks after being accelerated away from them, in the second case you will have the miniwatches record more time than the watches after being accelerated away from the watches: the accelerated ones end up ticking faster in this second case. That result is fully compatible with LET, but not with STR.

Then suggest an empirical test in a universe without gravity and such that STR predicts incorrectly. Can’t do that?

That's precisely what I set out in my paper: a test which would show two identical sets of apparatus set up identically but with them moving relative to each other and where they produce different measurements due to their different absolute speeds of motion. Gravity or the lack of it wouldn't change the results. You can see from the other thought experiment that expanding space provides ways to pin down absolute speeds, and all I did was convert that approach to an experiment that could be done today without needing to set things up in the early days of the universe.

But STR doesn’t make any philosophical assertions. It’s all empirical.

It absolutely does: it asserts that there's no absolute time and that absolute speeds of motion don't exist. But mathematics says otherwise, and so does our expanding universe. STR has always been bad philosophy dressed up as science.

So you’re asserting physics is locally measurably different at different potentials? You’d notice time slowing? Seriously? How about at speed then?  If I move at .99c, will I notice everything moving slow? Just wondering where you stand on this.

What I'm saying is that nothing that's going on out there is incompatible with absolute time. It could be measured locally if you know how fast you're moving and how deep you are in the collective gravity wells that can influence the place where you are. You would never notice time slowing when time never slows: if you move at 0.99c you will have your functionality slowed down and you'll notice everything else happening fast (after adjusting for Doppler shift).

You misunderstand. I’m talking about time as measured by clocks at Earth potential and a different potential (neither at zero potential) of the distant observer. Both are stationary relative to the comoving coordinate system. We’re both measuring the ‘absolute’ speed of some mutually visible object, and getting different numbers because our clocks (neither of which has ever accelerated) tick at different rates. Clearly speed is relative if we’re getting different answers. Where’s the absolute clock that measures the time it takes the object to go distance X?

There doesn't have to be an absolute clock to measure that. There only needs to be absolute time to govern it, and while absolute time can be referred to as a clock of a kind, that doesn't guarantee that anyone can ever read it or determine exactly how fast it ticks. But if you assume that the functionality of both your well-separated observers have clocks that are ticking at the same rate as each other due to their similarly low speed and similar depth in the local collective gravity wells (i.e. the ones in the universe detectable from there), they will not get different speed measurements for an object half way between them. For them to get different answers, they would either have to be moving at different absolute speeds (which they could measure by using my experiment) or they would be at different depths in gravity wells (which they could assess by measuring the amount of material affecting them gravitationally and the degree to which it is doing so). If they adjust for both of those, they should agree on the speed of the object. If you still have a difference in the measurements after that though, then something else must be slowing one of the observers, and that could potentially result from additional slowing depending on how fast the local space fabric is moving through some medium external to the universe.

Without an absolute clock, the universe would fall apart through event-meshing failures in an instant.

I would just have said that absolute speeds are meaningless without such a clock, but if you want the universe to fall apart due to your assertions, who am I to argue?

If one object could take a shorter time-length path into the future than another, they would be incapable of meeting up again with different times on their clocks because when one arrives at the meeting point, the other would not be able to keep the appointment as it would be late in arriving there, even though it has to pass through that same spacetime location. That's not quite "falling apart", but it's a reasonable description of the result. The only way they can actually meet up again with different times on their clocks is if one of them has been ticking slow under the governance of absolute time.

express it as a proportion of c.

Light doesn’t move at c in your absolute universe. It only moves at c at zero potential. This has been demonstrated. Relativity would say that it empirically moves at c ‘here’, using local rulers and clocks, but at least one of those is wrong in your interpretation.

As I've said before, there's absolute speed and there's absolute speed. It's the same with the speed of light: there's the speed of light and the speed of light, and they can differ because they're not the same thing. Where the "speed of light" is lower than the actual speed of light, "absolute speeds" will be higher than the actual absolute speeds. When you make a measurement of absolute speed using my experiment, you're using the "speed of light" and you're calculating "absolute speeds" accordingly. If you want absolute absolute speeds then you need to know what the absolute speed of light is and then adjust for that accordingly. What matters for the sake of this conversation is the speed of objects relative to the local speed of light, and once you have that, you can then measure the one-way speeds of light in different directions relative to the apparatus while always being fully aware that those are not the same thing as absolute absolute speeds. STR doesn't even allow for these "absolute speeds" that are proportions of the local speed of light, so you're just taking things off on an unnecessary diversion in an attempt to muddy the waters.

There are two key things that matter here. (1) If accelerated watches tick slower than unaccelerated clocks while accelerated miniwatches (that are comoving with clocks from moments after their creation having been accelerated and then decelerated a moment later) are ticking more quickly than watches, then STR is making incorrect predictions about the result either of the first acceleration or the second acceleration. (2) If two sets of identical apparatus set up the same way at the same location but moving at a different speeds don't produce a null result like the MMX, STR is making incorrect predictions, while if the local space is expanding, there cannot be a null result. Nitpicking about what exactly absolute speeds are is a sideshow: we have them regardless.

[Halc]

STR it denies the existence of absolute time and absolute speeds of motion
…
[STR] asserts that there's no absolute time and that absolute speeds of motion don't exist.

Where does it do that? Quote the 1905 paper please. That would indeed constitute a metaphysical claim. I don't see how that could be demonstrated from the premises.

We have a clock and a watch sitting near each other which the scientist look at and travel to and fro between them to confirm what they're doing

Clocks not in each other’s presence cannot be unambiguously compared. If they’re near each other and millions of years apart, then either they were never in sync or the slow one has been accelerated towards the faster one and will eventually meet it, in which case said scientist would not need to travel between them. You seem to be making up wrong numbers. How did they get millions of years apart if they’re ‘near each other?’ Is one continuously accelerating back and forth or something?

The ones that were moving fast early on have slowed to a near halt now

This language seems to assume absolute speeds. If you want to prove your interpretation, you can’t beg it up front. Only relative to this cosmological coordinate system do inertial things slow down over time, and I can assign such coordinates to any preferred event in spacetime, meaning that frame references are still necessary.

When you compare that set of watches with one set of miniwatches though, which ones are behind with their times and were accelerated?

Acceleration is absolute. There is no question about which ones have done this.

STR can't handle that precisely because both these cases can happen in the same system, and if in the first case you have the watches recording less time than the clocks after being accelerated away from them, in the second case you will have the miniwatches record more time than the watches after being accelerated away from the watches: the accelerated ones end up ticking faster in this second case. That result is fully compatible with LET, but not with STR.

Sorry, but I cannot parse what you’re trying to convey. It sounds like an empirical result claimed incompatible with STR, but I cannot follow it. What is a ‘same system’ as opposed to a different system? No systems were defined.

You have accelerated watches which at times pass by comoving clocks that have never been accelerated. The can be compared at this point and will be slow by time T. You then eject a miniwatch at each clock so it stays forever with the clock while the watch continues on. But the miniwatch will forever be slow by time T then relative to the clock in its presence.
That’s all I got from your description. STR doesn’t predict anything different, but I think there was more to it.
Please be specific about when things happen and what change of speed is done.

That's precisely what I set out in my paper: a test which would show two identical sets of apparatus set up identically but with them moving relative to each other and where they produce different measurements due to their different absolute speeds of motion. Gravity or the lack of it wouldn't change the results.

I don’t remember the paper. I remember something about an experiment performed just outside the solar system, which will very much be affected by gravity, so you’re lying to yourself if you suggest otherwise. If the experiment is done in without gravity, then it need not be performed away from (nonexistent) mass. Anyway, I forgot how it went, but it seemed to be begging since frame references were missing. It assumed its conclusions. Maybe I remember incorrectly.

What I'm saying is that nothing that's going on out there is incompatible with absolute time. It could be measured locally if you know how fast you're moving and how deep you are in the collective gravity wells that can influence the place where you are. You would never notice time slowing when time never slows: if you move at 0.99c you will have your functionality slowed down and you'll notice everything else happening fast (after adjusting for Doppler shift).

Pick a specific example then.  On Jan 1 (noon, absolute time, to which your watch is set), you jump towards a very large black hole (one large enough that tidal forces aren’t a bother even after 10 subjective minutes inside).  After one day (your watch, noon Jan 2), you cross the event horizon, noticing nothing different. At 10 minutes past noon (your watch), what absolute time is it?
I know I didn’t give all the specifics like the actual mass. Not looking for some fancy calculation.  I claim the question is unanswerable, and that makes it indeed incompatible with absolute time. Your hand-wave assertion to the contrary shows me only that you don’t have an answer.
Absolute time cannot be ‘measured locally’. Our falling guy has no defined speed or gravity depth. These things are not defined under your proposed coordinate system. He has exited your chosen coordinate system. That’s my point.

There doesn't have to be an absolute clock to measure that. There only needs to be absolute time to govern it, and while absolute time can be referred to as a clock of a kind, that doesn't guarantee that anyone can ever read it or determine exactly how fast it ticks.

So just another thing that is there, but functionally inaccessible.

clocks that are ticking at the same rate as each other due to their similarly low speed and similar depth in the local collective gravity wells

Gravity well depth is absolute. It isn’t a local thing. Speed differences aside, two clocks will tick in sync only if they’re at the same potential, not at the same ‘local’ potential. This is true even between clocks separated by far more than the size of the visible universe.

or they would be at different depths in gravity wells (which they could assess by measuring the amount of material affecting them gravitationally and the degree to which it is doing so).

That was my point. At what point do you decide to cut this off? Very distant star X affects my gravitational potential, but star Y one AU further away does not. Seems fishy, especially since the distant objects contribute more to the potential than the nearby ones do.

There are two key things that matter here. (1) If accelerated watches tick slower than unaccelerated clocks

Begging statement, meaningless under relativity. Try harder. Use empirical language. Don’t say what rates things tick. Say what will be measured at specific events.

(2) If two sets of identical apparatus set up the same way at the same location but moving at a different speeds don't produce a null result like the MMX, STR is making incorrect predictions

Galilean PoR says both apparatus (each in motion relative to the other) will measure the same local thing. You’re weren’t real specific about what you want measured.

while if the local space is expanding, there cannot be a null result.

And why does it take 20 posts to get the specifics of this non-null result? So far all I have is accelerated watches that are slow by exactly the amount predicted by relativity.

[David Cooper (OP)]

STR ... asserts that there's no absolute time and that absolute speeds of motion don't exist.

Where does it do that? Quote the 1905 paper please. That would indeed constitute a metaphysical claim. I don't see how that could be demonstrated from the premises.

Why restrict things to that specific paper when you know that Einstein insisted that there's no absolute time or absolute speeds of motion? You must know full well what the theory asserts. In that original paper, which at no point even refers to a theory of relativity, he was initially careful not to overstate the case, so in paragraph two of that paper he says, "Examples of this sort, together with the unsuccessful attempts to discover any motion of the earth relatively to the 'light medium,' suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest." ... "The introduction of a “luminiferous ether” will prove to be superfluous inasmuch as the view here to be developed will not require an “absolutely stationary space” provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place."

Later on we have, "So we see that we cannot attach any absolute signification to the concept of simultaneity, but that two events which, viewed from a system of co-ordinates, are simultaneous, can no longer be looked upon as simultaneous events when envisaged from a system which is in motion relatively to that system."

All of these things became stated more strongly over time, leading to everyone in physics recognising that he was ruling out absolute time and absolute speeds. STR further evolved with Minkowski's input with the idea of spacetime, which leads to there being more than one STR model. But what was very clearly ruled out by Einstein was LET, because if it was merely LET, it wouldn't be Einstein's theory at all.

We have a clock and a watch sitting near each other which the scientist look at and travel to and fro between them to confirm what they're doing

Clocks not in each other’s presence cannot be unambiguously compared. If they’re near each other and millions of years apart, then either they were never in sync or the slow one has been accelerated towards the faster one and will eventually meet it, in which case said scientist would not need to travel between them. You seem to be making up wrong numbers. How did they get millions of years apart if they’re ‘near each other?’ Is one continuously accelerating back and forth or something?

It's really quite simple. If there's a clock here and another one a thousand miles away over there, I can note the time on the clock here, then travel a thousand miles to look at the clock there, note down its time, then come back to the first clock and look at its time again and note that down. If the first time is 13.8 billion, the second time is 13.75 billion and the third time is 13.8 billion, then it's clear that the clock over there is behind the clock over here with its timing. The two clocks might even be sitting side by side though, eliminating the need to make trips between them.

If we're able to look at the clocks a minute after they're created though, a million years after the big bang, we can see that some of the clocks have registered a minute passing since they were created, while the watches that were sent out from them at 0.866c from them ten seconds after the clocks were created have only registered 35 seconds passing since they and the clocks were created, and we can see these passing each other to confirm that. Let's have cameras built into them which can photograph their clock and any watch that comes by to say hello when they give each other a high five (or twelve) - that will leave us with lasting photographs that document the action without us having to be there at all: photos showing after a year that when clocks pass watches the watches have only registered half a year passing while the clocks have registered a whole year. The expansion of space is so slight in that length of time that it barely slows the watches speed of travel in that time. And when some of the miniwatches that were sent out from the watches ten seconds after the watches were sent out from the clocks, well, lo and behold, the photos show some of them passing watches with a year recorded on their dials to the half year on the dials of the watches, and when clocks and miniwatches drift into close contact, they are both shown to have a year recorded on them. That's just one set of photos though. There will be others that show a clock meeting a watch where the watch has 20 years on it while the watch only has 10 years. And so on. You can fill in the rest using your own imagination.

The ones that were moving fast early on have slowed to a near halt now

This language seems to assume absolute speeds. If you want to prove your interpretation, you can’t beg it up front. Only relative to this cosmological coordinate system do inertial things slow down over time, and I can assign such coordinates to any preferred event in spacetime, meaning that frame references are still necessary.

I assume nothing of the kind. It's about looking at the options as to what may be the case, and all options need to be covered. If the clocks are stationary and the watches are moving at 0.866c, then the watches will tick half as often as the clocks, but if the watches are stationary and the clocks are moving at 0.866c, then the watches will tick twice as often as the clocks, and if the clocks and watches are moving at the same speed as each other, then they will tick at the same rate as each other too. When you compare them as they pass each other, you will see those timing distances and will be able to tell a lot about what their absolute speeds must be (with the complication that you need to measure it in three dimensions and not just one, so you need to compare clocks passing each other in different directions to get the full picture.

When you compare that set of watches with one set of miniwatches though, which ones are behind with their times and were accelerated?

Acceleration is absolute. There is no question about which ones have done this.

Both the watches and the miniwatches have accelerated, but the clocks haven't. And when we're considering the action that only involves the watches and miniwatches, only the miniwatches have accelerated. In the first case we have the watches accelerate away from the clocks and tick more slowly as a consequence. In the second case we have one set of miniwatches accelerate away from the watches and tick more quickly as a consequence. And we have conformation of this by the fact that when we compare neighbouring miniwatches and comoving clocks, they are ticking at the same rate as each other. So, if the watches were accelerated and ticked more slowly as a result, then the miniwatches were decelerated and ticked more quickly as a result. (The "if" and "then" in that are important because it could be that the watches were decelerated and the miniwatches were accelerated, but you'd see the difference between those two possibilities by comparing the times on watches and miniwatches when they pass each other. The ones with more time recorded on them must have been decelerated.

You say that I assumed absolute speeds, but these are dictated by the twins paradox: if you don't have absolute speeds, then accelerating the watches and decelerating the miniwatches won't change their ticking rates at all, so whenever any of these timers pass other timers they would all have to read the same time. Or, if you're relying on some kind of magic with the accelerations to govern the timings, then the deceleration of the miniwatches would have to be an acceleration too and they would be left ticking slower than the watches, which would lead to clocks and miniwatches sitting side by side with one ticking at four times the rate of the other.

Sorry, but I cannot parse what you’re trying to convey. It sounds like an empirical result claimed incompatible with STR, but I cannot follow it. What is a ‘same system’ as opposed to a different system? No systems were defined.

The system is the universe in which these clocks are operating. Case 1 is what happens in relation to the clocks and watches. Case 2 is what happens in relation to the watches and miniwatches, but we're particularly interested in the miniwatches sent out in such a way that they end up sitting at rest relative to the nearby clocks. In case 1 we have accelerated watches which tick half as fast as the clocks after that acceleration. In case 2 we have accelerated miniwatches which tick twice as fast as the watches after their acceleration away from those watches. That means we have two cases of timers being accelerated which STR predicts will tick more slowly as a result of the acceleration, and yet in the second case the opposite happens: we instead see them behave in the way that LET predicts.

But the miniwatch will forever be slow by time T then relative to the clock in its presence.

Given the ten-second delay between the two accelerations, we can ignore that tiny difference in the timings a year later, but yes, there will be a slight lag.

That’s all I got from your description. STR doesn’t predict anything different, but I think there was more to it.
Please be specific about when things happen and what change of speed is done.

I was specific, but it takes time for people to take the details in with something like this and understand what's going on well enough to be able to recognise the point of it all. That's why it's so hard to get anywhere discussing this when 99.99% of people don't want to know what it reveals and would rather just say it's wrong without understanding it.

Normally when you run a twins paradox, you can't get a definitive answer as to which clock might be ticking faster than another clock that moves past it, but with expanding space we can because it enables us to separate clocks and know that any that are at rest, if there is such a thing as at rest, will display the same time on them when we bring them together, whereas if one is moving and another is at rest, then when we bring those together (with apparently identical accelerations), the one with the higher absolute speed will have recorded less time than the other. And if there are no absolute speeds, then none of them can have recorded different amounts of time passing because they were all created at the same time and none of them could be ticking slow, but the twins paradox bans that result because three of the clocks can pass each other in the manner, A passes B, B passes C, then C passes A, and if they were all ticking at the same rate then timing A (between clock A's encounters with B and C) will be equal to timings B plus C (their timings being the time between their encounters with the other two clocks), but the twins paradox demands that timing A > B+C, and as soon as you have A > B+C, you have either clock B or C ticking at a lower rate than clock A because of its higher absolute speed. In normal cases, you can't tell which clocks have higher or lower absolute speeds, but in this case with the expanding universe, you can: you can see it whenever clocks pass each other because they weren't separated by movement through space, but by expansion of space, and the latter does not affect their relative ticking rates, whereas the former does. I never start from the assumption that absolute speeds exist: their existence is forced by the twins paradox. People then deny that the twins paradox reveals that, even though it does, and they do this with the feeble excuse that you can't tell which clocks are moving faster or slower than which, but in these thought experiments with expanding space, you can tell that.

[post length limit, so only half way here...]

[David Cooper (OP)]

[...2nd half]

I don’t remember the paper. I remember something about an experiment performed just outside the solar system, which will very much be affected by gravity, so you’re lying to yourself if you suggest otherwise.

If you had actually read the paper carefully and understood it, you would know that gravity does not prevent it from producing good results. If you were to move the apparatus along at 0.866c (and I use this high speed just to illustrate the way it works by making the difference in measurements stark), the expansion of space between the two outer clocks would lead to light signals from them to the central clock taking extra time to reach the central clock, but that extra time taken would be getting on towards fifteen times longer from the trailing clock than from the lead clock, and that difference is not cancelled out by synchronisation differences in the way that happens at the start of the experiment before the space has expanded. (In the paper I actually switch though to not allowing the clocks to move apart, but to hold them at a fixed separation instead and to allow space to move through them as it expands - the trailing clock will then move through the extra space at a higher speed relative to it than the lead clock does, making it tick slower while they maintain their actual separation, but the end result is the same difference in the timings. The paper can be seen here: https://independent.academia.edu/DavidCooper173 - very few views registered there because I normally send people to a copy on my site instead as that only takes one click, but it's unreliable free hosting and has been unavailable a lot in recent days.)

Pick a specific example then.  On Jan 1 (noon, absolute time, to which your watch is set), you jump towards a very large black hole (one large enough that tidal forces aren’t a bother even after 10 subjective minutes inside).

Hold it right there. LET predicts that the functionality of a clock halts at the event horizon, and if you could get the clock inside the black ball, it would be halted there too, so there is no such thing as 10 subjective minutes inside. LET agrees with GTR about all predicted measurements that can be accessed from outside the black hole, but they differ radically when it comes to what goes on inside.

After one day (your watch, noon Jan 2), you cross the event horizon, noticing nothing different. At 10 minutes past noon (your watch), what absolute time is it?

My watch has been stopped for who knows how long, so it never reaches ten past noon, but absolute time has continued to run at the same constant rate for the whole universe and all its content.

I know I didn’t give all the specifics like the actual mass. Not looking for some fancy calculation.  I claim the question is unanswerable, and that makes it indeed incompatible with absolute time. Your hand-wave assertion to the contrary shows me only that you don’t have an answer.

Your assertions are the result of you assuming that GTR is right, and its incompatibility with absolute time is just one of a number of symptoms of its brokenness. I do have an answer, and it's that a clock only goes on ticking inside a black hole in broken theories. But time continues to operate in there; it's just that any clock governed by the speed of light will be halted. Absolute time is not governed by the speed of light, but instead has a role in governing the speed of light.

Absolute time cannot be ‘measured locally’. Our falling guy has no defined speed or gravity depth. These things are not defined under your proposed coordinate system. He has exited your chosen coordinate system. That’s my point.

He hasn't. He's descended to the event horizon and stopped there with his functionality frozen. He can only go inside the event horizon by more stuff falling on top of him and increasing the energy density there to make the event horizon migrate out past him, and still his is frozen motionless. He might stay there for trillions of years of absolute time before he is destroyed by the process that generates Hawking radiation. (Trillions is a guess - maybe it's quadrillions or quintillions, but I'll just stick with trillions for now even if its not enough.) Meanwhile, GTR has him continue down to a singularity instead and he stays there for an infinite amount of the time external to the black hole, even though he is actually destroyed by that Hawking radiation process within mere trillions of years of that time external to the black hole. He has at no time exited my proposed coordinate system: you are merely attributing your own warped one that doesn't add up onto me, but I don't allow that kind of magic in the model. He cannot travel infinitely far timewise into the future and also be destroyed here within mere trillions of years. That brokenness of GTR is a big hint that it's wrong.

So just another thing that is there, but functionally inaccessible.

It's hard for anything to happen without it. It's one of nature's key fundamentals, just like space.

Gravity well depth is absolute. It isn’t a local thing.

Of course its local: you wouldn't have clocks tick at different rates in a lab by being on shelves at different heights otherwise. One is at deeper total depth than the other in all the gravity wells affecting them. Different localities are frequently at different depths. (Some are obviously at the same depth as each other though.) The important point here is that one of the observers may live in a much more massive galaxy than the other observer and his clock will therefore be ticking slower than the other observer's, so he would have to adjust for that for both observers to agree on the speed of the mutually observed object half way between them.

At what point do you decide to cut this off? Very distant star X affects my gravitational potential, but star Y one AU further away does not. Seems fishy, especially since the distant objects contribute more to the potential than the nearby ones do.

The very distant ones are going to affect both observers to almost the same extent, and while the local mass of stuff may make a lesser contribution, it can still be the main cause of a difference in the rate their respective clocks tick at, so they most need to cancel that part of it out in order to come close to agreeing on the speed of the observed object.

There are two key things that matter here. (1) If accelerated watches tick slower than unaccelerated clocks

Begging statement, meaningless under relativity. Try harder. Use empirical language. Don’t say what rates things tick. Say what will be measured at specific events.

Not meaningless at all. I can't shackle it by describing it through the lens of broken theories that don't fit the case in point. In the thought experiment with the clocks being created near the time of the big bang, we see that accelerated watches are ticking slower than unaccelerated clocks because we can look at the photos that show their times when they encounter each other and show that the clocks have registered more time passing. Those photos are the measurements. In previous posts I had observers comparing them and they were making the measurements. The measurement all show the clocks ticking faster than the watches, unless they don't, in which case we're dealing with a case where the watches were decelerated rather than accelerated, or a case in which the timings match and the watches were first decelerated to zero speed and then accelerated. Three different cases, but in each case the comparisons of times will tell us a lot about their absolute speeds, and when we look at how the miniwatches behave too (sent out in two opposite directions from the watches), we are going to see differences in timings when some of these timers meet up: the twins paradox demands that, and so absolute speeds are revealed as existing in all three cases.

(2) If two sets of identical apparatus set up the same way at the same location but moving at a different speeds don't produce a null result like the MMX, STR is making incorrect predictions

Galilean PoR says both apparatus (each in motion relative to the other) will measure the same local thing. You’re weren’t real specific about what you want measured.

It's all spelt out in the paper. What we're measuring is signals sent at the speed of light from the two end clocks to a central clock. The space expands between them, and the extra distance the signals have to travel will be covered at different speeds if the clocks are moving in their direction of alignment, leading to a timing difference. There is no timing difference at the start of the experiment due to one clock being ahead of the other in its timing if the clocks are moving along that line: they are synchronised at the start by a light signal being sent out to them from the central clock. The outer clocks then send signals back to the central clock which initially arrive simultaneously at the central clock, but as the space expands between the clocks, the signals go out of sync unless the clocks were initially at absolute rest. It's that simple. If the clocks aren't at rest, then the clocks must go out of sync due to that expansion. If they don't, there cannot be any expansion.

And why does it take 20 posts to get the specifics of this non-null result? So far all I have is accelerated watches that are slow by exactly the amount predicted by relativity.

It shouldn't take 20 posts. You had it all two and a half months ago, but you didn't want to understand it back then, and you probably still don't. You appear to misunderstand almost every point on purpose as a stalling tactic.

[Halc]

I remember something about an experiment performed just outside the solar system, which will very much be affected by gravity, so you’re lying to yourself if you suggest otherwise.

If you had actually read the paper carefully and understood it, you would know that gravity does not prevent it from producing good results.

OK, so you’re lying to yourself. Has anybody with any physics knowledge actually reviewed this? Do you dismiss any review that points out errors? For one, you seem to assume that gravity somehow just shuts off ‘outside the solar system’.
You put two relatively stationary objects in interstellar space, the local stars around it will usually tend to pull the two objects apart.  The galaxy as a whole will also accelerate them as it accelerates our solar system.  If the two objects are aligned radially with the galaxy, they’ll tend to move apart. If aligned axially, they’ll tend to move together, but probably a lesser effect than the nearby stars pulling them apart.  If they’re aligned tangentially, they’ll tend to rotate about each other.  This is all simple orbital mechanics, having nothing to do with relativity.
Trying to measure expansion within a bound object is like trying to do it by tracking the distance between a pair of buildings over time. Such motion has been measured, but it’s continental drift, not space expansion that explains it.

So let’s at least be reasonable and put this setup in deep space between galaxy clusters in a place with minimal gravity gradient. Otherwise the gravity effects will totally dwarf any claimed expansion effects.

The paper talks about putting two objects in space, relatively stationary. If they’re separated by some distance, then they’ll have different peculiar velocities.  If the near end has zero peculiar velocity, the far end will have a peculiar velocity in the direction of the near end. Space might expand past it, but that object will remain a fixed distance from the near end over time unless a force (gravity say) accelerates it.  So the two ends will remain a fixed separation indefinitely. Your paper seems to naively assume that expansion is a force that somehow accelerates things, like there’s some kind of drag with the aether or something. That nobody has pointed this out seems to indicate that nobody has actually reviewed the paper.

If you were to move the apparatus along at 0.866c

No frame reference. If you’re not begging your conclusion, then a speed is meaningless without a reference.
I will assume a peculiar velocity of .866c, and I’ll take a guess that it is along the line separating the two ends, but that also isn’t specified. I shouldn’t have to assume all these things. You should specify them.
You should also put the objects much further apart like a megaparsec so these things I’m pointing out become more obvious. It’s a thought experiment, so don’t be afraid to scale it up to make it stark, as you say. If it was actually a valid thing, then we can work to scale it down to practical distances and super-high precision measurements.  At a megaparsec, you don’t need many significant digits, but you need more time.

the expansion of space between the two outer clocks would lead to light signals from them to the central clock taking extra time to reach the central clock

That would be remarkable…  I deny this claim unless there are external forces involved accelerating things.
You’ve described clocks synced relative to their own inertial frame, and if that inertia is maintained (no acceleration), then the proper separation between the two ends will be maintained and the measurement taken in the middle will get signals simultaneously from either end.
You’re describing a local test in supposedly gravity-free conditions (which interstellar space isn’t).  The cosmological frame cannot be detected by a local test.

Hold it right there. LET predicts that the functionality of a clock halts at the event horizon

That seems to be an awful mark against LET then. It’s like looking at a flat map of Earth (like google maps) and noting that Greenland appears larger than Brazil despite the fact that it’s about a quarter the size of Brazil. That’s just a coordinate difference, and there is a coordinate singularity that makes both poles infinitely distant, so they’re never shown on such a map. LET would seem to assert that the south pole therefore doesn’t exist, asserting a physical singularity to what is a mere abstract coordinate singularity.  In fact, one can go to the south pole and not be able to tell there’s anything special going on there. One can draw a map of it, but only by choosing a different coordinate system. LET on the other hand refuses the validity of any but the one coordinate system, and thus metaphorically denies the existence of the south pole.  Ditto with black holes. Local spacetime at the event horizon is perfectly Minkowskian, and thus physics goes on as normal, as evidenced by a simple choice of a different abstract coordinate system such as the local inertial one of the guy falling in, or something non-local like Kruskal–Szekeres coordinates.

So LET acknowledges and runs away from the problem with hands on the ears, whereas relativity has no trouble with it. Defeated by confusing the map for the territory. So sad.

Of course [gravity well depth is] local

I’m saying that the difference in depth between two events is not frame dependent. Your comment comparing very distant events (say outside each other’s visible universe) seemed to suggest otherwise.

Use empirical language. Don’t say what rates things tick. Say what will be measured at specific events.

In the thought experiment with the clocks being created near the time of the big bang, we see that accelerated watches are ticking slower than unaccelerated clocks because we can look at the photos that show their times when they encounter each other and show that the clocks have registered more time passing.

Much better. Clocks are being compared in each other’s presence. No mention of tick rates which require a frame reference. The photo seems hardly necessary. The measurement can be logged and emailed for later comparision. No actual scientist need be present.

[David Cooper (OP)]

If you had actually read the paper carefully and understood it, you would know that gravity does not prevent it from producing good results.

OK, so you’re lying to yourself. Has anybody with any physics knowledge actually reviewed this? Do you dismiss any review that points out errors? For one, you seem to assume that gravity somehow just shuts off ‘outside the solar system’.

If you imagine doing the experiment with two sets of the apparatus moving at high relativistic speed relative to each other, the impact of gravity on it is rendered utterly irrelevant. If you do it with a very low relative speed, you then do have to be careful to correct for the interference of gravity where one of the clocks may have spent more of its time at a lower depth in a gravity well than the other, but you can calculate those differences by knowing the distribution of the local massive bodies that cause that difference. Distant objects won't cause measurable differences.

You put two relatively stationary objects in interstellar space, the local stars around it will usually tend to pull the two objects apart.

That's discussed in the paper, and that's precisely why after setting out a version of the experiment in which the clocks are left free to move apart (to show people the principle of how it works), I then set out a preferred version where the clocks positions are controlled to prevent them moving apart. If one of them is deeper in a local gravity well than the other during some part of the experiment, the can be corrected for, but you'd obviously plan the positioning of the experiment carefully to try to make it equal on average.

... This is all simple orbital mechanics, having nothing to do with relativity.

And it's all predictable stuff that we can correct for.

Trying to measure expansion within a bound object is like trying to do it by tracking the distance between a pair of buildings over time. Such motion has been measured, but it’s continental drift, not space expansion that explains it.

It doesn't matter whether you call it a bound object or not. If the space is expanding between the two clocks and we are actively maintaining the distance between them, we are moving them through the amount of new space that has appeared between them, and that affects their timings. It also affects their timings differently if the central clock isn't at rest, and with a bigger difference in how much it affects their timings the further from being at rest the central clock is.

So let’s at least be reasonable and put this setup in deep space between galaxy clusters in a place with minimal gravity gradient. Otherwise the gravity effects will totally dwarf any claimed expansion effects.

Ideally that's what we would do, but it could take millions of years to get it there. We don't need to wait that long though because we can correct for gravity well depth differences as they are predictable, so we can actually do the experiment on our own doorstep.

The paper talks about putting two objects in space, relatively stationary. If they’re separated by some distance, then they’ll have different peculiar velocities.  If the near end has zero peculiar velocity, the far end will have a peculiar velocity in the direction of the near end. Space might expand past it, but that object will remain a fixed distance from the near end over time unless a force (gravity say) accelerates it.  So the two ends will remain a fixed separation indefinitely. Your paper seems to naively assume that expansion is a force that somehow accelerates things, like there’s some kind of drag with the aether or something. That nobody has pointed this out seems to indicate that nobody has actually reviewed the paper.

If the central clock is at rest, both the outer clocks will be moving through space in order to maintain their distance to the central clock, as you recognise - this must happen in expanding space. There is no force acting on the outer clocks unless we apply one to keep them at the right separation if they drift away from that, but if we get their speeds just right at the start, they'll hold station automatically, so the only corrections will be to deal with gravity's interference. What will cause the clocks to run slow in this case is their speed through space which is not zero if it is zero for the central clock. That equality in the slowing for the outer clocks will result in a null result for that set of apparatus. But we always do the experiment with two sets of apparatus. The other set has the central clock moving through space. One of the outer clocks may be at rest in space this time, in which case the other outer clock will be moving through space twice as fast as the middle clock. That would lead to a clear loss of synchronisation between the outer clocks, leading to a non-null result.

If you were to move the apparatus along at 0.866c

No frame reference. If you’re not begging your conclusion, then a speed is meaningless without a reference.

It has a very clear meaning in LET and we're talking about measuring absolute speeds, so you shouldn't have any difficulty understanding what it means. The difference in results for the two sets of apparatus that you have to get in expanding space shows that absolute speeds are involved. STR says that they don't exist, so it requires a null result from both sets of apparatus, and in doing so it violates the rules of the twins paradox, as is spelt out in the paper.

I will assume a peculiar velocity of .866c, and I’ll take a guess that it is along the line separating the two ends, but that also isn’t specified.

The direction is clearly specified as being along the straight line connecting the clocks.

I shouldn’t have to assume all these things. You should specify them.

Indeed you shouldn't have to assume them: they are all spelt out clearly in the paper.

You should also put the objects much further apart like a megaparsec so these things I’m pointing out become more obvious.

The paper describes an experiment that could practically be carried out during this century - that is why the distances were made small. If you want to make it bigger, that's an easy thing to translate to.

the expansion of space between the two outer clocks would lead to light signals from them to the central clock taking extra time to reach the central clock

That would be remarkable…  I deny this claim unless there are external forces involved accelerating things.

The slowing of clocks isn't about accelerations, but about absolute speeds through space. The twins paradox carried out by three clocks that never accelerate demonstrate that. In the experiment we either have the outer clocks moving at the same speed as each other through space (in opposite directions) while the central clock is at rest, or we have one of the outer clocks moving through space faster than the other. It's a very low speed difference, but it all adds up to a timing difference.

You can understand that easily enough when you think about how when you try to separate two clocks very slowly, you end up with the same synchronisation as if you separated them very quickly to the same distance apart. No matter how slowly you move them, you get the same end result, but if you move the clock slowly, you have to move it for a lot longer.

Now, transfer that understanding to the experiment: we have two clocks moving at speeds through space that may only be a little different, but they move through space at different speeds for the same length of time as each other with one of them moving through more space than the other. That leads to a change in their synchronisation.

You’ve described clocks synced relative to their own inertial frame, and if that inertia is maintained (no acceleration), then the proper separation between the two ends will be maintained and the measurement taken in the middle will get signals simultaneously from either end.

The synchronisation is only maintained if the central clock is at rest. If it is moving, one of the outer clocks will be slowed more than the other because it will be moving faster through space. The synchronisation will be skewed, of course, if the central clock is moving (along the straight line connecting the clocks), but it will initially look perfect in the frame in which the central clock is at rest. As time passes though, one of the outer clocks lags further and further behind the other, and the signals coming back to the central clock from the outer clocks will go out of sync with each other.

You’re describing a local test in supposedly gravity-free conditions (which interstellar space isn’t).  The cosmological frame cannot be detected by a local test.

But it can be. We can calculate the impact of gravity and adjust for it, working out how much slower one clock would be ticking than the other based on their relative depth in local gravity wells so that we aren't misled by that aspect of the result.

Hold it right there. LET predicts that the functionality of a clock halts at the event horizon

That seems to be an awful mark against LET then.

Quite the reverse.

It’s like looking at a flat map of Earth (like google maps) and noting that Greenland appears larger than Brazil despite the fact that it’s about a quarter the size of Brazil...

No. It's like looking at a globe and seeing that the speed of light reaches zero at the event horizon while everything from there on down is functionally frozen: a black ball of stuff like the fuzzballs of string theory.

Local spacetime at the event horizon is perfectly Minkowskian, and thus physics goes on as normal, as evidenced by a simple choice of a different abstract coordinate system such as the local inertial one of the guy falling in, or something non-local like Kruskal–Szekeres coordinates.

Spacetime is just a contrived abstraction. LET uses a Euclidean metric with the speed of light reducing in gravity wells, and that leads to it making the same predictions about things we can measure as GTR, but different ones about ones that we can't measure inside black holes. What shows us that LET is a more trustworthy account is the way that GTR has things travel down to a singularity where they run straight on into an infinitely far off future without delay, only to be destroyed in the near future of now (mere trillions of years rather than infinitely far beyond that) by the process that evaporates black holes and produces Hawking radiation. The problems you keep coming up with are all the product of applying a broken theory and seeing everything through its cracked lens.

So LET acknowledges and runs away from the problem with hands on the ears, whereas relativity has no trouble with it. Defeated by confusing the map for the territory. So sad.

What would be sad would be if it pandered to the broken predictions of GTR which can't handle time properly. Instead of that, it sets out how things could more rationally function.

I’m saying that the difference in depth between two events is not frame dependent. Your comment comparing very distant events (say outside each other’s visible universe) seemed to suggest otherwise.

I had no intention of suggesting otherwise.

Much better. Clocks are being compared in each other’s presence. No mention of tick rates which require a frame reference. The photo seems hardly necessary. The measurement can be logged and emailed for later comparision. No actual scientist need be present.

Indeed. There are multiple valid ways of doing it.

[Halc]

It would really help if you actually put some numbers to what you expect to happen. I know numbers are not your thing, but the language of physics is mathematics, and you haven’t proposed anything if you haven’t worked out what you think will happen. I’m left guessing as to your guesses because you’re speaking the wrong language. The paper has almost no computations.
I see 100 au expanding by 50m in a month. That’s an actual computation. Care to show how you got 50m? I got about twice that.  Are you asserting that the relatively stationary objects are going to move apart 50m in a month?  I might agree with that only because the pull of the nearby stars might do that. Absent gravity and such, they stay 100 au apart relative to the inertial frame in which they were initially stationary, all per Newton’s first law of motion, which still applies.

Anyway, I can run your assertion to a contradiction if that’s the setup. Make sure you specify which coordinate system you are using because the paper switches back and forth between peculiar (what you call absolute) velocities and ‘frames A - H’ which I presume are inertial frames, but you don’t say that. It’s important, because you are working with inertial and non-inertial frames and you seem to treat them the same. You have things relatively moving when you assert them to be relatively stationary, a contradiction with inertial frames.

If the space is expanding between the two clocks and we are actively maintaining the distance between them, we are moving them through the amount of new space that has appeared between them, and that affects their timings.

You're trying to measure the slowing of a clock due to nearly zero peculiar velocity? First of all, it won't work, and second of all, I don't think 40 digits of precision would be enough if it was valid. You’re mixing inertial and non-inertial frames to get this conclusion. It’s wrong. You synced the clocks in an inertial frame, so the clocks will stay synced relative to that frame. They were never in sync relative to the cosmological frame in which the expansion takes place, but you seem to assume that they are.

Ideally that's what we would do, but it could take millions of years to get it there.

Who cares? It only has to be possible. Being practical is only a goal if you expect anyone to actually do this. It’s a forum post, not a grant application. The experiment can take as long as you like as well. The reasons that it doesn’t work become far more apparent if you put your objects say a billion parsecs apart. Keeping it small only means all the instruments need to have 30 digits of precision instead of 2.

If the central clock is at rest, both the outer clocks will be moving through space

Only in the cosmological coordinate system, which isn’t an inertial one.

There is no force acting on the outer clocks unless we apply one to keep them at the right separation if they drift away from that

We’re doing this without gravity or dark energy, so they won’t drift. You seem to not so much be interested in keeping them relatively stationary as much as computing their time dilation due to their peculiar motion? But your clocks were never synced in that coordinate system, so no comparison can be made. All clocks will stay in sync forever in the inertial frame in which all of them are stationary.
As I said, it becomes more obvious if you scale up the thing much more than just 100 AU.

What will cause the clocks to run slow in this case is their speed through space which is not zero if it is zero for the central clock.

Oops! To measure that, you’d have to sync the clocks relative to the cosmological frame, and you haven’t done that.

[.866c, no reference] has a very clear meaning in LET and we're talking about measuring absolute speeds, so you shouldn't have any difficulty understanding what it means.

Fine. .866c peculiar velocity, which I already said I assumed.  That has meaning. Dropping the reference is begging your conclusion. I don’t accept LET, so I’m not going to accept a conclusion that is assumed in the description of the setup.
The experiment will behave the same. All clocks will stay in sync relative to the interial frame in which all clocks are stationary. Even LET does not suggest otherwise. It make the exact same empirical predictions (except for the experience of crossing into a black hole apparently).

The difference in results for the two sets of apparatus that you have to get in expanding space

There is no difference unless external forces are involved, changing the proper separation of the objects. Any other result would falsify LET for one thing.

Indeed you shouldn't have to assume them: they are all spelt out clearly in the paper.

Forgive me for not pouring over the details in the paper. It’s wrong right out of the gate, so I didn’t see all the details. I shouldn’t have said that such things needed to be spelt out when I hadn’t checked if they were.

the expansion of space between the two outer clocks would lead to light signals from them to the central clock taking extra time to reach the central clock

That would be remarkable…  I deny this claim unless there are external forces involved accelerating things.

The slowing of clocks isn't about accelerations, but about absolute speeds through space.[/quote]Fine, but you’re not measuring the absolute time of the signals with your setup. You’re measuring the time relative to the inertial frame in which you synced all the clocks. The signal travel time will remain fixed for all eternity relative to that frame.
You have to change the setup if you want to measure the time relative to the cosmological frame, but then it’s relative to that frame, not absolute. Hence I don’t accept that the cosmological frame is absolute. I can create other such frames that behave exactly the same (with the primary clocks ejecting A and B watches and all that). It’s simply a coordinate system relative to an event rather than relative to an inertial frame. Of course the cosmological frame is still unique (preferred if you will) since there is but one obvious objective event in the universe, and it is relative to that event.

think about how when you try to separate two clocks very slowly, you end up with the same synchronisation as if you separated them very quickly to the same distance apart.

Umm… no. You yourself say that it’s all about speed. Doing it fast results in a sync different from a slow transport. Neither method is a valid synchronization method. There are ways to do it. If you wanted to sync a pair of clocks relative to your ‘absolute’ frame, how would you do it? Assume both have known zero peculiar velocity, but it should also be possible between any set of clocks all with the same peculiar speed.

Now, transfer that understanding to the experiment: we have two clocks moving at speeds through space that may only be a little different, but they move through space at different speeds for the same length of time as each other with one of them moving through more space than the other. That leads to a change in their synchronisation.

No it doesn’t, since they were not synced ‘with space’. They will maintain the synchronization which they were initially given.

Spacetime is just a contrived abstraction.

Then LET apparently gives physical meaning to a contrived coordinate abstraction if it denies reality beyond said contrived abstraction.

[David Cooper (OP)]

It would really help if you actually put some numbers to what you expect to happen.

I thought the paper contained all the numbers it needs, but there are actually big mistakes in it which I would have found if I'd just worked out more numbers. The result is that a new paper needs to be written, but there was never any danger of this approach failing: the results merely show up differently from the way I'd previously thought. More on that below.

I see 100 au expanding by 50m in a month. That’s an actual computation. Care to show how you got 50m? I got about twice that.

I got 100m too, which means each one has an additional 50m to send it signal back across to the central clock in the case where we don't maintain the separations, but it isn't 50:50 for all speeds, and that's where I made one of the big mistakes.

Are you asserting that the relatively stationary objects are going to move apart 50m in a month?  I might agree with that only because the pull of the nearby stars might do that. Absent gravity and such, they stay 100 au apart relative to the inertial frame in which they were initially stationary, all per Newton’s first law of motion, which still applies.

Even without any gravity acting on them from anywhere, you can either have them move apart as the space between them expands or you can have them maintain separation simply by setting up their initial speeds differently. I introduced the idea by having them moving in order to help people understand how there is an effect to measure, but I then switched to maintaining the original distance between them so that the extra space being generated between them pushes extra space through them instead. That removed all the problems that the original idea suffered from. We then have a system in which if there's no expansion, all three clocks will remain in sync throughout the entire duration of the experiment, but if the space is expanding and the central clock is at rest, the two outer clocks will still remain in sync with each other throughout the experiment but will both lag behind the middle clock, and the amount by which they lag behind will be the same time that it takes for light to travel 50m. We know that because that's how much a clock will lag by if you move it 50m regardless of the speed you move it across those 50m. Light travels 50m in 167 millionths of a second (which is 167 ticks of a 1GHz processor) and is easy to measure: so easy, indeed, that we likely could reduce the separation to an astronomical unit, but let's just stick with 100 au for now.

If the space is expanding and the clocks are moving along through space such that one of the outer clocks is actually stationary, then the middle clock is going to move along through 50m of space and be 16.7 billionths of a second behind in its timing by the end of a month, while the other outer clock will have moved along though 100m of space and will be twice as far behind with its timing by the end of that month. The original synchronisation will have been skewed of course to fit the chosen speed of travel of the middle clock, because the synchronisation signal from the central clock will have reached the tail clock before the lead clock, but at that time, signals pinged straight back would still have reached the central clock simultaneously. After a month though, that will no longer happen: the signal from the tail clock will return 167 millionths of a second early and the signal from the lead clock will return 167 millionths of a second late, as measured by the central clock, so we have a clear measurable difference.

What happens if we move the clocks faster through space? Let's have the tailing clock move 50m through space over the course of the month while the middle clock moves 100m and the lead clock moves 150m. We now have the same difference in synchronisation as we had in the previous case, so we can't measure the speed difference between the two in the way I originally thought we could: we merely know that the clocks are moving in the same direction as before. So, it turns out that we can't work out their absolute speed from any running of the experiment unless its done in the range of transition where the clocks are nearly at rest. I need to write a new paper to describe this properly. What actually happens then is that we have a constant delay for a wide range of speeds on either side of being at rest, but with the opposite direction of delay for each of those sides. In between we have a rapid transition from a delay one way to a delay the opposite way. That makes it possible to pin down absolute rest with far higher precision than I previously thought could be achieved, and the changeover point would be a clear signal regardless of any gravitational interference, so you wouldn't even have to compensate for that. The downside is that it would take more runs of the experiment to find that zone of changeover. Initially, we would merely find out our direction of travel, and then we'd have to send the apparatus the opposite way at faster and faster speeds each time until we get the signal to reverse.

This is precisely why I wanted to run the paper past you before publishing it, but you weren't interested last time, so I had to publish it in a hurry due to things I'd already put out there about the case involving clocks being made near the time of the big bang which provided an opportunity for someone else to get in first with an experiment that can be done for real. I needed someone like you to push me into debugging it properly, and now that's finally happening, so it'll lead to a better second paper. If I sent my ideas to a journal in the normal way, there would be an opportunity to discuss and correct it before publication, but I can't go down that route as something this big would be stolen in a flash and have someone else's name put on it, so I have to publish directly every time, and having done that, it's no longer within their rules for it to be submitted to them. Now with this new finding, the first place that this latest bit has been published is right here on this forum. I will immediately put it up elsewhere afterwards too though as I like to get multiple time and date stamps on everything.

We’re doing this without gravity or dark energy, so they won’t drift.

Of course they'll drift. If you have the central clock at rest while the outer two are maintaining distance from it with the space expanding in between, those outer clocks have to be moving through space while the middle clock is not moving through any, so they must tick slower than it. If they don't fall behind, they would then have to be moving through space at the same speed as the central clock, but that would mean there could not be any expansion of the space between them.

You seem to not so much be interested in keeping them relatively stationary as much as computing their time dilation due to their peculiar motion? But your clocks were never synced in that coordinate system, so no comparison can be made. All clocks will stay in sync forever in the inertial frame in which all of them are stationary.

The whole point is that they can't all be stationary because of the expansion of space: they have to be moving at different speeds through the expanding space in order to maintain their separation distances, and clearly that's going to show. I imagined incorrectly before how the space was moving through them when they're moving at high speeds, and that made me think you'd get a bigger and bigger change in synchronisation between them the faster you move the apparatus through space, but no: I now think it's constant, except where it makes the transition from going one way to the opposite way, and at that point there's a massive signal in the change in direction of the lag when the tail clock switches over to being the lead clock. So, what you actually want to do is run the experiment to find out what the lag is, and that tells you the direction the clocks are moving in. You then slow it down by decelerating the system in the direction of the tail clock, and you just keep on doing so repeatedly. Once it reaches the point where the lead clock is at rest, the direction of the lag will change, reversing after the middle clock is at rest.

To measure that, you’d have to sync the clocks relative to the cosmological frame, and you haven’t done that.

You don't. All you do is send out a signal from the central clock to the outer ones, and then they send signals back to the central clock many times. You keep sending signals both ways, of course, to maintain the same separation between them, but you don't keep correcting the main clocks: you just let them drift and look at the lags in the arrival of their specific signals.

The experiment will behave the same. All clocks will stay in sync relative to the interial frame in which all clocks are stationary. Even LET does not suggest otherwise. It make the exact same empirical predictions (except for the experience of crossing into a black hole apparently).

No: LET predicts that the clocks are moving through space at different speeds and that they will tick at different rates as a result. STR predicts that they are all moving at the same speed relative to each other and that they will all tick at the same rate. That opens the way to test the theories by experiment and either disprove STR in expanding space, or disprove the idea that the space there is expanding, which would be devastating a much more important theory. If the space is expanding, you necessarily have a different speed of light relative to the lead clock than the tail clock in both directions along the line, and that is why STR cannot handle this case correctly. If you make the experiment big with the lead clock in one distant galaxy and the tail clock in another as far away from us in the opposite direction, then both of them are hurtling through those galaxies at relativistic speeds to maintain their distance to us, and yet we know that those galaxies are approximately at rest in their local space.

The slowing of clocks isn't about accelerations, but about absolute speeds through space.

Fine, but you’re not measuring the absolute time of the signals with your setup. You’re measuring the time relative to the inertial frame in which you synced all the clocks. The signal travel time will remain fixed for all eternity relative to that frame.

The travel time for the signals does indeed remain constant, but when the tail clock is moving through space at a lower speed than the lead clock, the lead clock sends those signals out with a longer and longer delay each time, so they arrive late.

think about how when you try to separate two clocks very slowly, you end up with the same synchronisation as if you separated them very quickly to the same distance apart.

Umm… no. You yourself say that it’s all about speed. Doing it fast results in a sync different from a slow transport. Neither method is a valid synchronization method.

Of course it's valid. One method of synchronising clocks is to send out simultaneously pulses of light to two clocks in opposite directions from half way between them, and they set themselves to zero when the signals arrive. If instead, from the same starting point, you send two synchronised watches out with one covering the distance to one clock in an hour and the other taking a day to get to the other clock, and then when those transferred watches read a particular time you set the two destination clocks to zero, you have sychronised them for the same frame as before. The speed at which you move a clock through space does not lead to a different synchronisation for the target clocks. Moving a clock delays it, and the delay that you get is the same size for a given distance of movement, and that delay is identical to the amount of time light takes to cross that distance. So, the delay to a clock from having space pass through it is the same as the time it takes for light to travel through that space.

Spacetime is just a contrived abstraction.

Then LET apparently gives physical meaning to a contrived coordinate abstraction if it denies reality beyond said contrived abstraction.

Spacetime is a contrived abstraction of something else that fits reality more accurately, and LET describes that reality more accurately by not making irrational predictions about what goes on inside black holes: that's where the predictions between GTR and LET diverge. But at the moment we're dealing with a place where the predictions of STR and LET diverge, so exploring that is the priority for the moment.

[Halc]

I then switched to maintaining the original distance between them so that the extra space being generated between them pushes extra space through them instead. That removed all the problems that the original idea suffered from. We then have a system in which if there's no expansion, all three clocks will remain in sync throughout the entire duration of the experiment, but if the space is expanding and the central clock is at rest, the two outer clocks will still remain in sync with each other throughout the experiment but will both lag behind the middle clock

But they won’t lag, for the reasons I repeatedly pointed out, and that you will not see because you’re too busy knowing that you’re right.

and the amount by which they lag behind will be the same time that it takes for light to travel 50m.

That is even more wrong. If the clocks had been synced relative to what you call the absolute frame, the lag will be a month of time dilation from the blistering motion of a millimeter per minute. I don’t have a calculator with enough digits to express that. Irrelevant because the clocks were not synced that way, so they’ll not lag at all.
Say Earth is stationary. The ISS moves relative to Earth about 660000 km (about 2.2 light seconds) each day. According to you a clock on the ISS would run 2.2 seconds slow per day instead of the actual figure of about 26 microseconds.

This is precisely why I wanted to run the paper past you before publishing it

It is hard to review because you don’t have any mathematics in it. None of what I’m pointing out above is in the paper. Nowhere do you mention something like 167 milliseconds.
This is why I wanted numbers because I could have shown all this ages ago. It is difficult to critique a paper which doesn’t spell out what numbers are expected.

an opportunity for someone else to get in first

Time is not of the essence. Nobody is racing to find this, since it doesn’t demonstrate anything. Both interpretations predict the exact same numbers. If you don’t get identical numbers, you’re making a mistake. Thus there is no conclusion since there’s no distinct results from one interpretation or the other.

We’re doing this without gravity or dark energy, so they won’t drift.

Of course they'll drift.

Yes, they will, because the real universe has gravity. A thing in orbit cannot be inertial. I cannot think of an object in the universe that isn’t accelerating all the time relative to any coordinate system you can think of except its own proper local frame, and even then…
This is why I’m concentrating on the gravity-free hypothetical case. A test that doesn’t work in the ideal case doesn’t need to worry about being made practical.

You seem to not so much be interested in keeping them relatively stationary as much as computing their time dilation due to their peculiar motion? But your clocks were never synced in that coordinate system, so no comparison can be made. All clocks will stay in sync forever in the inertial frame in which all of them are stationary.

The whole point is that they can't all be stationary because of the expansion of space: they have to be moving at different speeds through the expanding space in order to maintain their separation distances, and clearly that's going to show.

This is what I mean. I tell you what’s wrong, and you don’t hear it. Actually read what I say and don’t just assume I’m wrong.
You didn’t sync your clocks ‘with space’, so it doesn’t show what you’re trying to show. If you did sync them that way (no proposed method to do this is mentioned in the paper, which is probably good since clocks ticking at different rates cannot be meaningfully synced), then indeed, relative to that non-inertial coordinate system, the moving ones will lag (by a number far to small to measure by current technology) and this lag is exactly predicted by relativity as well, so it doesn’t falsify either interpretation.

All you do is send out a signal from the central clock to the outer ones, and then they send signals back to the central clock many times. You keep sending signals both ways, of course, to maintain the same separation between them

Sending signals does not help maintain separation. If they’re stationary relative to some inertial frame, they’ll stay that way. Unclear what all these repeated signals do. One signal sent from the central place is enough to sync (to set to zero say) the outer ones with each other.  After that, any subsequent signals will be received by the center in exact normal rate with no additional lag at all, even under your interpretation. You seem entirely unaware of this.
Even in your interpretation, if the central clock is ‘stationary’ and the outer ones are moving inward slowly to maintain constant proper distance, the signals from the outer clocks (sent every local second say) will arrive at the central clock every second, exactly. The 3 clocks are not in (absolute) sync with each other, but that doesn’t change the rate at which the central clock will receive the signals.

No: LET predicts that the clocks are moving through space at different speeds and that they will tick at different rates as a result.

That’s a metaphysical assertion, not an empirical prediction. LET does not make different empirical predictions (again, apparently excepting the black hole thing, which is sort of like religion making a different empirical prediction about the afterlife: The experiment can be performed, but the observer is safely prevented from reporting his findings to the rest of us).

STR predicts that they are all moving at the same speed relative to each other and that they will all tick at the same rate.

STR makes no such metaphysical assertions, and you’ve declined to provide a reference where it does. STR only predicts what will be measured at specific events. Do you understand the difference? Your experiment can only be based on measurements, not on assertions. You can’t directly measure the separation between two things because you can’t be at both ends at once, so be very specific about how you’re going to know the separation of things and which coordinate system is used to express the result.

The travel time for the signals does indeed remain constant

Have you computed that or is this just another guess? This would be come far more apparent if you scaled it up to gigaparsecs instead of 7 light hours. Don’t guess.
You set it up with constant proper separation of the clocks relative to an inertial frame so say the clocks are held separated with a 100 AU rigid stick.  Using the cosmological coordinate system, the distance between clocks is always shorter than 50 AU due to length contraction of the moving ends. The proper separation of those clocks is increasing due to that motion slowing down over time.

think about how when you try to separate two clocks very slowly, you end up with the same synchronisation as if you separated them very quickly to the same distance apart.

Doing it fast results in a sync different from a slow transport. .

If instead, from the same starting point [equidistant between two end points], you send two synchronised watches out with one covering the distance to one clock in an hour and the other taking a day to get to the other clock, and then when those transferred watches read a particular time you set the two destination clocks to zero, you have sychronised them for the same frame as before.

This is nonsense even in your interpretation, which is apparently the one you’re using due to the lack of frame references. The watch spending an hour at speed is going to be behind the one that did the same distance in a day.  Say the separation is .95 light hours each way. Both watches are zeroed and sent out at midnight. The fast watch moves at .95c, gets there at 1AM and reads 12:18:45 which is 41:15 behind. The slow watch goes the same .95 LH distance in a day at .0396c and reads 11:58:52 PM which is 1:08 behind. That’s over 40 minutes out of sync. I think you need to review the basics. Everything of yours seems to be based on guesses. Run the numbers. Your reaction to all my posts seems to be a knee-jerk reaction to disagree with everything rather than to actually consider the possibility that your guesses are wrong.

[David Cooper (OP)]

But they won’t lag, for the reasons I repeatedly pointed out, and that you will not see because you’re too busy knowing that you’re right.

They'll only fail to lag if the space isn't expanding. You cannot have one clock at rest in space while the other two are moving through space with all their clocks ticking at the same rate. You asked me to go big with this and I did: I gave you an example with the two end clocks in distant galaxies on opposite sides of the sky from us while the central clock is here. To maintain the same separation, those distant clocks have to travel through those galaxies at relativistic speed. Clocks at rest in those galaxies are ticking at about the same rate as our clock here, but the distant clocks that are hurtling through those galaxies to maintain a constant distance from us can't tick at that same rate as those local clocks at rest without destroying the twins paradox locally where they are.

If the clocks had been synced relative to what you call the absolute frame, the lag will be a month of time dilation from the blistering motion of a millimeter per minute.

Why are you trying to synchronise them by any frame other than the one in which the central clock is at rest? Not that it actually matters though as all we need is a measure in the change in the synchronisation over a month, so any initial synchronisation at all would actually do. I had misremembered how slow clock transport works though, so you're right about that part of the problem: the separation between the clocks needs to be much bigger to get a significant speed difference through space for them, and that makes the experiment much harder to do, so again your help in debugging this has been invaluable.

Both interpretations predict the exact same numbers. If you don’t get identical numbers, you’re making a mistake.

They don't. When you put the outer clocks in distant galaxies you can see that: they must tick much more slowly than the central clock. We're now back to having a smooth change in the lag for the absolute speed of travel of the apparatus rather than a distinct signal as you do it within close range of it being at rest, so there's no sudden clear signal of the kind I imagined last night. But the principle remains right: the two theories do not predict the same numbers. Clearly the experiment may be a lot harder to do than I'd hoped, though, we have much more accurate atomic clocks now than we used to, so what do the numbers say about that:-

With an aeroplane moving at 500 mph we have a loss of 3 millionths of a second per month. (I found that at the bottom of this page http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/airtim.html where it gives the difference over 48 hours.) With our clocks 100 au apart we have roughly 60 mm per hour of speed difference, so that's a long way short: we'd need the clocks to be a trillion au apart for the same size of signal. However, we have much more accurate clocks available than at the time of Hafele Keating: our best atomic clocks can now measure ticks as small as 10^(minus19) seconds, or a tenth of a billionth of a billionth of a second. That's a tenth of a millionth of a trillionth, so we have ten trillion times as much accuracy as is needed to detect the loss of 3 millionths of a second in a month with a 500mph speed. That should allow us to bring the trillion astronomical units down a fair chunk, but I don't know how much? I can't get my calculator to make a prediction for the 500mph case as it runs out of precision along the way, so that makes it difficult to work with any lower speeds than that.

Edit: I've found a workaround for that. The speed 0.1c leads to a clock ticking 0.995 as often as a clock at rest. Try it again with 0.01c and you get 0.99995, so you just stick a couple of extra nines in there. Try it again with 0.001c  and you get 0.9999995, so again you just stick another pair of nines in, and that pattern goes on repeating. So, for every division of the speed by ten, we need a hundred times more resolution with the timers. That means that our ten trillion times (13 zeros in there) more precision than is needed for 500mph = 220m/s =  220000mm/s, we can get rid of at least six of those zeros, taking us down to under 2mm/s. It wouldn't surprise me if there's a big error in there somewhere, but I'm up late and I'm too tired to check it again right now.

A thing in orbit cannot be inertial.

We don't allow the clocks to follow orbital paths.

You seem to not so much be interested in keeping them relatively stationary as much as computing their time dilation due to their peculiar motion? But your clocks were never synced in that coordinate system, so no comparison can be made. All clocks will stay in sync forever in the inertial frame in which all of them are stationary.

The whole point is that they can't all be stationary because of the expansion of space: they have to be moving at different speeds through the expanding space in order to maintain their separation distances, and clearly that's going to show.

This is what I mean. I tell you what’s wrong, and you don’t hear it. Actually read what I say and don’t just assume I’m wrong.

You assert that it's wrong, but it isn't. Go back to the big version with the end clocks in distant galaxies maintaining their distance to us while those galaxies which are at rest in their local space move out past them. The end clocks must be ticking slower than the central clock is doing here. Clocks in those distant galaxies which are at rest are ticking at the same rate as the central clock here, but the end clocks aren't at rest in the places where they are..

You didn’t sync your clocks ‘with space’, so it doesn’t show what you’re trying to show. If you did sync them that way (no proposed method to do this is mentioned in the paper, which is probably good since clocks ticking at different rates cannot be meaningfully synced)...

The method to sync them is spelt out clearly: a signal is sent out from the middle clock. It doesn't matter that the clocks are ticking at different rates because they will both start timing when that signal reaches them and we don't require them to remain in sync - the whole point is to see how much they go out of sync from that moment on.

and this lag is exactly predicted by relativity as well, so it doesn’t falsify either interpretation.

It is not predicted by STR.

Sending signals does not help maintain separation.

In the paper I described how it does. The clocks are inside boxes which shield them from gas and dust, while these boxes can change their speed and direction of travel with ion thrusters. These boxes can be buffeted about a bit while using the continual series of signals to maintain the right separation, transferring energy to the clock inside to make it maintain that separation with greater accuracy by shooting photons at it.

After that, any subsequent signals will be received by the center in exact normal rate with no additional lag at all, even under your interpretation. You seem entirely unaware of this.

Of course they arrive without any lag: that's the whole point of them: they are used to maintain the separation, while this process does not update the clock in the box which is being used for the experiment.

That’s a metaphysical assertion, not an empirical prediction. LET does not make different empirical predictions

It most certainly does. In LET the ticking rates of clocks are governed by absolute speeds through space, and the clocks have different absolute speeds through space.

STR predicts that they are all moving at the same speed relative to each other and that they will all tick at the same rate.

STR makes no such metaphysical assertions, and you’ve declined to provide a reference where it does. STR only predicts what will be measured at specific events. Do you understand the difference?

Nonsense: STR is absolutely clear about what will happen to the three clocks which are not moving relative to each other - it does not allow them to tick at different rates. No reference is required for anything so fundamental to the theory.

Your experiment can only be based on measurements, not on assertions. You can’t directly measure the separation between two things because you can’t be at both ends at once, so be very specific about how you’re going to know the separation of things and which coordinate system is used to express the result.

It is sufficient to maintain the separation which has its length measured using the frame in which the central clock is at rest: that's a trivial thing to measure as you can just ping a light pulse out to the ends and back and time that round trip.

The travel time for the signals does indeed remain constant

Have you computed that or is this just another guess?

Why would you argue against that when you've made the same claim yourself? Remember this: "After that, any subsequent signals will be received by the center in exact normal rate with no additional lag at all, even under your interpretation. You seem entirely unaware of this."

Using the cosmological coordinate system, the distance between clocks is always shorter than 50 AU due to length contraction of the moving ends. The proper separation of those clocks is increasing due to that motion slowing down over time.

You don't need to consider that as the separations are controlled by the central clock and must remain equal in length: they are not length contracted if the central clock is at rest. The central clock will complain if the signals are returned too soon.

Edit:

The problem of interference by gravity can be addressed by running a double-length version of the experiment alongside two sets of the standard length version. This places the clocks of different versions nearly side by side with clocks in other sets where they're at the same depth in gravity wells as each other. The bigger version will amplify the amount of "time dilation" caused by the difference in speed between its outer clocks while the component of slowing caused by gravity will not change. This should make it possible to separate the latter effect from the one we want to measure and allow the former to be measured with high precision (and with higher and higher precision as we continue to make more accurate clocks).

[Halc]

Apologies. Been a while, but I’ve actually been running some numbers to get a better feel for how this all works. A great deal of the trouble with communication between us is your refusal to specify the coordinate system you’re using. It would be OK if you consistently used only one, but you don’t, and you switch back and forth between them and think some fact that’s true in one coordinate system (the sync of clocks, the distance between them, etc.) will be the same, when they’re not. It doesn’t help that you’ve picked an example that so completely local (only ~7 light hours between clocks) that the differences are immeasurable, but your proposal is to measure exactly that, and you will fail because A) you haven’t computed what you expect to measure, and B) You are not setting up the scenario using cosmological coordinates, but you switch to those coordinates when you want to assert something like this:

They'll only fail to lag if the space isn't expanding.

No coordinate system specified, so this metaphysical statement is ambiguous, and I didn’t assert otherwise. I said there would be no measured lag at the central point or wherever it is the measurements are being taken.
If you want to make a metaphysical assertion like that, be specific with a coordinate system, else we just keep going round in circles. Your paper says the 3 clocks are stationary relative to inertial frame A (the paper just says 'frame A', but doesn't say inertial). An inertial coordinate system is a different coordinate system than the one with the lag. Same spacetime, but different ordering of events. It’s a purely abstract difference. What matters is what is measured. That’s not abstract. That’s empirical, and the clock in the center will get signals at regular intervals from the end clocks, not lagged at all. This, not being a metaphysical assertion, must be true regardless of coordinate system of choice.
If the one clock is 7 light hours (LH) away as measured in inertial coordinates, then using the cosmological coordinates, the separation between those clocks will be < 7LH, but increasing. The time it takes to get a signal from the distant clock will be >7 hours and decreasing. This is because space expands between them while the signal is in flight, so it has further to go. Yes, the clock lags, but since the travel time is decreasing, the measurement taken at the central clock will be exactly 1 second apart, exactly as predicted by all theories involved.
All t his would be far more apparent if you scaled up the experiment to significant distances so the difference isn’t all the way into the 40th decimal place (I didn’t work it out, my calculator doesn’t have enough digits).

Why are you trying to synchronise them by any frame other than the one in which the central clock is at rest?

Which frame would that be, the inertial one or the cosmological one? The central clock can be at rest in both of them. So still ambiguous. Be clear!
In cosmological coordinates, if two objects maintain separation distance at a given time (which is different than having identical velocity), then that constant separation distance will only be temporary, and they’ll start to move together and eventually meet. It would require proper acceleration of one or both of the objects to maintain this constant separation as measured in cosmological coordinates. This is one of the things I found out when working through the numbers.

Both interpretations predict the exact same numbers. If you don’t get identical numbers, you’re making a mistake.

They don't.

Then either your proposal differs from LET, or you assert that LET is falsifiable. Somehow I don’t think your grasp of the theory is up to the latter, so you’re making up new stuff now.

When you put the outer clocks in distant galaxies you can see that: they must tick much more slowly than the central clock.

Depends on your choice of abstract coordinate system. You never specify it. Want me to count how many times in one post you do it? This is about 4 now.

With an aeroplane moving at 500 mph we have a loss of 3 millionths of a second per month.

5.  Maybe the aeroplane is more stationary when it flight. The H-K experiment certainly showed this with the westbound flight.

Edit: … So, for every division of the speed by ten, we need a hundred times more resolution with the timers.

Yes.

A thing in orbit cannot be inertial.

We don't allow the clocks to follow orbital paths.

You put in in interstellar space just outside the solar system. That puts it in orbit about the galaxy, involving acceleration that will dwarf the sort of time differences you’re trying to measure. That’s why I put it in a universe completely free of gravity and dark energy. Your setup needs to be stationary and needs to stay that way without proper acceleration.

The method to sync them is spelt out clearly: a signal is sent out from the middle clock.

But are your outer clocks moving apart? In which coordinate system are they maintaining constant separation, because it can’t be both. You didn’t specify how you accomplished it. In particular, no mention of coordinate system was made. Things were not ‘spelt out clearly’. It very much matters because constant separation in one coordinate system gives different empirical results than constant separation in a different coordinate system.

In the paper I described how it does. The clocks are inside boxes which shield them from gas and dust

There is no gas and dust in our ideal universe with no galaxy yanking the thing around. That’s a practical concern, but we’re nowhere near the practical yet.

These boxes can be buffeted about a bit while using the continual series of signals to maintain the right separation, transferring energy to the clock inside to make it maintain that separation with greater accuracy by shooting photons at it.

Fair enough. We can have something shoot photons from the opposite direction to cancel that.  Or (if you accept the inertial coordinates) we could just attach all the parts to a stick or a slab of granite like they do in the lab. That method doesn’t work in cosmological coordinates.

That’s a metaphysical assertion, not an empirical prediction. LET does not make different empirical predictions

It most certainly does. In LET the ticking rates of clocks are governed by absolute speeds through space

That’s not an empirical measurement. It’s a metaphysical assertion. You seem not to know the difference at all.

STR is absolutely clear about what will happen to the three clocks which are not moving relative to each other - it does not allow them to tick at different rates.

STR makes no such assertion, and it certainly cannot be demonstrated from the premises.

It is sufficient to maintain the separation which has its length measured using the frame in which the central clock is at rest

It’s at rest in both coordinate systems, so you still need to specify the coordinate system if you want to be clear.

that's a trivial thing to measure as you can just ping a light pulse out to the ends and back and time that round trip.

That is an empirical prediction. Using cosmological coordinates, if you are stationary and there is a mirror out there held at a constant distance (as measured by said cosmological coordinates), the round trip times will shorten over time. The first one will take longer than the second one. Do you not know this? It’s kind of obvious if you think about it. Point is here, you can’t use such a method to maintain constant separation relative to that kind of coordinate system. It only works for inertial coordinates. Ditto with the granite slab.

The travel time for the signals does indeed remain constant

Have you computed that or is this just another guess?

Why would you argue against that when you've made the same claim yourself?

Travel time is an abstract concept is constant in this scenario only using inertial coordinates.

Remember this: "After that, any subsequent signals will be received by the center in exact normal rate with no additional lag at all, even under your interpretation.

That makes no mention of travel time (a relationship dependent on one’s abstract coordinate system of choice). It mentions only what will be measured at one location, which is a coordinate system independent empirical claim. You really don’t know the difference.

Edit:
The problem of interference by gravity can be addressed

If you’ve no grasp of the ideal situation, it’s not time to try to deal with the real universe with its gravity and such.