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Apr 19, 2022, 3:21:44 AMApr 19

to

In the lift stopped at the floor, the bodies accelerate both towards=20

the floor and towards the center of the Earth (the two directions=20

coincide).

If the cables break and the elevator goes into free fall, the two=20

gravitational accelerations no longer coincide.

The bodies stop accelerating towards the floor but continue to=20

accelerate towards the center of the Earth.

Doesn't this mean that in the free-falling elevator the force of=20

gravity has not disappeared at all but is well active?

the floor and towards the center of the Earth (the two directions=20

coincide).

If the cables break and the elevator goes into free fall, the two=20

gravitational accelerations no longer coincide.

The bodies stop accelerating towards the floor but continue to=20

accelerate towards the center of the Earth.

Doesn't this mean that in the free-falling elevator the force of=20

gravity has not disappeared at all but is well active?

Apr 19, 2022, 9:39:24 AMApr 19

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"stationary" frame there is a "force" of gravity causing free objects to

accelerate downwards. Note however this this frame of reference is

not an inertial frame. Per the Equivalence Principle, this frame is

equivalent to one in space that is accelerating "upward" at 1 g.

For a reference frame that is stationary wrt the falling bodies, there

is no force acting at all, everything is in free fall and "weightless".

This IS an inertial frame because in this frame if you release a free

body, it remains stationary wrt this frame. There is no force acting

on it. With respect to this inertial frame it is the earth that is

accelerating upward. (I am ignoring tidal effects, which is a

second order effect.)

In the modern interpretation gravity is not a force, but what we

attribute to the force of gravity is really a non-Euclidean space-

time in the neighborhood of massive objects. The only real force

is the one at your feet that is accelerating you upwards at 1 g.

When you are stationary on the surface of the earth you are not

in an inertial frame, but in one that is accelerating upwards at

1 g. It is the free falling objects that are in an inertial frame and

not accelerating.

Rich L.

Apr 19, 2022, 9:58:55 PMApr 19

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Richard Livingston <richali...@gmail.com> writes:

>In the modern interpretation gravity is not a force, but what we

>attribute to the force of gravity is really a non-Euclidean space-

>time in the neighborhood of massive objects. The only real force

>is the one at your feet that is accelerating you upwards at 1 g.

"Accelerating" means "changing the speed",
>In the modern interpretation gravity is not a force, but what we

>attribute to the force of gravity is really a non-Euclidean space-

>time in the neighborhood of massive objects. The only real force

>is the one at your feet that is accelerating you upwards at 1 g.

and "speed" means "change of position", right?

a = dv/dt, v = dx/dt, a = 1 g ==> dv/dt = 1 g.

v = g t + v0, x = (1/2) g t^2 + v0 t + x0.

Assuming: v0 = 0 and x0 = 0: x = (1/2) g t^2.

I assume that the Australians are my antipodes.

So, I am accelerated since a while with 1 g upwards, as you

say above, (=change of my velocity upwards (=change of my

location upwards)) and the Australians with 1 g downwards.

Shouldn't I then be moving further and further away from

Australians?

[[Mod. note -- In order to add/subtract an acceleration vector "here"

to/from an acceleration vector "there", we need a common inertial reference

frame that contains both "here" and "there". If were in a flat spacetime,

that would be easy, since in a flat spacetime inertial reference frames

are of infinite extent. But we don't live in a flat spacetie, we live

in a curved spacetime, and in a curved spacetime an inertial reference

frame is only an approximation valid in a small region. (The precise

definition of "small" depends on how good of an approximation you want,

i.e., how small you want an acceleration to be in order to call it

"negligable".)

As you've just observed, the opposite sides of the Earth are too far

apart to be contained in a common inertial reference frame (assuming

that we're not willing to treat +/- 1 g accelerations as "negligable").

That is your 1 g "up" acceleration is measured with respect to a

*different* inertial reference frame from the the Australian's "1 g down",

and hence you can't just add/subtract them without taking into account

the non-trivial transformation (induced by spacetime curvature) between

those two different inertial reference frames.

-- jt]]

Apr 21, 2022, 3:24:49 AMApr 21

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Richard Livingston marted=EC 19/04/2022 alle ore 15:28:38 ha scritto:

> With respect to this inertial frame it is the earth that is=20

> accelerating upward.=20

This is incomprehensible.

Acceleration occurs in the presence of a force (F=3Dma).

The force existing between the 300 kg lift and the Earth is worth 300=20

kg-weight.

This force justifies the downward acceleration of the elevator but=20

could never justify the acceleration of the entire earth mass upward!

> With respect to this inertial frame it is the earth that is=20

> accelerating upward.=20

This is incomprehensible.

Acceleration occurs in the presence of a force (F=3Dma).

The force existing between the 300 kg lift and the Earth is worth 300=20

kg-weight.

This force justifies the downward acceleration of the elevator but=20

could never justify the acceleration of the entire earth mass upward!

Apr 22, 2022, 1:39:49 PMApr 22

to

On 4/21/22 2:24 AM, Luigi Fortunati wrote:

> Richard Livingston marted=EC 19/04/2022 alle ore 15:28:38 ha

> scritto:

>> With respect to this inertial frame it is the earth that is

>> accelerating upward.
> Richard Livingston marted=EC 19/04/2022 alle ore 15:28:38 ha

> scritto:

>> With respect to this inertial frame it is the earth that is

>

> This is incomprehensible.

Not really. But one must be thinking in terms of General Relativity

(GR), not Newtonian mechanics (NM).

> Acceleration occurs in the presence of a force (F=ma).

But there quite clearly is a force: for an object sitting at rest on the

surface of the earth, there is an upward force on it, which we call

"weight".

> This force justifies the downward acceleration of the elevator but

> could never justify the acceleration of the entire earth mass

> upward!

You need more precision in your thoughts and words. "Acceleration" by
> upward!

itself is insufficiently defined -- use either "proper acceleration" or

specify a (locally) inertial frame relative to which it is measured.

"The entire earth mass" is likewise ill defined -- consider just a small

portion of its surface. A small object at rest on earth's surface has a

proper acceleration of 9.8 m/s^2 (directed upward); in GR this is in

response to the (upward) force exerted on the object by the earth's surface.

[In physics, "proper" means "relative to the instantaneously

co-moving inertial frame of the object in question".]

In NM, near the surface of the earth, we generally use coordinates in

which that surface is at rest. This hides the underlying issue -- these

coordinates hide the force that the surface exerts on such objects. NM

then adds a gravitational force to cancel the force the surface exerts,

yielding net zero force -- this is CLEARLY WRONG as we humans can feel

the force from the surface on our bodies, and it is clearly not zero. GR

corrects this conceptual error:

In GR, near the surface of the earth, locally inertial frames are all

accelerating downward at 9.8 m/s^2, so an object at rest on the surface

is accelerating (upward) relative to them -- responding to the force

that the surface exerts on such objects.

Tom Roberts

Apr 25, 2022, 3:35:55 AMApr 25

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earth's

surface (reacting), while for Einstein it is the earth's surface

exerting

an upward force on us (reacting).

And you say Einstein is right and Newton is wrong.

But action and reaction are INTERCHANGEABLE!

The two opposing forces are both actions and they are both reactions.

And there is nothing INERTIAL in either.

Accelerating force is one and accelerating force is the other.

Neither is privileged.

Just think of two bodies of equal mass: how would you determine who is

acting

and who reacts?

Luigi Fortunati

[[Mod. note -- Assuming a person standing on (at rest with respect to)

the Earth's surface: In Newtonian mechanics

(a) Newtonian gravity exerts a downward force on the person, AND

(b) The person's feet exert a downward force on the Earth's surface, AND

(c) the Earth's surface exerts an upwards reactive force (reacting

against (b)) on the person's feet.

The net vertical force acting on the person (= the sum of (a) and (c))

is zero

[(b) is not included in the sum because it's not acting

on the person, but rather on the Earth's surface]

, and hence the person has zero vertical acceleration with respect to

the Earth's surface.

In general relativity,

(a) isn't there, AND

(c) is still true, AND

(b) is now categorized as a downwards reactive force on the Earth's

surface, reacting against (c).

The net vertical force acting on the person is now just (c), and is

upwards. Thus the person accelerates upwards at 1 g acceleration

relative to an inertial reference frame. But in GR, an inertial

reference frame is *free-falling*, so near the Earth's surface an

inertial reference frame must have a 1 g accelreation downwards

relative to the Earth's surface. Thus the person's acceleration with

respect to the Earth's surface is zero (= same as the Newtonian mechanics

analysis).

It's not that "Einstein is right and Newton is wrong". More accurately,

both descriptions are internally consistent ways of describing physics.

Newtonian mechanics is the slow-motion weak-gravitational-field limit

of general relativity, so if you only look at weak gravitational fields,

and you move much slower than the speed of light, then you'll see only

tiny difference between the two, and it's reasonable to continue using

Newtonian mechanics.

But if you make very precise measurements (atomic clocks & suchlike),

and/or you measure things in strong gravitational fields (neutron stars,

black holes, & suchlike), then these theories are distinguishable, and

you need general relativity to accurately describe observations.

-- jt]]

Apr 26, 2022, 3:21:54 PMApr 26

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> [[Mod. note -- Assuming a person standing on (at rest with respect to)

> the Earth's surface: In Newtonian mechanics

> (a) Newtonian gravity exerts a downward force on the person, AND

> (b) The person's feet exert a downward force on the Earth's surface, AND

> (c) the Earth's surface exerts an upwards reactive force (reacting

> against (b)) on the person's feet.

> The net vertical force acting on the person (=3D the sum of (a) and (c))
> the Earth's surface: In Newtonian mechanics

> (a) Newtonian gravity exerts a downward force on the person, AND

> (b) The person's feet exert a downward force on the Earth's surface, AND

> (c) the Earth's surface exerts an upwards reactive force (reacting

> against (b)) on the person's feet.

> is zero

> [(b) is not included in the sum because it's not acting

> on the person, but rather on the Earth's surface]

> , and hence the person has zero vertical acceleration with respect to

> the Earth's surface. =20
> [(b) is not included in the sum because it's not acting

> on the person, but rather on the Earth's surface]

> , and hence the person has zero vertical acceleration with respect to

>

> In general relativity,

> (a) isn't there, AND

> (c) is still true, AND

> (b) is now categorized as a downwards reactive force on the Earth's

> surface, reacting against (c).

> The net vertical force acting on the person is now just (c), and is

> upwards. Thus the person accelerates upwards at 1 g acceleration

> relative to an inertial reference frame. But in GR, an inertial

> reference frame is *free-falling*, so near the Earth's surface an

> inertial reference frame must have a 1 g accelreation downwards

> relative to the Earth's surface. Thus the person's acceleration with

> respect to the Earth's surface is zero (=3D same as the Newtonian mechanics
> In general relativity,

> (a) isn't there, AND

> (c) is still true, AND

> (b) is now categorized as a downwards reactive force on the Earth's

> surface, reacting against (c).

> The net vertical force acting on the person is now just (c), and is

> upwards. Thus the person accelerates upwards at 1 g acceleration

> relative to an inertial reference frame. But in GR, an inertial

> reference frame is *free-falling*, so near the Earth's surface an

> inertial reference frame must have a 1 g accelreation downwards

> relative to the Earth's surface. Thus the person's acceleration with

> analysis).

> -- jt]]

You and Einstein say that the reference frames in free fall are

inertial.

Ok.

The elevator in free fall (relative to the Earth) is an inertial

reference frame.

And why is the Earth in free fall (relative to the elevator) NOT an

inertial reference frame?

Still, both of them are in free fall!

Apr 28, 2022, 3:05:56 AMApr 28

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On Tuesday, April 26, 2022 at 2:21:54 PM UTC-5, Luigi Fortunati wrote:

...

The center of gravity of the earth is in free fall (around the sun), but

a reference frame tied to the surface of the earth is not, due to the

distortion of space-time by the mass of the earth. An elevator on

one side of the earth in free fall is an inertial frame, but an elevator

in free fall on the opposite side of the earth is a different inertial

frame. Each of these inertial frames will see the other as accelerating.

That doesn't mean either of these frame are not inertial. The property

of being an inertial frame is a local thing.

The earth is not "in free fall relative to the elevator". Relative to the

elevator the earth is accelerating upwards. It should not be

considered an inertial frame because in that frame it is accelerating.

That is, an object in the surface-of-the-earth frame can only be

stationary in that frame if it has a force accelerating it upwards.

Rich L.

...

> The elevator in free fall (relative to the Earth) is an inertial

> reference frame.

>

> And why is the Earth in free fall (relative to the elevator) NOT an

> inertial reference frame?

>

> Still, both of them are in free fall!

You need to be more precise about what frame you are talking about.
> reference frame.

>

> And why is the Earth in free fall (relative to the elevator) NOT an

> inertial reference frame?

>

> Still, both of them are in free fall!

The center of gravity of the earth is in free fall (around the sun), but

a reference frame tied to the surface of the earth is not, due to the

distortion of space-time by the mass of the earth. An elevator on

one side of the earth in free fall is an inertial frame, but an elevator

in free fall on the opposite side of the earth is a different inertial

frame. Each of these inertial frames will see the other as accelerating.

That doesn't mean either of these frame are not inertial. The property

of being an inertial frame is a local thing.

The earth is not "in free fall relative to the elevator". Relative to the

elevator the earth is accelerating upwards. It should not be

considered an inertial frame because in that frame it is accelerating.

That is, an object in the surface-of-the-earth frame can only be

stationary in that frame if it has a force accelerating it upwards.

Rich L.

Apr 29, 2022, 3:59:28 AMApr 29

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Richard Livingston giovedě 28/04/2022 alle ore 09:05:51 ha scritto:

> You need to be more precise about what frame you are talking about.

> The center of gravity of the earth is in free fall (around the sun)...
> You need to be more precise about what frame you are talking about.

The center of gravity of the elevator is also in free fall around the

sun.

And both (Earth and elevator) are in free fall also with respect to

Jupiter,

Mars and all the other planets.

We want to talk only about the Earth and the elevator without third

party

inconveniences which, moreover, act on both and not on just one?

And therefore, in ALL references the free-fall elevator does not move

at random

but accelerates exactly in the direction that goes towards the center

of the Earth.

In ALL references the free-falling Earth does not move haphazardly but

accelerates

exactly in the direction that goes towards the center of the elevator.

They are two opposite free falls where the center of gravity of each

mass goes exactly towards the center of gravity of the other mass.

The surface of the Earth has nothing to do with it just as the surface

of the elevator has nothing to do with it.

The interaction is between two masses (whose centers of gravity tend

to approach each other) and not between two surfaces.

[[Mod. note -- The fundamental difference between the elevator and

the Earth is that the Earth is a self-gravitating system -- different

parts of the Earth have a non-trivial gravitational interaction with

each other. That means that (a) an inertial reference frame (IRF)

on one side of the Earth (right next to the elevator), (b) an IRF at

the center of mass of the Earth, and (c) an IRF on the other side of

the Earth, are three DISTINCT IRFs.

As measured with respect to IRF (a), the free-falling elevator is

unaccelerated (stationary or moving uniformly).

If we were to try to extend the Earth-center-of-mass IRF (b) to cover

the entire Earth and its immediate neighbourhood, we'd find that with

respect to the extended IRF (b), IRF (a) and the free-falling elevator

are both accelerating at 1 g in the (vector) direction from the elevator

towards the center of the Earth, while IRF (c) is accelerating at 1 g

in the (vector) direction from the center of the Earth towards the

elevator.

As Richard Livingston said in a previous article in this thread,

> Each of these inertial frames will see the other as accelerating.

> That doesn't mean either of these frame are not inertial. The property

> of being an inertial frame is a local thing.

So, one reasonable answer to the question you asked in a previous posting
> That doesn't mean either of these frame are not inertial. The property

> of being an inertial frame is a local thing.

in this thread,

> And why is the Earth in free fall (relative to the elevator) NOT an

> inertial reference frame?

is that the center of mass of the Earth (and its corresponding IRF (b))
> inertial reference frame?

*is* in free-fall with respect to the elevator. But no part of the Earth's

surface is in free-fall (it's all supported in a non-free-fall state by

the solid body of the Earth).

-- jt]]

May 1, 2022, 5:45:27 AMMay 1

to

Luigi Fortunati giovedì 28/04/2022 alle ore 19:59:24 ha scritto:

> [[Mod. note -- The fundamental difference between the elevator and

> the Earth is that the Earth is a self-gravitating system -- different

> parts of the Earth have a non-trivial gravitational interaction with

> each other. That means that (a) an inertial reference frame (IRF)

> on one side of the Earth (right next to the elevator), (b) an IRF at

> the center of mass of the Earth, and (c) an IRF on the other side of

> the Earth, are three DISTINCT IRFs.

If so, then there are not only 3 inertial reference frame but there are
> [[Mod. note -- The fundamental difference between the elevator and

> the Earth is that the Earth is a self-gravitating system -- different

> parts of the Earth have a non-trivial gravitational interaction with

> each other. That means that (a) an inertial reference frame (IRF)

> on one side of the Earth (right next to the elevator), (b) an IRF at

> the center of mass of the Earth, and (c) an IRF on the other side of

> the Earth, are three DISTINCT IRFs.

infinite of them and they are all directed radially towards the center

of the Earth, right?

May 1, 2022, 5:45:27 AMMay 1

to

Luigi Fortunati giovedì 28/04/2022 alle ore 19:59:24 ha scritto:

> [[Mod. note -- The fundamental difference between the elevator and

> the Earth is that the Earth is a self-gravitating system -- different

> parts of the Earth have a non-trivial gravitational interaction with

> each other. That means that (a) an inertial reference frame (IRF)

> on one side of the Earth (right next to the elevator), (b) an IRF at

> the center of mass of the Earth, and (c) an IRF on the other side of

> the Earth, are three DISTINCT IRFs.

If each free-fall elevator becomes a distinct inertial reference frame
> the Earth is that the Earth is a self-gravitating system -- different

> parts of the Earth have a non-trivial gravitational interaction with

> each other. That means that (a) an inertial reference frame (IRF)

> on one side of the Earth (right next to the elevator), (b) an IRF at

> the center of mass of the Earth, and (c) an IRF on the other side of

> the Earth, are three DISTINCT IRFs.

from all other free-fall elevators, then there are not only 2 or 3

distinct inertial reference frame but there are infinite, one for each

possible elevator.

And all of these distinct inertial reference frame converge towards the

center of the Earth.

> As Richard Livingston said in a previous article in this thread,

>> Each of these inertial frames will see the other as accelerating.

>> That doesn't mean either of these frame are not inertial. The property

>> of being an inertial frame is a local thing.

>

> So, one reasonable answer to the question you asked in a previous posting

> in this thread,

>> And why is the Earth in free fall (relative to the elevator) NOT an

>> inertial reference frame?

> is that the center of mass of the Earth (and its corresponding IRF (b))

> *is* in free-fall with respect to the elevator. But no part of the Earth's

> surface is in free-fall (it's all supported in a non-free-fall state by

> the solid body of the Earth). -- jt]]

Whoever is in the center of the Earth is stationary at the exact point

of maximum inertia, where there is no force (Newton) and where there is

no "curvature" (Einstein).

Whoever stands in the center of the Earth (where all the free-falling

elevators converge) sees the elevators accelerating towards him.

How does he (totally inert) accelerate to all the elevators?

And if he actually accelerated toward the elevator coming down from the

north pole, how would he accelerate toward the elevator coming from the

south pole as well?

May 2, 2022, 4:36:53 AMMay 2

to

[Moderator's note: Too much quoted text deleted. -P.H.]

I'm afraid you are missing the concept that in a gravitational field the

concept of an inertial reference frame is very localized. Yes, there

ARE an infinite number of possible reference frames. And for each one

if you get very far from the origin of that frame (i.e. the location

where a free object floats without acceleration) then you are no longer

in an inertial frame FROM THE POINT OF VIEW OF THAT FRAME. That is,

while an object inside your freely falling elevator will not accelerate

when released, if you place that object a short distance outside your

elevator it will begin to accelerate when released.

And from the point of view of each of these localized inertial frames,

objects falling freely in other frames are accelerating, even though in

their local inertial frames those objects are "weightless".

Rich L.

I'm afraid you are missing the concept that in a gravitational field the

concept of an inertial reference frame is very localized. Yes, there

ARE an infinite number of possible reference frames. And for each one

if you get very far from the origin of that frame (i.e. the location

where a free object floats without acceleration) then you are no longer

in an inertial frame FROM THE POINT OF VIEW OF THAT FRAME. That is,

while an object inside your freely falling elevator will not accelerate

when released, if you place that object a short distance outside your

elevator it will begin to accelerate when released.

And from the point of view of each of these localized inertial frames,

objects falling freely in other frames are accelerating, even though in

their local inertial frames those objects are "weightless".

Rich L.

May 2, 2022, 4:37:24 AMMay 2

to

I asked the moderator to cancel my last two posts because I wanted to

improve them but something went wrong and they were published anyway: I

apologize to everyone.

[Moderator's note: Posts are distributed among the active moderators.

So such a request sent as if it were a post will probably not go to the

same moderator. Even if it did, he could really "cancel" it only if he

hadn't already posted it, as many NNTP servers no longer honor requests

to cancel posts. Note that there is another address which reaches all

active moderators, which should be used for such requests. See

http://www.astro.multivax.de:8000/spr/spr.html -P.H.]

After some thought, my final answer (which replaces the previous two)

is the following.

> [[Mod. note -- The fundamental difference between the elevator and

> the Earth is that the Earth is a self-gravitating system -- different

> parts of the Earth have a non-trivial gravitational interaction with

> each other. That means that (a) an inertial reference frame (IRF)

> on one side of the Earth (right next to the elevator), (b) an IRF at

> the center of mass of the Earth, and (c) an IRF on the other side of

> the Earth, are three DISTINCT IRFs.

>

> As measured with respect to IRF (a), the free-falling elevator is

> unaccelerated (stationary or moving uniformly).

> ...

and those of the 2 free-falling elevators from the north and south

poles are accelerated.

Instead, Einstein argues that all three motions are inertial.

If one of the two is right, the other is wrong: it is obvious.

How can we determine who is right and who is wrong?

In my opinion, a good way to judge is the following.

Any measurement of their reciprocal speeds (that of one elevator

relative to the other and of each of the 2 elevators relative to the

center of the Earth) guarantees us that ALL their reciprocal motions

are accelerated and that there is no mutual velocity that is uniform.

This mutual acceleration is justified if the motion of the elevators is

accelerated (as Newton argues) but it is not at all justified if the

motion of the elevators and the center of the Earth are all inertial

(as Einstein argues).

In fact, if all reciprocal motions were truly inertial, where would the

mutual acceleration we measure come from?

improve them but something went wrong and they were published anyway: I

apologize to everyone.

[Moderator's note: Posts are distributed among the active moderators.

So such a request sent as if it were a post will probably not go to the

same moderator. Even if it did, he could really "cancel" it only if he

hadn't already posted it, as many NNTP servers no longer honor requests

to cancel posts. Note that there is another address which reaches all

active moderators, which should be used for such requests. See

http://www.astro.multivax.de:8000/spr/spr.html -P.H.]

After some thought, my final answer (which replaces the previous two)

is the following.

> [[Mod. note -- The fundamental difference between the elevator and

> the Earth is that the Earth is a self-gravitating system -- different

> parts of the Earth have a non-trivial gravitational interaction with

> each other. That means that (a) an inertial reference frame (IRF)

> on one side of the Earth (right next to the elevator), (b) an IRF at

> the center of mass of the Earth, and (c) an IRF on the other side of

> the Earth, are three DISTINCT IRFs.

>

> As measured with respect to IRF (a), the free-falling elevator is

> unaccelerated (stationary or moving uniformly).

> So, one reasonable answer to the question you asked in a previous posting

> in this thread,

>> And why is the Earth in free fall (relative to the elevator) NOT an

>> inertial reference frame?

> is that the center of mass of the Earth (and its corresponding IRF (b))

> *is* in free-fall with respect to the elevator. But no part of the Earth's

> surface is in free-fall (it's all supported in a non-free-fall state by

> the solid body of the Earth).

> -- jt]]

Newton says that the reference of the center of the Earth is inertial
> in this thread,

>> And why is the Earth in free fall (relative to the elevator) NOT an

>> inertial reference frame?

> is that the center of mass of the Earth (and its corresponding IRF (b))

> *is* in free-fall with respect to the elevator. But no part of the Earth's

> surface is in free-fall (it's all supported in a non-free-fall state by

> the solid body of the Earth).

> -- jt]]

and those of the 2 free-falling elevators from the north and south

poles are accelerated.

Instead, Einstein argues that all three motions are inertial.

If one of the two is right, the other is wrong: it is obvious.

How can we determine who is right and who is wrong?

In my opinion, a good way to judge is the following.

Any measurement of their reciprocal speeds (that of one elevator

relative to the other and of each of the 2 elevators relative to the

center of the Earth) guarantees us that ALL their reciprocal motions

are accelerated and that there is no mutual velocity that is uniform.

This mutual acceleration is justified if the motion of the elevators is

accelerated (as Newton argues) but it is not at all justified if the

motion of the elevators and the center of the Earth are all inertial

(as Einstein argues).

In fact, if all reciprocal motions were truly inertial, where would the

mutual acceleration we measure come from?

May 2, 2022, 11:24:13 AMMay 2

to

On 5/2/22 3:37 AM, Luigi Fortunati wrote:

> Newton says that the reference of the center of the Earth is inertial

> and those of the 2 free-falling elevators from the north and south

> poles are accelerated.

>

> Instead, Einstein argues that all three motions are inertial.

No. GR says that the three are LOCALLY inertial. You cannot omit
> Newton says that the reference of the center of the Earth is inertial

> and those of the 2 free-falling elevators from the north and south

> poles are accelerated.

>

> Instead, Einstein argues that all three motions are inertial.

"locally", and that is the crux of your confusion.

> If one of the two is right, the other is wrong: it is obvious.

contexts. Both are true within their respective contexts. But your

imprecise and ambiguous language hides that.

> How can we determine who is right and who is wrong?

ambiguous statements is useless, as is logic applied to statements

belonging to different contexts.

Statements containing ambiguous words like "acceleration" can be

ambiguous: neither true nor false. Correct statements must avoid all

such words, and be precise enough to be adjudged true.

"Proper acceleration" and "coordinate acceleration" are precise enough

here, while unqualified "acceleration" is not. Newtonian mechanics does

not have the concept of proper acceleration; GR introduced it to avoid

the ambiguity that is confusing you.

> In my opinion, a good way to judge is the following. [... useless

> method using speeds]

The correct way is to distinguish proper acceleration from coordinate

acceleration (which you failed to do).

The proper acceleration of a (pointlike) object is its acceleration

relative to its instantaneously co-moving locally inertial frame; it is

invariant (independent of coordinates -- all observers agree on its

value), while coordinate accelerations are not invariant. This is true

independent of whether the object is in freefall (zero proper

acceleration), or not (nonzero proper acceleration).

In the first paragraph quoted above, objects at rest in the center of

the earth and at rest in each elevator have zero proper accelerations.

When one uses the coordinates of their locally-inertial frame, each has

zero coordinate acceleration. When one uses the coordinates of one of

those frames to describe an object at rest in a different one, the

coordinate acceleration is nonzero.

(In general, the coordinates of a locally inertial frame

might not be valid far away -- they are LOCAL.)

Bottom line: complicated and subtle subjects like modern physics require

precision in thought and word. You need to make more precise statements

that are not ambiguous.

Tom Roberts

May 3, 2022, 3:58:41 AMMay 3

to

Tom Roberts lunedì 02/05/2022 alle ore 17:24:10 ha scritto:

> ....

> These can be statements containing ambiguous words such as "acceleration".

the

Earth and of the center of the Earth towards the free-falling elevator

are not ambiguous, because they are observable and measurable in all

references.

>....

> In the first paragraph cited above, objects at rest in the center of

> the ground and at rest in each lift have their own zero accelerations.

The acceleration of the object in the elevator is really (obviously)

null as all the accelerations with respect to themselves are null but

what does it have to do with gravity?

The acceleration of gravity of the object in the elevator is directed

towards the center of the Earth and not towards the elevator!

> ....

> These can be statements containing ambiguous words such as "acceleration".

> ambiguous: neither true nor false.

The accelerations of the free-falling elevator towards the center of
the

Earth and of the center of the Earth towards the free-falling elevator

are not ambiguous, because they are observable and measurable in all

references.

>....

> In the first paragraph cited above, objects at rest in the center of

> the ground and at rest in each lift have their own zero accelerations.

The acceleration of the object in the elevator is really (obviously)

null as all the accelerations with respect to themselves are null but

what does it have to do with gravity?

The acceleration of gravity of the object in the elevator is directed

towards the center of the Earth and not towards the elevator!

May 3, 2022, 4:18:00 AMMay 3

to

Richard Livingston luned=EC 02/05/2022 alle ore 10:36:50 ha scritto:

> I'm afraid you are missing the concept that in a gravitational field the

> concept of an inertial reference frame is very localized.
> I'm afraid you are missing the concept that in a gravitational field the

Gravity is not very localized because it does not go from man to

elevator.

Gravity goes from the man-elevator to the center of the earth!

[Moderator's note: Even if gravity is not localized, the concept of an

inertial frame can be. -P.H.]

May 5, 2022, 3:26:53 AMMay 5

to

Luigi Fortunati martedì 03/05/2022 alle ore 10:17:57 ha scritto:

> [Moderator's note: Even if gravity is not localized, the concept of an inertial frame can be. -P.H.]

Ok, so let's ask ourselves who is at rest and who is not in the "local"
> [Moderator's note: Even if gravity is not localized, the concept of an inertial frame can be. -P.H.]

reference.

Let us ask ourselves: if the man in the elevator stopped at the floor

drops the ball he is holding, is it the ball that falls towards the

floor (Newton) or is it the floor that falls towards the ball

(Einstein)?

It is entirely reasonable to imagine that there may be a force capable

of accelerating the ball downwards but it takes a lot of faith to be

able to accept that there may be a force capable of accelerating the

entire Earth towards the ball.

May 5, 2022, 4:05:24 PMMay 5

to

On Thursday, May 5, 2022 at 2:26:53 AM UTC-5, Luigi Fortunati wrote:

I think this will be my last post on this issue:

-"Who is at rest?" is the wrong question. The relevant question is "who

is in an inertial frame?" If you are in an inertial frame you can let go

of an object and it will float where you left it. If you let go of an

object and it accelerates away, then you are not in an inertial frame.

-In the paradigm of General Relativity there are no "forces" due to

gravity, only curvature of space-time. The result is that a reference

frame that is at a fixed position away from the center of mass of

a large massive object is no longer an inertial frame. That is, if you

release an object that is initially stationary in that frame it will start

to accelerate away from you. In this paradigm the released object

has no forces on it, it is merely following its normal world line through

space-time. You, on the other hand, feel a force on your feet that is

accelerating you upwards relative to the inertial frame that is

accelerating downwards wrt you.

-You can choose to ignore this point of view and say the released

object is experiencing a force downwards, but if that is the case

why does someone in free fall feel "weightless"? If you were inside

an elevator far from any mass you would feel weightless. If you

were in an elevator in free fall near a large mass you would again

feel weightless. In one case you would say there is no force, in the

other you would say there is. What difference does it make?

-If you don't want to think in terms of the curvature of space-time and

the effect that has on an object's world line, you will not progress

much in understanding General Relativity.

Rich L.

-"Who is at rest?" is the wrong question. The relevant question is "who

is in an inertial frame?" If you are in an inertial frame you can let go

of an object and it will float where you left it. If you let go of an

object and it accelerates away, then you are not in an inertial frame.

-In the paradigm of General Relativity there are no "forces" due to

gravity, only curvature of space-time. The result is that a reference

frame that is at a fixed position away from the center of mass of

a large massive object is no longer an inertial frame. That is, if you

release an object that is initially stationary in that frame it will start

to accelerate away from you. In this paradigm the released object

has no forces on it, it is merely following its normal world line through

space-time. You, on the other hand, feel a force on your feet that is

accelerating you upwards relative to the inertial frame that is

accelerating downwards wrt you.

-You can choose to ignore this point of view and say the released

object is experiencing a force downwards, but if that is the case

why does someone in free fall feel "weightless"? If you were inside

an elevator far from any mass you would feel weightless. If you

were in an elevator in free fall near a large mass you would again

feel weightless. In one case you would say there is no force, in the

other you would say there is. What difference does it make?

-If you don't want to think in terms of the curvature of space-time and

the effect that has on an object's world line, you will not progress

much in understanding General Relativity.

Rich L.

May 6, 2022, 8:22:13 PM (13 days ago) May 6

to

Richard Livingston gioved=EC 05/05/2022 alle ore 22:05:20 ha scritto:

> -"Who is at rest?" is the wrong question. The relevant question is "wh=

o

> is in an inertial frame?" If you are in an inertial frame you can let =

if you let go of an object, it accelerates toward the floor if the

gravity is that of a black hole and if the object is below the center

of the elevator where gravity acting on the object is greater than

gravity acting on the entire elevator!

[[Mod. note -- No, the correct conclusion is to observe that inertial

frames are always of limited size, with the actual size limit depending

on your tolerance (threshold) for how small an acceleration difference

(a.k.a tidal acceleration) is "negligable".

If your freely-falling elevator is big enough that you notice the

acceleration differences between different free-falling objects in

the elevator (all of which were initially at rest with respect to

the elevator), and/or between these and the elevator itself, that's

a statement that your elevator is too big for any one inertial frame

to cover the entire elevator. If you want to apply the concept of

"inertial frame" in the elevator, then you need a smaller elevator

and/or a looser tolerance for acceleration differences.

-- jt]]

> -"Who is at rest?" is the wrong question. The relevant question is "wh=

o

> is in an inertial frame?" If you are in an inertial frame you can let =

go

> of an object and it will float where you left it. If you let go of an

> object and it accelerates away, then you are not in an inertial frame.

And, therefore, the free-fall elevator is not an initial frame because
> of an object and it will float where you left it. If you let go of an

> object and it accelerates away, then you are not in an inertial frame.

if you let go of an object, it accelerates toward the floor if the

gravity is that of a black hole and if the object is below the center

of the elevator where gravity acting on the object is greater than

gravity acting on the entire elevator!

[[Mod. note -- No, the correct conclusion is to observe that inertial

frames are always of limited size, with the actual size limit depending

on your tolerance (threshold) for how small an acceleration difference

(a.k.a tidal acceleration) is "negligable".

If your freely-falling elevator is big enough that you notice the

acceleration differences between different free-falling objects in

the elevator (all of which were initially at rest with respect to

the elevator), and/or between these and the elevator itself, that's

a statement that your elevator is too big for any one inertial frame

to cover the entire elevator. If you want to apply the concept of

"inertial frame" in the elevator, then you need a smaller elevator

and/or a looser tolerance for acceleration differences.

-- jt]]

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