# How would the photon clock experiment work according to Lorentzian relativity?

EDIT: How is Lorentz' interpretation of STR considered "unpublished"?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!

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.

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.