Question regarding an elevator

[vallor]

[ This is a repost of the following article: ]
[ From: vallor <val...@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.)

--
-v

[vallor]

On Fri, 30 Jun 2023 12:29:05 -0700 (PDT), mitchr...@gmail.com wrote:

> On Friday, June 30, 2023 at 11:37:37 AM UTC-7, vallor wrote:
>> 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)
>

> The strength of gravity is equal in contractile curvature.
> There is no inner gravity drop off. Feynman was a problem
> where he replaced original GR by inner drop off.
> At a BH how can there be Feynman's inner drop off gravity?
> He said it would go to zero. So how could gravity in a BH
> do it?

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

> Accelerating is increased speed it is not the force of gravity.
> Motion is like force. It can get weight.

Thank you for the response, very much appreciated.

I was referring to the observation that Einstein made that one
couldn't tell the difference from within an elevator in either
situation. I was pointing out that with sensitive enough instruments,
you can tell the difference. The gedanken-experiment might
not hold up:

Perhaps the concept of "locality" might have something
to do with "how sensitive are your instruments"... What do you think?

Thanks,

-Scott

cc: comp.ai.shells, where the discussion first began
fu2: sci.physics

>
> Mitchell Raemsch

[Sn!pe]

vallor <val...@vallor.earth> wrote:

> (I am but an egg.)

Which of us came first?

Can the chatbot can answer that?
Maybe the gravitational question too?

--
^Ï^. – Sn!pe – <https://youtu.be/_kqytf31a8E>

My pet rock Gordon just is.

[vallor]

On Fri, 30 Jun 2023 20:55:33 +0100, Sn!pe wrote:

> vallor <val...@vallor.earth> wrote:
>
>> (I am but an egg.)
>
> Which of us came first?
>
> Can the chatbot can answer that?

User
which came first, the chicken? or the chicken egg? or...?

ChatGPT
The question "which came first, the chicken or the egg?" is often used as
a metaphor for the dilemma of causality and it dates back to Ancient
Greece. In the literal sense, it questions whether birds (such as the
chicken) or their eggs were the first to exist.

From a scientific perspective, in the realm of evolution, the egg came
first. The concept here is that an animal similar to a chicken, but not
quite a chicken, laid an egg that hatched into what we would now recognize
as a chicken. This is due to small genetic mutations that occur over time.

In this model, the "egg" -- or the mechanism through which offspring with
variations and mutations are produced -- is fundamental to the process of
evolution. This mutation would have occurred in the embryo inside the egg,
so technically, the egg would have come before the chicken.

This situation is a product of evolution, which functions through gradual
changes over many generations. The first chicken would have been a product
of non-chickens breeding and producing offspring with small mutations,
until eventually, there was an animal we'd recognize as a chicken. So, in
that sense, the egg came first, but it was laid by a bird that was not
quite a chicken.

This answer, of course, depends on the definition of a "chicken egg". If a
"chicken egg" is an egg from which a chicken emerges, then the egg came
first. If a "chicken egg" is an egg laid by a chicken, then the chicken
came first.

It's important to remember that this is a simplified model of how
evolution works and actual processes are complex, involving many genes and
environmental factors.

> Maybe the gravitational question too?

One at a time, please. :)

(Dinosaurs had eggs, so eggs came first.)

--
-v

[vallor]

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

[Sn!pe]

Interesting.

> > Maybe the gravitational question too?
>
> One at a time, please. :)
>
> (Dinosaurs had eggs, so eggs came first.)
>

Some hold that we avians are descended from the dinosaurs.
I do hope that doesn't mean that I'm one of the hemi-reptiloid
rulers of this sorry sphere; I'd hate think that I might be in part
responsible for the woes of poor old Spaceship Earth.

[Sn!pe]

[comp.ai.shells only]

vallor <val...@cultnix.org> wrote:
[...]

> Perhaps the concept of "locality" might have something
> to do with "how sensitive are your instruments"... What do you think?
>
> Thanks,
>
> -Scott
>
> cc: comp.ai.shells, where the discussion first began
> fu2: sci.physics
>

I don't read sp so I will take no further part in this discussion.

[Sn!pe]

[...]

Lacking context, I have nothing to add.

[vallor]

On 1 Jul 2023 11:44:31 GMT, Stefan Ram wrote:

> vallor <val...@cultnix.org> writes:
>>I was referring to the observation that Einstein made that one couldn't
>>tell the difference from within an elevator in either situation. I was
>>pointing out that with sensitive enough instruments,
>>you can tell the difference.
>

> The gravitational potential at the bottom of the elevator is
>
> V( x )= -GM/x, where
>
> x is the distance from the center of the Earth to the bottom
> of the elevator,
> G is the gravitational constant, and M the mass of the Earth.
>
> At the top, it's
>
> V( x + h )= -GM/( x + h ), where
>
> h is the height of the elevator.
>
> So the difference is
>
> -GM/( x + h )-( -GM/x )= GMh/( x^2 + hx )~ GMh/x^2.
>
> This difference can be made as small as wanted by reducing the height
> of the elevator. We also should reduce the size of the floor as
> otherwise the direction of the force differs between different points
> of the floor. So, it seems to me that for such gedanken-experiments
> one uses elevators of infinitesimal size!

Thank you so much for doing the math. It's been a while.

Also, it seems to me that for an elevator accelerating at 1G
in free space, the "top" accelerometer will actually
register _heavier_ than the "bottom" accelerometer, due to
gravity from the mass of the elevator.

--
-v