[Halc]

Now now, the condition is that the galaxy is stationary as you defined above.

There are two cases, and you're homing in on the one that doesn't directly show up anything. You have to look at the other case that you see what matters here.

There is no other case. The FLRW model doesn't allow for a fast moving object unless it has recently accelerated. There's nothing in existence massive and energetic enough to accelerate an entire galaxy to significant speeds, so there is no other case.  Hence my firing the clock out of the galaxy. Acceleration at some point is necessary.  12 billion years ago isn't 'recently', so it will not pass us by at any particularly great velocity, as per the FLRW solution to Einstein's field equations.

Computations please.  You make it sound like some other theory predicts different numbers.

You should be able to fit your own numbers to it without needing help from me.

I'm not the one making a claim about a difference in a pair of theories. You're the one claiming some sort of inconsistency with a theory. You should be able to show where the numbers don't work out. I should be able to show the errors in your calculations, but I've seen none.

I gave you numbers. "Much younger" contains a number. "Ages more" contains a number.

Fair enough.  GR predicts the clock will have less than 12 billion years on it when it gets here.  No contradiction so far.  Not sure what you consider to be 'much less'.  My gut says maybe 9-10 billion years on the clock, but that's just my gut. That doesn't sound like 'much less'.

In case 2, the speed of the galaxies is any high relativistic speed, so you can make that anything from 0.99999999c or 0.9c.

But no theory posits a galaxy moving at a speed like that, except in a local exotic inertial frame (such as the inertial frame of a muon striking Earth), which, being local, is pretty meaningless at a larger scale. The muon was recently accelerated. The galaxy cannot be.

I don't know why you want me to choose specific numbers when I'm giving you a free choice.

I did choose.  I said relative speed between the clock and the galaxy that ejects it is arbitrarily close to light speed. I chose a case where it gets here now given a ballistic trajectory from a point in time when the universe appears 1.7 GY old. I specifically pushed it that far back so that the clock wasn't 'recently accelerated'.
I used a clock since that is a better indication of age than that of a hypothetical immortal human. Not sure why there needs to be observers travelling with clocks, but you can add them if you want.

In case 2, all the multuplets are created at the same time again

No, they're not created at the same time since you're not ordering their ages in the same way as the FLRW coordinate system. In any inertial frame, the ages multuplets from case 1 are all out of sync. Or are you unware of RoS?

Case 1: the galaxies are stationary. The multuplets ejected from them at 0.999...c practically stop aging as they travel through space, so when multuplets pass us, we see them in an ancient state.

Oopsie. This only happens in a SR universe, and you said you were not using that model.  And we would see them in a very young state, almost no time on the clocks.
Use a model where the universe is expanding. They'll pass by quite slowly, and have billions of years on their clocks.

Case 2: the galaxies are moving at 0.999...c.

No theory allow this, not LET and not GR. Of course it will fail.

Some of he multuplets ejected from them are moving through space at zero, and when we run across them we can see that we are the ones in an ancient state compared to them.

Oopsie again. What they see is objective fact, and cannot differ just due to an abstract coordinate change. If your theory predicts the above statement, then it is wrong. They will see our unaccelerated clocks with more time on them than on their accelerated clocks. Acceleration is objective after all.

you fall in line behind [establishment nonsense] instead of trusting your own mind.

I trust my mind fine. I've not looked at any websites or anything during this discussion. I've managed to point out several mistakes in your 'numbers' above, mostly due to failure to apply RoS through a coordinate system change. You're making amateur mistakes.

Case 1: galaxy speeds = 0. Travelling multuplets' speed, a fraction under c. Age of all travelling multuplets is much younger than the stay-at-home multuplets in the galaxies they're passing.

They'd have to continuously accelerate to do something like that. But they're posited as being ballistic, so this isn't true. There are galaxies that their light will reach but their ballistic selves will never reach, which would not be true if all these galaxies are flying by in pretty much negligible time. There are further galaxies that even their light would never reach, which would not be true in any universe described by STR at a large scale. Even continuously accelerating observers could never reach these galaxies since there is no way to overtake their own light which cannot reach them.

Why the heck would anyone need to ask for specific values about their exact ages for that when the travelling ones must be younger in all possible illustrations of case 1?

Because your assertions are wrong, and numbers show this better than talk. Otherwise I wouldn't much need it.

Again, why the heck would anyone need to ask for specific values about their exact ages for that when this subset of the travelling multuplets must be older in all possible illustrations of case 2?

Because you did a frame change and still asserted that all their ages were the same. RoS says that cannot be.  FLRW says nothing is capable of accelerating a galaxy to the kinds of speeds you're talking about.  If it cannot accelerate, and the mass/energy from which it is composed has existed since the big bang, then it is still stationary.  Motion slows under FLRW coordinates, which is why nothing can move fast for long, and why the clock will pass us by at a sedate speed no matter the power of the explosion that sent the thing our way.

Either you should accept that or you should provide your numbers for a counterexample which breaks the above claims.

I did. I said 'no fast galaxies' and 'sedate speed'.

[David Cooper]

Now now, the condition is that the galaxy is stationary as you defined above.

There are two cases, and you're homing in on the one that doesn't directly show up anything. You have to look at the other case that you see what matters here.

There is no other case.

Of course there's another case. There are two possible cases, and both of them can be combined into a single case, which is how the proof works. If you aren't prepared to try to understand case 2 for ideological reasons, you're rendering yourself incapable of grasping a crucial part of the the method.

When we're dealing with case 1 where the multuplets are all formed in systems that aren't moving at relativistic speed, they're intelligent enough to see what you keep missing, which is the thing that I came up with in the space of ten seconds two days ago and which you still haven't caught up with. They realise that even if they're in  a case 1 universe, they can create case 2 within it. They all have the wit to send out travelling multuplets at relativistic speeds in many directions, and those travelling multuplets then send out clocks at relativistic speeds relative to them in many directions. Each of those clocks comes with recorded details of its past. Set A of the travelling multuplets are all the ones moving along parallel paths aligned with the direction we call north. Each of them will have defined that direction with reference to distant objects in the universe straight ahead of and behind them, and the name "set A" is applied to them retrospectively when they've been grouped with others moving along parallel paths. The same documentation is carried by all the clocks that they send out. Some of those clocks will be sent out ahead at even higher relativistic speed, but others will be sent out behind and will end up with non-relativistic speed. Set A of multuplets and the clocks sent out by that set serve as a case 2 scenario within a case 1 scenario.

Ten seconds is all it took for me to spot this, and I didn't have anyone else spelling it out to help me, so what's taking you so long? But you're still the fastest mind I've found to discuss this kind of thing with.

I'm not the one making a claim about a difference in a pair of theories. You're the one claiming some sort of inconsistency with a theory. You should be able to show where the numbers don't work out. I should be able to show the errors in your calculations, but I've seen none.

You've been given numbers which are fully adequate. What's stopping you working with them? "More" is a number. "Less" is a number. Learn how to use them.

I gave you numbers. "Much younger" contains a number. "Ages more" contains a number.

Fair enough.  GR predicts the clock will have less than 12 billion years on it when it gets here.  No contradiction so far.  Not sure what you consider to be 'much less'.  My gut says maybe 9-10 billion years on the clock, but that's just my gut. That doesn't sound like 'much less'.

If we go for really extreme speeds, you don't need to reach for a calculator at all to handle this. The high relativistic speed can be so close to c that we can just treat it as c and assume practically no aging at all for the object moving at that speed. Suppose the multuplets are all created a billion years after the big bong. Some of them are sent out in many directions at close to c. These travellers are encountered by other stay-at-home multuplets in other galaxies ten billion years later, and in case 1 they find that the travelling multuplets are a year old while the stay-at-home ones who meet them are ten billion years old. If it's case 2 though, it's radically different. The stay-at-home multuplets have aged a year while the travelling ones moving in some directions have aged ten billion years (while the ones moving in the opposite direction have aged only a fraction of a second). The case 2 result allows the absolute frame's identity to be pinned down to a small range. The case 1 result also does this, but it only becomes clear that this is so after you've realised that case 1 and case 2 have to be able to coexist in the same system.

The multuplets sent out from case 1 galaxies (when the universe is a billion years old) who immediately send out clocks in many directions become a case 2 system within a case 1 system. Set A of those multuplets can look at clocks passing them which were sent out by other set A multuplets and the find that the clocks in that set are aging faster then them if they're moving relative to them in one direction and slower than them if they're moving in the opposite direction. This provides a means to break relativity within a single system.

But no theory posits a galaxy moving at a speed like that, except in a local exotic inertial frame (such as the inertial frame of a muon striking Earth), which, being local, is pretty meaningless at a larger scale. The muon was recently accelerated. The galaxy cannot be.

It doesn't matter that no theory suggests the galaxies are moving at relativistic speed, but LET says that they could be (while STR has difficulty doing the same because it wants everything to be stationary and plays illegal frame-changing games to try to make that so). The proof doesn't depend on galaxies moving that fast, but that case must be considered as a possible reality. Even then, the proof still doesn't depend on them moving that fast because it doesn't need fast-moving galaxies to create a case 2 system. It can make a case 2 system within a case 1 system by sending out multuplets at relativistic speed who then send out clocks at what look to them like relativistic speeds.

I don't know why you want me to choose specific numbers when I'm giving you a free choice.

I did choose.  I said relative speed between the clock and the galaxy that ejects it is arbitrarily close to light speed. I chose a case where it gets here now given a ballistic trajectory from a point in time when the universe appears 1.7 GY old. I specifically pushed it that far back so that the clock wasn't 'recently accelerated'.

I have no problem putting numbers to this, and you shouldn't have any either. I'm not going to complete your calculations for you when it's so obvious that the results will confirm what I've said.

I used a clock since that is a better indication of age than that of a hypothetical immortal human. Not sure why there needs to be observers travelling with clocks, but you can add them if you want.

They are essential to create a case 2 system within a case 1 system. If you only have a case 2 system, you only need to see the age of multuplets passing you to be able to pin down the absolute frame. If you have a case 1 system you can actually do the same thing, but you don't necessarily realise that until you think things through with a case 2 system created within a case 1 system where you can then appreciate that you can't have a case 1 system within a case 1 system where the two case 1 systems are moving relative to each other. One of them has to be a case 2 system, and the existence of a case 2 system allows you to pin down the absolute frame. All case 1 systems are capable of hosting a case 2 system, so in all systems you can pin down the absolute frame, though it's tricky to do and takes a long time. The next step is to try to reducing the time needed to run an experiment of this kind to see if it can be turned into one that could be done within the space of a few decades rather than needing billions of years, but it may not be possible without the help of intelligent aliens in other galaxies who can serve as other groups of multuplets, and it may be impossible to get the results in less than hundreds of billions of years given how long it's actually going to take before we can all begin the experiment.

In case 2, all the multuplets are created at the same time again

No, they're not created at the same time since you're not ordering their ages in the same way as the FLRW coordinate system. In any inertial frame, the ages multuplets from case 1 are all out of sync. Or are you unware of RoS?

They are all created at around the same time after the big bang. We aren't using the time of a skewed frame: we have an expanding universe with an even expansion across the part of the universe we're using, and with the galaxies all moving in such a way that they're close to being at rest in space rather than moving through it at relativistic speed, they are aging at the same rate and starting the experiment the same length of time after the big bang in each galaxy.

Case 1: the galaxies are stationary. The multuplets ejected from them at 0.999...c practically stop aging as they travel through space, so when multuplets pass us, we see them in an ancient state.

Oopsie. This only happens in a SR universe, and you said you were not using that model.  And we would see them in a very young state, almost no time on the clocks.

This happens in an LET universe. It happens in our universe - we know that because we've tested it. Those multuplets will have their functionality practically halted as they move at c. STR also requires them to age hardly at all between leaving one galaxy and arriving at another. These assessments of ages are also not things that vary for different observers: all observers see them as being the same specific age when they arrive at another galaxy. The same traveller on reaching galaxy X cannot be seen as being older than the native multuplets of that galaxy by one observer and younger than them by another observer. The measured ages are invariant facts.

Use a model where the universe is expanding. They'll pass by quite slowly, and have billions of years on their clocks.

If you're imagining the travellers slowing down and aging a lot as a result, then that's fine: they're still going to be moving faster through space than the stay-at home multuplets and will age less than them in case 1, whereas in case 2, they would age more than the stay-at-home ones.

Case 2: the galaxies are moving at 0.999...c.

No theory allow this, not LET and not GR. Of course it will fail.

LET does allow for it. The lack of any obvious mechanism for all the galaxies being made to move so fast straight out of the big bang doesn't allow us not to consider the possibility of it happening, but again we don't need to rely on being in a case 2 universe because we can create a case 2 system within a case 1 universe, and that's why you should make the effort to understand how a case 2 system works instead of failing to do the necessary thinking on the basis that you don't believe a case 2 universe can happen. We don't need it to happen, but to understand the proof, you need to get your mind round it regardless and stop sabotaging your own thinking.

Some of he multuplets ejected from them are moving through space at zero, and when we run across them we can see that we are the ones in an ancient state compared to them.

Oopsie again. What they see is objective fact, and cannot differ just due to an abstract coordinate change. If your theory predicts the above statement, then it is wrong. They will see our unaccelerated clocks with more time on them than on their accelerated clocks. Acceleration is objective after all.

Ten seconds, it took for me to see the whole thing. I'm not going to call it two days for you as that would be unfair, but given the amount of writing you've now done about this, we're talking about a good few minutes. What they see is facts agreed on by all observers. In a case 1 system, the travellers all age less than the non-travellers. In a case 2 system, some of the travellers age less than the non-travellers, and this is measured by all observers (after the fact, when images of the travellers meeting the non-travellers reach them). We're not making any coordinate change: we're dealing with single systems in which we either get a case 1 result or a case 2 result. And if we set up a case 2 system within a case 1 universe, we can see case 2 results and use them to pin down the absolute frame.

I trust my mind fine. I've not looked at any websites or anything during this discussion.

You've brought all that establishment baggage along for the ride and it's hampering your efforts to understand the proof.

I've managed to point out several mistakes in your 'numbers' above, mostly due to failure to apply RoS through a coordinate system change. You're making amateur mistakes.

On the contrary, you have found no mistakes in my numbers, but have merely mauled the maths. You are the one making amateur/professional mistakes.

Case 1: galaxy speeds = 0. Travelling multuplets' speed, a fraction under c. Age of all travelling multuplets is much younger than the stay-at-home multuplets in the galaxies they're passing.

They'd have to continuously accelerate to do something like that. But they're posited as being ballistic, so this isn't true.

We don't need to care about them slowing down: they are going to be moving faster than their stay-at-home equivalents in case 1 thoughout their trips, and some of them will be moving slower than their stay-at-home equivalents in case 2 throughout their trips. The age differences will thus reverse between the two cases regardless of this factor.

There are galaxies that their light will reach but their ballistic selves will never reach, which would not be true if all these galaxies are flying by in pretty much negligible time.

We don't need them to be able to travel from every galaxy to every other galaxy. It is sufficient for some of them to make a trip between two galaxies taking long enough to do so for the age differences to show up. I've been talking about billions of years, but if the speeds of travel are close to c and the universe is young with the galaxies close together, and if the timers are accurate, we can use much shorter trips. All that matters is that enough travellers meet enough non-travellers for us to get the data we need about their relative ages. This experiment could have be done in a small chunk of an observable universe. It's like with the Michelson-Morley experiment: if we want to show it visually in a software demo, we might have it travel at 0.866c to provide a clear understanding of what's going on, but in real life we move it at very low speed and depend on high-precision measurements instead. The same applies here: I've illustrated the idea using a thought experiment that uses extreme speeds to help people visualise it, but in the real world it would be done with low speeds and we'd be looking to use very accurate timers instead of just looking at multuplets and trying to assess their age by how gray their hair is.

Why the heck would anyone need to ask for specific values about their exact ages for that when the travelling ones must be younger in all possible illustrations of case 1?

Because your assertions are wrong, and numbers show this better than talk. Otherwise I wouldn't much need it.

My assertions are right, and there are no numbers that can overturn that.

Again, why the heck would anyone need to ask for specific values about their exact ages for that when this subset of the travelling multuplets must be older in all possible illustrations of case 2?

Because you did a frame change and still asserted that all their ages were the same.

No - I gave you two different cases involving different universes to illustrate the two possibilities. I then combined the two cases within a single universe, and observers using all frames agree about the relevant facts there about the relative ages of multuplets when they meet up.

RoS says that cannot be.  FLRW says nothing is capable of accelerating a galaxy to the kinds of speeds you're talking about.  If it cannot accelerate, and the mass/energy from which it is composed has existed since the big bang, then it is still stationary.  Motion slows under FLRW coordinates, which is why nothing can move fast for long, and why the clock will pass us by at a sedate speed no matter the power of the explosion that sent the thing our way.

That's all barking up the wrong tree. You've fixated on trying to rule out case 2 instead of focusing on understanding its rules, and the result is that you never understood that the direction the proof is driving in is that can we recreate a case 2 system within a case 1 universe and use that to pin down the absolute frame.

Either you should accept that or you should provide your numbers for a counterexample which breaks the above claims.

I did. I said 'no fast galaxies' and 'sedate speed'.

You should have got beyond that irrelevant objection within the first few seconds.

[Halc]

Of course there's another case. There are two possible cases, and both of them can be combined into a single case, which is how the proof works.

OK, but you need to fix the RoS mistakes you make that I pointed out, not a trivial task under GR.

Set A of the travelling multuplets are all the ones moving along parallel paths aligned with the direction we call north.

Each of them will have defined that direction with reference to distant objects in the universe straight ahead of and behind them, and the name "set A" is applied to them retrospectively when they've been grouped with others moving along parallel paths. The same documentation is carried by all the clocks that they send out. Some of those clocks will be sent out ahead at even higher relativistic speed, but others will be sent out behind and will end up with non-relativistic speed. Set A of multuplets and the clocks sent out by that set serve as a case 2 scenario within a case 1 scenario.

Ten seconds is all it took for me to spot this, and I didn't have anyone else spelling it out to help me, so what's taking you so long? But you're still the fastest mind I've found to discuss this kind of thing with.

So far so good, but you haven't got to the point where you assert that all the case-2 clocks carried by the 'stationary' observers are somehow still in sync. I got what you're describing, but you falter on that point, and draw conclusions based on an assumption that their clocks will be in sync in some (what??) coordinate system.   In what sort of coordinate system are all these observers all stationary?  You need to find a solution to the Einstein equations which combine FLRW spacetime with relativistic motion, and neither of us is up to that task.
Also, I object to your term 'multiplets' which implies that they are all twins born at the same time and place, which is violated by you putting them all in different galaxies without explanation of how they got separated like that. So I'm using the more accepted term 'observer'.

My gut says maybe 9-10 billion years on the clock, but that's just my gut. That doesn't sound like 'much less'.

I must retract this. Apparently the traveler clock reads a minimal value. I ran some numbers, and it seems I made some invalid assumptions.
So I throw a rock at 0.4c to the north. Somewhere 5.4 GLY north is a galaxy receding at that pace, so in a way, the rock is stationary relative to that galaxy.  But as time goes on, the Hubble 'constant' changes to a lower value, which increases the velocity of our rock relative to that distant galaxy from zero to something positive. That's the part I didn't take into account, that something could accelerate without force relative to the distant thing. So it eventually gets there, and seemingly will pass it at 0.4c, not something less as my initial thoughts suggested.

So, OK, I'm willing to say that the clock arriving from 12 billion years ago still reads a tiny time, and flings by us at nearly c. Still working it out, but this seems the more plausible answer now.

The ages at any meeting of observers are objective events, so both case 1 and case 2 must yield identical results.  The traveling observers see the galaxies fly by in moments, their separation contracted to very short distances. But each takes longer than the next to go by, and eventually no more galaxies are witnessed passing the window. There's a finite number of them, then no more.  This can take say an hour on his clock if his initial acceleration is enough.

If we go for really extreme speeds, you don't need to reach for a calculator at all to handle this.

You do if you want to do the coordinate translation.

The high relativistic speed can be so close to c that we can just treat it as c and assume practically no aging at all for the object moving at that speed.

I'll agree to that.

Suppose the multuplets are all created a billion years after the big bong.

Some of them are sent out in many directions at close to c. These travellers are encountered by other stay-at-home multuplets in other galaxies ten billion years later, and in case 1 they find that the travelling multuplets are a year old while the stay-at-home ones who meet them are ten billion years old.

Those are objective (not coordinate system dependent) observations, so that will be observed in case 2 as well. You don't seem to realize that.

If it's case 2 though, it's radically different.

Because you're doing it wrong. The observations are in fact identical, as they must be. I've pointed out where you go wrong.  OK, we'll go with the traveler aging one year, and the stay-at-home guy 10 GY.

The stay-at-home multuplets have aged a year

No, in both cases, the accelerated guy ages a year, who is apparently stationary in case 2  How long the stay-at-home guy ages depends on your coordinate system, but you're using a Minkowskian transformation over a coordinate system that isn't Minkowskian. You can't apply SR to this situation. You explicitly specified using constant cosmological time for the the frame in case-1, not some Minkowskian inertial frame. You cannot translate freely between the two.

Maybe if you keep the experiment local, it would make more sense because you could reduce it to a simple SR case.  Two planets stationary in the cosmological frame (unaccelerated since the big bang when their clocks were set to zero) 10 LY apart, and a guy that travels between them in one subjective minute.  Now you can use the simpler inertial mathematics, and indeed the planet guys each age under a microsecond in the traveler frame. So what?  He still observers each planet guy being 10 years older than the one on the planet he left. Increasing the scale to one that involves expansion just complicates what is a simple situation.

The case 2 result allows the absolute frame's identity to be pinned down to a small range.

OK. This isn't news. The identity of that frame (called the comoving frame, or the cosmological coordinate system) has been well known for nearly 100 years. Surely you know this already. Calling it an absolute frame is a choice. The physics community simply identifies the foliation as the only one symmetrical at cosmological scales. It is overwhelmingly the choice of absolute frame for those that posit the meaningfulness of such a thing. It doesn't foliate all of spacetime, which seems to be a fatal flaw in declaring it to be absolute, but that's just my observation.

If you only have a case 2 system, you only need to see the age of multuplets passing you to be able to pin down the absolute frame.

I can see that from Earth, no expensive experiment needed. It's been pinned down for a long time. Get with the program. The only thing different is that they don't call it that name.
For instance, the term 'peculiar velocity' is the velocity of something relative to that frame, and not to any other. Earth currently has a peculiar velocity around 0.14c.

And if we set up a case 2 system within a case 1 universe, we can see case 2 results and use them to pin down the absolute frame.

and the result is that you never understood that the direction the proof is driving in is that can we recreate a case 2 system within a case 1 universe and use that to pin down the absolute frame.

Twice more, your goal seems to be to pin down this one special coordinate system, which has already been done. Is that your point? I agree, such a frame has been identified. GR uses it. Can we go home now?

The case 1 result also does this, but it only becomes clear that this is so after you've realised that case 1 and case 2 have to be able to coexist in the same system.

Agree. No problem.

The multuplets sent out from case 1 galaxies (when the universe is a billion years old) who immediately send out clocks in many directions become a case 2 system within a case 1 system.

By defining case2 within case 1 like that, you seem to have defined a coordinate system with non-orthogonal axes which is the only way to keep all those different clocks in sync in this new case 2 coordiante system. Nothing wrong with that, but the mathematics is more complicated, and you have the axes so close to parallel that the tiniest change along the space axis will result in a massive change in the time axis. So the 10 BY change is expected in one year of time in this squashed coordinate system. But your conclusions assume orthogonal axes, where two events separated on a spatial line would have an unchanged coordinate on the other axes.

Set A of those multuplets can look at clocks passing them which were sent out by other set A multuplets and the find that the clocks in that set are aging faster then them if they're moving relative to them in one direction and slower than them if they're moving in the opposite direction.

You lost me here. What case are we talking?  Who is Set A? The accelerated observers?  How can any clock overtake them if they all accelerated identically.
How is the tick-rate of the passing clock measured?  Using a local inertial frame, or by looking at a successive clock assumed to be synced with it? The two methods will yield vastly different numbers.

Not sure why there needs to be [biological] observers travelling with clocks, but you can add them if you want.

They are essential to create a case 2 system within a case 1 system.

I cannot think of one thing that a human can do better in any of these scenarios that isn't better done with clocks, lasers, mirrors, and other machines. All the human does is read the numbers from the machines, which can be done via email. He just doesn't need to be there. In my universe, people aren't special, but that's just my bias against anthropocentrism.

They are all created at around the same time after the big bang.

Relative to the cosmological frame, yes. Not relative to the case2 'frame' that you've not really worked out, but you seem suddenly to assume there's an inertial frame or something where all these observers are stationary (there isn't) and far worse, where their clocks are still in sync, said amateur mistake that seem to fall back on some kind of Newtonian thinking.

We aren't using the time of a skewed frame: we have an expanding universe with an even expansion across the part of the universe we're using

Not in the case 2 frame it isn't. There's only the one frame that has even expansion, and it isn't an inertial one. This is what I mean by case 2 not being valid until you come up with a coordinate system that has the properties you claim of it. The one with the non-orthogonal curved axes was the best I could think of.  It is sort of a polar coordinate system except the polar axis is a very tight spiral instead of a straight ray. If you want to work with that, fine, otherwise, you need to come up with said solution to the field equations that satisfies your scenario.

STR also requires them to age hardly at all between leaving one galaxy and arriving at another.

STR is inapplicable, but I agree that GR also describes this. It describes the time between galaxies to continuously increase, while STR would have them going by at a steady pace, never ending.

These assessments of ages are also not things that vary for different observers: all observers see them as being the same specific age when they arrive at another galaxy. The same traveller on reaching galaxy X cannot be seen as being older than the native multuplets of that galaxy by one observer and younger than them by another observer.

Agree.

Use a model where the universe is expanding. They'll pass by quite slowly, and have billions of years on their clocks.

If you're imagining the travellers slowing down and aging a lot as a result

I was, and I'm retracting that part. The Hubble constant isn't a constant, so apparently the peculiar velocity is maintained. I've been working out the numbers, and that bit didn't hold up.

Case 2: the galaxies are moving at 0.999...c.

No theory allow this, not LET and not GR. Of course it will fail.

LET does allow for it.

Of course it doesn't. LET asserts an absolute frame, so the speed of any object is a property of the object, not a relation with an abstract frame. The speed of any galaxy is pretty much stopped under that view.

Some of he multuplets ejected from them are moving through space at zero, and when we run across them we can see that we are the ones in an ancient state compared to them.

Oopsie again. What they see is objective fact, and cannot differ just due to an abstract coordinate change. If your theory predicts the above statement, then it is wrong. They will see our unaccelerated clocks with more time on them than on their accelerated clocks. Acceleration is objective after all.

Ten seconds, it took for me to see the whole thing. I'm not going to call it two days for you as that would be unfair, but given the amount of writing you've now done about this, we're talking about a good few minutes.

Well maybe you should take more than 10 seconds, giving you more time to realize that clocks synced in one frame are not synced in another.

What they see is facts agreed on by all observers. In a case 1 system, the travellers all age less than the non-travellers.
In a case 2 system, some of the travellers age less than the non-travellers

Frame reference omitted big time. What manner of coordinate system is used to make this statement?  It seems to just be a 'case 2 system', which is not a description of a coordinate system. Case 1 used the cosmological frame. OK, I get that. But case 2 system is undefined, especially since you added all these travelers going every which way. Pick one maybe, and then describe how to relate the others, because in his local inertial frame, most of the other observers don't even exist.
I could not describe such a coordinate system, especially in 10 seconds. Your admission of this indicates you are not putting thought to your scenario, and seeming just using Newtonian physics with time dilation, as if that's all that relativity is. Of course you get contradictions using that. It's wrong.

You've brought all that establishment baggage along for the ride

So I have, since it has withstood an insane amount of scrutiny. Nobody follows the dogma of established physics since there's not a buck in doing so. Fame and fortune is taken by those that find flaws in established theory, and especially those that propose theories that make better predictions. That's why LET gets no traction since it adds more premises without benefit of better predictions. Better predictions is what sells.

On the contrary, you have found no mistakes in my numbers

Hmm....

All that matters is that enough travellers meet enough non-travellers for us to get the data we need about their relative ages.

Can't do that unless they meet those non-travellers more than once, else they don't know the age of them (in their own frame) when they started. But you've made no mistakes in your numbers, so my pointing this out must be me not knowing my Newtonian mechanics properly.
So I meet a non-traveler on a planet and he's 10 billion and I'm a child. So he was born way before me. I've not shown anything else.

some of them will be moving slower than their stay-at-home equivalents in case 2 throughout their trips. The age differences will thus reverse between the two cases regardless of this factor.

What do you mean by 'age differences'?  It's not like a pair of people ever meet more than once for an objective comparison, so if one is a year old and the other is 10 billion, it might just be because the one started out at a microsecond less than 10 billion. So what do you mean by those words, and what do you think that shows? Remember your coordinate references when answering. Oh right, you've not defined a coordinate system, so you can just make up nonsense.

We don't need them to be able to travel from every galaxy to every other galaxy. It is sufficient for some of them to make a trip between two galaxies taking long enough to do so for the age differences to show up.

Agree. Why not just use a pair of stars 100 LY apart, stationary in the cosmological frame?  It makes the math so much simpler. Why the stupid big scale that forces these exotic coordinate systems?

I've been talking about billions of years, but if the speeds of travel are close to c and the universe is young with the galaxies close together, and if the timers are accurate, we can use much shorter trips.

Putting it closer to the BB doesn't solve any of the problems since the GR math still needs to be used. The trick is to get away from that event. We're assuming we've already pinned down this special frame. It's really easy to do with a simple microwave measurement in say 6 places in the night sky.

It's like with the Michelson-Morley experiment: if we want to show it visually in a software demo, we might have it travel at 0.866c to provide a clear understanding of what's going on, but in real life we move it at very low speed and depend on high-precision measurements instead.

High speed is fine with me. It's not like we're funding a real thing. My problem is the usage of curved coordinate systems that you don't understand, and the lack of known solutions to the field equations to allow a frame shift like you describe. Keep it local and the same thing can be demonstrated with simpler inertial coordinate systems.

but in the real world it would be done with low speeds and we'd be looking to use very accurate timers instead of just looking at multuplets and trying to assess their age by how gray their hair is.

Which is why I use clocks right from the start instead of trying to measure time by the paint peeling from the walls. I still haven't figured out what function the biological observers fill, except to be low-resolution clocks.

I gave you two different cases involving different universes to illustrate the two possibilities. I then combined the two cases within a single universe, and observers using all frames agree about the relevant facts there about the relative ages of multuplets when they meet up.

If they all agree, where's the contradiction? What are we trying to demonstrate again?  Oh right, pinpointing the special frame, which is as simple as a couple trivial measurements done from Earth. I'm not contesting that conclusion.

[David Cooper]

but you need to fix the RoS mistakes you make that I pointed out, not a trivial task under GR.

There are no such mistakes to fix. In case 1 there is a universe expanding from a big bang with the galaxies separating due to expansion of space between them, so they aren't moving at high speed through that expanding space fabric. The amount of time it takes for those galaxies to evolve is the same everywhere with none of them slowed by any significant speed of movement through space.

In case 2 it's similar, but all the galaxies are moving through the expanding space fabric at relativistic speed. It takes longer for them to evolve due to their slowed functionality, but again they all reach the same stages of development at the same time because they all have the same amount of slowed functionality.

]So far so good, but you haven't got to the point where you assert that all the case-2 clocks carried by the 'stationary' observers are somehow still in sync. I got what you're describing, but you falter on that point, and draw conclusions based on an assumption that their clocks will be in sync in some (what??) coordinate system.

Set A of multuplets all set out from galaxies which are at rest and which are at the same stage of their evolution. All the multuplets in set A accelerate to relativistic speed in the same direction in an identical manner and their clocks slow identically. There is no way for them to go out of sync. (Indeed, the same applies to the clocks of all other travelling multuplets as they are all travelling from galaxies which are at rest, but we can't rely on being in a case 1 universe, so we should restrict ourselves to a single set to guarantee that their clocks are equally affected by whatever they do.)

In what sort of coordinate system are all these observers all stationary? You need to find a solution to the Einstein equations which combine FLRW spacetime with relativistic motion, and neither of us is up to that task.

The correct coordinate system to use for this is one that expands with the universe. You should not be attempting to use one in which we are fixed in place while other galaxies are moving and where some (outside the observable universe) are moving through that grid at superluminal speeds.

Also, I object to your term 'multiplets' which implies that they are all twins born at the same time and place, which is violated by you putting them all in different galaxies without explanation of how they got separated like that. So I'm using the more accepted term 'observer'.

What do you mean, "without explanation"? They are like twins precisely because they do all come into being at the same time. They were separated by the expansion of space having been created together at the big bang. It actually takes a bit of time after that before they form, but in a thought experiment we're entitled to have them form just a moment after the big bang, and then they're separated by large distances simply by the universe expanding while they remain at rest in space. This already destroys RoS.

The ages at any meeting of observers are objective events, so both case 1 and case 2 must yield identical results.

But with case 2 you get a very different result because it's the galaxies that are moving fast while all the travellers moving in one particular direction are at rest, so for them the journeys take vast amounts of time and they arrive at galaxies where very little has had a chance to happen due to their almost completely frozen functionally.

Those are objective (not coordinate system dependent) observations, so that will be observed in case 2 as well. You don't seem to realize that.

No - it can't be the same in case 2. We know this because we can build a case 2 system within a case 1 system, and those two systems operate at the same place. We have our case 1 galaxies and set A of travelling multuplets playing the role of case 2 galaxies, while the clocks sent out by the set A multuplets play the role of case 2 multuplets, and we're interested most in the clocks that they send back the way they came because they stop and hold station relative to the case 1 galaxies, so they actually represent case 1 galaxies. Set A multuplets (case 2 galaxies) pass case 1 galaxies and we see that these multuplets (case 2 galaxies) have aged less than the case 1 galaxies. When set A multuplets encounter clocks sent backwards by other set A multuplets, you're asserting that those clocks will also have to run slow, practically frozen functionally, and the set A multuplets will be much older than them when they meet them, but no: these clocks are effectively case 1 galaxies and the set A multuplets age more slowly than those, so they must age more slowly than that group of clocks too, so you're not allowed to have the galaxies age faster than the set A multuplets and the set A multuplets age faster than the clocks they sent out behind them (as soon as they left their galaxies) - these particular clocks effectively remain with their galaxies and must age at the same rate as them. Two clocks sitting side by side will tick at the same rate (ignoring the gravity well influences, but they're trivial - we're not putting any of our timers anywhere near a black hole).

How long the stay-at-home guy ages depends on your coordinate system, but you're using a Minkowskian transformation over a coordinate system that isn't Minkowskian. You can't apply SR to this situation. You explicitly specified using constant cosmological time for the the frame in case-1, not some Minkowskian inertial frame. You cannot translate freely between the two.

If STR can't apply to this, it has no business being applied to our universe at all. We have galaxies which have all existed for the same length of time since the big bang and they provide the basis for a coordinate system which expands along with the universe That's the right coordinate system to use for this. If a multuplet moves from one galaxy to another at nearly c, no time will pass for it while it makes that trip, but the galaxies will age a lot, and that will show up clearly when it arrives at the next one. When it encounters a clock sent out behind from a fellow set A multuplet, that clock reveals that it has aged as much as the galaxies. The clock serves as a case 2 multuplet and the multuplet serves as a case 2 galaxy. The case 1 galaxies say to the case 1 multuplet, "you were the one who moved", and the case 2 galaxies (the multuplet) say to the case 2 multuplet (the clock), "I was the one who moved". They have pinned down the local absolute frame in their region of the universe.

OK. This isn't news. The identity of that frame (called the comoving frame, or the cosmological coordinate system) has been well known for nearly 100 years. Surely you know this already. Calling it an absolute frame is a choice. The physics community simply identifies the foliation as the only one symmetrical at cosmological scales. It is overwhelmingly the choice of absolute frame for those that posit the meaningfulness of such a thing. It doesn't foliate all of spacetime, which seems to be a fatal flaw in declaring it to be absolute, but that's just my observation.

With this thought experiment though, we show that it is the absolute frame of the kind which objects can either be at rest in or moving through and where they have absolute speeds of motion through it which determine how fast their clocks tick. That's the bit that's news, and it's the mistake you made that hid that from you because you mistakenly thought the same observations would be made in case 2 as case 1, but you actually get the opposite result.

Twice more, your goal seems to be to pin down this one special coordinate system, which has already been done. Is that your point? I agree, such a frame has been identified. GR uses it. Can we go home now?

This is about pinning down the absolute frame at a location. It isn't merely about pinning down a coordinate system.

By defining case2 within case 1 like that, you seem to have defined a coordinate system with non-orthogonal axes which is the only way to keep all those different clocks in sync in this new case 2 coordiante system. Nothing wrong with that, but the mathematics is more complicated, and you have the axes so close to parallel that the tiniest change along the space axis will result in a massive change in the time axis. So the 10 BY change is expected in one year of time in this squashed coordinate system. But your conclusions assume orthogonal axes, where two events separated on a spatial line would have an unchanged coordinate on the other axes.

I don't know where you're getting all that imagined complexity from. We simply have set A multuplets moving "north" relative to galaxies and set-A-south clocks which are at rest relative to the galaxies. It's really simple. We run the experiment and it tells us that the galaxies have an absolute speed of close to zero and the set A multuplets have an absolute speed close to c. If the experiment produces the opposite result, then we know that our galaxies are actually set 2 galaxies and that they have an absolute speed of nearly c while the set A multuplets have an absolute speed close to zero.

Set A of those multuplets can look at clocks passing them which were sent out by other set A multuplets and the find that the clocks in that set are aging faster then them if they're moving relative to them in one direction and slower than them if they're moving in the opposite direction.

You lost me here. What case are we talking?  Who is Set A? The accelerated observers?  How can any clock overtake them if they all accelerated identically.

Multuplets were sent out from galaxies in all directions, but we're only interested in the ones that went north, and those are classed as set A. The multuplets all send out clocks in all directions once they're up to maximum speed themselves, and we're only interested in clocks sent out by set A multuplets, and we're most interested in the clocks that they send out southwards because those will then be at rest relative to the galaxies. That is how we put case 2 right on top of case 1 and show that they must have completely opposite results.

How is the tick-rate of the passing clock measured?  Using a local inertial frame, or by looking at a successive clock assumed to be synced with it? The two methods will yield vastly different numbers.

We don't care about the tick rate: the Doppler effect will guarantee that we learn nothing from that. We only care about the time that the clock has measured, and the reading of that value when the clock meets a multuplet, or when a travelling multuplet meets a stay-at-home multuplet in a galaxy, will be the same for all observers. There is no option of that value being both smaller and bigger than the value on the clock of the other party.

I cannot think of one thing that a human can do better in any of these scenarios that isn't better done with clocks, lasers, mirrors, and other machines.

Well, you need them to make clocks and to decide to do the experiment. You don't technically need to send any multuplets anywhere when you can just send clocks which then send out more clocks, but because this is akin to a twins paradox and that's traditionally done by sending a person, I've done the same here.

They are all created at around the same time after the big bang.

Relative to the cosmological frame, yes. Not relative to the case2 'frame' that you've not really worked out, but you seem suddenly to assume there's an inertial frame or something where all these observers are stationary (there isn't) and far worse, where their clocks are still in sync, said amateur mistake that seem to fall back on some kind of Newtonian thinking.

In case 2 they are all moving at the same speed through space and in the same direction, so their clocks must remain in sync, so I'm not making any mistake. And case 2 can be created in case 1 as well: we have all our stationary galaxies which are only moving apart because the space between them is expanding, and we send out the travelling multuplets at the same time universally, and a moment after they've been sent out and reached nearly c, they send out their clocks, so all those clocks start their timings (in case 1) at the same universal delay after the big bang. The timings of those clocks will then diverge as they're going in lots of different directions with some stopping relative to the galaxies and others going much faster relative to the galaxies than the multuplets that sent them out. If you're working with a universe in which galaxies are moving apart because the space between them is expanding rather than because they are moving at different speeds through space, there is no mechanism to make their clocks run at different rates relative to each other so they will all age the same as each other whether they're in a case 1 system or a case 2.

[Post too long - needed to be split...]

[David Cooper]

Part 2 of a split post:-

We aren't using the time of a skewed frame: we have an expanding universe with an even expansion across the part of the universe we're using

Not in the case 2 frame it isn't. There's only the one frame that has even expansion, and it isn't an inertial one. This is what I mean by case 2 not being valid until you come up with a coordinate system that has the properties you claim of it.

A case 2 system can exist within case 1, so you have the same non-skewed frame for both. The expansion is identical. The only difference is that the galaxies are all moving north.

STR also requires them to age hardly at all between leaving one galaxy and arriving at another.

STR is inapplicable, but I agree that GR also describes this.

STR comes into this because it denies the existence of absolute speeds, so if it's to apply to the universe at all, it should be testable in this experiment. STR says that the traveller is aging less than the stay-at-home by magic and that the stay-at-home is also aging less than the traveller by magic at the same time. However, we have results that show that some stay-at-homes age definitively more, and that other stay-at-homes age definitively less. The travelling multuplet in case 1 serves a stay-at-home in case 2. All our case 2 travellers (set A's south-sent clocks) are aging more than their stay-at-homes, and they're doing that by having lower absolute speeds. We know here that if we run a local twins paradox experiment with a travelling twin leaving a galaxy with a set A travelling multuplet where we have already established that a set A travelling multuplet ages less than the galaxy, then we know for certain that the travelling twin's clock is ticking slower than the galaxy's clocks too on the outward leg of his trip, and the same for the return leg. We can also do this with a stay-at-home twin who is moving along with the set A multuplet while a travelling twin accelerates to remain with the galaxy for a while before chasing to catch up. On the first leg of his trip, we know for certain that his clock was ticking faster than the stay-at-home twin's clock. This shows that STR does not fit our universe.

Case 2: the galaxies are moving at 0.999...c.

No theory allow this, not LET and not GR. Of course it will fail.

LET does allow for it.

Of course it doesn't. LET asserts an absolute frame, so the speed of any object is a property of the object, not a relation with an abstract frame. The speed of any galaxy is pretty much stopped under that view.

Of course LET allows it, exactly as it allows the set A multuplets move through the absolute frame in case 1. In case 2, the galaxies do exactly what the multuplets do in case 1.

Well maybe you should take more than 10 seconds, giving you more time to realize that clocks synced in one frame are not synced in another.

Ten seconds was sufficient. We don't need to care about what incorrect frames assert about clock synchronisation, and even if we've pinned down the absolute frame, we don't misuse of LET by ignoring the expansion of space and making out that the rest of the universe has slower functionality because it's moving relative to us. We take the expansion into account and correct for that.

What they see is facts agreed on by all observers. In a case 1 system, the travellers all age less than the non-travellers.
In a case 2 system, some of the travellers age less than the non-travellers

Frame reference omitted big time. What manner of coordinate system is used to make this statement?

These are observations made by all observers regardless of any frame they're misusing.

It seems to just be a 'case 2 system', which is not a description of a coordinate system. Case 1 used the cosmological frame. OK, I get that. But case 2 system is undefined, especially since you added all these travelers going every which way. Pick one maybe, and then describe how to relate the others, because in his local inertial frame, most of the other observers don't even exist.

Case 1 and case 2 can operate in the same place and share the same objects with different names attached to them. The set-A south-sent clocks and the galaxies are essentially interchangeable. This was the 10 second idea, and it stands up well three days on.

I could not describe such a coordinate system, especially in 10 seconds. Your admission of this indicates you are not putting thought to your scenario, and seeming just using Newtonian physics with time dilation, as if that's all that relativity is. Of course you get contradictions using that. It's wrong.

The ten seconds was how long it took to spot this trick. I spent a lot more time checking it afterwards to make sure it worked, and it does work. You already can't have STR for reasons of all the other disproofs, but this is a particular way in which you cannot have it along with a universe that expands - that destroys STR by introducing demonstrable absolute speeds.

You've brought all that establishment baggage along for the ride

So I have, since it has withstood an insane amount of scrutiny.[/quote]

It hasn't survived it any more than the impossible Gods of religions have survived being disproved. You simply have a vast number of deluded people clinging to broken models and brainwashing everyone about how the universe supposedly works and insulting other people who point out the fatal faults, shouting them down and calling them crackpots while systematically trying to hide all heretical discussion through deletions, bans, and throwing threads into special forums filled with so much crackpot action that no one normal ever reads them. That's not withstanding scrutiny, but running away from it.

Nobody follows the dogma of established physics since there's not a buck in doing so.

Same with religion, unless you're a superpreacher. Physics has a good few of those.

Fame and fortune is taken by those that find flaws in established theory, and especially those that propose theories that make better predictions. That's why LET gets no traction since it adds more premises without benefit of better predictions. Better predictions is what sells.

LET is infinitely simpler as it removes all the magic where contradictions have to be tolerated, and it doesn't break at every turn by generating event-meshing failures, and it allows for real causation rather than depending on infinite magic to account for fake causation, and it also makes better predictions because it doesn't produce nonsense about what goes on in black holes.

All that matters is that enough travellers meet enough non-travellers for us to get the data we need about their relative ages.

Can't do that unless they meet those non-travellers more than once, else they don't know the age of them (in their own frame) when they started. But you've made no mistakes in your numbers, so my pointing this out must be me not knowing my Newtonian mechanics properly.

The method doesn't depend on meeting anyone repeatedly. It's sufficient that the details of who aged how much from all these encounters all tell the same story about which frame is the local absolute frame.

So I meet a non-traveler on a planet and he's 10 billion and I'm a child. So he was born way before me. I've not shown anything else.

You need to be patient and wait for more data to come in. But if this experiment had been started nearer to the time of the big bang, we could have been collecting that data for billions of years as travellers pass us and tell us about their encounters with clocks sent out by their own set. We don't have the data, but we do have this thought experiment, and it tells us that this could be done and that it would give us a result that lets us pin down the absolute frame.

some of them will be moving slower than their stay-at-home equivalents in case 2 throughout their trips. The age differences will thus reverse between the two cases regardless of this factor.

What do you mean by 'age differences'?  It's not like a pair of people ever meet more than once for an objective comparison, so if one is a year old and the other is 10 billion, it might just be because the one started out at a microsecond less than 10 billion.

All the multuplets set out the same length of time after the big bang. All set A's clocks were sent out soon after, again the same length of time after the big bang as each other. If it's a case 1 universe with stationary galaxies, the set A south-sent clocks are stationary too while the multuplets are moving at close to c. If it's a case 2 universe, some of the multuplets are stationary (and we retrospectively call them set A after we have the results in) while their south-sent clocks are moving south with the galaxies at nearly c. A microsecond difference of timing when something's moving at nearly c will be a long delay, but if you collect enough data and average it out, clear differences will show up. But in case 1 you can't get a significant difference anyway as everything's functioning fast until the multuplets are sent out, and in case 1 you also get all the results you need just from looking at how young they are when they arrive at other galaxies. It's with sending out the clocks to create case 2 within case 1 that you'll get small differences in timings adding up to huge differences, but because the clocks whose timings you depend on most are at rest relative to the galaxies, you can see that any variations in their ages are related to how far they were released out from their home galaxy, so it's easy to correct for that. In case 2, all the galaxies are slowed enormously, so there could be big delays between multuplets being sent out as measured by the travelling multuplets, but all of those galaxies have similar low values on their clocks, and all of the travelling multuplets moving in one particular direction have huge values on their clocks as the pass other galaxies compared with the values on the clocks of those galaxies - there might be a lot of variation in the times on those multuplets' clocks, but that doesn't matter, and they also record where they originated from, so you have a timing for the trip over a known distance. We'll have a clear reversal in the results between a case 1 universe and a case 2 one.

So what do you mean by those words, and what do you think that shows? Remember your coordinate references when answering. Oh right, you've not defined a coordinate system, so you can just make up nonsense.

By older, I mean manifestly massively older, and by younger I mean manifestly massively younger - there will be no possibility of mixing them up. The coordinate system to use is obvious - you just have to allow it to expand with the universe.

Why not just use a pair of stars 100 LY apart, stationary in the cosmological frame?  It makes the math so much simpler. Why the stupid big scale that forces these exotic coordinate systems?

We need to use locations which have expanding space between them. You won't register much of that over 100 LY. We use the expansion to separate a pair of twins, then we move one of them through space to reunite them, and when we do that, we pin down the absolute frame. If the travelling twin ages less, his absolute speed through space is higher that that of the stay-at-home twin. If he ages more than the stay-at-home twin though, his absolute speed must be lower than that of the stay-at-home twin.

Putting it closer to the BB doesn't solve any of the problems since the GR math still needs to be used.

It would solve a problem if there had been lots of intelligent species about sooner to start carrying out the experiment in time for us to have collected lots of results now.

The trick is to get away from that event. We're assuming we've already pinned down this special frame. It's really easy to do with a simple microwave measurement in say 6 places in the night sky.

In a case 2 universe, you'd expect the CMB to have the same skew as the galaxies which are all moving the same way at nearly c, so it would look to observers in those galaxies as if they're stationary if they assume the CMB data is a reliable guide to that.

High speed is fine with me. It's not like we're funding a real thing. My problem is the usage of curved coordinate systems that you don't understand, and the lack of known solutions to the field equations to allow a frame shift like you describe.

There isn't one that I don't understand. You're just failing to work with the right one.

Keep it local and the same thing can be demonstrated with simpler inertial coordinate systems.

If you try to do that, you either shut out the expansion that the thought experiment depends on or render the effect very small, and you then shackle yourself to a coordinate system that goes out of alignment with the absolute frame over distance. You need a frame that expands with the universe.

I gave you two different cases involving different universes to illustrate the two possibilities. I then combined the two cases within a single universe, and observers using all frames agree about the relevant facts there about the relative ages of multuplets when they meet up.

If they all agree, where's the contradiction? What are we trying to demonstrate again?  Oh right, pinpointing the special frame, which is as simple as a couple trivial measurements done from Earth. I'm not contesting that conclusion.

What we're showing is that the case 2 galaxies age less than the case 2 travellers, while the case 1 galaxies age more than the case 1 travellers, and when we put a case 2 system in a case 1 universe, we discover that we can use these measurements to pin down the absolute frame, even if all we use are galaxies and primary travellers: if the travellers age less, we're in a case 1 universe, but if they age more, we're in a case 2 universe.

[phyti39]

David;

These two flashes of light travel alongside each other all the way to the observer who sees them both arrive simultaneously. How did the two flashes of light know to travel at the same speed as each other? Did they decide to travel at c relative to one ship rather than the other ship?

Light does not propagate relative to an object!
The propagation speed of light in space is constant and INDEPENDENT of its source.
The big word being the most significant, meaning light does not acquire the speed of the source. This distinguishes light motion from material object motion.

In a plane moving at a constant speed v, every element in the plane has acquired the speed v.
As seen by an observer outside the plane:
With no air turbulence, if a passenger tosses a ball perpendicular to the aisle at speed w, to another passenger, the motions are simultaneous and add as vectors.
If the v component is removed from all elements within the plane, and the ball tossed in the same manner, the scenario would be equivalent to the plane being at rest on the ground. This demonstrates the equivalence of inertial motion and rest, and an example of SR postulate 1, the same description of physics is valid in all inertial frames.
It also shows a need for a definition of 'rest' different from that of Newton. There is only motion and 'rest' is a special case when two systems A and B, have identical velocities.
Thus each can be in motion while at rest relative to each other.

Replacing the plane with a spaceship moving at .1c, the ball with a photon, and a detector in the opposite seat, the simultaneous motions do not add as vectors.
As seen by an observer outside the ship:
The photon vector is rotated in the direction of the detector but at a constant speed c.
This results in a small gap between photon and detector, i.e. v and c don't meet. The photon spends a small portion of its energy chasing the detector, thus requires a little more transit time. As the ship moves faster nearing c, the gap becomes more significant.   

LET assumes an ether. SR postulate 2 assumes independent light propagation (AS IF  from a fixed position in space). Events do not move. Both produce the same results since the coordinate transformations are the same.
Einstein later replaced the redundant Lorentz ether with the gravitational field in GR, with a similar status as Newton's absolute space.

The MGP experiment
The motion can be represented as a cylinder with the ct axis through the origin, and d equal to the circumference. The cylinder is unrolled to a flat surface with only constant velocities, the origin (black) and light (blue). Light speed is constant in SR. The rotation is absolute motion, with the origin approaching in the cw direction and receding in the ccw direction.

MGP.gif (4.35 kB . 459x434 - viewed 3376 times)

Einstein's insistence that the speed of light is always c relative to any observer is nothing more than a contrived mathematical abstraction

I can agree with you on this part but only within the correct context.
"That light requires the same time to traverse the same path A to M as for the path B to M is in reality neither a supposition nor a hypothesis about the physical nature of light, but a stipulation which I can make of my own freewill in order to arrive at a definition of simultaneity."
Relativity The Special and the General Theory
Albert Einstein 1961 Crown Publishers Inc. pg 23

The simultaneity convention has to satisfy the expectations of an observer at rest.

Assuming a pseudo rest frame is a choice, not a mandate.

Making measurements in motion, includes the effects of time dilation and length contraction, which result in measured light speed equal to c.
Are those effects included in your simulations?

When considering motion, light speed is c, object speed is v.
It is necessary to use the forms of c-v and c+v in calculations, as closing speeds, rates of change for a spatial separation. There is no physical thing moving at those speeds.

[phyti39]

Jano;

Consider the popular example of reciprocal time dilation.
A and B with a relative velocity, observe each other's clock rate as slower than their own. This is not a case of each watching the other clock and seeing doppler effects.
The red calibration curves denote a constant time where intersecting an observer time line.
With clocks set to t=0 at the origin, each sends a signal at t=1, which triggers the remote clock to send a time encoded signal which returns at t=2.15.
What is the basis for their conclusion?
The SR clock synch convention defines the light transit times out and back to be equal, which would be the expectation of a rest frame observer.
The (green) axis of simultaneity, established when synchronizing the clocks in each frame, assigns the distant clock event to a later time on the observers clock. Clock event 1.47 is assigned to (1+2.15)/2=1.58.
It's observer perception, what each thinks after all analysis is complete.
The variation in assigned times depends on the directions of the target and the signals, the same or opposite.
U would claim the B clock is running slower than the A clock.
What time is it? It depends on who you ask!

td-recip slow.gif (5.34 kB . 423x484 - viewed 3393 times)

[phyti39]

Jano:

simultaneity and length contraction required for reciprocity

SR requires both ends of an object be measured simultaneously.
A is black,  B is green, each ship is length d, g=gamma.
The near end of both ships are at 0 for all measurements.

left (with no length contraction):
A measures length of green ship as d, on his axis of simultaneity Ax.
B length/A length =d/d=1.
B measures length of black ship as e, on his axis of simultaneity Bx.
A length/B length =e/f=1/g^2.
Measurements are not reciprocal.

right (with length contraction):
A measures length of green ship as d/g, on his axis of simultaneity Ax.
B length/A length =1/g.
B measures length of black ship as e, on his axis of simultaneity Bx.
A length/B length e/f=1/g.
Measurements are reciprocal


SR reciprocity2.gif (8.29 kB . 907x474 - viewed 3370 times)

[Halc]

There are no such mistakes to fix.

In that case you’re talking about your own new theory where simultaneity isn’t frame dependent.  That’s consistent for an absolutist, but having the galaxies being the thing moving is not consistent with the view.  So you’ve alienated every view I can think of. If you find an inconsistency, it just means the new theory doesn’t work so well.

In case 2 it's similar, but all the galaxies are moving through the expanding space fabric at relativistic speed. It takes longer for them to evolve due to their slowed functionality, but again they all reach the same stages of development at the same time because they all have the same amount of slowed functionality.
…
The correct coordinate system to use for this is one that expands with the universe.

This is what I mean. I cannot think of any known coordinate system where this is the case, which is why I’ve said case 2 doesn’t exist.  FLRW metric is such a solution, but that metric does not have frame rotation operators defined like SR does with Minkowski coordinates, so there’s just the one frame.
You’re free to find a solution to Einstein’s field equations that satisfies all these conditions, but until then, there’s little to discuss about it.

You should not be attempting to use one in which we are fixed in place while other galaxies are moving and where some (outside the observable universe) are moving through that grid at superluminal speeds.

FLRW metric does not have anything moving at superluminal speeds. Motion is defined as peculiar velocity in the metric, and that is bounded by light speed anywhere.

But with case 2 you get a very different result because it's the galaxies that are moving fast while all the travellers moving in one particular direction are at rest, so for them the journeys take vast amounts of time and they arrive at galaxies where very little has had a chance to happen due to their almost completely frozen functionally.

This is wrong. You’re using a Minkowskian property on a non-Minkowskian coordinate system. You’re also denying Minkowskian RoS above, but still attempting to apply dilation with Minkowskian rules. You’re not being self consistent.

Those are objective (not coordinate system dependent) observations, so that will be observed in case 2 as well. You don't seem to realize that.

No - it can't be the same in case 2.

It must be. If objective observations are different from one case to the other, then one of the cases is wrong, which is what I’ve said from the beginning.

If STR can't apply to this, it has no business being applied to our universe at all.

Much better.  And yet you’re trying to use it above, but incorrectly.

With this thought experiment though, we show that it is the absolute frame of the kind which objects can either be at rest in or moving through and where they have absolute speeds of motion through it which determine how fast their clocks tick. That's the bit that's news

It’s not news. The general idea has been known for 90 years.  It still doesn’t foliate all of spacetime, which suggests that there is no absolute frame at all. This is just a special one, but not necessarily absolute. If you want to demonstrate the latter, you need to find a valid way to falsify the view that there isn’t one.

This is about pinning down the absolute frame at a location. It isn't merely about pinning down a coordinate system.

A frame has a location? If not, what’s the difference between a coordinate system and a frame? They’re the same thing to my knowledge.

What are the absolute coordinates of our solar system? Seems funny to call it absolute if you can’t answer that.  “2nd star to the right and straight on till morning” is a relative reference for example.

akin to a twins paradox and that's traditionally done by sending a person

Every physical demonstration of the twins scenario has been done with atomic clocks, never people.

In case 2 they are all moving at the same speed through space and in the same direction, so their clocks must remain in sync so I'm not making any mistake.

Ouch. Why do I bother if this is your understanding?

[David Cooper]

Light does not propagate relative to an object!

If it leaves an object or arrives at one, it has propagated relative to one at a speed greater then zero

The propagation speed of light in space is constant and INDEPENDENT of its source.

And if the source is an observer, then that means it moves at speeds other than c relative to that observer, so you've already rejected part STR. Of course, STR does that too by saying two incompatible things and thereby contradicting itself.

The big word being the most significant, meaning light does not acquire the speed of the source. This distinguishes light motion from material object motion.

Which is fine until you demand that it is c relative to all observers. It's when you want two incompatible things at once that your theory breaks.

This demonstrates the equivalence of inertial motion and rest, and an example of SR postulate 1, the same description of physics is valid in all inertial frames.
It also shows a need for a definition of 'rest' different from that of Newton. There is only motion and 'rest' is a special case when two systems A and B, have identical velocities.
Thus each can be in motion while at rest relative to each other.

There are two ways of interpreting that. One of them has been disproved, and the other depends on "same" meaning that it looks the same and not that it is the same, as with LET.

The MGP experiment
The motion can be represented as a cylinder with the ct axis through the origin, and d equal to the circumference. The cylinder is unrolled to a flat surface with only constant velocities, the origin (black) and light (blue). Light speed is constant in SR. The rotation is absolute motion, with the origin approaching in the cw direction and receding in the ccw direction.

You can represent it in lots of ways to try to hide what it actually reveals. I showed you what it reveals and that can't be undone.

Are those effects included in your simulations?

Wherever they're relevant, yes.

When considering motion, light speed is c, object speed is v.
It is necessary to use the forms of c-v and c+v in calculations, as closing speeds, rates of change for a spatial separation. There is no physical thing moving at those speeds.

Indeed, and the relative speeds (closing speeds) vary: that's why a ship at rest is different from a moving ship in the way that light travels about within it. The physics of what's happening within them is different, but if you try to measure each case while moving with it, they appear to be the same. This gives us two contradictory interpretations of what STR says, and some people try to use both of them, asserting that STR means one whenever the other is shown to be wrong, and then asserting things that depend on the disproved interpretation and justifying that interpretation on the basis of that interpretation being a viable interpretation of the words, even though it's only the other interpretation that holds. It's like a farmer who only has bulls expecting them to give birth to calves on the basis that a bull is a male cow and cows can give birth to calves.

[David Cooper]

There are no such mistakes to fix.

In that case you’re talking about your own new theory where simultaneity isn’t frame dependent.

When I find faults in someone else's theory, it doesn't become my theory on the basis that I label it as faulty while its owners put an incorrect label on it claiming it isn't faulty. There are two models in play here, and both belong to the establishment. One has an expanding universe with space expanding between galaxies and the other is STR. If the two models can't coexist, one of them does not describe our universe and belongs in the bin. If you want them both to fit, something's got to give. We have case 1 travellers aging less than case 1 stayers, and we have case 2 travellers aging more than case 2 stayers, and we have them all in the same system such that the case 1 travellers are the case 2 stayers and the case 2 travellers are the case 1 stayers. That is the necessary consequence of applying the rules of an expanding universe and also applying the rules of relativity. It enables the absolute frame to be pinned down and thereby eliminates STR which denies the existence of such a frame.

That’s consistent for an absolutist, but having the galaxies being the thing moving is not consistent with the view.  So you’ve alienated every view I can think of. If you find an inconsistency, it just means the new theory doesn’t work so well.

We don't have the galaxies moving in case 1 with a case 2 system set up within it, so we are not dealing with a new theory of any kind. We are revealing a fault in the establishments models: STR is not compatible with expanding space. You can't save both models. STR's the one to ditch anyway though as it's been disproved in so many ways already.

The correct coordinate system to use for this is one that expands with the universe.

This is what I mean. I cannot think of any known coordinate system where this is the case, which is why I’ve said case 2 doesn’t exist.  FLRW metric is such a solution, but that metric does not have frame rotation operators defined like SR does with Minkowski coordinates, so there’s just the one frame.
You’re free to find a solution to Einstein’s field equations that satisfies all these conditions, but until then, there’s little to discuss about it.

Just use the coordinate system that I've described. The galaxies remain more or less at fixed locations while the distance between grid points grows over time while the universe expands. I don't see why you have a problem with that for case 2 and not with case 1 because they are identical other than that the content is moving, and in case 1 we can set some material moving in the same manner without anything breaking.

]FLRW metric does not have anything moving at superluminal speeds.

I was referring to superluminal speeds relative to us. They are not doing superluminal speeds relative to their local space fabric, but are moving through that at close to zero speed.

But with case 2 you get a very different result because it's the galaxies that are moving fast while all the travellers moving in one particular direction are at rest, so for them the journeys take vast amounts of time and they arrive at galaxies where very little has had a chance to happen due to their almost completely frozen functionally.

This is wrong. You’re using a Minkowskian property on a non-Minkowskian coordinate system. You’re also denying Minkowskian RoS above, but still attempting to apply dilation with Minkowskian rules. You’re not being self consistent.

It is fully self-consistent. The whole point is that the Minkowskian stuff doesn't fit an expanding universe. I'm using the rules of the expanding universe to dictate how the galaxies and other things age, and then I'm using their encounters to show up which have aged more than which. Case 1 appears compatible with STR, in part at least, because the case 1 travellers age as predicted by STR, but STR gets the predictions wrong for case 2 (and this can be case 2 within case 1) due to the lack of symmetry in the system. STR is ruled out by this for our universe. Well, there is one trick you could try to use to make it look as it it's viable, but that means getting rid of the expansion and having all the galaxies move at different absolute speeds, and as soon as you try that, you have to throw out STR again for another reason. It's just a hopeless theory, and everyone should have seen that from the start because it rests on contradiction anyway. It was never viable.

No - it can't be the same in case 2.

It must be. If objective observations are different from one case to the other, then one of the cases is wrong, which is what I’ve said from the beginning.

Case 2 travellers are case 1 stayers and case 1 travellers are case 2 stayers - they are interchangeable. When a case 2 traveller meets a case 2 stayer and finds that case 2 stayer to be older, we can translate that to: when a case1 stayer meets a case 1 traveller, he must find the case 1 traveller to be older. You are claiming that the stayer will be older in both cases, but that requires one clock to have two radically different times on it at the same time

If STR can't apply to this, it has no business being applied to our universe at all.

Much better.  And yet you’re trying to use it above, but incorrectly.

I'm using it absolutely correctly. You're four days into this now and still haven't caught up with the bit in the previous paragraph where you don't realise you're requiring a clock to provide two different timings at the same time with one of those times many orders of magnitude greater than the other.

With this thought experiment though, we show that it is the absolute frame of the kind which objects can either be at rest in or moving through and where they have absolute speeds of motion through it which determine how fast their clocks tick. That's the bit that's news

It’s not news. The general idea has been known for 90 years.  It still doesn’t foliate all of spacetime, which suggests that there is no absolute frame at all. This is just a special one, but not necessarily absolute. If you want to demonstrate the latter, you need to find a valid way to falsify the view that there isn’t one.

Clearly it is news, because it shows that STR is incompatible with an expanding universe. Every point in the universe must have an absolute frame in it. If you project the wrong kind of coordinate system out from that and find it goes out of sync with the absolute frame at other locations, then that's another error you're making. If you're requiring this kind of absolute frame to be the same frame as some external frame that doesn't expand and which might be more fundamentally absolute, then again you're making an error. We've discussed this before and you shouldn't still be mixing them up.

This is about pinning down the absolute frame at a location. It isn't merely about pinning down a coordinate system.

A frame has a location? If not, what’s the difference between a coordinate system and a frame? They’re the same thing to my knowledge.

The comparison was between an absolute frame and a coordinate system; not any old frame.

What are the absolute coordinates of our solar system? Seems funny to call it absolute if you can’t answer that.  “2nd star to the right and straight on till morning” is a relative reference for example.

Coordinates aren't part of the real universe: we just map them to it in an arbitrary way, so you can make the coordinates anything you like. You can do the same for a second object, then after that you have less choice. Once you've done it for a third object, all the rest may be forced.

akin to a twins paradox and that's traditionally done by sending a person

Every physical demonstration of the twins scenario has been done with atomic clocks, never people.

Fine - it would be the same with this. And in thought experiments it's done with twins, which is why I've built this one in the same style.

In case 2 they are all moving at the same speed through space and in the same direction, so their clocks must remain in sync so I'm not making any mistake.

Ouch. Why do I bother if this is your understanding?

What other understanding of it can there be? What extra factors are you imagining to make them age differently while they move at the same speed in the same direction? The model's very simple and I'm applying it. If you want to complicate the model to make it different from that, go ahead and try, but you'll just make a mess that doesn't fit our universe.

[phyti39]

Assuming the subject is still SR reciprocity,
Jano;

Here is another example of reciprocal time dilation.
The red line has been substituted for the calibration curve in the previous example, using the arc method for the one time needed.

On the left is A's description of B moving at .5c to right.
If A sent a signal at At=.500 to B, it would get a return time of Bt=.866.
A concludes the B clock is slow by a factor of .866.
B sends a signal at Bt=.289 and gets a return time of At=.500.

On the right is B's description of A moving at .5c to left.
B assigns the At=.500 to Bt=.577.
B concludes the A clock is slow by a factor of .500/.577=.866.
The td is reciprocal.

Using the coordinate transformations/LT,

x'=g(x-vt)=(0 - .5*.5000)/.866 = -.289

t'=g(t-vx)=(.500-.5*0)/.866 = .577

The answers agree with the spacetime graphics showing they are a geometric interpretation of the coordinate transformations.


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[xersanozgen]

https://www.academia.edu/44028129/Special_Relativity_the_Clock_Absurdity


https://www.academia.edu/42973938/EINSTEINS_TERRIBLE_TWINS_and_Other_Tales_of_Relativistic_Woe?email_work_card=title

These papers may explain reciprocity in SR better.

[Jaaanosik (OP)]

Gentlemen,
I need to catch up to the latest posts,
Jano

[Jaaanosik (OP)]

Phyti,
how about the second leg of the blue light roundtrip?
It takes 2s in the stay home frame.
It takes 7s in the moving frame.
Do both observers agree on this analysis?
Does the moving observer agree with the stay home observer about the time analysis?
Jano