1. Imagine two rockets approach each other at a speed of v. They broadcast regular timing signals at different radio frequencies so the two signals can be distinguished. Each rocket makes a prolonged recording of the signals from both itself and the other rocket. The rockets then decelerate equally and they stop in the same inertial frame so the two recordings can be compared.

The arrival frequency of the approaching signals can be reduced by v/c to compensate for the reducing distance. Hence the adjusted rates of the signals would be identical if there were no time dilation. For each rocket, the signals could then be aligned at the start of their recordings and no time lag would develop.

SR predicts that A will find B’s signals are slower and that B will find A’s are slower. In other words the signals would be found to progressively lag each other. If the two sets of time lags were plotted as lines on a graph, A’s would be to the left of B's and B's would be to the left of A's.

Please will someone tell me how this is possible.

2.

3. Perhaps I should add that symmetry dictates that the rockets' speeds are the same at all times. Hence either special relativity is wrong or else the rockets exist in different realities/worlds/universes that somehow temporarily lag behind each other before catching each other up.

If there are multiple realities, what experiments have demonstrated their existence? Or is SR based on an untestable and unscientific hypothesis?

4. Relativity of Simultaneity. Both rocket's agree as to what their respect clocks read upon meeting, but they don't while separated. This does not mean there are separate "realities". You can show this by assuming that in a frame where both rockets are approaching from opposite directions at the same speed relative to this frame. If you put two clocks at points an equal distance from the point where the rockets meet, someone in this frame will say that the rocket each pass one of the clocks at the same time before continuing on to meet up later. Further, we will say that according to this observer, the clocks of the rockets read the same time upon passing the clocks. Then he will see the rocket clocks run slower than his own and meet up reading the same times.

Each rocket will agree that their respective clocks read the same upon meeting and read the same time as our external observer saw them reading. They will also agree that his clock, while passing one of the above clocks read the same as the other rocket's clock read while passing the other external clock. Both rockets will also agree as to the time on both external clocks were when each rocket passed them. They however will not agree that both rockets passed the external clocks at the same moment, nor will they say that both external clocks were synchronized with each other.

This does not involve any different realities. Every local event is agreed upon by all observers. They just won't agree on the exact order in which these events occurred.

To use an analogy, imagine two people standing in a room and facing in different directions. If you were to ask them where a particular lamp was relative to themselves, One might say "five feet in front of me" while the other would say "four feet in front of me and three feet to my left". This does not mean that there are two different realities with the lamp in a different place in each reality. There is just one lamp, which each man sees from a different orientation ( if each man were to walk to where he says the lamp is they would meet at the same spot.)

With Relativity something similar is happening, but instead of just dealing with spatial directions, time is included in the mix. We measure events in space-time, but observers with relative motion with respect to each other have different "orientations" in space-time, and don't always agree on the space separation or time separation between any two events.

5. As Janus said. The two frames are symmetric, but they do not share the same notion of simultaneity. What SR basically tells us is that the separation between events in spacetime ( the line element ) is invariant, so everyone agrees on it; this necessarily means that concepts of space and time - taken separately - are observer-dependent.

6. My thanks to both Janus and Markus for the clarity of their replies.

I am unconvinced by the simultaneity explanation. The observed difference in time rates obviously depends on the Lorentz factor, but it seems to me that differences arising from simultaneity involve a further factor which looks like v^2/c^2. I may be wrong about this, but if the expressions for dilation and simultaneity are not identical then I don't see how simultaneity could explain the time rate differences for all values of v. I have also searched in vain for experiments that have confirmed the predicted simultaneity effect. Perhaps you could point me in the right direction. Otherwise we would be using one unconfirmed prediction to try to support another unconfirmed prediction.

I don't think the analogy involving the lamp is a fair one. Each observer's measurement of the bearings and distances of other objects can be reconciled. No inconsistency arises between their reference frames so there is no need to doubt the existence of a single reality. I raised the issue of multiple realities as a possible way to explain SR's different predictions for what ought to be a single variable, e.g. A's clock rate divided by B's clock rate. But thanks again for the reply. It's good to talk about these intriguing things.

7. I don't see how simultaneity could explain the time rate differences for all values of v
The key is to realise that there are no differences in "time rate" or "space rate" - all clocks tick at exactly 1 second per second in their own local frames, and all rulers measure exactly 1 meter per meter in their own local frames. This means that the line element remains invariant when going from one inertial frame to another. On a very practical, experimental level, this means simply that all inertial frames experience the same laws of physics - there is no local (!) experiment you can perform that distinguishes one frame from another. This is pretty intuitive - when you switch on your laptop in your living room, and you switch it on in a rocket that moves inertially at nearly the speed of light relative to Earth, you would expect it to work the exact same way, wouldn't you ? That includes all the electromagnetism, the quantum mechanics etc etc that go on within its components. This is experimental fact.

Now, you can go and ask yourself - what mathematical operation in Minkowski spacetime leaves the line element invariant ? The answer turns out to be the group of hyperbolic rotations; meaning, inertial frames in relative motion are just rotated by an angle in spacetime. We'll ignore boosts here for simplicity. So, in your specific experiment, the coordinate frames - when plotted - are rotated by an angle about the origin, in opposite directions. Hence, when you choose a point on the space axis, then you get a different time value for each frame, and vice versa as well, because the coordinate axis do not coincide.

That's relativity of simultaneity right there.

To experimentally test for relativity of simultaneity, you can check how speeds add up in spacetime - if the notion of time was the same in all frames, speeds would always add linearly; you could fix a light onto a rocket and shine it forward, and the light would move at c+ speeds. Evidently that is not what happens in the real world. We find that the maximum propagation speeds for information is exactly c in all frames, regardless of how fast that frame moves relative to some reference point. Holding the spatial distance of that motion constant, we find that it is the concept of time that is not shared between observers.

It comes down to this - if we want inertial frames to experience the same laws of physics, regardless of their relative state of motion, then their concepts of space and time cannot be the same, and hence we have relativity of simultaneity. Only the spacetime interval must be the same, which is exactly what we find in the real world.

8. I initially discounted simultaneity because I thought this arose from an inability to synchronise moving clocks, and synchronization of the rockets' clocks seemed to be irrelevant. Recordings could be made over weeks or even years, and it wouldn't matter whether comparisons were made between signals sent "at the same time" or those that were out of sync by hours or days. What matters is the times between the signals not the times of the signals. If you are both right about this being an issue then, as I say, I can't see how the maths might work.

If you are right then we are still left with the explanation that the recorded differences arise from different reference frames. My fundamental question is what does this actually mean? An apparently single object is meant to have different times, sizes and masses in different frames. This may work if there are multiple objects - a different one for each frame - but not if there really is only one object and one reality.

If identical clocks are compared under identical conditions then the ratio of their rates is exactly 1. The simplest comparison can of course be made at rest on the Earth at the same altitude. The comparison also works, as Janus said, for an observer who sends rockets at identical speeds in opposite directions, or in any direction. If the rockets have identical directions, not only can the observer measure the clock ratio to be 1 but this ratio is also found from recordings made by the two rockets. Inconsistencies only arise between rockets moving in different directions - even though their speeds are the same. My point is that the rockets' identical clocks are always being compared under identical conditions, so their time rates must remain identical. There is no physical difference that can account for any deviation from a ratio of 1. The clocks are affected by the accelerations they experience, but these are also identical. Inconsistent measurements only arise from observers moving in different directions, but of course this doesn't physically affect the clocks. More to the point, the moving observers know they cannot influence the clock rates.

9. My fundamental question is what does this actually mean? An apparently single object is meant to have different times, sizes and masses in different frames.
The quantities differ only as measured from different frames. These are coordinate quantities. So in other words, all the effects of relativity are manifestations of the relationships between frames in spacetime - masses, sizes, times etc etc never vary locally in any observer's own frame. This is what is meant when we say that "the laws of physics are the same in all inertial frames". There is no physical change in anything, just a shift of perspective that influences how different observers measure things that are not in their own rest frame.

There is really nothing mystical or special going on here at all - we are just literally looking at the same things from different angles in spacetime. When you look at a donut sitting on a table top from sideways, you see only a lump of dough; look at it from the top, and you see a ring with a hole in the middle. The two observers fundamentally disagree about what the donut looks like, but of course there is really no contradiction at all - they just look at the same thing from two different angles. It's just a trick of perspective - the contradiction is simply an illusion.

Relativity is exactly the same - you are just looking at intervals of time and space from different angles ( in a quite literal sense ), so observers appear to disagree. But of course, in actual fact they don't. They just have different perspectives on the same thing. It's all simple geometry. It seems strange and counterintuitive to us only because we are used to considering time and space as completely separate entities, whereas in fact they are not.

10. It's much like this :

11. Originally Posted by Markus Hanke

There is really nothing mystical or special going on here at all - we are just literally looking at the same things from different angles in spacetime. When you look at a donut sitting on a table top from sideways, you see only a lump of dough; look at it from the top, and you see a ring with a hole in the middle. The two observers fundamentally disagree about what the donut looks like, but of course there is really no contradiction at all - they just look at the same thing from two different angles. It's just a trick of perspective - the contradiction is simply an illusion.

Relativity is exactly the same - you are just looking at intervals of time and space from different angles ( in a quite literal sense ), so observers appear to disagree. But of course, in actual fact they don't. They just have different perspectives on the same thing. It's all simple geometry. It seems strange and counterintuitive to us only because we are used to considering time and space as completely separate entities, whereas in fact they are not.
I thought SR's predicted real differences rather than differences that are analogous to illusions. On the other hand, moving observers know they cannot influence the rate of clocks or the sizes of objects in different frames. I still think we lack experimental evidence of simultaneity effects and distance contraction (I don't have a problem with accelerated particles contracting) so I remain unconvinced. I think we've probably said enough on my rocket question, so thanks again to you and Janus for your time on this.

12. Originally Posted by Andrew?
I thought SR's predicted real differences rather than differences that are analogous to illusions. On the other hand, moving observers know they cannot influence the rate of clocks or the sizes of objects in different frames. I still think we lack experimental evidence of simultaneity effects and distance contraction (I don't have a problem with accelerated particles contracting) so I remain unconvinced. I think we've probably said enough on my rocket question, so thanks again to you and Janus for your time on this.
The differences are indeed real - in the illustration in my last post, the square really is a square, and the circle really is a circle, and they really are different. That's physical reality. However, neither of them is a true representation of the actual object; they are just angle-dependent projections of some aspects of the object onto lower-dimensional surfaces.

Same in relativity - observers measure only lower-dimensional projections; either time with clocks, or space with rulers. Those projections depend on the perspective in spacetime, but they are real in their own right, just not complete representations. In actual fact, reality is 4-dimensional, and there are no contradictions - which is why the laws of physics look the same for everyone if we write them down with tensors, instead of 3-vectors. If we could directly see spacetime separations between events, rather than just space and time differences, there would no longer be squares and circles, just the cylinder.

So the differences are "illusions" only in the sense that they are not complete representations of what is happening, in the same way as the shadows on the wall aren't complete representations of the original object. But of course the shadows themselves are nonetheless quite real. Perhaps I should not have used the term "illusion", as this could indeed be misunderstood. Time dilation, length contraction etc are all real phenomena, with real physical consequences; they are just not the full picture.

As for length contraction, this is straightforward ( but resource intensive ) to experimentally test, and has been done many times. For example this :

https://www.bnl.gov/rhic/physics.asp

Look at how the incoming ions are Lorentz-contracted into thin disks - if they weren't, the end products of the collision would be very different; I think you probably wouldn't get a quark-gluon plasma at all. Another, perhaps less direct, test would be the classic atmospheric muon experiment. So it's a very real phenomenon.

13. Thanks for your clarification on the intended reality of SR's predictions. I've seen people disagreeing about this, but I'm sure your interpretation is correct. Einstein said “A priori it is quite clear that we must be able to learn something about the physical behaviour of measuring rods and clocks from the equations of transformation …”. (My emphasis).

Our experiences obviously do lie in 4D not 3D. However, saying that the measured timing differences can be explained in Minkowski's 4D space is of no help to me. Minkowski space is based on the same principles as SR, so saying that SR's predicted effects can be explained in Minkowski terms is like saying SR's predictions can be explained by SR' assumptions.

For me, experiments are the only way to test SR. As I say, I am happy about particles or ions contracting but not distances. I cannot find any experiment that has measured distance contraction. The speed of an observer cannot change the actual distances between stationary objects. They can only appear to change. You describe the muon situation as perhaps a less direct test, but I would say it is no test whatsoever. The contraction of the atmosphere (and the Earth and the rest of the universe) is merely a prediction. No contraction of atmospheric thickness has actually been measured.

If we think of a set of particles around the ring of an accelerator, the particles may contract but not the distances between them. Even a small contraction of the total circumference of the inter-particle distances at CERN should result in them not fitting in the beam. (The following is a quote from Wikipedia on the Ehrenfest paradox: "The paradox has been deepened further by Albert Einstein, who showed that since measuring rods aligned along the periphery and moving with it should appear contracted, more would fit around the circumference, which would thus measure greater than 2πR.")

Again, I can find no experimental verification of the predicted simultaneity effects. So Minkowski notwithstanding, I do not see how SR can be correct about the two rocket situation.

Whilst time dilation is an experimental fact, the symmetrical dilation predicted by SR has been experimentally disproved. It is the symmetrical time dilation that I was criticising in this thread. I hope you are not taking my statements personally. I'm impressed by the depth of your knowledge of physics and your dedication to explaining it. You obviously know far more about physics than I do. I just think physics students are required to learn many difficult things very quickly and they don't have time to question the underlying beliefs. As time goes on it can be increasingly difficult for anyone to question their own beliefs. Mine too of course.

14. Originally Posted by Andrew?
My thanks to both Janus and Markus for the clarity of their replies.

I don't think the analogy involving the lamp is a fair one. Each observer's measurement of the bearings and distances of other objects can be reconciled. No inconsistency arises between their reference frames so there is no need to doubt the existence of a single reality. I raised the issue of multiple realities as a possible way to explain SR's different predictions for what ought to be a single variable, e.g. A's clock rate divided by B's clock rate. But thanks again for the reply. It's good to talk about these intriguing things.
No inconsistency arises in Relativity either. All observers can reconcile all events even if they don't agree as to their space and time separations. You can't analyze the situation using time dilation alone, as it is only one of the Relativistic effects in play.

The easiest way to analyze the scenario is through the use of space-time diagrams.

For example, here is the space-time diagram for this scenario according to the rest frame of the midpoint where the rockets meet.

Separation in space is along the horizontal axis and time is along the vertical axis. Events that lie on the same horizontal line are simultaneous for the frame.
The red line is the midpoint
The dark blue line is clock "A",
The light blue line is clock "B",
The orange line is rocket 1
The green line is rocket 2
The yellow lines radio signals traveling from one rocket to another.

As rocket 1 passes clock A, and rocket 2 passes clock B, they all set their clocks to zero, and the rockets start emitting their signals. The start of the signals cross at the midpoint sometime later, and the midpoint can use them (and the known distance to clocks A and B to set his clock, so that it would have also read 0 when the rockets passed the clocks. Note that the midpoint clock and clocks A&B are synced for the whole time. Also the Clocks on rockets A&B always read the same, though run slow compared to the the Midpoint clock and clocks A&B.

Rocket 1 receives the start of the signal from Rocket 2 just a bit before his clock reads 3, and Rocket 2 receives the start of the signal from Rocket 1 when his clock reads just a little bit before 3 (the slight difference apparent in the diagram is due to my inaccuracy in placement of the lines.) Both rockets receive signals from the other until they meet at the midpoint clock, which will read 5 (as well will clocks A&B), while their own clocks read somewhat over 4. Thus each rocket records the whole trip of the other rocket in the last third of their trip.

Now here are the same events according to Rocket 1.

Rocket 2's frame would look like this:

Basically a mirror image of Rocket 1's frame.

The point is that at the end, everyone agree on what events occurred and everyone agrees on the outcome of the events and what an observer in each of these frames would have recorded. No separate realities, just the same reality measured from different perspectives.

To use Markus Hanke's analogy, when we measure space and time, we are only measuring the "shadow" that space-time casts, And observers in relative motion measure shadows cast from different "directions". This does not create separate realities, just a different "view" of a reality that extents beyond our ability to directly measure. This does not however make our measurements illusions. If an ant is crossing a shadow cast by an object he must travel a set distance to cross it. If the lighting is changed for that object or the object rotated so that the shadow elongates, the ant has to travel a longer distance to cross the shadow, even if the object casting it hasn't changed its size. This increased distance traveled by the ant is not an illusion but very real.

In the same way, time dilation, length contraction, and the relativity of simultaneity are the results of projections of space-time as measured by us. This does not make the measurement we make and the outcomes we record unreal.

15. Wow, that's pretty impressive. I feel rather humbled by your efforts. The diagrams do a good job of explaining SR's predictions.

A problem I have personally is the assumption of non-simultaneity. As I say, this seems not to have been experimentally verified. Another problem is why in one rocket's frame would the other rocket have a different signal rate. Both rockets have experienced the same acceleration so there is no physical difference between them. Hence the signal rates should be identical, as of course they are in the first diagram. I don't see how a moving observer can physically change a rocket.

Given the time you have put into this, I'll try to find time to give the subject of simultaneity more thought. Thanks again.

16. Originally Posted by Andrew?
Wow, that's pretty impressive. I feel rather humbled by your efforts. The diagrams do a good job of explaining SR's predictions.

A problem I have personally is the assumption of non-simultaneity. As I say, this seems not to have been experimentally verified.
relativity of simultaneity is not an assumption, it is a natural consequence of the invariant speed of light (which has been experimentally verified.)
Another problem is why in one rocket's frame would the other rocket have a different signal rate. Both rockets have experienced the same acceleration so there is no physical difference between them. Hence the signal rates should be identical, as of course they are in the first diagram. I don't see how a moving observer can physically change a rocket.

I'm not sure exactly what you mean here, Both rockets start sending when they pass a clock and they set their clock to 0, and they stop sending once they meet up with the other rocket and their clock reads a bit past 4 This is true no matter what frame you are observing this from. Nothing is physically being changed for either rocket. If you are asking why rocket 2 seems to send at slower rate according to rocket 1, that is time dilation. Rocket 1 measures the signal coming in at a higher rate and for a shorter time, but that is due to Doppler shift. After taking into account that part caused by the decreasing distance, Rocket 1 would conclude that Rocket 2 transmitted at a slower rate and for longer than he did. This is because the Doppler shift he measures is Relativistic Doppler shift which combines the effects of classical Doppler shift with the effects of time dilation. (This also results in another piece of experimental evidence for SR. Classical and Relativistic Doppler shifts give different results for an source traveling at a given speed. Experiment shows that Relativistic Doppler shift gives the correct value in real-life measurements for sources moving at known speeds.)

Time dilation is due to the fact that rocket 1 and rocket 2 measure time differently than each other because of their relative motion.

Given the time you have put into this, I'll try to find time to give the subject of simultaneity more thought. Thanks again.[/QUOTE]

17. Minkowski space is based on the same principles as SR
Minkowski spacetime is Special Relativity; it is what you get when you have a region of spacetime with a vanishing Riemann tensor, i.e. negligible gravity. Remember in this contex also that SR is just a special case of GR.

the symmetrical dilation predicted by SR has been experimentally disproved
I am not aware of any experiments that are in contradiction to SR. Could you please provide a link to the experiment you are referring to, along with its peer review ?

they don't have time to question the underlying beliefs
In physics, we do not use beliefs; we use the scientific method. The underlying tenet in the theory of relativity is that all inertial observers experience the same laws of physics; rejecting this means saying that observers in different states of motion are subject to different laws of physics. It would also mean that gravity does not behave the way we see it working. If that were so, our universe would be a very strange place indeed !

18. I've tried a few times to reply in detail but the system keeps locking up, so I'll be brief.

I think the first postulate was an assumption because Einstein had no way of proving or disproving it. I believe it has since been disproved by observations from Hubble’s time onwards. The universe appears to be expanding away from a point that is at rest with the centre of the visible universe. If we view the expansion using a frame moving at v with respect to the universe, this vector is added to the basically symmetrical motion of distant objects. The universe is then seen to be evolving differently for high speed inertial observers for whom the symmetry of Hubble’s law is broken.

I believe SR does not conserve mass or energy between frames and this is a big problem for me.

I also think symmetrical time dilation has been disproved because experiments such as Hafele and Keatings' always reveal asymmetric dilations. For example westbound clocks get faster. This directly contradicts SR's prediction that observers A and B see each other's clock has slowed. This is a difficult subject because physicists usually say these experiments validate SR, but some say it's a GR situation and so no conclusions can be drawn about SR. However, the rotation of the Earth is irrelevant to SR's predictions. The only determining factor is the relative speed between two observers, e.g. the counter rotating planes.

19. Originally Posted by Andrew?
I've tried a few times to reply in detail but the system keeps locking up, so I'll be brief.

I think the first postulate was an assumption because Einstein had no way of proving or disproving it. I believe it has since been disproved by observations from Hubble’s time onwards. The universe appears to be expanding away from a point that is at rest with the centre of the visible universe. If we view the expansion using a frame moving at v with respect to the universe, this vector is added to the basically symmetrical motion of distant objects. The universe is then seen to be evolving differently for high speed inertial observers for whom the symmetry of Hubble’s law is broken.
The universe is not expanding away from a central point at rest or otherwise. The universe doesn't have a center point anymore than more than a point on the surface of a sphere could be called as being the center of the surface.

I believe SR does not conserve mass or energy between frames and this is a big problem for me.
KE is not conserved between frames in Newtonian physics either. And mass (in that the modern meaning of mass refers to the rest or invariant mass) is conserved.

I also think symmetrical time dilation has been disproved because experiments such as Hafele and Keatings' always reveal asymmetric dilations. For example westbound clocks get faster. This directly contradicts SR's prediction that observers A and B see each other's clock has slowed. This is a difficult subject because physicists usually say these experiments validate SR, but some say it's a GR situation and so no conclusions can be drawn about SR. However, the rotation of the Earth is irrelevant to SR's predictions. The only determining factor is the relative speed between two observers, e.g. the counter rotating planes.
1. You are confusing time dilation, which is the relative tick rate between clocks measured between frames by each frame, with the "total difference in accumulative time between two clocks that have been separated and brought back together. The results of the mentioned experiment measured the later, which were the end result of Relativistic effects that included, but were not limited to Time dilation.

2.The rotation of the Earth was, in fact, instrumental to the results of this experiment. You had 3 rotating frames. The clock on the surface of the ground which rotated with the Earth, one traveled opposite to the rotation of the Earth and one traveling with the rotation of the Earth. Now the stipulation that only Relative velocity determines time dilation only holds for inertial frames. Since these frame were traveling in circles they were not inertial but accelerating frames. Now acceleration doesn't effect your tick rate, but it does effect measurements made from that frame. And while during the moment any of these clocks were passing each other they would have measured each other as running slow, this would not have been the case during all the times they were separated during their respective trips. If they had been able to make direct measurements of the other clocks, they would have measured periods when the other clocks ran fast compared to their own. Since each clock was in a slightly different accelerated frame from the others, the total time they would measure on having passed on the other clocks from meeting to meeting would be different than what passed on their own, But all three clocks would agree on each meeting what each respective clock reads, even though during any given moment they won't agree on how fast the clocks were ticking compared to itself.
The Predictions that SR made on how much those clocks differed from each other when brought back together, and which were matched by in the actual experiment, were based on the same precepts that predicts symmetric time dilation between inertial frames. To say the experiment disproves symmetric time dilation to say that you don't understand the experiment.

So far this has been the case with all of your objections to SR. They are based on a limited and sometimes mistaken understanding of Relativity.

The "flaws" you are uncovering are in your own grasp of the subject rather than in the theory itself.

20. “The universe is not expanding away from a central point at rest or otherwise. The universe doesn't have a center point anymore than more than a point on the surface of a sphere could be called as being the center of the surface.”

I was talking about Hubble’s observed expansion from the centre of the visible universe. Are you saying this view is wrong? What about the point I was making about the lack of expansion symmetry for an observer moving at high speed with respect to the visible universe?

“KE is not conserved between frames in Newtonian physics either. And mass (in that the modern meaning of mass refers to the rest or invariant mass) is conserved.”

I referred to energy, not just KE. Newtonian mechanics does not require observers to consider themselves atrest. Suppose two masses of 1kg and 10kg are fastened together with a compressed spring between them. When the spring is released one can calculate how the PE is converted into the two different KE’s of the two moving masses. In SR, only one mass is moving in each frame, so in one frame the total KE = 0.5(1)v^2 and in the other the total KE =0.5(10)v^2.

When I said mass I meant to say momentum. But whilst on the subject, if A’s rocket has a mass of 1 tonne and B’s is 10 tonnes, A measures the total mass to be 1 + 10γ whilst B finds it to be γ+ 10.

“You are confusing time dilation, which is the relative tick rate between clocks measured between frames by each frame, with the total difference in accumulative time between two clocks that have been separated and brought back together.”

You are right. I assumed that the total relative tick rate would add up to the total time difference. I don’t see why that is not the case.

“Now acceleration doesn't effect your tick rate, but it does effect measurements made from that frame.”

I thought acceleration was equivalent to a gravitational field which affects tick rate. If the tick rate is unaffected, I don’t see why this would affect measurements made from that frame.

“And while during the moment any of these clocks were passing each other they would have measured each other as running slow, this would not have been the case during all the times they were separated during their respective trips.”

So when a westbound clock passes a ground clock or an eastbound clock, the overall faster westbound clock is found to be slower?

“If they had been able to make direct measurements of the other clocks, they would have measured periods when the other clocks ran fast compared to their own.”

So an eastbound clock can be faster than a westbound clock when it is out of sight? I really am confused now. I thought the calculations were done from the frame of an “observer” at the centre of the Earth. Why do the rates change when the clocks are passing each other?

Possibly it would help if you would please answer the following question. If eastbound and westbound planes were to momentarily fly in a completely straight line whilst they were measuring each other’s tick rate, i.e. if they corrected for the Earth's curvature, what would they find?

21. Just a quick one to say that SR requires Minkowski spacetime to apply; the expanding universe is a different geometry, it's FLRW spacetime. You cannot apply SR to the universe as a whole.

As for conservation - in SR, the object that is conserved is the energy-momentum tensor, not energy on its own ( ref Noether's theorem ). That's not quite the same thing. When you go on to GR then, there is no law of energy conservation at all - in fact, that notion does not make sense in a curved spacetime.

22. Originally Posted by Markus Hanke
Just a quick one to say that SR requires Minkowski spacetime to apply; the expanding universe is a different geometry, it's FLRW spacetime. You cannot apply SR to the universe as a whole.
Thanks but I'm not trying to apply SR to the visible universe, I am saying that the principle of relativity that it is based on has been disproved.

Originally Posted by Markus Hanke
As for conservation - in SR, the object that is conserved is the energy-momentum tensor, not energy on its own ( ref Noether's theorem ). That's not quite the same thing.
At everyday speeds, energy and momentum are conserved in Newtonian mechanics. They aren't in SR when a body's frame is considered to be at rest and it has no KE or momentum. Suppose I think the mass of the visible universe is m and its energy is E. If I then increase my speed in the direction of Leo by v its energy becomes E+0.5mv^2. Quite an achievement. I think the conservation of energy and momentum are two of the best ideas in physics and it bothers me that they are not built into SR.

23. Thanks but I'm not trying to apply SR to the visible universe
You were talking about "expansion symmetry" of moving observers wrt the visible universe; but the universe is not a valid frame of reference, so you cannot apply SR and it's symmetries here.

They aren't in SR when a body's frame is considered to be at rest and it has no KE or momentum.
Why do you think that ? Energy and momentum are conserved within a single frame, both in SR and in Newtonian dynamics; objects in SR do not need to be at rest. But obviously they are not conserved between frames - which is again true in both SR and Newtonian physics. However, if you consider energy and momentum together, then that object ( energy-momentum ) is always conserved in SR, even between different frames. This is in perfect accord with Noether's theorem.

24. Originally Posted by Markus Hanke
You were talking about "expansion symmetry" of moving observers wrt the visible universe; but the universe is not a valid frame of reference, so you cannot apply SR and it's symmetries here.
Why do you say the first postulate of SR cannot be tested wrt the visible universe?

I was talking about a point at rest with its visible universe, e.g. it experiences a symmetrical CMBR. This provides a preferred inertial frame in which the expansion of the universe is symmetrical and the universe is seen to be evolving under the influence of a symmetrical expansive force. In other frames the laws of physics differ because an asymmetric expansive force must be explained. This disproves the first postulate.

Why do you say this preferential frame of reference is not valid? This frame is the only non-arbitrary frame we have for describing the speed of the galaxies. I expect it is the frame astronomers use to model the universe's expansion. Can any astronomers comment on this?

Originally Posted by Markus Hanke
Energy and momentum are conserved within a single frame, both in SR and in Newtonian dynamics; objects in SR do not need to be at rest. But obviously they are not conserved between frames - which is again true in both SR and Newtonian physics.
Newtonian mechanics are not based on analysing events from two frames, such as those of two mutual observers. A single preferred frame is the one (as with the visible universe) that is at rest with the centre of gravity of the system under consideration. In the example I gave, Newton himself would say that if I accelerate to a speed of v then the Earth would imperceptibly move in the opposite direction so that momentum is conserved. He would not say that I should also consider myself to be at rest such that by expending a calorie or two I had given the universe a gigantic amount of KE and momentum.

25. Originally Posted by Andrew?
I was talking about a point at rest with its visible universe, e.g. it experiences a symmetrical CMBR. This provides a preferred inertial frame in which the expansion of the universe is symmetrical and the universe is seen to be evolving under the influence of a symmetrical expansive force. In other frames the laws of physics differ because an asymmetric expansive force must be explained. This disproves the first postulate.

Why do you say this preferential frame of reference is not valid? This frame is the only non-arbitrary frame we have for describing the speed of the galaxies. I expect it is the frame astronomers use to model the universe's expansion. Can any astronomers comment on this?
It is common to ask why the frame of reference in which the CMBR is symmetric is not a preferred frame of reference. The reason is that the CMBR is an object and being able to measure one's velocity relative to an object is not what is meant by a preferred frame of reference. A preferred frame of reference would require that one be able to determine one's absolute velocity without measuring the velocity relative to any object. Otherwise, that velocity is just a relative velocity that is relative to that object.

Originally Posted by Andrew?
Newtonian mechanics are not based on analysing events from two frames, such as those of two mutual observers. A single preferred frame is the one (as with the visible universe) that is at rest with the centre of gravity of the system under consideration. In the example I gave, Newton himself would say that if I accelerate to a speed of v then the Earth would imperceptibly move in the opposite direction so that momentum is conserved. He would not say that I should also consider myself to be at rest such that by expending a calorie or two I had given the universe a gigantic amount of KE and momentum.
Newton? There has been a lot of progress in physics since the time of Newton, even before the modern physics of relativity and quantum mechanics. Have you ever heard of Lagrangian mechanics? What about Hamiltonian mechanics? Both of these deal with generalised coordinate systems and can be considered a precursor to relativity. Indeed, in a way, these go even further than general relativity in terms of the types of coordinates considered, though they still treat time as absolute, which is where the breakthrough of Einstein's relativity is.

26. Originally Posted by KJW
It is common to ask why the frame of reference in which the CMBR is symmetric is not a preferred frame of reference. The reason is that the CMBR is an object and being able to measure one's velocity relative to an object is not what is meant by a preferred frame of reference. A preferred frame of reference would require that one be able to determine one's absolute velocity without measuring the velocity relative to any object. Otherwise, that velocity is just a relative velocity that is relative to that object.
I disagree with physicists' view. SR's frame equivalence deprives events of their context, and hence Minkowski's space-time is incomplete: it ignores prior times. A muon moving at high speed through the atmosphere is supposedly indistinguishable from a high speed Earth colliding with the muon. Yet this completely ignores the histories of the two bodies that led to their current energies. The muon is time dilated and not the Earth.

It is impossible to understand life on Earth or current affairs without taking the past into account. Similarly it is impossible to fully understand events in physics when they are stripped of their connection to the visible universe. The principle of relativity is a shallow misconception inherited from the Middle Ages.

Originally Posted by Andrew?
Newton? There has been a lot of progress in physics since the time of Newton, even before the modern physics of relativity and quantum mechanics.
I mentioned Newton in answering an earlier comment, but I think it's time someone answered my question.

27. Spacetime is the set of all events - i.e. all spatial points at all times. Nothing is being ignored. We describe the dynamics of bodies by looking at their worldlines, which is their entire history. In the case of the muon experiment, the world line is straight in spacetime, meaning that proper acceleration is zero at all points. Simply put, it is an inertial frame.

28. Originally Posted by Andrew?
The muon is time dilated and not the Earth.
This represents a misunderstanding of time dilation. Objects themselves aren't time dilated. It is the measurement of one object from a different frame of reference that is time dilation. The objects themselves aren't affected by the motion.

Originally Posted by Andrew?
A muon moving at high speed through the atmosphere is supposedly indistinguishable from a high speed Earth colliding with the muon. Yet this completely ignores the histories of the two bodies that led to their current energies.
In terms of the impact force that each experiences from the other, it makes no difference whether it is the muon or the earth that is travelling at high speed. Even Newtonian mechanics says that.

Originally Posted by Andrew?
The principle of relativity is a shallow misconception
Actually, the principle of relativity is an essential part of reality. Without it, one would not be able to make sense of reality. The very concept of measurement itself relies on objects having consistent properties when transferred from one context to another. Without this, one would be unable to state the properties of an object in any context because one would be unable to determine the context or how the change in context affects the properties of the object. Thus, if a clock ticks 1 second, it is measuring 1 second of time along its trajectory in spacetime regardless of how the clock is moving. Similarly for a ruler than is measuring a length of 1 metre. That's doesn't mean that a ruler can't experience forces that distort its length. For example, a spring (used as an example in the "Simultaneity" thread) can be stretched or compressed, but its natural length, the length it has in the absence of forces, is consistent across different frames of reference. It is quite natural that objects have intrinsic properties that do not depend on the context.

29. Originally Posted by KJW
Actually, the principle of relativity is an essential part of reality. Without it, one would not be able to make sense of reality. The very concept of measurement itself relies on objects having consistent properties when transferred from one context to another. Without this, one would be unable to state the properties of an object in any context because one would be unable to determine the context or how the change in context affects the properties of the object. Thus, if a clock ticks 1 second, it is measuring 1 second of time along its trajectory in spacetime regardless of how the clock is moving. Similarly for a ruler than is measuring a length of 1 metre. That's doesn't mean that a ruler can't experience forces that distort its length. For example, a spring (used as an example in the "Simultaneity" thread) can be stretched or compressed, but its natural length, the length it has in the absence of forces, is consistent across different frames of reference. It is quite natural that objects have intrinsic properties that do not depend on the context.
Don't want to nit pick but I have often heard this statement that time ticks at "one second per second" in all self referential frames of reference.

I get what it means but would I be right to think that this actual statement is not to be parsed literally? ("one second per second " sounds to me like a mathematical statement that whilst not actually wrong does not actually in itself mean anything and almost has the same construction as a joke)

30. Originally Posted by geordief
I get what it means but would I be right to think that this actual statement is not to be parsed literally? ("one second per second " sounds to me like a mathematical statement that whilst not actually wrong does not actually in itself mean anything and almost has the same construction as a joke)
You are quite correct. Saying that a clock ticks at "one second per second" in its own frame of reference is really quite meaningless but is an attempt to describe a tricky concept in relativity. A very common error in relativity is to think that motion actually alters the clocks, that time dilation is a slowing down of the clock itself. It isn't. And it is the principle of relativity that says that clocks behave the same in their own frame of reference regardless of that frame of reference. This is key to understanding relativity.

31. Originally Posted by KJW
Originally Posted by geordief
I get what it means but would I be right to think that this actual statement is not to be parsed literally? ("one second per second " sounds to me like a mathematical statement that whilst not actually wrong does not actually in itself mean anything and almost has the same construction as a joke)
You are quite correct. Saying that a clock ticks at "one second per second" in its own frame of reference is really quite meaningless but is an attempt to describe a tricky concept in relativity. A very common error in relativity is to think that motion actually alters the clocks, that time dilation is a slowing down of the clock itself. It isn't. And it is the principle of relativity that says that clocks behave the same in their own frame of reference regardless of that frame of reference. This is key to understanding relativity.
thanks ,another of my bugbears I can dispense with. One of my failings is I am too literalist I have decided (maybe it is a failing I share with the cranks we encounter from time to time on these forums)

32. I struggled with Special Relativity for years. The relativity of simultaneity made no more sense than the un-fishcakeness of fishcakes - it simply doesn't compute. There does also seem to be a long drawn out game involving (effectively) the assumption that you will be able to reverse engineer Pythagoras' Triangle Theorum from a succession of cryptic clues.

Calling the invariant spacetime interval s, the 'reveal' (the Pythagoras Theorum of Special Relativity) the hypoteneuse isn't so much equal to the sum of the opposing sides but its still pretty simple ...
s²=-x²-y²-z²+c²t² << that's it ... with more time I'd have changed + to - but it makes no difference...
As a quick check..
Looking at the muon experiment (see hyperphysics the muon experiment ) once you're away from the fishcakeness of cakes it gets much easier to see...
In this case we can discard y and z because its one dimension and time so...
where v is the muon velocity we have x=vt,y=0,z=0.
From Earth frame time t (and muon frame time T)...
s²=-v²t²+c²t²
In the muon frame s²=c²T²
so c²T²=-v²t²+c²t²
Or
T=t√(1-v²/c²) <<- time dilation just jumps out like fleas from a cat.

I can do that in more (and clearer) steps if anyone is interested.

33. Originally Posted by KJW
A very common error in relativity is to think that motion actually alters the clocks, that time dilation is a slowing down of the clock itself. It isn't. And it is the principle of relativity that says that clocks behave the same in their own frame of reference regardless of that frame of reference. This is key to understanding relativity.
An error in relativity, but not in reality as determined by observations. If I have two clocks and I lower one of them then I know it has been physically altered. Observations from its frame will show it is slower. I can be certain of this because I can see I did not deplete my energy reserves enough to raise all the other clocks that are visible in the universe. Thus it is with an accelerated inertial clock at the same altitude as one that remains at rest.

34. Observations from its frame will show it is slower
Which is precisely what we do not find in the real world; all clocks tick at the same rate in their own frame. It is only the relationship in spacetime between clocks that changes.

accelerated inertial clock
There is no such thing; a clock is either accelerated, or it is inertial. It can't be both at the same time.

35. Originally Posted by Andrew?
If I have two clocks and I lower one of them then I know it has been physically altered. Observations from its frame will show it is slower.
Actually, even if the clocks were physically altered, one would still be unable to observe that the clocks are slower from the same frame. This is because it would be necessary to compare the clocks with other clocks which also would have slowed.

By what physical mechanism causes a clock, any clock, to slow by the correct amount specified by relativity?

36. [QUOTE=Markus Hanke;605762]
Observations from its frame will show it is slower
Which is precisely what we do not find in the real world; all clocks tick at the same rate in their own frame. It is only the relationship in spacetime between clocks that changes.

So observers in valleys will not find their clocks are slower than clocks up mountains? I don't see how "all clocks tick at the same rate in their own frame" helps as this seems obvious. I was talking about comparing different frames.

Originally Posted by Markus Hanke
There is no such thing; a clock is either accelerated, or it is inertial. It can't be both at the same time.
When a rocket stops accelerating it has accelerated and is inertial. Einstein's inertially moving train must have accelerated at some point in the past. I don't see what you mean.

PS In reading various books on relativity, including Einstein's, I have not come across a distinction between inertial frames that have previously been accelerated and those that have never been accelerated. I don't know how one would know that a body had never been accelerated. The only transformation equations I have seen just involve the current relative speed, not previous accelerations.

37. Originally Posted by KJW
By what physical mechanism causes a clock, any clock, to slow by the correct amount specified by relativity?
There is no point explaining my own views.

38. Originally Posted by Andrew?
Originally Posted by KJW
By what physical mechanism causes a clock, any clock, to slow by the correct amount specified by relativity?
There is no point explaining my own views.
There is every point, as they are what are driving all of your "sr is wrong" threads

39. Originally Posted by Paleoichneum
There is every point, as they are what are driving all of your "sr is wrong" threads
What drove me was being unable to find any experimental evidence of distance contraction or symmetrical time dilation. This was followed by the realisation that SR does not conserve total momentum or energy in consecutive frames, i.e. frames separated by acceleration. The more I looked into it the more problems I found.

40. Originally Posted by Andrew?
When a rocket stops accelerating it has accelerated and is inertial. Einstein's inertially moving train must have accelerated at some point in the past. I don't see what you mean.
The confusion here is between two uses of "accelerated" (as a verb and as an adjective). You are using it to mean, as you know say, "a frame that has previously been accelerated"; everyone else (including me) assumed it to mean "a frame that is undergoing acceleration" (which is, to my mind, the more natural interpretation).

PS In reading various books on relativity, including Einstein's, I have not come across a distinction between inertial frames that have previously been accelerated and those that have never been accelerated.
Because there is no such distinction.

41. Originally Posted by Andrew?
What drove me was being unable to find any experimental evidence of distance contraction or symmetrical time dilation.
Muon decay. (And, indirectly, every experiment or measurement that is consistent with SR.)

This was followed by the realisation that SR does not conserve total momentum or energy in consecutive frames, i.e. frames separated by acceleration.
These are observer dependent; so not conserved between different frame of reference.

42. Originally Posted by Andrew?
There is no point explaining my own views.
There is every point.

43. I agree.
I expect that explanation to be forthcoming in your next post.

44. The only transformation equations I have seen just involve the current relative speed, not previous accelerations.
The relativistic transformations between accelerated frames are summarised here :

SR treatment of arbitrarily accelerated motion

Note that accelerated frames are not symmetric. However, if you perform an experiment where two frames are inertial during the course of the experiment, then any periods of acceleration prior or subsequent to that window of observation are irrelevant to the outcome ( i.e. they depend only on relative speed ); you are just synchronising the clocks at the beginning of the experiment, then comparing inertial with inertial, so there is full symmetry.

If you insist on taking into account previous accelerations, then you are of course welcome to do that, but you will find that it makes no difference at all to the outcome within the window of observation - which is inertial and symmetric. Only if the experimental window is widened to include periods of non-zero acceleration, will such accelerations play a role, because there no longer is symmetry between frames.

45. Let me ask you this - can you provide repeatable, testable experimental evidence that observers in relative motion experience different laws of physics ? Specifically, in light of your comments on EM, we would like to see evidence that the speed of light is different between inertial frames, meaning that different inertial observers are subject to different sets of field equations for the EM field.

Essentially, this is a test of Lorentz invariance; if that symmetry is violated, then SR is not valid, otherwise it is guaranteed to be valid.

Note that I am looking for objective experimental data, not beliefs or thought experiments.

46. Originally Posted by Andrew?
This was followed by the realisation that SR does not conserve total momentum or energy in consecutive frames, i.e. frames separated by acceleration.
One thing that has been overlooked throughout this discussion is that accelerated frames of reference are outside the scope of special relativity. Although special relativity can deal with accelerated objects that are observed from inertial frames of reference, accelerated frames of reference require some of the mathematics of general relativity, in particular, an explicit metric, Christoffel symbols, and the covariant derivative.

47. Originally Posted by Strange
The confusion here is between two uses of "accelerated" (as a verb and as an adjective). You are using it to mean, as you know say, "a frame that has previously been accelerated"; everyone else (including me) assumed it to mean "a frame that is undergoing acceleration" (which is, to my mind, the more natural interpretation).
Thanks Strange for taking the time to resolve this point.

Silly me. Fancy not realising that a past participle is a more natural way to describe the present.

48. Originally Posted by Andrew?
Fancy not realising that a past participle is a more natural way to describe the present.
Live and learn.

49. Originally Posted by Strange
Originally Posted by Andrew?
What drove me was being unable to find any experimental evidence of distance contraction or symmetrical time dilation.
Muon decay. (And, indirectly, every experiment or measurement that is consistent with SR.)
Exactly. The contraction of the Earth's atmosphere is merely a prediction. No distance contraction has ever been measured. High speed particles may well contract, but not the distances between them. As I say, if low speed particles are arranged around a circular accelerator and then accelerated, the distance between them is predicted to contract (Ehrnfest's paradox). Their total circumference would be much less than that of the accelerator ring.

50. Originally Posted by Andrew?
Exactly. The contraction of the Earth's atmosphere is merely a prediction. No distance contraction has ever been measured.
You don't have a clue how science works, do you. You are bit short on clue generally.)

As I say, if low speed particles are arranged around a circular accelerator and then accelerated, the distance between them is predicted to contract (Ehrnfest's paradox). Their total circumference would be much less than that of the accelerator ring.
That is because the distance between them is kept constant (in our frame of reference) by the applied forces. In their frame of reference they would get further apart.

But you have obviously closed your mind to rational thought so there is probably little point anyone trying to change your quasi-religious views. I note that you have not provided any theory, mathematics or evidence to support your ideas. All you have as an argument is sticking your fingers in your ears and saying "tra-la-la don't believe you". Pathetic.

51. Originally Posted by Dywyddyr
I agree.
I expect that explanation to be forthcoming in your next post.
I started the post by asking how two sets of lines on a graph could each be to the left of each other. The answer does not depend on my personal views. I did not move the question into the forum for personal ideas. Had I started a thread in this section, I would naturally have wanted to explain my views.

Some forty odd posts later, the question has still not been answered. In fact, none of my questions has yet been answered as far as I am concerned (though I'm hopeful that KJW will provide an answer to my second simultaneity question). Simply restating what physicists believe about SR does not answer my questions. I did not ask what physicists believe. I have tried to ask direct questions about, for example, the simple algebra that describes the observable acceleration of charges. I have said I completely reject SR in order to try to stop people from repeatedly explaining it. Clearly this has not worked.

Asking me about my views just seems to be a diversionary tactic. Every other contributor so far has been perfectly happy with SR, so reading about alternative theories would be a waste of their time. It would certainly be a waste of mine. As there seems to be no point in continuing this thread I will though conclude by saying a little about my ideas. Unfortunately I have run out of time for now, my better half takes a dim view of me asking questions on the forum, but I hope to find more time on Monday.

52. Originally Posted by Andrew?
Some forty odd posts later, the question has still not been answered. In fact, none of my questions has yet been answered as far as I am concerned .
"La la la. Can't hear you."

my better half takes a dim view of me asking questions on the forum
She is obviously very smart.

53. Originally Posted by Markus Hanke
Note that accelerated frames are not symmetric. However, if you perform an experiment where two frames are inertial during the course of the experiment, then any periods of acceleration prior or subsequent to that window of observation are irrelevant to the outcome ( i.e. they depend only on relative speed ); you are just synchronising the clocks at the beginning of the experiment, then comparing inertial with inertial, so there is full symmetry.

If you insist on taking into account previous accelerations, then you are of course welcome to do that, but you will find that it makes no difference at all to the outcome within the window of observation - which is inertial and symmetric. Only if the experimental window is widened to include periods of non-zero acceleration, will such accelerations play a role, because there no longer is symmetry between frames.
Thanks for the explanation and the link, I'll have a look at it later. For me, the KE that arises from acceleration is the key to time dilation. I accept this is not the case in SR.

54. Originally Posted by Markus Hanke
Let me ask you this - can you provide repeatable, testable experimental evidence that observers in relative motion experience different laws of physics ? Specifically, in light of your comments on EM, we would like to see evidence that the speed of light is different between inertial frames, meaning that different inertial observers are subject to different sets of field equations for the EM field.
As I've said, I consider that observations of the visible universe provide this evidence. For an observer at rest with the visible universe, the laws of physics lead to a symmetrical expansion. For moving observers these laws do not work. Their inaccuracy increases with the speed of the observer.

You are obviously correct in your deduction about my views on the speed of light. I think the necessary evidence already exists, but this would entail more threads and hence more personal abuse and more time wasted. We will just have to agree to differ now rather than later. Thanks again for your time.

55. Originally Posted by Andrew?
I have said I completely reject SR...
Given this then it's not surprising that
none of my questions has yet been answered as far as I am concerned
is it?

Asking me about my views just seems to be a diversionary tactic.
Apart from us finding out exactly where you're going wrong.

but I hope to find more time on Monday.
Monday it is...

56. Originally Posted by Andrew?
We will just have to agree to differ now rather than later. Thanks again for your time.
Ok, that is fair enough.
Good luck.

57. Originally Posted by Andrew?
We will just have to agree to differ now rather than later. Thanks again for your time.
You are, of course, entitled to your opinion. You do, however, have the not-insignificant disadvantage of being wrong.

58. Originally Posted by Dywyddyr
Monday it is...
My own ideas start from the assumption that we can regard the visibleuniverse as having zero net momentum. This is obviously not a testable idea but it is logicallyconvenient. If physicists’ cosmologicalprinciple is correct then the universe continues indefinitely in alldirections. My assumption is then thatthe whole universe has no net momentum, and there can be no basis outside theuniverse for asserting that the universe is moving.

In the language of SR, maybe I should say the visible universe is aninertial frame. Apart from that ofcourse my view could not differ more from that of SR. I base everything on the principle that thevisible universe conserves its momentum, and this directly contradicts SR. It means that a frame in which a muon has avelocity of v cannot be equated with a frame in which the universe has avelocity of –v. This would violate theprinciple that the momentum of the visible universe is conserved. (For convenience one can obviously treat abody such as the Earth as having no momentum provided one ignores its relationto the rest of the universe.) Theconservation of the universe’s momentum overall is ensured by conserving itlocally, as in Newton’s laws of motion.

Observers in our galaxy can then agree on the speeds of differentstars, e.g. ours is moving at about 370km/s. These are objective and measurable speeds relative to the visible universe. What more preferred framework for measuringspeeds could there be? The universe isthe absolute reference.

Distant galaxies of course have their own visible universes. They have frames that are equivalent to ours,but speeds are still objectively measurable. Here again I am defining speed in relation to the locally visibleuniverse. Other properties of bodies,such as length, are also objectively measurable and unique.

Someone asked how I derive the time dilation factor. It just comes out of the idea that for a bodyin thermal equilibrium its total energy through space and time isconserved. The greater its KE and speedthrough space, the less its energy and rate through time. This is consistent with the experimentalevidence about asymmetric time dilation and the absence of distancecontraction. It leads to my view ofspacetime which is too radical to explain on the forum, but it resolves all thecontradictions that had troubled me.

So these are my principles. You cannow ridicule the crackpottery of a physics based on the conservation ofmomentum and on the unity of an objective universe.

59. Originally Posted by Dywyddyr
Monday it is...
My own ideas start from the assumption that we can regard the visible universe as having zero net momentum. This is obviously not a testable idea but it is logically convenient. If physicists’ cosmological principle is correct then the universe continues indefinitely in all directions. My assumption is then that the whole universe has no net momentum, and there can be no basis outside the universe for asserting that the universe is moving.

In the language of SR, maybe I should say the visible universe is an inertial frame. Apart from that of course my view could not differ more from that of SR. I base everything on the principle that the visible universe conserves its momentum, and this directly contradicts SR. It means that a frame in which a muon has a velocity of v cannot be equated with a frame in which the universe has a velocity of –v. This would violate the principle that the momentum of the visible universe is conserved. (For convenience one can obviously treat a body such as the Earth as having no momentum provided one ignores its relation to the rest of the universe.) The conservation of the universe’s momentum overall is ensured by conserving it locally, as in Newton’s laws of motion.

Observers in our galaxy can then agree on the speeds of different stars, e.g. ours is moving at about 370km/s. These are objective and measurable speeds relative to the visible universe. What more preferred framework for measuring speeds could there be? The universe is the absolute reference.

Distant galaxies of course have their own visible universes. They have frames that are equivalent to ours, but speeds are still objectively measurable. Here again I am defining speed in relation to the locally visible universe. Other properties of bodies, such as length, are also objectively measurable and unique.

Someone asked how I derive the time dilation factor. It just comes out of the idea that for a body in thermal equilibrium its total energy through space and time is conserved. The greater its KE and speed through space, the less its energy and rate through time. This is consistent with the experimental evidence about asymmetric time dilation and the absence of distance contraction. It leads to my view of spacetime which is too radical to explain on the forum, but it resolves all the contradictions that had troubled me.

So these are my principles. You cannow ridicule the crackpottery of a physics based on the conservation of momentum and on the unity of an objective universe.

60. Originally Posted by Andrew?
(For convenience one can obviously treat a body such as the Earth as having no momentum provided one ignores its relation to the rest of the universe.)
With this statement, you have just contradicted yourself. Throughout your post, you have been telling us of the importance of the frame of the visible universe and of the velocities relative to this frame. Then you say that the frame of the visible universe can be ignored and that the earth can be treated as being at rest. If you are to maintain that the visible universe is a preferred frame, then you have to explain why the earth can be treated as having no momentum. Otherwise, you've just admitted to the principle of special relativity.

Originally Posted by Andrew?
Someone asked how I derive the time dilation factor. It just comes out of the idea that for a body in thermal equilibrium its total energy through space and time is conserved. The greater its KE and speed through space, the less its energy and rate through time.
This is not enough. How does having greater KE mean it has less energy? How does having more KE or less energy mean it has less rate through time? In particular, I also asked how this lower rate through time is quantitatively the same as that obtained from special relativity.

61. Originally Posted by KJW
Originally Posted by Andrew?
(For convenience one can obviously treat a body such as the Earth as having no momentum provided one ignores its relation to the rest of the universe.)
With this statement, you have just contradicted yourself.
There is no contradiction in treating the Earth as having no momentum if one is ignoring its relation to the rest of the universe. The Earth still has momentum which can be ignored for local purposes. One could add the Earth's momentum to those of the particles or snooker balls etc. being considered but it can be cancelled out at the end. If one is considering the Earth's orbit in the solar system then it would be convenient to treat the solar system as having no momentum. If one is considering a star's orbit in a galaxy then one could treat the galaxy as having no momentum. But if you want to understand the motion of the galaxy and its red shift then this needs to be done using the frame of the visible universe.

Originally Posted by KJW
How does having greater KE mean it has less energy? How does having more KE or less energy mean it has less rate through time? In particular, I also asked how this lower rate through time is quantitatively the same as that obtained from special relativity.
I just assume a particle has KE plus binding energy plus an energy through time. Time rate is proportional to the square root of time energy just as speed is proportional to the square root of KE. I can try pasting some equations in but I don't know how they would fare from the spacing problem.

62. Originally Posted by Andrew?
Originally Posted by KJW
Originally Posted by Andrew?
(For convenience one can obviously treat a body such as the Earth as having no momentum provided one ignores its relation to the rest of the universe.)
With this statement, you have just contradicted yourself.
There is no contradiction in treating the Earth as having no momentum if one is ignoring its relation to the rest of the universe. The Earth still has momentum which can be ignored for local purposes. One could add the Earth's momentum to those of the particles or snooker balls etc. being considered but it can be cancelled out at the end. If one is considering the Earth's orbit in the solar system then it would be convenient to treat the solar system as having no momentum. If one is considering a star's orbit in a galaxy then one could treat the galaxy as having no momentum.
In other words, you are invoking the principle of relativity.

Originally Posted by Andrew?
But if you want to understand the motion of the galaxy and its red shift then this needs to be done using the frame of the visible universe.
This is outside of the scope of special relativity, so is irrelevant to any discussion about special relativity.

Originally Posted by Andrew?
I just assume a particle has KE plus binding energy plus an energy through time. Time rate is proportional to the square root of time energy just as speed is proportional to the square root of KE. I can try pasting some equations in but I don't know how they would fare from the spacing problem.
What is "time energy"? Didn't you say earlier that time dilation is related to KE?

63. Originally Posted by KJW
In other words, you are invoking the principle of relativity.
Everything is relative, and everything can be related to the visible universe, but this is not the same as Einstein's principle of relativity.

Originally Posted by KJW
This is outside of the scope of special relativity, so is irrelevant to any discussion about special relativity.
A body at rest with the visible universe should not be outside the scope of SR. This body shares the same frame is the one I am describing.

Originally Posted by KJW
What is "time energy"? Didn't you say earlier that time dilation is related to KE?
Conventional forms of energy allow speeds to be calculated. However, SR predicts equal time rates for mutual observers whereas experiments measure unequal ones. Hence I wanted to find a form of energy from which unequal time rates could be predicted. I spoke of time energy in order to convey a general impression, but I actually think of it as process energy. This is the energy that determines the rate of a particle's processes and the rate it interacts with other particles. Process rate, or time rate, is proportional to the square root of process energy - just as the speed through space is proportional to the square root of KE. The obvious principle to choose is to say that the sum of KE and process energy is conserved.

Given the equivalence of space and time, I assume process energy and KE are symmetrical. When a body is at rest, its KE is zero but its process energy is a maximum. If a body travelled at its maximum speed of c its KE would at a maximum but its process energy would be zero, and so would its process rate. This gives the Lorentz factor quite easily. The faster the speed through space, the slower the speed through time.

There is obviously a lot more to it than this, but I avoid the difficulties of, for example, one twin having to age rapidly when the other twin in a rocket decelerates, or the complications of simultaneity between frames. For me there is just one objective universe, so in the rest frame of the visible universe each clock has just one time rate and each body just one length.

64. You CANT ignore the motion of earth though. Pretending we are not moving, just to create supposed incongruity is incorrect and visibly wrong

65. Originally Posted by Paleoichneum
You CANT ignore the motion of earth though. Pretending we are not moving, just to create supposed incongruity is incorrect and visibly wrong
I don't see what you mean. I'm saying the Earth has motion with respect to the visible universe, for the Sun it's about 370km/sec. Similarly the Earth also has spin in relation to the visible universe. It is SR that assumes the Earth's linear motion can always be ignored.

66. No that's not what sr says. You are the one saying that earth should not be considered in motion

67. Originally Posted by Andrew?
This is consistent with the experimental evidence about asymmetric time dilation
What evidence is there of asymmetric time dilation between inertial frames of reference?

Originally Posted by Andrew?
Everything is relative
That's not true. For example, acceleration is not relative. If an observer accelerates away from an inertial observer, then there is no ambiguity as to who is accelerating. Also, that observer can determine they are accelerating whilst in a sealed room without looking out into space.

Originally Posted by Andrew?
everything can be related to the visible universe
No-one says that they can't. What is being said is that it is unnecessary to relate everything to the visible universe. The visible universe is not a preferred frame of reference, but is an acceptable frame of reference.

Originally Posted by Andrew?
this is not the same as Einstein's principle of relativity
You require that all inertial frames are equivalent. How is that different from Einstein's principle of relativity?

Originally Posted by Andrew?
... Given the equivalence of space and time ... If a body travelled at its maximum speed of c ...
How is it that people can accept some parts of special relativity while rejecting other parts? Special relativity comes as a package. You either accept all of it or reject all of it. You can't simply choose which bits you like and which bits you don't like. Because special relativity is mathematically derived from a very small set of axioms, all the various aspects are logically connected and not separable. By accepting some parts of relativity while rejecting other parts of relativity, you are proposing a reality that is illogical.

68. Originally Posted by KJW
What evidence is there of asymmetric time dilation between inertial frames of reference?
It seems any evidence that is obtained close to the Earth can be disputed on the basis that the Earth is not inertial. Gravitational effects are obviously very important, but other things being equal, SR predicts that when two observers have a relative speed, they see that each other's clock is symmetrically slower than their own. As you know, a ground based observer will see that a westbound clock runs faster, but the westbound observer sees the ground clock is slower. Similarly an eastbound observer will see that a ground based clock runs faster. To overcome these asymmetric dilations, calculations are carried out for an "observer" at the centre of the Earth. This clock seems immune to any symmetrical slowing effect that SR predicts would be observed from the other clocks.

Originally Posted by KJW
That's not true. For example, acceleration is not relative.
It is in my book.

Originally Posted by KJW
The visible universe is not a preferred frame of reference, but is an acceptable frame of reference.
It is preferred if one wants to understand red shifts and the expansion of the universe.

Originally Posted by KJW
You require that all inertial frames are equivalent. How is that different from Einstein's principle of relativity?
I keep saying that all frames are not equivalent. The laws of physics are at their simplest in a frame at rest with its visible universe.

Originally Posted by KJW
How is it that people can accept some parts of special relativity while rejecting other parts? Special relativity comes as a package. You either accept all of it or reject all of it.
I reject all of it, and Einstein doesn't have a patent on experimental results or ideas. Anyone is entitled to think that bodies travelling faster than light may lead to problems.

69. Originally Posted by Andrew?
Originally Posted by KJW
What evidence is there of asymmetric time dilation between inertial frames of reference?
It seems any evidence that is obtained close to the Earth can be disputed on the basis that the Earth is not inertial. Gravitational effects are obviously very important, but other things being equal, SR predicts that when two observers have a relative speed, they see that each other's clock is symmetrically slower than their own. As you know, a ground based observer will see that a westbound clock runs faster, but the westbound observer sees the ground clock is slower. Similarly an eastbound observer will see that a ground based clock runs faster. To overcome these asymmetric dilations, calculations are carried out for an "observer" at the centre of the Earth. This clock seems immune to any symmetrical slowing effect that SR predicts would be observed from the other clocks.
I explicitly said INERTIAL frames of reference. The Hafele–Keating experiment involves accelerated clocks. A clue to the non-inertial nature of the experiment is that the clocks start together and end together. So this experiment is not evidence of asymmetric time dilation between inertial frames of reference. Indeed, the Hafele–Keating experiment is a test of relativity, and its results are in agreement with the predictions of relativity. The twin clock paradox experiment does produce an asymmetric time dilation because of the differences in acceleration of the two paths in spacetime.

Originally Posted by Andrew?
Originally Posted by KJW
That's not true. For example, acceleration is not relative.
It is in my book.
Well your book would be wrong. An observer can determine if they are accelerating or inertial simply by dropping an object. If they are accelerating, the object will fall, whereas if they are inertial, the object will float. It is worth noting that in the twin clock paradox experiment, if each observer is looking at the other observer's Doppler shift, then there is a difference between when the two observers observe the change from redshift to blueshift as the travelling observer starts the return journey. The travelling observer, whose turn-around is an acceleration, observes the change from redshift to blueshift immediately, whereas the stay-at-home observer doesn't observe the change from redshift to blueshift until the light from the turn-around has travelled the distance to reach the stay-at-home observer. This indicates that the change in direction is not merely relative, but that it is the travelling observer and only the travelling observer that truly turned around.

Originally Posted by Andrew?
Originally Posted by KJW
You require that all inertial frames are equivalent. How is that different from Einstein's principle of relativity?
I keep saying that all frames are not equivalent.
But you also said that you can treat the earth as having zero momentum. You can't have it both ways. All inertial frames are locally equivalent, and globally equivalent in flat (Minkowskian) spacetime.

Originally Posted by Andrew?
The laws of physics are at their simplest in a frame at rest with its visible universe.
Actually, being the simplest does not make a frame of reference preferred. In fact, by expressing the laws of physics in covariant form, the laws of physics will have the same form in all frames of reference.

Originally Posted by Andrew?
Anyone is entitled to think that bodies travelling faster than light may lead to problems.
Why? Why the speed of light? Particles can travel faster than light in a medium. This doesn't produce any problems, although it does produce Cherenkov radiation if the particles are charged.

70. Originally Posted by KJW
I explicitly said INERTIAL frames of reference.
Yes, and I said that Earth based experiments can be disputed on the grounds that they are not inertial. In my original question I asked about the logic of two clocks being slower than each other whilst they were inertial. If no one wants to talk about this inertial time dilation then it seemed reasonable to mention the classic non-inertial experiment. The time differences between clocks and ground observers are not explained by their observed relative speeds as predicted by SR. They involve their speeds relative to the Earth's centre. Anyway, we will never agree on this so there is no point in discussing it further.

Originally Posted by KJW
That's not true. For example, acceleration is not relative.
In my view if an observer at the top of a mountain and an observer in a valley observe an acceleration event, the latter would observe a faster rate of acceleration because their slower is clock. These relative differences in acceleration measurements can be resolved in the frame of the universe.

Originally Posted by KJW
But you also said that you can treat the earth as having zero momentum. You can't have it both ways.
I keep saying the Earth does have momentum but for local purposes it can be treated as zero because it cancels out.

Originally Posted by KJW
Actually, being the simplest does not make a frame of reference preferred.
Einstein thought of his first postulate as a proper scientific hypothesis. He explained in his book on relativity how it could be falsified, namely if the laws of physics were at their simplest in a given frame then this frame would be "absolutely at rest". The laws governing the expansion of the universe are at their simplest in the frame of the universe, hence his first postulate has been falsified. We will obviously not agree on this, so thanks for your thoughts but there is no point in continuing this discussion.

71. He explained in his book on relativity how it could be falsified, namely if the laws of physics were at their simplest in a given frame then this frame would be "absolutely at rest".
Can you please provide an exact reference for this quotation.

72. Einsteins "little" relativity book, section one, chapter five, about the middle of paragraph six.

73. Originally Posted by Andrew?
I said that Earth based experiments can be disputed on the grounds that they are not inertial.
Not if they are properly designed experiments. Disputing an experiment simply on the grounds that it is earth based is cargo cult science. Motion in the horizontal plane can be considered as inertial if the distances involved are small in comparison to the curvature of the earth.

Originally Posted by Andrew?
In my original question I asked about the logic of two clocks being slower than each other whilst they were inertial.
It has already been mentioned that neither clocks actually slow down but it is how each clock appears relative to the other that is slower. A spacetime diagram would be helpful here, but the equivalence of the two inertial frames of reference ensure that they both see the each other in the same way. The logic is not as strange as you might think. For example, consider two clocks that are one light-second apart, at rest relative to each other, and synchronised with respect to each other. An observer at each clock sees the other clock as one second behind their own clock. How can each clock be one second behind the other clock?

Originally Posted by Andrew?
If no one wants to talk about this inertial time dilation then it seemed reasonable to mention the classic non-inertial experiment.
Except that I asked for evidence for asymmetric time dilation between inertial frames of reference, and the Hafele–Keating experiment isn't the evidence I asked for.

Originally Posted by Andrew?
The time differences between clocks and ground observers are not explained by their observed relative speeds as predicted by SR.
The results of the experiment are in agreement with predictions from relativity.

Originally Posted by Andrew?
They involve their speeds relative to the Earth's centre.
It doesn't matter what frame of reference is used because the time value of a clock is invariant. But the metric is simpler in the frame of the earth's centre, so calculating the time value of the clocks will be easier (this doesn't make that frame any more valid).

Originally Posted by Andrew?
Originally Posted by KJW
That's not true. For example, acceleration is not relative.
In my view if an observer at the top of a mountain and an observer in a valley observe an acceleration event, the latter would observe a faster rate of acceleration because their slower is clock. These relative differences in acceleration measurements can be resolved in the frame of the universe.
I was talking about an observer in an accelerated frame of reference determining that they are in an accelerated frame of reference and not in an inertial frame of reference,

Originally Posted by Andrew?
Originally Posted by KJW
But you also said that you can treat the earth as having zero momentum. You can't have it both ways.
I keep saying the Earth does have momentum but for local purposes it can be treated as zero because it cancels out.
And I'm saying you can't treat the earth's momentum as zero if you think there is a preferred frame of reference.

Originally Posted by Andrew?
Anyway, we will never agree on this so there is no point in discussing it further.
...
We will obviously not agree on this, so thanks for your thoughts but there is no point in continuing this discussion.
Then what was the point of starting the discussion in the first place?

74. Then what was the point of starting the discussion in the first place?
I am wondering the same thing. If you have already made up your mind on something, as is evidently the case here, why go on a public forum and ask questions ? None of the replies will matter in the slightest, regardless of what they are

75. Originally Posted by Markus Hanke
If you have already made up your mind on something, as is evidently the case here, why go on a public forum and ask questions ?
I am not the only person on the forum to have made up their mind on on something.

I started with a question about the logic of two clocks being slower than each other. I was told this could be explained by a lack of simultaneity, so I've now asked a question about synchronized clocks around the edge of a rotating platform. Symmetry shows these clocks are synchronized in the rotating frame as well as in the stationary frame. This is not supposed to happen. No one has yet explained why this does not show SR to be inconsistent.

It isn't surprising I haven't changed my mind about SR as the evidence against it is so strong. I don't just mean the falsification of its first postulate by the expansion of the universe.

Circular accelerators are built because people ignore the predicted contraction of the ring of particles (Ehrnfest's paradox). GPS works because people ignore the predicted symmetrical time dilation between satellites and the Earth's centre, all of which are inertial in my opinion as the satellites are in free fall. The satellites' clocks slow down, but in the frame of a satellite the Earth's frame does not slow equally. The dilation is asymmetric. In fact no evidence has emerged against the natural assumption that there is one objective universe containing objects having a single length and time rate.

Of course E=mc^2 is independent of SR, and Einstein wasn't even the first person to have this idea.

I have asked these questions because I thought there may be someone else who is interested in finding a better way to explain our observations of the universe.

76. It isn't surprising I haven't changed my mind about SR as the evidence against it is so strong.
I am getting a different impression, because I have seen this countless times before - I think you haven't changed your mind because you do not want to change your mind. You have arrived at a particular idea about how the world should work, and you will do everything within your power to support this idea - this includes strategies like selectively isolating information, misrepresenting information, ignoring evidence, refusing to properly learn SR ( seriously - you have very large gaps in knowledge and understanding of the model, as evidenced by your responses here ! ), and others. It is called confirmation bias. The starting point for all your arguments is not the scientific method, but your personal ideas.

Examples of this - you keep repeating that SR has been "falsified" by the expansion of the universe, in spite of the fact that you have repeatedly been told by several people here that "the universe" is not actually an SR frame of reference featuring symmetry wrt the earth-bound observer. You keep repeating that there is no evidence that Lorentz invariance exists in the real world, in spite of overwhelming experimental and observational evidence to the contrary; pointing out this evidence to you results in responses such as "I don't see any evidence". You keep applying principles of SR wrongly, and then take it as "evidence that SR is inconsistent" if things don't work out etc. I could go on, but you get the idea.

The reason why there is no one else here - or indeed within the world of established science - who is looking to abandon SR is that the Theory of Relativity is in full accord with the scientific method, and hence works very well as a framework to understand the universe. On the other hand, it is manifestly evident that notions of absolute time and space are not in accord with the scientific method, and the real world; this had already been recognised as far back as the late 1800s. The Theory of Relativity was developed precisely because space/time absolutism does not work.

So for yourself, you are going to have to make a choice here :

1. Go on believing that every single scientist and learned person ( including myself, KJW, and others involved in this discussion here, who have studied this stuff for years, both formally and informally ) since the inception of SR/GR is a brainless sheep who just regurgitates orthodox dogma, and is simply too stupid - or too heavily indoctrinated - to recognise the obvious failings of SR/GR. Scientists are either simple-minded, or are all part of a conspiracy to suppress dissidents. All experimental evidence has been misunderstood and misinterpreted, for the past 100+ years. Obvious evidence against SR/GR is deliberately being ignored. All other disciplines of physics - QFT, RQM, etc - are equally flawed, since relativity is an integral part of them too. The scientific method is just a tool to exclude deviant opinions, and of no other value. Essentially, go on believing that "it does not make sense to me, hence it must be wrong. Absolutism does make sense to me, hence it must be right."
2. Consider the fact that the problem may not actually be the Theory of Relativity, but rather your own mind. Consider the possibility that your understanding of the model is flawed and incomplete. Consider the possibility that you have fallen victim to confirmation bias, which is often a subconscious process. Consider the possibility that "it does not make sense to me / I don't like it" is not an objective way to evaluate a scientific model. Consider the possibility that you simply may be wrong in your opinions.

Choose wisely, and choose objectively. Bayesian rationality may be a good tool for this; you have already acknowledged that others here know more about physics and SR than you do. Given that, what do you think are the probabilities of

a) There being a grand conspiracy among physicists over the past 100 years to defend a model that is manifestly wrong
b) Every physicist and learned person over the past 100 years - except yourself - being too stupid to see the faults in relativity, or them being merely mindless, unthinking, non-critical regurgitators of textbooks who can't see the flaws
c) Your own idea of relativity simply being inaccurate

This is an assessment you are going to have to make for yourself, and you will be the owner of that decision along with all its consequences. It has nothing to do with any of us. As things stand, we could go on for weeks and weeks with these discussions, to no avail at all - we are not going to convince you that SR works, no matter what we say/quote/show, unless you look at your own motivations first; and you are certainly not going to convince any person who bases his/her view of the world on the scientific method that SR within its domain of applicability is somehow wrong or inconsistent ( the latter one can be shown not to be the case in a general and trivially easy manner ).

77. The dilation is asymmetric
Of course it is asymmetric. The satellite and the earth-bound clock sit at different points in a gravitational field, so - while each frame is locally inertial - the global situation is one where you need to account for gravitational effects, hence it's a GR problem. There cannot be any Lorentz symmetry between these frames.

I do not know if this persistent tendency of yours to apply SR wrongly in one way or another is due to your lack of knowledge on this subject, or whether it is a wilful and conscious act. We can help you with the former, if you let us, but not with the latter.

78. No one has yet explained why this does not show SR to be inconsistent.
Again, it is because the metric on the rotating disc is not Minkowski ( it is approx the Langevin-Landau-Lifschitz metric ), so you cannot just apply SR to this and expect everything to work out. SR, like any other model, has a limited domain of applicability, and you need to know those limits, and apply the appropriate models.

It is never a good idea to reject a model of physics that you do not fully understand yourself.

79. I just want to point out that nothing I have written here is in any way, shape or form meant as a personal attack, so in case that's how you perceive it, I apologise in advance.

I wrote these things, because I know from my own personal experience what it is like to be stuck in the confirmation bias trap - there have been times when I was absolutely convinced of the veracity of certain things, and it really did feel to me like everyone else just failed to understand the subject matter - including experts in the field. I defended those beliefs of mine tooth and nail, in a wholly irrational manner, without even realising it. I picked information and twisted it to suit my needs, ignored evidence that was pointed out to me, and simply refused to even consider any other angle on the subject.

It took one particularly patient and persistent poster to make me see "over the wall" - so to speak - and realise that I had been wrong all along. I was challenged to support my view with maths, and was given the necessary tools to do so; when the result wasn't what I expected it to be, I was baffled and perplexed - it was a genuine shock to the system. But the universe is what it is, you cannot argue with it; we are all entitled to our own opinions, but not or own facts.

So I had to eat humble pie, and come back and admit I was wrong, right there in public. It was a very important experience, and really took my understanding of physics to a completely new level.

So what I am trying to say is that I wrote the below for no other reason but in the hopes that might start questioning yourself a little, which can only be a good thing. Ultimately it is of no consequence to me what you believe or not, but I don't like to see obvious intelligence wasted.

Make the best of it.

80. Thanks Markus for explaining your position and that of others who believe in SR, but I'm trying to focus on experimental results and logical arguments about them.

Do you think Einstein was wrong to base SR on a testable hypothesis concerning absolute motion, or do you think the expansion of the universe is not symmetrical when viewed from a point at rest with the visible universe, or that it is not asymmetric in other frames, or that a law of symmetric expansion is not simpler than one of asymmetric expansion?

In reply to my original question of how two clocks could logically be slower than each other, I was told this could be explained by non-simultaneity. However it seems to me that non-simultaneity can only apply to observations of more than one clock in a moving frame. In this case an observer receives signals from a single moving clock in another rocket. How can this clock be non-simultaneous with itself?

As for the circular rotating discs that are synchronized by a central signal, I have asked about the actual pattern of sync gaps. You say "it is approx the Langevin-Landau-Lifschitz metric" but this tells me nothing about the actual sync gaps.

In the case of a rectangle formed from four lines of clocks moving at constant speed around a rectangle, the clock in the middle of each line can similarly be synchronized by a central signal. The remaining clocks in each line can then be synchronized in the normal manner. Stationary observers along each line should see a progressive sync gap along each line and around each corner. As this sync gap progresses in the direction of motion, e.g. clockwise, I still do not see why the sync gaps do not lead to each clock becoming out of sync with itself.

81. Originally Posted by Markus Hanke
The dilation is asymmetric
Of course it is asymmetric. The satellite and the earth-bound clock sit at different points in a gravitational field, so - while each frame is locally inertial - the global situation is one where you need to account for gravitational effects, hence it's a GR problem. There cannot be any Lorentz symmetry between these frames.

I do not know if this persistent tendency of yours to apply SR wrongly in one way or another is due to your lack of knowledge on this subject, or whether it is a wilful and conscious act. We can help you with the former, if you let us, but not with the latter.
I was referring to the time dilation that physicists attribute to SR, i.e. the 7 microseconds daily slowing of satellite clocks, not the 45 attributed to GR. My point is that this SR time dilation is supposed to be symmetrical. The satellites should also find that the Earth's central frame has slowed down by 7 microseconds, but they just find that the Earth frame is 7 microseconds faster.

82. Thanks Markus for explaining your position and that of others who believe in SR, but I'm trying to focus on experimental results and logical arguments about them.
That is what the scientific method does too - it takes the mathematical model ( "logical argument" ), extracts predictions from it, and compares those predictions to experimental results. "Belief" never comes into it. This has been done thousands upon thousands of times since SR's inception over a hundred years ago, and the thing is this - based on those results, every scientist since then has come to the conclusion that it is an exceptionally successful and well-working model. This is why we are using it on a daily basis in science and engineering, and this is why it has become an integral part of pretty much all areas of the natural sciences, from quantum field theory to chemistry.

You say otherwise.

All I am asking you to do is consider what this rejection really means, for yourself. I'm sure you are well aware that your approval or rejection of SR is entirely irrelevant in the grand scheme of things; it will continue to be used, since the deciding factor is consensus among the scientific community. That being the case, the only reason why I am still responding here is because I want to help you.

But maybe let me ask you outright - is there actually anything me or anyone else here could say to you that would make you change your mind ? I would appreciate an honest answer; if there is not, then that is fine, we'll just let this go. If there is, then you might give us a rough idea what we could do to help, and we'll try our best.

83. My point is that this SR time dilation is supposed to be symmetrical.
The symmetry is only between inertial frames; even if you disregard the difference in gravitational potential, a frame stationary on the Earth's surface is still not inertial, since its worldline isn't straight - unlike the satellite, which traces out a geodesic. So again, this is not a pure SR situation, which matters if you compare two such frames.

Luckily ( in terms of computational effort ), due to certain symmetries of the Schwarzschild metric, we still get the correct magnitude of the relative velocity effect ( 7 microseconds ), but the sign has to come from GR.

Earth : 45-7 = 38 microseconds
Satellite : -45-(-7) = -38 microseconds

If I can make a suggestion to you - if you wish to disprove specifically Lorentz symmetry on the basis of experimental results, I would very much recommend you stick to purely inertial frames in flat spacetime, since that is the domain of applicability of Lorentz symmetry. GPS satellites are really within the domain of GR, and you are just making your own life really hard if you bring up such examples.

Lorentz symmetry ( which is the symmetry between inertial frames you keep referring to ) can be directly tested in a lab, which has been done many, many times with very high levels of accuracy :

https://en.m.wikipedia.org/wiki/Mode...entz_violation

If you wish to show SR wrong, you need to reference a repeatable, controlled, peer-reviewed experiment that shows a Lorentz violation. To the best of my knowledge no such experimental data exists to date; on the other hand, the above link ( as well as the references therein ) shows a large list of results that indicates that Lorentz symmetry - and hence SR - are indeed valid.

I should also mention that Lorentz symmetry is equivalent to CPT symmetry, so if it were violated, we would have spotted that long ago in particle accelerator high energy collisions.

84. It's worth noting that in the case of asymmetric time dilation between inertial frames of reference, and the visible universe as the preferred frame of reference, the result of measurements using the Doppler effect will vary with the time of day as well as the time of year due to the different velocities of a given fixed location on the surface of the earth with respect to the preferred frame.

Have you ever heard of Mössbauer spectroscopy? Basically, a solid target containing particular nuclei is probed with gamma radiation photons of resonant frequency emitted recoil-free from a solid source containing nuclei that decay to form the same nuclei as the target. For example, cobalt-57 decays by electron capture to an excited state of iron-57, which in turn decays to the ground state by emitting a gamma radiation photon of very precise energy. This gamma radiation photon is very close to the precise energy needed to be absorbed by ground state iron-57 in the target. However, the precise energy of the gamma radiation photons that the iron-57 in the target will absorb depends on the environment of the individual iron-57 nuclei, for example, the electron density of the s-orbitals at the nuclei. This is useful to chemists and biochemists studying iron compounds. But, the energy of the source gamma radiation will generally not precisely match the resonant energy of the target nuclei. So, the source is accelerated through a range of velocities, producing a changing Doppler shift between the source and target, the particular relative velocities at which absorption occurs being recorded as a spectrum. A typical range of velocities for iron-57 may be around ±11 mm/s, so the measurement would be extremely sensitive to the time of day or the time of year as well as the latitude if the visible universe is the preferred frame of reference. Surely, such a variation of the spectra for a given compound with respect to the time of day would have been noticed by now if it exists.

85. Originally Posted by Markus Hanke
The symmetry is only between inertial frames; even if you disregard the difference in gravitational potential, a frame stationary on the Earth's surface is still not inertial, since its worldline isn't straight - unlike the satellite, which traces out a geodesic. So again, this is not a pure SR situation, which matters if you compare two such frames.
I made it clear I was talking about the Earth's centre, not its surface, and I referred to the 7 microsecond dilation that physicists themselves say is due to SR.

Thank you for the Wikipedia link which I found interesting. It mentioned the Ives-Stillwell experiment which validated asymmetric dilation. Ives believed his experiment disproved SR, but I have not found an explanation of why. The Kennedy-Thorndike experiment is described as disproving the idea of the Earth moving through an aether, but I have never thought such motion was plausible anyway.

There is also mention of the Robertson-Mansouri-Sexl framework. The latter two wrote a paper in 1976 which said the CMBR "has shown that cosmologically a preferred system of reference does exist." It seems their paper presents a theory of absolute simultaneity which is kinematically equivalent to SR.

The more I read the more sure I become of my own ideas. I notice you have not answered my questions again:

"Do you think Einstein was wrong to base SR on a testable hypothesis concerning absolute motion, or do you think the expansion of the universe is not symmetrical when viewed from a point at rest with the visible universe, or that it is not asymmetric in other frames, or that a law of symmetric expansion is not simpler than one of asymmetric expansion?

In reply to my original question of how two clocks could logically be slower than each other, I was told this could be explained by non-simultaneity. However it seems to me that non-simultaneity can only apply to observations of more than one clock in a moving frame. In this case an observer receives signals from a single moving clock in another rocket. How can this clock be non-simultaneous with itself?

As for the circular rotating discs that are synchronized by a central signal, I have asked about the actual pattern of sync gaps. You say "it is approx the Langevin-Landau-Lifschitz metric" but this tells me nothing about the actual sync gaps.

In the case of a rectangle formed from four lines of clocks moving at constant speed around a rectangle, the clock in the middle of each line can similarly be synchronized by a central signal. The remaining clocks in each line can then be synchronized in the normal manner. Stationary observers along each line should see a progressive sync gap along each line and around each corner. As this sync gap progresses in the direction of motion, e.g. clockwise, I still do not see why the sync gaps do not lead to each clock becoming out of sync with itself."

86. Originally Posted by KJW
It's worth noting that in the case of asymmetric time dilation between inertial frames of reference, and the visible universe as the preferred frame of reference, the result of measurements using the Doppler effect will vary with the time of day as well as the time of year due to the different velocities of a given fixed location on the surface of the earth with respect to the preferred frame.
A very reasonable point, but in my view the Earth's centre moves in such a way as to cancel out the net forces from the Sun and the rest of the universe. The universe provides a reference frame for red shifts of the Earth's centre, but local time dilation is based on KE/mass, i.e. speed relative to the Earth's inertial centre. Changes in the Earth's time rate would affect local observers and local experimental light sources alike.

87. Originally Posted by Andrew?
but in my view the Earth's centre moves in such a way as to cancel out the net forces from the Sun and the rest of the universe

How?

88. I made it clear I was talking about the Earth's centre, not its surface, and I referred to the 7 microsecond dilation that physicists themselves say is due to SR.
The 7 microsecond time dilation is between a satellite in orbit, and a receiver at the surface of the Earth. That is where the GPS receivers are located, not at the center of the Earth. If you wish to discuss GPS, then at the very least you need to stick to the actual setup.

89. Originally Posted by Andrew?
Originally Posted by KJW
It's worth noting that in the case of asymmetric time dilation between inertial frames of reference, and the visible universe as the preferred frame of reference, the result of measurements using the Doppler effect will vary with the time of day as well as the time of year due to the different velocities of a given fixed location on the surface of the earth with respect to the preferred frame.
A very reasonable point, but in my view the Earth's centre moves in such a way as to cancel out the net forces from the Sun and the rest of the universe. The universe provides a reference frame for red shifts of the Earth's centre, but local time dilation is based on KE/mass, i.e. speed relative to the Earth's inertial centre. Changes in the Earth's time rate would affect local observers and local experimental light sources alike.
There would still be a variation of the Mössbauer spectrum for a given compound with respect to the latitude of the laboratory as well as the orientation of the gamma radiation beam relative to the earth's spin axis.

90. Originally Posted by Andrew?
Stationary observers along each line should see a progressive sync gap along each line and around each corner. As this sync gap progresses in the direction of motion, e.g. clockwise, I still do not see why the sync gaps do not lead to each clock becoming out of sync with itself."
As was explained in the other thread, there is no progression of sync gaps as one goes around the loop. The relation "is simultaneous to" is not transitive (where it is understood that in the expression "X is simultaneous to Y", simultaneity is with respect to Y). This is because the notion of simultaneity with respect to one frame is independent of the notion of simultaneity with respect to another frame.

91. Originally Posted by Andrew?
Circular accelerators are built because people ignore the predicted contraction of the ring of particles (Ehrnfest's paradox).
The Ehrenfest paradox doesn't apply to particles travelling around a particle accelerator. The Ehrenfest paradox is about spinning rigid discs. Also, length contraction is in the direction of motion, not in the direction perpendicular to the motion. Thus, while there is contraction around the circumference, there isn't contraction of the radius. It should be noted that the trajectory of a particle around the accelerator ring is actually a spiral in four-dimensional spacetime, and it is in four dimensions that the length contraction applies.

92. Originally Posted by Paleoichneum
Originally Posted by Andrew?
but in my view the Earth's centre moves in such a way as to cancel out the net forces from the Sun and the rest of the universe

How?
The Earth's centre accelerates with respect to the rest of the universe in accordance with the forces from the rest of the universe. Hence it is in free fall. The acceleration of a mass is equivalent to the force from a gravitational field.

"Do you think Einstein was wrong to base SR on a testable hypothesis concerning absolute motion, or do you think the expansion of the universe is not symmetrical when viewed from a point at rest with the visible universe, or that it is not asymmetric in other frames, or that a law of symmetric expansion is not simpler than one of asymmetric expansion?

In reply to my original question of how two clocks could logically be slower than each other, I was told this could be explained by non-simultaneity. However it seems to me that non-simultaneity can only apply to observations of more than one clock in a moving frame. In this case an observer receives signals from a single moving clock in another rocket. How can this clock be non-simultaneous with itself?

In the case of a rectangle formed from four lines of clocks moving at constant speed around a rectangle, the clock in the middle of each line can similarly be synchronized by a central signal. The remaining clocks in each line can then be synchronized in the normal manner. Stationary observers along each line should see a progressive sync gap along each line and around each corner. As this sync gap progresses in the direction of motion, e.g. clockwise, I still do not see why the sync gaps do not lead to each clock becoming out of sync with itself."

93. Originally Posted by Markus Hanke
I made it clear I was talking about the Earth's centre, not its surface, and I referred to the 7 microsecond dilation that physicists themselves say is due to SR.
The 7 microsecond time dilation is between a satellite in orbit, and a receiver at the surface of the Earth. That is where the GPS receivers are located, not at the center of the Earth. If you wish to discuss GPS, then at the very least you need to stick to the actual setup.
The 7200ns is between a satellite and an axis through the Earth's centre and poles. The 7200ns is not a property of the Earth's surface because the satellite's relative speed varies over the surface. The rotational speed of the equator means the dilation here is 6300ns.

The basic point remains that the "SR" dilation is asymmetric.

94. Originally Posted by KJW
There would still be a variation of the Mössbauer spectrum for a given compound with respect to the latitude of the laboratory as well as the orientation of the gamma radiation beam relative to the earth's spin axis.
Relativists often assume there are just three models of light transmission: SR, the ballistic theory or the ether. The ballistic theory, whereby the speed of light is fixed by its source, sounds very sensible but is obviously wrong. The idea that c is constant for an ether through which the Earth moves was discredited a long time ago. Kennedy-Thorndike's use of Mossbauer is another attack on the defunct ether theory. The assumption being that as it disproves the ether theory more successfully than Michelson & Morley, and because the ballistic theory has also been disproved, we are left with SR. There are though other theories, mine being one of them. As I have no need of the defunct ether theory I see no reason why the experimental results would be affected by latitude or orientation.

95. Originally Posted by KJW
The relation "is simultaneous to" is not transitive (where it is understood that in the expression "X is simultaneous to Y", simultaneity is with respect to Y). This is because the notion of simultaneity with respect to one frame is independent of the notion of simultaneity with respect to another frame.
I accept that SR's notion of simultaneity is independent of frames, but not that it can be independent of logic. If each observer sees their clock is behind the clock behind and ahead of the clock ahead, then logically there is a cumulative sync gap. One can consider the frame of a single clock that receives timing signals from the other clocks via a wire or fibre optic cable around the edge of the disc. If sync gaps occur then they should increase positively in one direction and negatively in the other. If so, what happens at the clock diametrically opposite?

96. Originally Posted by KJW
The Ehrenfest paradox is about spinning rigid discs. ... It should be noted that the trajectory of a particle around the accelerator ring is actually a spiral in four-dimensional spacetime, and it is in four dimensions that the length contraction applies.
Yes, you're right that Ehrnfest was referring to rigid bodies, but of course his paradox arises from the more general one that a circumference in a rotating frame is predicted to contract but the diameter does not. I keep being told these things make sense in SR's four dimensions, but they do not make sense in the real four dimensions of accelerating particles. I see no point in saying Minkowski space - which is based on SR's assumptions - proves SR is correct. This would be the case even if SR's assumptions had not been invalidated. Similarly, there would be no point in me saying my idea of spacetime proves that my idea of spacetime is correct.

The fact is that experiments have failed to validate distance contraction. As in the muon/Earth's atmosphere experiment, distance contraction is assumed to occur otherwise SR would not make sense. But there must surely be ways that distance contraction could be demonstrated if it occurred. For example, the distance between stars would vary on a quarterly basis depending on whether it was parallel or perpendicular to the Earth's direction of orbit.

97. Originally Posted by Andrew?
Originally Posted by KJW
There would still be a variation of the Mössbauer spectrum for a given compound with respect to the latitude of the laboratory as well as the orientation of the gamma radiation beam relative to the earth's spin axis.
I see no reason why the experimental results would be affected by latitude or orientation.
It is because the speed of a point on the earth's surface relative to the earth's centre varies with latitude, a point closer to the equator being faster than a point closer to the poles. With the source moving relative to the target at a given speed, the speeds of the source and of the target vary with the orientation as well as the latitude.

Originally Posted by Andrew?
Relativists often assume there are just three models of light transmission: SR, the ballistic theory or the ether. The ballistic theory, whereby the speed of light is fixed by its source, sounds very sensible but is obviously wrong. The idea that c is constant for an ether through which the Earth moves was discredited a long time ago. Kennedy-Thorndike's use of Mossbauer is another attack on the defunct ether theory. The assumption being that as it disproves the ether theory more successfully than Michelson & Morley, and because the ballistic theory has also been disproved, we are left with SR. There are though other theories, mine being one of them. As I have no need of the defunct ether theory I see no reason why the experimental results would be affected by latitude or orientation.
I made no mention of the aether. My argument is against asymmetric time dilation.

98. Originally Posted by Andrew?
I see no point in saying Minkowski space - which is based on SR's assumptions - proves SR is correct.
I did not suggest that Minkowskian spacetime proves that special relativity is correct. Rather, Minkowskian spacetime provides an explanation of special relativity. However, Minkowskian spacetime does prove that special relativity is consistent. Hence, my signature below.

99. Originally Posted by Andrew?
Originally Posted by KJW
The relation "is simultaneous to" is not transitive (where it is understood that in the expression "X is simultaneous to Y", simultaneity is with respect to Y). This is because the notion of simultaneity with respect to one frame is independent of the notion of simultaneity with respect to another frame.
I accept that SR's notion of simultaneity is independent of frames, but not that it can be independent of logic. If each observer sees their clock is behind the clock behind and ahead of the clock ahead, then logically there is a cumulative sync gap. One can consider the frame of a single clock that receives timing signals from the other clocks via a wire or fibre optic cable around the edge of the disc. If sync gaps occur then they should increase positively in one direction and negatively in the other. If so, what happens at the clock diametrically opposite?
By considering the situation in terms of Minkowskian spacetime, it is clear that there are no sync gaps. And because Minkowskian spacetime is fully consistent, any logic that indicates a cumulative synch gap leading to inconsistency has to be invalid in some way.

100. Originally Posted by KJW
I made no mention of the aether. My argument is against asymmetric time dilation.
I know you didn't, but the Wikipedia article makes it clear that the relative velocity being considered is that of "the hypothetical aether", not the centre of the Earth.

Are you saying the experiment separately measured the time dilation of the apparatus and the aether and proved them to be equal?

101. Originally Posted by KJW
I did not suggest that Minkowskian spacetime proves that special relativity is correct. Rather, Minkowskian spacetime provides an explanation of special relativity. However, Minkowskian spacetime does prove that special relativity is consistent. Hence, my signature below.
It doesn't matter that Minkowski spacetime is consistent with itself, it needs to be consistent with reality. Depending on which version is used, either its times or its distances are imaginary. This shows it does not apply to the real world. The statement that SR has no internal inconsistencies is no basis for claiming it does not lead to real world inconsistencies and paradoxes.

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