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]]