Frames of reference in Special Relativity

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Suppose we have two observers ,A and B (who are in inertial motion wrt one another)   that are observing a series of events at a third  location(O).

I understand that  both observers will agree  on the timing and nature of  events playing out at O.

Does that mean that both A and B  apply Lorentz transformations in spacetime  in order to  change their own frame of reference to that of the events  they are observing at O ?

Do they ,as it were  "get into and walk in the shoes" of the third observer at O?

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They can do it either way: they can transform their measurements to O (which could be one way of A and B comparing their own local measurements). O they can transfer O to A or B, respectively.

7 minutes ago, geordief said:

I understand that  both observers will agree  on the timing and nature of  events playing out at O.

Hang on. They won't agree on the time between events in O (as they measure it in A and B). They might not even agree on the relative ordering of events in O.

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Posted (edited)
8 minutes ago, Strange said:

Hang on. They won't agree on the time between events in O (as they measure it in A and B). They might not even agree on the relative ordering of events in O.

They will agree on the timing as seen from an observer at O though won't they ?

Edited by geordief

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3 minutes ago, geordief said:

They will agree on the timing as seen from an observer at O though won't they ?

Yes. Because the Lorentz transform is reversible (I'm sure there is a proper mathematical term; linear?) so the events get transformed from O to A and to B, then if you transform them back to O you end up where you started.

So, they might not agree about the ordering of events in their frames, but they will agree about what is seen by an observer in O.

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8 minutes ago, geordief said:

Won't they agree on the timing as seen from an observer at O ?

None of their clocks will agree, if there is relative motion. (you don’t specify if O is in a third frame)

edit: As Strange said, they will agree on anything reconstructed with the Lorentz transform, but that’s not what “agreeing on the timing” means to me

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Posted (edited)
10 minutes ago, swansont said:

None of their clocks will agree, if there is relative motion. (you don’t specify if O is in a third frame)

Yes O is a third frame. What I am asking is whether A and B  can calculate correctly  what O's  spatio-temporal measurement of processes occuring in its vicinity would be.

Suppose A is based on Earth and B is based on  Jupiter can both know exactly what an observer  on Mars is measuring by taking account of the correct Lorentz Transformations? (and in similar locations where relative velocities were relativistic)

11 minutes ago, swansont said:

edit: As Strange said, they will agree on anything reconstructed with the Lorentz transform, but that’s not what “agreeing on the timing” means to me

Yes but that is what I was getting at. (my wording was no doubt loose)

Edited by geordief

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Posted (edited)
44 minutes ago, Strange said:

Yes. Because the Lorentz transform is reversible (I'm sure there is a proper mathematical term; linear?) so the events get transformed from O to A and to B, then if you transform them back to O you end up where you started.

So, they might not agree about the ordering of events in their frames, but they will agree about what is seen by an observer in O.

Symmetric is the term your looking or in this case also commutative.

(Under constant velocity)

This is shown as the inner product of the Minkowskii group is symmetric via

$\mu \cdot \nu=\nu \cdot \mu$

The equations are linearized however that doesn't necessarily describe reversible functions.

Edited by Mordred

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They will not agree on the timing of events at O, from their respective frames, A and B.
And they will need to know their relative velocities ( compared to the O frame ) to apply the transforms, and get the temporal ordering in the O frame.

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29 minutes ago, MigL said:

They will not agree on the timing of events at O, from their respective frames, A and B.
And they will need to know their relative velocities ( compared to the O frame ) to apply the transforms, and get the temporal ordering in the O frame.

What I was asking (and I feel I have got the answer =yes) was whether they would be able  by taking everything ** into account  to effectively place themselves behind the eyes of the observer O (at some stage in the past)  and so in theory  see the physical processes in her vicinity just as if they themselves were then  present.

Suppose the observer O was looking at an episode of Only Fools and Horses then I expect A and B  by applying the Lorentz transformation to the stream of digits arriving from O to be able to view the episode at their leisure.

At first it would be gibberish  but after the transformation it would  be viewing material .

** ie esp their own motion relative to O whether inertial or accelerated

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