*Post by xray4abc**Post by Luigi Fortunati*In my animation

https://www.geogebra.org/m/veezhbrr

there is a train moving at relativistic speed and there are two photons

leaving at the same time from the center of the wagon towards points A

and B where the ends of the dilated spring are fixed.

When the photons reach A and B, they release the mechanism that holds

the ends in place, so that the spring (no longer fixed) can contract.

However, in the reference of the train, the two photons arrive at their

destination at the same time and the (released) spring compresses

symmetrically, remaining in the center of the wagon.

But, in the ground reference, one photon arrives before the other and

the spring contracts asymmetrically, so that it does not stay in the

center of the wagon but moves to the side.

Since the spring cannot contract in two different ways, one of the two

contractions must be wrong: which of the two is correct and which is

wrong?

Well, let us imagine... that those 2 photons arriving to the centre of

the wagon , activate the detonator of a bomb ..IFF and ONLY IFF they

arrive simultaneously.

Only if they arrive at the same time "in which reference"?

*Post by xray4abc*Regards, Laszlo Lemhenyi

Luigi.

[[Mod. note -- I have several comments.

First, note that Luigi's animation shows the entire spring responding

*instantaneously* to the release of the endpoints. That's not possible

(in special relativity). Rather, when each endpoint is released, a

wave of rarefaction will propagate along the spring away from the

endpoint. That propagation can't happen any faster than the speed of

sound in the material making up the spring, and for a realistic spring

would be considerably slower. I won't try to analyze this in detail

here.

For the rest of what I'm going to write, let's set aside the

speed-of-sound issue, and consider instead some other interesting

physics questions posed by Luigi's animation.

First, it's useful to introduce a bit of terminology:

Let's call the release of the left end of the spring "event L".

And, let's call the release of the right end of the spring "event R".

Luigi's animation poses the following two questions:

(a) If event's L and R each send a photon (i.e., a signal which travels

at the speed of light) back to the wagon's central point, which

photon (left-end or right-end) arrives first?

(b) Which end of the spring is released first, i.e., which of events

L and R happens first?

Let's first consider question (a):

In relativity, the relative temporal ordering of different events

*along a single observer's worldline* is universal: all observers

agree on this ordering. (Since these events are all located along a

single observer's worldline, they are necessarily *timelike*-separated.)

That means that question (a) has a universal answer, i.e., the answer

to question (a) does *not* change from one reference frame to another.

This in turn means that we can compute the answer by using whatever

reference frame (RF) is most convenient. In this case, the wagon RF

is very convenient: the problem is fully symmetric, and it's clear

that in this frame both the left-end and right-end photons arrive

back at the wagon center at the *same* time. By the argument given

in the previous paragraph, that statement ("the left-end and right-end

photons arrive back at the wagon center at the *same* time") is

necessarily true in *any* RF.

Exercise for the reader: explicitly work out the photon propagation in

the ground RF and show that the two photons also arrive simultaneously

in this RF.

Now let's consider question (b):

In relativity, the relative temporal ordering of different

*spacelike-separated* events isn't universal: different observers (RFs)

will in general disagree on this ordering.

Events L and R are spacelike-separated, so they have *no* universal

temporal ordering. So, question (b) as I've written it is inherently

observer-dependent. As we've seen, in the wagon RF events L and R

are simultaneous. But in the ground RF, events L and R are *not*

simultaneous. That is:

(1) In the wagon RF, the time coordinate of event L is equal to the

time coordinate of event R. In other words, the two ends of the

spring are released at the same time, so the spring contracts

symmetrically.

(2) In the ground inertial reference frame, the time coordinate of

event L is *not* equal to the time coordinate of event R. In

other words, the two ends of the spring are released at different

times, so the spring contracts *asymmetrically).

Both statements (1) and (2) are correct.

So, the statement

*Post by xray4abc*Since the spring cannot contract in two different ways, one of the two

contractions must be wrong: which of the two is correct and which is

wrong?

is ill-posed. The correct statement is that *both* pictures are correct;

the notion of "symmetrical contraction" is observer-dependent, i.e.,

the answer to the question "is the spring contracting symmetrically"

varies from one RF to another.

-- jt]]