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. Thatís 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 Newtonís 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.
Weíre doing this without gravity or dark energy, so they wonít 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, youíd have to sync the clocks relative to the cosmological frame, and you havenít 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.
QuoteThe slowing of clocks isn't about accelerations, but about absolute speeds through space.Fine, but youíre not measuring the absolute time of the signals with your setup. Youíre 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.
Quotethink 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.UmmÖ no. You yourself say that itís 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.
QuoteSpacetime 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.