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I know that they have proven time dilation in the moving frame from the perspective of the stationary frame, eg comparing two cesium clocks in the jumbo jet test.
But have tests been done on the other side of the equation; testing to show time dilation in the stationary frame from the perspective of the moving frame?

I know that this goes to the heart of relativity, and I certainly know of the formulas for Lorentz transformation.
I just want to know if this has been actually tested.

Edit, there seems to be some confusion over the twin paradox. The issue is if a twin takes a rocket to a distant star. The twin on earth will see the rocket moving away and will see a clock on the rocket moving slower, But the twin in the rocket will see the earth moving away, so will see the earth clock moving slower. The paradox is when the rocket twin returns who is younger? They can't both be younger.

So my question, again, is has it been actually tested if a twin in the rocket sees the earth moving away, and thus sees an earth clock moving slower. Has this been tested in any way? I know that it has been tested that the earth bound twin will see a clock in the rocket moving slower. But has the opposite been tested?

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  • $\begingroup$ Lorentz symmetry guarantees that verifying time-dilation in the "stationary" frame verifies the corresponding result in the "moving" frame. Where we have to be careful about the terms "stationary" and "moving" since they are not meaningful in special relativity. $\endgroup$
    – Charlie
    Oct 11 '20 at 20:17
  • $\begingroup$ @Charlie I understand all of that. Just wondering if it has actually been tested. They've done several sophisticated tests on the first half. Have they done any on the second half? $\endgroup$ Oct 11 '20 at 20:22
  • $\begingroup$ Wasn't the test with the Jumbo Jet designed to test general relativity? To see if a clock higher in a gravity field ticks faster than lower in the field? $\endgroup$ Oct 11 '20 at 20:24
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    $\begingroup$ Could you clarify what you mean by this: “testing to show time dilation in the stationary frame from the perspective of the moving frame?” I don’t understand the test that is being sought. $\endgroup$
    – Dale
    Oct 11 '20 at 20:24
  • $\begingroup$ @DescheleSchilder Yes, exactly. It showed that the clock in the jumbo jet ran slower than the clock on the ground, because of kinetic time dilation. $\endgroup$ Oct 11 '20 at 20:30
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Indeed, an inertial observer can ascribe himself a state of "proper rest" or "proper motion". However, in SR an observer rarely founds himself in a "moving frame", an observer is usually "at rest" in his own frame. Two spatially separated and Einstein - synchronized clocks of his "rest frame" measure longer time interval than a single clock, which is changing spatial position (is moving) in his frame (time dilation).

SR recognizes only one synchronization of spatially separated clocks - Einstein's .

However, there were Mossbauer rotor experiments (time dilation tests) in centrifuge;

  • if an observer (absorber) is at rest in the center of the centrifuge and a source of radiation is attached to the rim of centrifuge, this observer would measure $\gamma$ times lower frequency of radiation, or "moving clock is running slower than his own"

  • If an observer (absorber) is attached a rim of an centrifuge and a source of radiation is located in the center, this observer would measure $\gamma$ times higher frequency of radiation, or that the a "clock at rest is running faster than his own"

  • If two observers are located on the opposite sides of a rim of rotating ring, they would measure absence of dilation of each other clocks (Champeney and Moon time dilation test)

The circumference can be of arbitrarily large diameter; i.e. this rotating observer can be quasi - inertial; that doesn't change things much. Rotating observer simply cannot ascribe himself state of rest.

Good to note, that A. Einstein in his celebrated 1905 paper teaches, that from the point of view of "moving observer" a clock "at rest" is ticking $\gamma$ times faster than his own.

One clock is slower that the other and vice versa - is nonsense - even in Special Relativity

@Mohammad Javanshiry, I have provided the quote already. The quote was taken straight from Einstein‘s paper, just please read it carefully. Einstein clearly indicated that the source was „at rest“ and the observer was „moving“. Note that Einstein attached time dilation to the observer. Indeed, relativistic Doppler blueshift doesn‘t mean that the source‘s clock is running faster. It doesn‘t also mean, that it is running slower. It means, that source‘s clock is running either slower, or faster, or at the same rate – at any rate you wish, that purely depends on what an observer thinks about his own motion. One can attach time dilation either to the observer, or to a source or even to the both.

If it is still not clear, please read 34-6 The Doppler effect, Relativistic effects in radiation, Feynman lectures. Note that Feynman considers the effect in the frame of the stationary observer AND in the frame of the stationary source. In the first case he attaches time dilation to the source (34.12), in the second to the moving observer. In the second case(34.14) Feynman divides source‘s frequency by $\sqrt {1-v^2/c^2}$.

If an observer is moving towards a stationary source of radiation, frequency of the source increases (blueshift) due to dilation of observer‘s clock. Since his clock is running slower, the „outside world“ appears to him as if in fast-forward mode.

@foolishmuse I don’t know why they debate twin paradox. Twin paradox has trivial resolution in the framework of Lorentz Ether Theory.

I don't also know why they have decided that the speed of light is isotropic in all frames of reference.

If an observer in inertial laboratory wants to measure rate of “moving” clock, he must set up laboratory equipment first, or synchronize two spatially separated clocks within his laboratory, say A and B. So as to synchronize these clocks, he must know, how long a light pulse travels from clock A to clock B, i.e. he must to know the one – way speed of light. But, so as to measure the one - way speed of light he must synchronize clocks. Hence, there is a circular reasoning. It is not possible to measure one – way speed of light prior to certain synchronization scheme. However, it is possible to measure speed of light back – and – forth by means of single clock.

Since one – way speed of light depends on synchronization convention, one - way dilation also depends on synchronization convention. All that is clear for 100+ years, Einstein understood that perfectly well.

SR assumes, that one – way speed of light is isotropic in all relatively moving reference frames, but it is not experimentally confirmed fact. It is a convention, a.k.a. Einstein synchronization, or standard synchrony convention. If every observer synchronizes clock according to Einstein, every “moving” relatively to him clock would appear running slower than his own, spatially separated ones.

Einstein’s synchrony convention is only a special case of Reichenbach’s synchrony convention, or non – standard synchronization. This synchronization allows anisotropic one – way speeds of light, but keeps two – way speed of light isotropic.

For example, this observer can assume, that his laboratory is moving relatively to a “stationary” clock. In this case he must take into account his own velocity in the stationary clock’s frame and re-synchronize clocks in his laboratory according to anisotropic (Reichenbach’s) synchrony convention. In this case “stationary” clock would measure longer interval of time, or would appear running faster.

The same is about the relativistic Doppler effect. As soon as you re-adjust laboratory equipment or change interpretation, you can make “moving clock” running at any rate you wish - slower (if you think, that clock is moving within your frame) or faster (if you think, that you are moving himself relatively to a stationary clock).

However, raving fans of SR do not want to admit, that an observer can be “moving” himself, even though they admit, that motion is relative. This is the paradox.

I wrote this note so as to avoid synchronization issue and work it out only by means of relativistic Doppler effect; this demonstrates that these wonders like “one clock is slower than the other and vice versa” is simply a piece of nonsense.

By the way, there is a good article which addresses twin paradox.

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  • $\begingroup$ I think that this answer is another confirmation of the solution to the twin paradox. Because the test is done in a centrifuge, the rotating ring is constantly changing inertial frames, so yes, it would see the clock in the centre as running faster. I think that in order to do the test I'm asking about, the moving frame would have to be running in a straight line away from the stationary frame, and not return. $\endgroup$ Oct 11 '20 at 21:52
  • $\begingroup$ "A. Einstein in his celebrated 1905 paper teaches, that from the point of view of "moving observer" a clock "at rest" is ticking γ times faster than his own." Would you please give a direct reference to this? Remember that the blue-shift of a moving source, due to the Doppler effect, does not indicate that the clock of the source runs faster. $\endgroup$ Oct 11 '20 at 22:00
  • $\begingroup$ @foolishmuse, an observer on the rim if a rotating ring sees the clock in the center as running faster because his own clock (and the observer himself) is running slower, not because he is constantly changing inertial frame. Please note that only when time dilation is measured on closed paths, it is not conventional and can unequivocally be measured like the two-way speed of light. One -way dilation depends on clock synchronization convention, Please read chapter the chapter "non-standard synchronizations" here: en.wikipedia.org/wiki/One-way_speed_of_light $\endgroup$
    – Albert
    Oct 12 '20 at 10:46
  • $\begingroup$ Hence, prior to measuring dilation of moving from point A to point B single clock one must synchronize two clocks in points A and B. Measured time dilation would depend on clock synchronization convention. pitt.edu/~jdnorton/teaching/HPS_0410/chapters/…. Now, the following problem arises: how one must synchronize clocks in an "stationary" frame and how in a "moving" one? Only after synchronization procedure one - way measurement can be conducted. $\endgroup$
    – Albert
    Oct 12 '20 at 10:51
  • $\begingroup$ @Albert the basis of the twin paradox in SR is that both the earth twin and rocket twin see the other as moving away, and thus both see the other clock as moving slower. It is only when the rocket twin changes direction and returns to earth that the resolution occurs, and this is because the rocket twin has changed inertial frames. You can see it all here: en.wikipedia.org/wiki/Twin_paradox Based on that resolution, an object orbiting an observer would be constantly changing inertial frames and thus there would be no paradox. $\endgroup$ Oct 12 '20 at 17:37
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Let's assume two identical objects being in relative motion wrt each other. Let's also assume they got their motion in a symmetrical way (by accelerating from each other with the same acceleration)). Their clocks are synchronized at the start.
If one of the two accelerates and decelerates to enter the other object, there will be a difference in time on the clocks.
This amounts indeed to the twin paradox, as is stated in a comment.
But it works the other way round too. That's why there is a symmetry between the two objects.

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