Explaining the Behavior of a Ball on a Tilted Platform

[Pelion]

Hi all,

Consider the following SR scenario:

In a frame S: A ball is resting on a platform that is parallel to the x axis. The platform is moving downward at a constant velocity parallel to the y axis. We assume a constant gravitational field whose lines of force are parallel to the y axis.

In a frame S': An observer moves with relativistic velocity, relative to S, parallel to the x axis.

The observer in S' will observe a tilted platform.

How does he explain the fact that he ball doesn't roll off the platform?

For S', it seems, there must arise a velocity-dependent 'extra-gravitational' force to keep the ball in place, in addition to the usual gravitational force. Is this true? If so, is this significant and thus far not noticed?

Cheers

 

[PeterDonis]

Consider the following SR scenario:

It isn't SR if this...

We assume a constant gravitational field whose lines of force are parallel to the y axis.

...is the case. You need to re-specify your scenario.

 

[Pelion]

It is an SR scenario: you can replace the constant gravity field with another force field...lets say, for example, a charged ball within a constant electric field.
GR effects do not come into play because we are only dealing with constant velocities (the platform, moving downward, and the frame S' moving left-right or right-left).
I use gravity because it may be case that an extra,velocity-dependent, gravitational component arises wrt to the observations of frame S', and this may be interesting and not yet noticed.

 

[Nugatory]

replace the constant gravity field with another force field...lets say, for example, a charged ball within a constant electric field.

How does the electromagnetic force transform from S to S'?

 

[PeterDonis]

you can replace the constant gravity field with another force field...lets say, for example, a charged ball within a constant electric field.

Yes, you can do this. But then, as Nugatory says, you need to transform the force correctly into frame S'.

GR effects do not come into play because we are only dealing with constant velocities

GR effects do not come into play with variable velocities. They come into play with spacetime curvature, i.e., tidal gravity. You could have set your scenario in an accelerating rocket in empty space, and SR would work perfectly well.

I use gravity because it may be case that an extra,velocity-dependent, gravitational component arises wrt to the observations of frame S'

Velocity-dependent forces arise in electromagnetism; the magnetic force on a charged particle is velocity-dependent.

Also, as already noted, there is no gravity in flat spacetime; more precisely, there is no "velocity-dependent gravitational component" of any force. (Gravity isn't a force anyway in relativity.) You can simulate some of the effects of gravity by being in an accelerating rocket; as I noted above, you could set your scenario in an accelerating rocket in empty space.