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?
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...
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?
On Thursday, 28 July 2022 at 12:07:50 UTC+2, 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?
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 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 theer
light rays come back together, i.e. at the center of the wagon, whichev=
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.
[[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?
[[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.
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.
[[Mod. note -- For example, suppose we mount a (level) protractor
on the wagon...
[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".
[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
[[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.
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?
On Thursday, July 28, 2022 at 6:07:50 AM UTC-4, 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?
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.
Regards, Laszlo Lemhenyi
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 isis ill-posed. The correct statement is that *both* pictures are correct;
wrong?
xray4abc mercoled=EC 16/11/2022 alle ore 19:44:27 ha scritto:Of the wagon of course!
On Thursday, July 28, 2022 at 6:07:50 AM UTC-4, 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?
Well, let us imagine... that those 2 photons arriving to the centre ofOnly if they arrive at the same time "in which reference"?
the wagon , activate the detonator of a bomb ..IFF and ONLY IFF they
arrive simultaneously.
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
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 isis ill-posed. The correct statement is that *both* pictures are correct;
wrong?
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]]
On Thursday, November 17, 2022 at 1:51:04 AM UTC-5, Luigi Fortunati wrote:
xray4abc mercoled=EC 16/11/2022 alle ore 19:44:27 ha scritto:
On Thursday, July 28, 2022 at 6:07:50 AM UTC-4, 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?
Of the wagon of course!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"?
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
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.
I would like to remind that ....The theory of special relativity..does not make theNow 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
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 mercoled=EC 16/11/2022 alle ore 19:44:27 ha scritto:
...
[[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.
where I added the blue wave of rarefaction that comes to the center ofhttps://www.geogebra.org/m/veezhbrr
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
where I added the blue wave of rarefaction that comes to the center ofhttps://www.geogebra.org/m/veezhbrr
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]]
Richard Livingston alle ore 16:53:38 di gioved=C3=AC 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.
Op 29/07/2022 om 12:57 schreef 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 https://youtu.be/AYpD9JRWjdU?list=PL5xDSSE1qfb6zyVKJbe8POgj-8ijmh5o0
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.
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