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[ChatGPT] The elevator (was: Re: Question regarding an elevator

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On Fri, 30 Jun 2023 19:08:03 GMT, vallor wrote:

> [ This is a repost of the following article:                            
>   ]
> [ From: vallor <vallor@cultnix.org>                                     
>   ]
> [ Subject: Question regarding an elevator                               
>   ]
> [ Newsgroups: sci.physics                                               
>   ]
> [ Message-ID: <u7n7da$2jpl7$1@dont-email.me>                            
>   ]
> 
> Thought experiment:
> 
> Einstein's elevator.
> 
> In an elevator sitting on the ground on Earth, gravity would be measured
> as higher near the floor than the ceiling, given sufficiently sensitive
> equipment. (1/d^2)
> 
> Accelerating the elevator at 1G, there won't be the difference in
> "gravity" from the ceiling to the floor.
> 
> What does that mean with regards to "locality"?  Is that just a measure
> of how sensitive the instruments you're carrying are?  Or...?
> 
> (I am but an egg.)

User
Thought experiment:

Einstein's elevator.  (Special relativity)

In an elevator sitting on the ground on Earth, gravity would be measured
as higher near the floor than the ceiling, given sufficiently sensitive
equipment. (1/d^2)

Accelerating the elevator at 1G, there won't be the difference in 
"gravity" from
the ceiling to the floor.

Wondering if that matters to Special Relativity, or if it
was just a broader gedanken experiment?  Or...?

Thank you for any insights you have on this. :)
ChatGPT
Einstein's "Elevator" thought experiment is a staple in our understanding 
of General Relativity (GR), not Special Relativity (SR). SR deals with 
inertial frames of reference, which means frames that are either at rest 
or moving at constant velocity. It does not account for the effects of 
gravity or acceleration, and therefore doesn't directly concern itself 
with the hypothetical elevator scenario.

When Einstein came up with his elevator thought experiment, he was trying 
to demonstrate a fundamental idea of General Relativity, which is the 
principle of equivalence. This principle essentially states that the 
effects of gravity and acceleration are locally indistinguishable. In 
other words, if you were in a closed elevator, you wouldn't be able to 
tell if you were being pulled downward by gravity on Earth, or if the 
elevator was being accelerated upward through space at a rate of 9.8 m/
s^2.

Now, to your question regarding the variation of gravity in an elevator 
resting on Earth (where gravity is stronger at the floor than at the 
ceiling due to the inverse square law) versus in an accelerating elevator 
in space (where the "gravity" feels uniform). While this difference exists 
and is indeed measurable with very sensitive equipment, it does not 
fundamentally challenge or change the principle of equivalence, because 
the principle is a local concept.

What do we mean by "local"? If the elevator is small enough (so that 
variations in gravitational field strength across its size are 
negligible), then there's no experiment you could conduct inside the 
elevator to determine whether it's stationary in a gravitational field or 
in free space being accelerated. That's the essence of the equivalence 
principle.

However, if the elevator is large enough that these variations in 
gravitational field strength are not negligible, then we'd say that the 
"locality" condition isn't satisfied. For example, you could imagine a 
scenario where the elevator is the size of a planet. Clearly, there would 
be a noticeable difference in gravity between the floor and the ceiling. 
But in this case, the equivalence principle isn't meant to apply, because 
the situation is no longer local.

So, in short, while the variation in gravitational strength is an 
interesting point and certainly real, it doesn't undermine the validity of 
the equivalence principle because this principle is only meant to apply to 
small, local regions of spacetime. For larger regions where the variation 
in gravitational strength becomes noticeable, one would need to apply the 
full machinery of General Relativity.

 _ _ _ _ _

-- 
-v

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Question regarding an elevator vallor <vallor@vallor.earth> - 2023-06-30 19:08 +0000
  Re: Question regarding an elevator snipeco.2@gmail.com (Sn!pe) - 2023-06-30 20:55 +0100
    [ChatGPT] Chicken or the egg? vallor <vallor@vallor.earth> - 2023-06-30 20:14 +0000
      Re: [ChatGPT] Chicken or the egg? snipeco.2@gmail.com (Sn!pe) - 2023-06-30 22:30 +0100
  [ChatGPT] The elevator (was: Re: Question regarding an elevator vallor <vallor@vallor.earth> - 2023-06-30 20:49 +0000
  Re: Question regarding an elevator snipeco.2@gmail.com (Sn!pe) - 2023-06-30 22:39 +0100

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