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]

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]

Richard Livingston alle ore 16:53:38 di giovedì 28/07/2022 ha scritto:
> On Thursday, July 28, 2022 at 5:07:50 AM UTC-5, Luigi Fortunati wrote:
>> 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]

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]

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]

Julio Di Egidio alle ore 08:42:01 di marted=EC 02/08/2022 ha scritto:
> 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]

Luigi Fortunati alle ore 12:00:40 di martedě 02/08/2022 ha scritto:
> [[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]

Luigi Fortunati alle ore 05:02:06 di mercoledě 03/08/2022 ha scritto:
> [[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]]

[Julio Di Egidio]

On Wednesday, 3 August 2022 at 02:00:45 UTC+2, Luigi Fortunati wrote:
> Julio Di Egidio alle ore 08:42:01 di marted=EC 02/08/2022 ha scritto:

<snip>

> > 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

[Luigi Fortunati]

Luigi Fortunati alle ore 09:44:22 di mercoledì 03/08/2022 ha scritto:
> [[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
>> 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.