| 1 Luigi Fortunati | Relativity of simultaneity | Thursday 28 July 2022 |
| 2 Luigi Fortunati | Re :Relativity of simultaneity | Wednesday 3 August 2022 |
| 3 Luigi Fortunati | Re :Relativity of simultaneity | Wednesday 3 August 2022 |
| 4 Luigi Fortunati | Re :Relativity of simultaneity | Wednesday 3 August 2022 |
Relativity of simultaneity
129 weergaven
https://groups.google.com/g/sci.physics.research/c/cojXWFv7iXA
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?
| > |
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. |
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]]
| > |
[[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]]
| > |
[[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]]
Back to USENET overview USENET
Back to my home page Contents of This Document