Relativity of simultaneity

[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?

[Richard Livingston]

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?

They are both correct and your final paragraph shows that you don't
understand the issue with simultaneity in special relativity.

BTW, one aspect of your simulation that is incorrect is that you are
showing the two springs contracting uniformly (i.e. the same
simultaneously along their length). What would really happen is
a wave of compression that starts at the end that is released, and
propagates at a speed much slower than the speed of light towards
the anchored end. But the fact that the springs are released at
different "times" in different frames is absolutely correct and
pretty well proven by experiment.

RIch L.

[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?

They are both correct...

Impossible!

If the spring remains in the center of the wagon it does not move to the
left and if it moves to the left it does not remain in the center of the
wagon: one condition excludes the other.

Luigi Fortunati

[Julio Di Egidio]

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?

As others have noted, it's your graphics that is wrong, what you draw
is not what happens: but indeed the problem to begin with is that you
keep drawing "(incorrect) animations", not space-time diagrams...

Julio

[Julio Di Egidio]

Post by Julio Di Egidio

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?

As others have noted, it's your graphics that is wrong, what you draw
is not what happens: but indeed the problem to begin with is that you
keep drawing "(incorrect) animations", not space-time diagrams...

I think you also tend to overcomplicate your setups: e.g. here you don't
need a spring, you could simply bounce light rays off the front and rear
walls (or even massive particles, with ideal bouncing), which is all 1-D
by disregarding transversal distances, and it is enough to see how the
light rays come back together, i.e. at the center of the wagon, whichever
the frame!

On that line, here is a little space-time diagram I have put together
with Desmos: <https://www.desmos.com/calculator/mngma52fol>
There are limitations to what can be done in Desmos: I had to use
coords of the form (x,t) and in most places t becomes y, plus I am
doing the inverse transformation, hence (-v) in some places: in fact,
to the point, **with Lorentz transformations I am going from what
happens in the frame of the wagon (represented by the 4 events
C,L,R,D), to what appears in the external frame** (which, if relativity
means what it means, is a/the valid procedure here).

It is then obvious by the diagram that, to the ground observer, the
bouncing of the light rays is (in general) not simultaneous, yet the
light rays must indeed rejoin at the center of the wagon whichever
the relative frame speed.

HTH,

Julio

[Luigi Fortunati]

I think you also tend to overcomplicate your setups: e.g. here you don'=

t

need a spring, you could simply bounce light rays off the front and rea=

r

walls (or even massive particles, with ideal bouncing), which is all 1-=

D

by disregarding transversal distances, and it is enough to see how the
light rays come back together, i.e. at the center of the wagon, whichev=

er

the frame!
On that line, here is a little space-time diagram I have put together
with Desmos: <https://www.desmos.com/calculator/mngma52fol>
There are limitations to what can be done in Desmos: I had to use
coords of the form (x,t) and in most places t becomes y, plus I am
doing the inverse transformation, hence (-v) in some places: in fact,
to the point, **with Lorentz transformations I am going from what
happens in the frame of the wagon (represented by the 4 events
C,L,R,D), to what appears in the external frame** (which, if relativity
means what it means, is a/the valid procedure here).
It is then obvious by the diagram that, to the ground observer, the
bouncing of the light rays is (in general) not simultaneous, yet the
light rays must indeed rejoin at the center of the wagon whichever
the relative frame speed.

With the light everything is normal, linear and correct, so I have no
questions to ask.

But the theory must also be valid with springs and not only with light
rays.

I updated my animation and added the spring drop all the way to the
floor:
<https://www.geogebra.org/m/mejqfmrf>

In the reference of the train, the fall is without inclinations and
without lateral displacements, neither to the right nor to the left:
the spring always remains in the center of the wagon.

In the ground reference, the spring tilts and does not stay in the
center of the wagon.

One condition excludes the other and, therefore, one of the two must be
wrong: which of the two?

[[Mod. note -- As others have noted, both of these "conditions" are
correct; there is no contradiction between them.

To understand how they can both be correct, it's useful to ask how
one could distinguish one condition from the other *observationally*.

That is, how could you *measure* whether whether the spring is or isn't
tilted? Presumably you'd need to measure the heights of the spring's
two ends and compare them. But the spring is falling, so you need
to measure the heights of the two ends at the same time. And that's
where the problem appears -- what does the phrase "at the same time"
mean in special relativity? Your apparent paradox is due to the fact
that the phrase "at the same time" does *not* have the same meaning for
different observers.

Similarly, how could you *measure* whether one end of the spring
hits the floor before the other end of the spring hits the floor?
You could, for example, have an inertial observer measure the time
when each end of the spring hits the floor, then compare those times.
But this leaves open the question of *which* inertial observer should
make these measurements? Again, your apparent paradox reflects the
fact that different inertial observers will in general disagree about
the relative times of spatially-separated events.

These issues aren't straightforward, and benefit a lot from more
carefully-thought-out and lengthly presentations than are possible
in a newssgroup discussion. I highly recommend studying a good book
or two on special relativity. My two personal favorites are:

@book {
author = "Edwin F. Taylor and John Archibald Wheeler",
title = "Spacetime Physics",
edition = "2nd",
publisher = "W. H. Freeman",
year = 1992,
isbn = "0-7167-2326-3 (hardcover) 0-7167-2327-1 (paperback)",
note = "free download at https://www.eftaylor.com/spacetimephysics/"
}

@book {
author = "N. David Mermin",
title = "Space and Time in Special Relativity",
publisher = "Waveland Press",
X-publisher-original-edition = "McGraw-Hill (1968)",
address = "Prospect Heights, Illinois, USA",
year = "1968, 1989",
isbn = "0-88133-420-0 (paper)",
}
-- jt]]

[Luigi Fortunati]

Post by Luigi Fortunati
[[Mod. note --
...
To understand how they can both be correct, it's useful to ask how
one could distinguish one condition from the other *observationally*.
That is, how could you *measure* whether whether the spring is or isn't
tilted?

It is the theory itself that tells me if the spring tilts or not.

If the theory tells me that the two extremities are released
simultaneously, I obviously deduce that (falling) it does not tilt.

If he tells me that one end is released before the other, I equally
obviously deduce that (falling) it tilts.

[[Mod. note -- What does the word "simultaneously" mean? In special
relativity simultaneity is observer-dependent, i.e., different observers
will in general not agree on whether two (spatially-separated) events
are simultaneous. There's no universal notion of "simultaneous".

In the same way, whether or not the spring tilts is observer-dependent;
there's no universal notion of tilt.

Your two "conditions" are each internally consistent and correct.
There's no contradiction between them; they're simply different ways
of describing the same events.
-- jt]]

[Luigi Fortunati]

Post by Luigi Fortunati
[[Mod. note -- What does the word "simultaneously" mean? In special
relativity simultaneity is observer-dependent, i.e., different observers
will in general not agree on whether two (spatially-separated) events
are simultaneous. There's no universal notion of "simultaneous".
In the same way, whether or not the spring tilts is observer-dependent;
there's no universal notion of tilt.

The tilt with respect to the floor of the wagon does not vary as the
observer changes!

[[Mod. note -- The whole point is that there's no generic
observer-independent "tilt with respect to the floor of the wagon".
Rather, different observers measure different tilts with respect to the
floor of the wagon.

If you disagree, please describe a way to (correctly) measure the tilt
which doesn't give different answers for different observers.
[For example, suppose we mount a (level) protractor
on the wagon and try to read the spring's tilt on the
protractor scale. We immediately run into the problem
that the spring is falling, so we need to read the two
sides of the protractor at the same time.... but different
observers disagree about "the same time".]

The underlying logic of your apparent paradox (and the resolution that
"tilt" is observer-dependent) is very similar to that of the well-known
"stick and hole" apparent paradox, e.g., see sections 5 and 6 of
https://en.wikipedia.org/wiki/Ladder_paradox
or
http://www.relativitysimulation.com/Tutorials/TutorialMeterstickAndHole.html
https://physics.stackexchange.com/questions/83520/a-relativistic-meter-stick-and-a-thin-disk
https://www.physicsforums.com/threads/meter-stick-slides-over-a-meter-wide-hole-at-a-high-speed.945765/
-- jt]]

[Luigi Fortunati]

[[Mod. note -- For example, suppose we mount a (level) protractor
on the wagon...

Done.

In my animation
<https://www.geogebra.org/m/zyarm93v>
I added the protractor and also a stop and go to be able to stop the animation at any time.

[Mod. note -- What does the word "simultaneously" mean? In special

Post by Luigi Fortunati
relativity simultaneity is observer-dependent, i.e., different observers
will in general not agree on whether two (spatially-separated) events
are simultaneous. There's no universal notion of "simultaneous".

This is exactly what happens in my animation.

The arrival of the two photons (and the release of points A and B) is simultaneous in the wagon reference but not in the ground reference.

[Mod. note -- The whole point is that there's no generic
observer-independent "tilt with respect to the floor of the wagon".
Rather, different observers measure different tilts with respect to the
floor of the wagon.
If you disagree, please describe a way to (correctly) measure the tilt

I agree, so much so that in my animation (which respects the criteria of
Relativity) the inclination in the reference of the wagon is different
from that in the reference of the terrain.

But what if there is an explosive bottle on the plane that explodes if
it slips (and bangs) but doesn't explode if it doesn't slip (and doesn't
slam)?

It happens that it does not explode for the observer for the observer on
the train (for which the plane does not tilt and the bottle does not
slip) but it explodes for the observer on the ground (for which the
plane tilts and the bottle slips).

And this is not acceptable.

[Julio Di Egidio]

<snip>

Post by Luigi Fortunati

Post by Julio Di Egidio
It is then obvious by the diagram that, to the ground observer, the
bouncing of the light rays is (in general) not simultaneous, yet the
light rays must indeed rejoin at the center of the wagon whichever
the relative frame speed.

With the light everything is normal, linear and correct, so I have no
questions to ask.
But the theory must also be valid with springs and not only with light
rays.

Indeed it is, because the basic experiment I have reduced it to is
sufficient to see that, *whatever happens* (there is something magic
about light, e.g. it sets the boundary for any exchange of classical
information, but exactly the same outcome you'd have with massive
particles, or even springs and combinations thereof...), as long as
what happens on the left side is exactly symmetric to what happens
on the right side, you are guaranteed a rendez-vous at the center *in
any frame*. Which is about what is essential and what is unneeded
complication in an ideal/thought experiment.

But overall, you even seem to miss fundamental notions like *event*
and what it means, i.e. what are we actually modelling, so I'd second
the moderator's suggestion that you at least go through some good
introductory books, and try and follow *that* progression: including
how to rather draw space-time diagrams (only once you got those
you can confidently build simulations...).

Julio

[Nicolaas Vroom]

Post by Luigi Fortunati
[[Mod. note -- What does the word "simultaneously" mean?

There are two definitions.
1) You can call this the global definition.
This definition depends on the question:
At any instant, in the evolution of the universe, are there
simultaneous events happening?
IMO the answer is Yes.
For example, at any instant, all the planets around the Sun have a
specific position. Each position can be considered as an event.
2) You can call this the local definition.
This definition is observer depended and is based on what an
observer sees.
For example: you can have three events A, B and C and three observers
1, 2 and 3.
Observer 1 can see A and B simultaneous; Observer 2 can see B and C
simultaneous and Observer 3 can see A and C simultaneous, but that
does not say anything about the order of the events A, B and C.
What makes all of this more complicated is that the observers also
can move relative of each other.
This problem sounds like the tower of Babel problem, where everyone
speaks a different language and nothing can be achieved.
(https://www.theatlantic.com/magazine/archive/2022/05/social-media-democracy-trust-babel/629369/
IMO the only way to solve this problem is, if all the three observers
agree to one reference frame and that all the clocks used are linked
to that frame.

Post by Luigi Fortunati
In special relativity simultaneity is observer-dependent, i.e.,
different observers
will in general not agree on whether two (spatially-separated) events
are simultaneous. There's no universal notion of "simultaneous".

In some way we all must agree on something.
There only exists one universe at each instant.

Post by Luigi Fortunati
In the same way, whether or not the spring tilts is observer
-dependent; there's no universal notion of tilt.

The physical reality (evolution) is not observer dependant.
What each of us observes is something different.

Post by Luigi Fortunati
Your two "conditions" are each internally consistent and correct.
There's no contradiction between them; they're simply different
ways of describing the same events.

In physics people should try to predict the future.
Whatever both observe, they should predict the same future.

https://www.nicvroom.be/

[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. The END RESULT should be good enough to show
clearly.."which of the two is correct", I think. :)

Regards, Laszlo Lemhenyi

[Luigi Fortunati]

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]]

[xray4abc]

Post by Luigi Fortunati

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"?

Of the wagon of course!
Then, if an explosion takes place, it is clear that NO MATTER what exactly
the theoretical predictions regarding simultaneity in the other frames of reference
are..the photons must have been arrived simultaneously, and the observers in the other frames
may scratch their heads as long as they want, to figure out...why the explosion occurred !
Regards, LL

Post by Luigi Fortunati

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.
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".
(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?
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.
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*
(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]]

[xray4abc]

Post by xray4abc

Post by Luigi Fortunati

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"?

Of the wagon of course!
Then, if an explosion takes place, it is clear that NO MATTER what exactly
the theoretical predictions regarding simultaneity in the other frames of reference
are..the photons must have been arrived simultaneously, and the observers in the other frames
may scratch their heads as long as they want, to figure out...why the explosion occurred !
Regards, LL

Post by Luigi Fortunati

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.
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".
(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?
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.
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*
(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]]

I would like to remind that ....The theory of special relativity..does not make the
connections between effective measurements made in 2 relatively moving
inertial reference frames, as we would like the case to be.
Max Born, in his book "Einstein's theory of relativity" says about relativistic effects,
on page 254 (Dover publicatons , New York)..."Thus the contraction is only a consequence of our way of
regarding things and is not a change of physical reality"
I say, same applies for any other measurements !
In my interpretation, this means:
We can not have/measure/possess the data from a moving reference frame! We can have only the data WE ATTRIBUTE
to that frame. The example with the explosion, I have given, shows though, that some things......
like simultaneity of a given event.....the signals reaching the detonator in this case, must apply in
in any reference frame.
Regards, LL

[Luigi Fortunati]

Post by Luigi Fortunati
...
[[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.

Right observation.

However, the speed of propagation of the rarefaction wave is not that
of light (absolute speed) but it is speed v<<c and, therefore, is not
influenced by the reference.

It is like the speed of the train which is the same in both references,
because what changes are the distances and times, not the speeds.

So, it doesn't affect the final result, as you can see from the updated
animation

Post by Luigi Fortunati

Post by Luigi Fortunati
https://www.geogebra.org/m/veezhbrr

where I added the blue wave of rarefaction that comes to the center of
the spring at the same instant in the train reference but not in the
wagon one.

[[Mod. note -- It's not true to say that the speed of the rarefaction
wave "is not influenced by the reference". In the reference frame of the
wagon the rarefaction wave propagates at a speed v. But to figure out
what it does in the ground reference frame, you have to use the
special-relativity velocity addition formula,
https://en.wikipedia.org/wiki/Velocity-addition_formula
-- jt]]

[Luigi Fortunati]

Post by Luigi Fortunati
However, the speed of propagation of the rarefaction wave is not that
of light (absolute speed) but it is speed v<<c and, therefore, is not
influenced by the reference.
It is like the speed of the train which is the same in both references,
because what changes are the distances and times, not the speeds.
So, it doesn't affect the final result, as you can see from the updated
animation

Post by Luigi Fortunati
https://www.geogebra.org/m/veezhbrr

where I added the blue wave of rarefaction that comes to the center of
the spring at the same instant in the train reference but not in the
wagon one.
[[Mod. note -- It's not true to say that the speed of the rarefaction
wave "is not influenced by the reference". In the reference frame of the
wagon the rarefaction wave propagates at a speed v. But to figure out
what it does in the ground reference frame, you have to use the
special-relativity velocity addition formula,
https://en.wikipedia.org/wiki/Velocity-addition_formula
-- jt]]

Right, you're right, I was wrong

Luigi

[wugi]

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?

They are both correct...

Impossible!
If the spring remains in the center of the wagon it does not move to the
left and if it moves to the left it does not remain in the center of the
wagon: one condition excludes the other.

If the wagon moves, the spring center moves with it.
In the standpoint of the rest frame, the wagon's "back" end will receive
the light signal first, and release the spring earlier; but the latter
has to do a longer trip to reach its rest point, since it is heading for
a "receding" spring center. And vice versa in the "front" end, where the
signal arrives later, but the spring end does a shorter trip as the
spring center is heading towards it.

Your example is not much different from the example of symmetrical light
clocks, exhibiting ROS together with time dilation and length
[[Mod. note -- I think by "ROS" the author means
"relativity of simultaneity" -- jt]]
contraction in light clock systems moving WRT each other.
See eg my video

Or also, from the rivet paradox case with the apparent incompatibility
of the rivet being stopped "head first" in its own system, and "tail
first" in the (stationary) hole system.
See my videos

and

[Luigi Fortunati]

Post by wugi

Post by Luigi Fortunati
Impossible!

If the wagon moves, the spring center moves with it.
Your example is not much different from the example of symmetrical light
clocks, exhibiting ROS together with time dilation and length
[[Mod. note -- I think by "ROS" the author means
"relativity of simultaneity" -- jt]]
contraction in light clock systems moving WRT each other.
See eg my video
http://youtu.be/AYpD9JRWjdU

I had already admitted that I was wrong on November 19, 2022.

[Moderator's note: Much quoted text trimmed. -P.H.]

[Rock Brentwood]

Post by Luigi Fortunati
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.

No it doesn't.

All the parts of the spring between the ends stay put
and don't change at all,
until the "I was released" signal reaches it,
the signal being conveyed by the action of the spring, itself.
It doesn't get to that part of the spring any faster
than the speed of sound in the spring, whatever that may be.

Until that sound signal reaches that part of the spring,
it remains in the whatever state of compression it was in
as if nothing had happened to the ends.

Your intuition is wrong.
It is grounded in small objects, where you don't see the propagation.
You've never worked with huge objects, by which I mean objects
hundreds or thousands of meters in length.
Even large trees exhibit this delayed reaction and response -
as those of us who are out and about all the time know full well.

No spring acts as a cohesive unit at all; there is no such thing.
That's an illusion borne of being of size too small for you to see its fluidity.
You have to treat it as a fluid, for all intents and purposes.