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.
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