Einstein's Elevator & Tidal Gravity

[Wes Tausend]

[Moderator's note: This is a portion of a post originally made in another thread, which has been moved due to being off topic there.]

Einstein's Equivalence principle is based on the realization that, "An observer in a windowless room cannot distinguish between being on the surface of the Earth, and being in a spaceship in deep space accelerating at 1g(2)". I'm not sure why the tidal effects quoted below in NOTES would not register in his elevator, as I thought I had worked that out with SR here before and the analogous fields actually appear indistinguishable, just as he said.

I'm fairly confident that a link between electrodynamics and GR will eventually be published, but since I'm not aware of any present peer reviewed submission, it's not open for me to discuss here. Keep in mind that Einstein's original Unified Field idea did not include the unknown strong and weak 'forces' (interactions), and today, 'unifying all' might better be called a Theory of Everything (T.O.E.).

Wes

NOTES
(1) From Wikipedia, "The special principle of relativity states that physical laws should be the same in every inertial frame of reference, but that they may vary across non-inertial ones. This principle is used in both Newtonian mechanics and the theory of special relativity. Its influence in the latter is so strong that Max Planck named the theory after the principle."

(2) From wikipedia, "So the original equivalence principle, as described by Einstein, concluded that free-fall and inertial motion were physically equivalent. This form of the equivalence principle can be stated as follows. An observer in a windowless room cannot distinguish between being on the surface of the Earth, and being in a spaceship in deep space accelerating at 1g. This is not strictly true, because massive bodies give rise to tidal effects (caused by variations in the strength and direction of the gravitational field) which are absent from an accelerating spaceship in deep space. The room, therefore, should be small enough that tidal effects can be neglected."

 

[Ibix]

I'm not sure why the tidal effects quoted below in NOTES would not register in his elevator, as I thought I had worked that out with SR here before and the analogous fields actually appear indistinguishable, just as he said.

Two chains hung side by side in a rocket under power in the absence of gravity will hang parallel. Two chains in a rocket resting on the surface of the Earth will point towards the centre of the Earth, so will be slightly closer together at the bottom than the top. That is a tidal effect. It's always present on the Earth if your measurements are sufficiently sensitive, and never present in the rocket.

 

[Wes Tausend]

Two chains hung side by side in a rocket under power in the absence of gravity will hang parallel. Two chains in a rocket resting on the surface of the Earth will point towards the centre of the Earth, so will be slightly closer together at the bottom than the top. That is a tidal effect. It's always present on the Earth if your measurements are sufficiently sensitive, and never present in the rocket.

"never present in the rocket" ??

Then I either have an insight, or am dead wrong. PF, Ibix, please pardon me while I seek an understanding. Perhaps I should start a separate thread, but I thought we might agree a full understanding of Einstein's Equivalence is important to this thread.

Ibix, I thought about your popular perspective and accepted it in the past. But then with suitable thought experiment, I realized that even if one found a portion of space completely devoid of external gravitational influence, the chains themselves would still be made of mass, thus we have hopelessly taken some gravity with us. I assumed Einstein would have considered this and thought the same.

So it seems a microscopic internal form of gravitational influence would invariably continue inside the rocket or elevator. The top of the chains can be assumed held apart by the supposedly rigid top attachment, but the bottom links, proportionally more free, would seem to tend to 'pull' ever so slightly together. Since the force holding the 'attractive' chains apart at the top, as opposed to the uniform acceleration trying to 'straighten' them, seems to me to invert proportionally all the way 'down', I thought all the chain links would then likely individually form a perfect vee.

Rather than chains, I did my original thought experiment with a simple pair of identical apples that I supposed my occupant (Newton's Ghost) was to simultaneously hold out to his sides and 'drop'. His apple 'masses' would then began to slightly move together in an observed vee immediately upon release and uniformly accelerate their apparent movement towards one another. I believe the apple/chain principle must be the same, except for the 'attachment force' keeping them from meeting. The restricted chains seem reminiscent of the Cavendish Experiment where Cavendish calculated this tiny restrictive force by measuring the amount of twist in his springy, fine suspension wire.

In addition, I even worked out in my head, that at a steady 32 feet/sec/sec, the vee of either apples or chain would seem to assume a complete vertice at approximately 4000 miles below the rocket or elevator. For a hoped proof, I had to use geometry, vectors and a continuous group of resultant vectors (the vee) in a mental diagram, since I am probably untrained in the complicated math more commonly employed. It seems to me the vertice entirely depends on the uniform constant acceleration of both actions which I believe is closely related to the reason for a gravitational constant per Cavendish.

If I am not first shot out of the saddle, while a blackboard in the same room would be easier, I might be able to demonstrate this here on PF by description alone. A more permissive alternative on PF would be by private conversation if you wish. The major appeal is that this perspective (if PF agrees it is an insight) entirely agrees with Einstein's statement that the two are indistinguishable. I think we might all at least agree Einstein was not often wrong, nor was he often careless.

Offhand, I had a different method of determining general tidal effects concerning elongation and Lorentz-like compaction, using SR mandates in a thought experiment upon the differences in an accelerating, and decelerating rocket.

Wes

 

[Ibix]

One could easily calculate the attractive force of the two chains and subtract out the effect and see if they would be parallel or not. Or repeat the experiment with lighter and lighter weight chains and see what the angle tends to as the mass tends to zero. Or use a curtain of chains so that the net force on the central ones is arbitrarily close to zero.

However you do it, you can calculate and subtract out the self-interaction of the chains. If no angle remains, you are in a rocket. Otherwise you are on a planet.

 

[PeterDonis]

Then I either have an insight, or am dead wrong.

The correct answer is (c): you are misunderstanding what this discussion is about. See below.

if one found a portion of space completely devoid of external gravitational influence, the chains themselves would still be made of mass, thus we have hopelessly taken some gravity with us

If you're going to go that route, the rocket itself has mass. But that mass is many, many orders of magnitude smaller than the mass of the Earth. Run the numbers and see.

His apple 'masses' would then began to slightly move together in an observed vee immediately upon release and uniformly accelerate their apparent movement towards one another.

"Slightly", yes, in an idealized experiment of infinite accuracy. Now run the numbers and see how much actual movement you would in principle see with actual apples, as compared to the tidal effect of the Earth. And then see how that compares with the actual accuracy that actual experiments can achieve.

I even worked out in my head, that at a steady 32 feet/sec/sec, the vee of either apples or chain would seem to assume a complete vertice at approximately 4000 miles below the rocket or elevator.

Yes, that's because the Earth's gravitational acceleration at the surface is 32 feet/sec/sec. But that does not mean the apples cause each other that kind of acceleration. Run the numbers and see. And in a spaceship accelerating in empty space, the Earth is not there, so the tidal gravity due to the Earth is not there. That means your calculation of apple trajectories is irrelevant to the case of a spaceship accelerating in deep space. For that case, the only sources of gravity are the apples themselves and the spaceship. None of those will produce the tidal gravity you calculated.

If I am not first shot out of the saddle, while a blackboard in the same room would be easier, I might be able to demonstrate this here on PF by description alone. A more permissive alternative on PF would be by private conversation if you wish.

None of these are going to happen.

(if PF agrees it is an insight)

PF doesn't. It was when Newton discovered it, but that was about 350 years ago.

entirely agrees with Einstein's statement that the two are indistinguishable

Einstein's never said tidal gravity was indistinguishable from no tidal gravity. Nor did he ever say the tidal gravity due to the Earth was indistinguishable from the (in principle present, but in practice unmeasurably tiny) tidal gravity due to a pair of apples and a spaceship in deep space.

 

[PeterDonis]

Now that the misconception in the OP has been addressed, this thread is closed.