1
$\begingroup$

EDIT: How is Lorentz' interpretation of STR considered "unpublished"? There's a ton of published scientific literature on it, see for example here or here. There were no grounds to close this question.

So, I’ve been reading up on the (neo-)Lorentzian interpretation of Special Relativity and absolute simultaneity, which is said to be empirically equivalent to Minkowski's and Einstein's interpretations (albeit a bit more metaphysical in nature). Yet there's one aspect of it that I just can't seem to wrap my head around no matter how hard I think on it, so I'm really hoping someone could help me see where I'm going wrong.

Consider the photon clock experiment where one observer (Alice) in motion passes by another observer (Bob) at rest, each of them holding a photon clock.

Now, according to the (neo-)Lorentzian interpretation, Alice would be in absolute motion whereas Bob would be closer to absolute rest.

Bob's perspective:

Bob would see Alice as being subject to time dilation, with Alice's clock subsequently ticking slower than Bob's.

Bob would conclude that his own perspective is privileged due to being closer to absolute rest, thus Alice and her clock are both running slower in an absolute sense.

Alice's perspective:

Alice would not be surprised to see her own clock ticking normally, since she too would conclude that her whole body and perceptions have absolutely slowed along with her photon clock.

So far, so good. HOWEVER...

Alice would also percieve Bob and his clock running slower than her own. But if it's postulated that...

  1. There exist relations of absolute simultaneity,
  2. Bob and his clock are absolutely running faster than Alice an hers, and
  3. Alice's perception of ALL events have been slowed due to her being in absolute motion,

then how does it still turn out that...

  1. Alice percieves Bob and his clock running slower than her own?

For Bob, there's no problem here. His present includes Alice's clock in absolute motion and thus running slower than his own, as it should. But what is Alice supposed to make of her perceived present where Bob's clock is running slow DESPITE being closer to absolute rest?

I've been racking my brain about this for weeks at this point, getting nowhere and starting to feel like I'm losing my mind a little. If you could offer some insight for a poor layman like myself, it would be greatly appreciated!

*NOTE: I'm aware that the Lorentzian (3D) interpretation is not as popular as Minkowski's (4D), but even if you don't happen to subscribe to it, please just humour me for the sake of the question.

Cheers!

$\endgroup$
2

2 Answers 2

4
$\begingroup$

The (neo-)Lorentzian interpretation is just standard special relativity except that the $t$ coordinate of one inertial frame is metaphysically identified as the true Newtonian time. That identification doesn't affect any prediction of the theory, so from a physical perspective it makes no difference.

Special relativity is sometimes taught as though for each person, there is only one "correct" reference frame, the one in which they're at rest. The truth is just the opposite: all reference frames are equivalent, so you can use any one to solve any problem. In particular, you can use the absolute reference frame of the Lorentzian interpretation to solve any problem, if you want.

In this problem, what you really mean by Alice's "perspective" is that there are a bunch of clocks moving at the same speed as Alice, that have been synchronized by Einstein's procedure or some equivalent method, and Alice takes the reading on a nearby clock from that family to be the "time" of any event.

Alice's clocks all run slow relative to the absolute time, but they are also desynchronized relative to the absolute time, with those in the forward direction showing an earlier time. After one second of absolute time, the clock that used to be near Bob has advanced by $1/γ$ second, but it is no longer the clock nearest Bob: the nearest clock is behind it and so shows a later time. The difference between the readings of the two clocks at the two times is $γ$ seconds.

$\endgroup$
1
$\begingroup$

I think your confusion arises because you mistakenly interpret time dilation as meaning that clocks slow down when they move relative to the absolute rest frame. That is only true in a very specific sense, and when you understand what I mean by that your confusion should clear.

Specifically, time dilation is a consequence of a loss of synchronisation of time across different frames. If you have a clock, A, in one frame that coasts between two clocks, B and C, in another, the elapsed time measured by the coasting clock A between the two encounters will be less than the difference between the reading of clock B at the first encounter and the reading of clock C at the second. In your thinking, you assume the difference arises because clock A is running slow. However, it really arises because clock C is out of sync with clock B (specifically it is running ahead of clock B), and really all the clocks are running at the same rate.

To see this, imagine you are walking along a corridor, and every ten seconds, according to your watch, you pass someone holding a clock. Let's suppose the clocks tick at exactly the same rate as your watch, but they are out of synch, so that every clock you pass is one second ahead of the clock before it. When you pass the first clock it will read 11s, while your watch will read 10s. When you reach the next clock it will read 22s, while you watch will read 20 s. The next clock your reach will read 33s while your watch will read 30s, and so on. To you and to the people you pass, your watch will be time dilated, but in reality it is ticking at exactly the same rate as the clocks, but lags progressively behind because of a lack of synchronisation.

To take this further, imagine that following you at ten second intervals are other people walking down the corridor, and their watches tick at exactly the same rate as yours, but they are each set a second ahead of the watch of the next person in line. To someone holding one of the clocks, they see you pass then they see each of the other people pass, and seemingly their clock is losing a second compared with each of the passing watches, so they think their clock is time dilated. So you have a situation in which any individual watch seems to be time dilated compared to the clocks it passes, while every individual clock seems dilated compared with the watches it passes even though all the watches and clocks are ticking at exactly the same rate.

Once you get your head around that, all of the mysteries of SR- whether the Lorenz or Einstein interpretation- should be resolved. Do not think of time dilation as meaning 'moving clocks run slow', but think of it as meaning 'moving clocks are not in synch with stationary clocks'.

As a final effort to make the point, imagine Bob is at rest in the absolute rest frame (in the Lorenz interpretation, obviously). If Alice and her friend coast past Bob at some speed, and Bob compares the time on his watch firstly to Alice's watch and then later to her friend's, he will conclude that his watch is running slow (ie dilated) even though he is absolutely at rest and Alice and her friend are moving. Again, his watch is not 'really' running slow- it is ticking at the same rate as the watches of Alice and her friend- what causes Bob's watch to appear to lose time is a synchronisation effect.

$\endgroup$
2
  • $\begingroup$ Thank you, those were quite helpful illustrations of the desynchronization effect you describe. But it's all still rather abstract, in that as far as I understand the retardation of clocks (and any objects) in motion is a consequence of the invariance of the speed of light. Yet if the supposed dilation is merely an apparent phenomenon, then doesn't that by extension mean that this desynchronization is void of any material causes? Are we to accept that it's just a quirk of the geometry of space and time, even in the Lorentzian framework of absolute space and time? $\endgroup$ Oct 15, 2022 at 22:52
  • $\begingroup$ That is certainly the conclusion I reached when I tried to figure out the significance of the Lorenzian view. The local time that appears in that view varies with distance, so you effectively have exactly the same tilted planes of simultaneity as you do in Einstein's version (which I suppose I should have guessed earlier, since both boil down to the same thing mathematically). $\endgroup$ Oct 16, 2022 at 6:15

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.