Does the bridge collapse under the weight of the train?

[Luigi Fortunati]

The bridge and the train have the same length at rest.

The bridge collapses only if the entire weight of the train rests on
it.

In the reference of the train (traveling at relativistic speed) the
bridge (contract) is shorter and the weight of the train never rests
entirely on the bridge: the passengers are safe.

Instead, in the reference of the ground, the train is shorter and there
is a time interval in which the weight of the train rests entirely on
the bridge which, therefore, collapses: for the observer on the ground
the passengers of the train are doomed.

Who's right? Are train passengers saved or not?

[Moderator's note: This is essentially the same puzzle as the ladder
paradox, which even has its own Wikipedia entry. In fact, it is closer
to the "man falling into grate" version originally discussed by the
late, great Wolfgang Rindler. -P.H.]

[Bruce Scott]

On 2020-11-13, Luigi Fortunati <fortuna...@gmail.com> wrote:
> The bridge and the train have the same length at rest.
>
> The bridge collapses only if the entire weight of the train rests on
> it.

[...]

> [Moderator's note: This is essentially the same puzzle as the ladder
> paradox, which even has its own Wikipedia entry. In fact, it is closer
> to the "man falling into grate" version originally discussed by the
> late, great Wolfgang Rindler. -P.H.]

The version we got in class (way back when) was the train entering the
barn with the doors opening/closing just in time. The answer, of
course, is relativity of simultaneity.

--
ciao, Bruce

[Luigi Fortunati]

Bruce Scott sabato 12/12/2020 alle ore 19:13:37 ha scritto:
>> The bridge and the train have the same length at rest.
>>
>> The bridge collapses only if the entire weight of the train rests on
>> it.
> [...]
>
>> [Moderator's note: This is essentially the same puzzle as the ladder
>> paradox, which even has its own Wikipedia entry. In fact, it is closer
>> to the "man falling into grate" version originally discussed by the
>> late, great Wolfgang Rindler. -P.H.]
>
> The version we got in class (way back when) was the train entering the
> barn with the doors opening/closing just in time. The answer, of
> course, is relativity of simultaneity.

But does the bridge collapse or does it not collapse?

[Moderator's note: Answer per moderator's note here, as this has been
solved long ago. The bridge collapses. Forget the complication of the
bridge and the weight of the train causing it to break; just have a gap
where the bridge should be. Does the train fall into the gap? Yes.
See the "paradox" due to Rindler above. Check this out:
https://www.youtube.com/watch?v=Xrqj88zQZJg I think that some of the
confusion comes from first assuming that when the train is on the bridge
or the gap then it will fall, but in practice if the train were moving
that fast then it would just sail over the gap. But if you assume that
it would fall when positioned over the gap, you also have to assume that
gravity is strong enough to pull it down. -P.H.]

[Roland Franzius]

With respect to gravity things are different. Objects at speed of light
follow "straight lines" near worldlines of light on local light cones.

If light rays traverse the bridge without beeing bend down to touch the
opposite wall, any massive train will reach the other side, too, in the
limit v->c. Since bridges are constructed using light rays, no extra
engeneering art is necessary.

For slow trains, the engineer should form the bridge as a ballistic
parabola in order to save steel.

The question of the bridge collapse is a question of energy-momentum
transfer in its rest system.

The train at the speed of light is releivistically compressed to a point
and acts like a point mass on a ballistic hyperbole at its perigaeum. It
does not transfer energy-momentum to the bridge. It will leave the earth
surface tangentially and will disappear somwhere behind Uranus.

--

Roland Franzius

[Douglas Eagleson]

On Monday, December 14, 2020 at 4:08:16 PM UTC-5, Luigi Fortunati wrote:
> Bruce Scott sabato 12/12/2020 alle ore 19:13:37 ha scritto:

> >> The bridge and the train have the same length at rest.
> >>
> >> The bridge collapses only if the entire weight of the train rests on
> >> it.

> > [...]

> >
> >> [Moderator's note: This is essentially the same puzzle as the ladder
> >> paradox, which even has its own Wikipedia entry. In fact, it is closer
> >> to the "man falling into grate" version originally discussed by the
> >> late, great Wolfgang Rindler. -P.H.]
> >

> > The version we got in class (way back when) was the train entering the
> > barn with the doors opening/closing just in time. The answer, of
> > course, is relativity of simultaneity.

> But does the bridge collapse or does it not collapse?
>
> [Moderator's note: Answer per moderator's note here, as this has been
> solved long ago. The bridge collapses. Forget the complication of the
> bridge and the weight of the train causing it to break; just have a gap
> where the bridge should be. Does the train fall into the gap? Yes.
> See the "paradox" due to Rindler above. Check this out:
> https://www.youtube.com/watch?v=Xrqj88zQZJg I think that some of the
> confusion comes from first assuming that when the train is on the bridge
> or the gap then it will fall, but in practice if the train were moving
> that fast then it would just sail over the gap. But if you assume that
> it would fall when positioned over the gap, you also have to assume that
> gravity is strong enough to pull it down. -P.H.]

Simultaneity says that if the bridge collapses in one frame of relativity
that it collapses in all frames. Sort of like that a life destruction
cannot alter to a many universes model.

Say a train is given a barn door pair to travel thru. And the train has
explosives in it, triggered by closed doors firing them if the train
trigger is centered in it. The train velocity to trigger is findable
by trial and error? But in fact the train is never at c. Meaning
that the trigger never fires. Indicating that the barn viewer
can never know when the barn doors are closed.