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Ufonaut99

Re: The Equivalence of Acceleration and Gravitation in General Relativity

December 22 2016, 7:46 AM 

Hi Nakayama,

nakayama: The crew can vary the direction of the space ship ... But, the thing of this level will be written somewhere. Or, is it my misunderstanding ?
...In Wikipedia (in Japanese), the equivalence principle is also written as follows. “In the infinite small area, acceleration of motion and of gravity cannot be distinguished". However, in general, vector of the two (the two are calculable) are different (unrelated than different : qualitatively and quantitatively). Even in the infinite small area (locally), it will be so (in general). A case that the two is difficult to distinguish is exceptional and is limited only to a point, to a line or to a plain. Why is that a principle ?
... Why infinite small area is specialized ?

You've given the answer yourself : A case that the two is difficult to distinguish ... is limited only to a point

And that's the equivalence principle happy.gif Note that it's not calculating nor comparing that measurement against some specific object like Earth (such a thing would be meaningless anyway, since gravity varies across the surface of the planet)

GR is about translation of the POINT (x, y, z, t) in one frame to the POINT (x', y', z', t') in another - so by definition in GR we're only interested in the principle applied LOCALLY to a POINT (or "infinite small area" )

Of course across wider spans there'll be differences as gravity diminishes with distance and pilots play acrobatics with their rocket ships, but those aren't local. Rather, they're a lot of points, each of which feels a force happy.gif

 
 
nakayama

Re: The Equivalence of Acceleration and Gravitation in General Relativity

December 23 2016, 12:47 AM 

Gravity and inertial force acting on a moving automobile are unrelated. Locally (at infinite small area), it will be the same. On an elevator cabin in free fall, there will be no meaning (in physics) worthy to be noted.

To Ufonaut99,
Thank you so much for your respond. But about the above, how do you think ?

 
 
Ufonaut99

Re: The Equivalence of Acceleration and Gravitation in General Relativity

December 23 2016, 7:13 AM 

You're welcome happy.gif

Gravity and inertial force acting on a moving automobile are unrelated

And yet they produce the same effect. That's rather the point wink.gif(*)

On an elevator cabin in free fall, there will be no meaning (in physics) worthy to be noted.

On the contrary, that's an equivalent picture that led Einstein to the equivalence principle in the first place. So let's ask the question :

You wake up in a windowless room, and feel weightless. Are you free-falling in a gravitational field, or floating "stationary" in space? For myself, I reckon that merits a "note" happy.gif



(*) And how do you know that they're unrelated? For example, to take the simple model that was still viable in Einstein's time, suppose "inertia" is nothing but the combined gravitational effect of all the stars and other stuff in the universe.
That would mean "gravity" and "inertial force" are not only related, but actually exactly the same thing !
Be careful about making assertions that you cannot justify ( **cough** wavelength **cough** wink.gif )

 
 
nakayama

Re: The Equivalence of Acceleration and Gravitation in General Relativity

December 24 2016, 9:53 PM 

To Ufonaut99,

Your respond (Dec 23) brings an idea as follows. I must thank you.

There are three pictures A, B and C, where the elevator cabin is falling. The density of air in the falling space is high in A, middle in B, and sparse in C. The acceleration observed on each floor was 0.6g for A, 0.4g for B, and 0.2g for C. This is supported by calculation with hydromechanics. When falling space were a vacuum (other circumstances are the same), gravity 1g will be acting also.

About free fall, I have written not a few responds to this thread.

 
 
nakayama

Re: The Equivalence of Acceleration and Gravitation in General Relativity

December 24 2016, 10:17 PM 

To Ufonaut99,

About a space ship without window, I wrote as follows (on Dec 8).

“In discussion on free fall, a starting point of falling, center of the gravity (center of the gravity source) cannot be ignored. When these are lacking, we will be unable to start talking. By the way, in free fall, acceleration, inertial force are self-evident, I believe.“

An observer outside will see the truth (when condition meets, he see a parabola). Or, plural observers must be welcomed.

 
 
nakayama

Re: The Equivalence of Acceleration and Gravitation in General Relativity

December 24 2016, 10:46 PM 

On acceleration, the same phenomenon (qualitatively, quantitatively) is seen everywhere of space (in dairy life also). In space, there will be one and only physical frame. Acceleration seems to be based only on this frame. Relativity of acceleration will be impossible (in free fall also).
P.S. Gyroscope with laser and with inertia seem to work the same. Aether to inertia also.
P.S. This frame seems not to rotate to celestial sphere.

 
 
nakayama

Re: The Equivalence of Acceleration and Gravitation in General Relativity

December 26 2016, 10:01 PM 

Inertial frame will be a frame that is not accelerated (at a standstill or in uniform motion) relative to aether frame. Not only light, but also acceleration / non acceleration will follow aether frame.

 
 
nakayama

Re: The Equivalence of Acceleration and Gravitation in General Relativity

December 26 2016, 10:10 PM 

In a plane, a passenger putting eye mask (blindfold) on his eyes says that he cannot distinguish whether plane is flying or on the ground. Sayings from other viewpoints are sealed ?

 
 
nakayama

Re: The Equivalence of Acceleration and Gravitation in General Relativity

December 27 2016, 8:46 PM 

In my previous post (Dec 24 : the first post) with three pictures (the density of air is high, middle, and sparse), compared was momentary values. But the comparison of terminal speed of a falling body will be more smart. Allow me to rewrite. Also in these pictures, common premise of hydromechanics will be gravity 1g. And in free fall too (will be).

 
 
Ufonaut99

Re: The Equivalence of Acceleration and Gravitation in General Relativity

December 28 2016, 6:51 PM 

Happy Christmas, Nakayama, and I hope you and everybody on the forum had a great day, and have a good year happy.gif

Or, is it my misunderstanding ?
...
An observer outside will see the truth (when condition meets, he see a parabola). Or, plural observers must be welcomed.
...
Sayings from other viewpoints are sealed ?
...
But the comparison of terminal speed of a falling body will be more smart.

You're not listening to what I (and that wikipedia page .... and Einstein) are saying.

I'm guessing you heard somewhere something like "The equivalence principle means it's impossible to tell whether someone is ....."
Nope; That's not the equivalence principle.

Look, Einstein's original picture of the Equivalence Principle was an individual in free-fall being weightless.
OF COURSE that individual knows "the truth" that he is in a gravitational field.

You mentioned a passenger in a plane, but we often use Einstein's original picture of a passenger in a train passing a platform.
That passenger was not blindfolded, so OF COURSE knows "the truth" that he's moving relative to the platform and to Earth, and "other viewpoints" are part of the picture.

Being unable to discover "the truth" in a given scenario is NOT what these principles are about, as Einstein's own illustrations make clear - so yes, you are still misunderstanding.

Let's take a concrete example of the Equivalence Principle, for example, your elevator C - in fact, let's take 2 elevators :
- Alice in C1 is being pulled along at just under 2 metres / second2
- Bob in C2 is suspended from a BIG tower at around 8000km above the earth's surface.

Alice and Bob are fully aware of their surroundings, and are also in regular contact with eachother (and anybody else).
Tell you what, you can also have as many "plural observers" as you like happy.gif

The equivalence principle in GR is that Alice and Bob both feel the same force of around 0.2g at (say) the centrepoint (x, y, z, t) in their elevator, and that all effects of that force will be the same for both.

So your argument against that is ..... ? happy.gif

 
 
Anonymous

Re: The Equivalence of Acceleration and Gravitation in General Relativity

December 28 2016, 9:16 PM 

>>>Look, Einstein's original picture of the Equivalence Principle was an individual in free-fall being weightless.
OF COURSE that individual knows "the truth" that he is in a gravitational field.

not in the way that Einstein talked about it!

 
 
nakayama

Re: The Equivalence of Acceleration and Gravitation in General Relativity

December 29 2016, 12:43 AM 

This is a trial of definition. The definition of encyclopedia seems to differ (the same external force mg does not cause the same inertial force).

Inertial frame: Frame where inertial force is not seen. It can be said also to be non accelerated frame.
Accelerated frame: Frame where inertial force is seen.

 
 
nakayama

Re: The Equivalence of Acceleration and Gravitation in General Relativity

December 29 2016, 2:09 AM 

Two glass tubes are standing vertically. Inside of one is vacuum and inside of the other is sparse air. The same bodies are falling. One is in free fall and the other is at a terminal speed. Acting of gravity will be evident.

Dear Ufonaut99,
Please give some time to respond.

 
 
nakayama

Re: The Equivalence of Acceleration and Gravitation in General Relativity

December 30 2016, 12:48 AM 

A disk is rotating vertically. At the edge of the disk, centrifugal force (inertial force) is 3g. And gravity is 1g. Acceleration acts on the each point of the disk depends on inertial force and gravity. Gravity acts on the each point like a free fall.

 
 
nakayama

Re: The Equivalence of Acceleration and Gravitation in General Relativity

December 31 2016, 1:12 AM 

In non gravitational field, a space ship is moving in a uniform accelerated motion (along a straight line). From the space ship, four bodies are sent horizontally like letter X. After a few seconds, four bodies the same again. Each locus seen from the space ship will draw parabola. Relativity of accelerated motion will not stand up. Assertion on free fall will not also.

When forces act on a body is gravity only (supposed from one direction only), the body will do an accelerated motion. So, free fall will be an accelerated motion.

The influence of voice of each infinite small point (area) of an elevator cabin in free fall must be equal.

 
 
nakayama

Re: The Equivalence of Acceleration and Gravitation in General Relativity

January 1 2017, 12:14 AM 

In previous post (Dec 29), definition of inertial frame was tried as follows “Inertial frame: Frame where inertial force is not seen”. Allow me to add that only frames at a standstill or in a uniform linear motion (relative to aether frame, probably) will be inertial frame. “Action of force” written in encyclopedia will be needless and unsuitable (the same external force mg does not guarantee the same inertial force).

 
 
nakayama

Re: The Equivalence of Acceleration and Gravitation in General Relativity

January 2 2017, 12:54 AM 

Two bodies at a standstill start free fall from each starting point. Height of the two differs. On the ground, falling speed (momentum also) is measured. Free fall seems not to be inertial frame.

 
 
nakayama

Re: The Equivalence of Acceleration and Gravitation in General Relativity

January 3 2017, 12:19 AM 

Inertial force caused by external force (except gravity) or by rotation can be calculable with internal force. Inertial force caused in a body falling vertically can be calculable from gravity and normal force (normal resistance). In free fall, normal force is zero.

 
 
nakayama

Re: The Equivalence of Acceleration and Gravitation in General Relativity

January 4 2017, 11:31 PM 

Falling of body that draws parabola starts. An optional point on the parabola can be regarded as a stationary (seen vertically). Then, the same parabola can be drawn. It shows that action of gravity is unrelated to the motion of body. In free fall also.

 
 
nakayama

Re: The Equivalence of Acceleration and Gravitation in General Relativity

January 6 2017, 12:31 AM 

Allow me to rewrite yesterday’s post.

Falling of body that draws parabola starts. At an optional point on the parabola, the same parabola can be drawn (seen from a selected inertial frame). It shows that action of gravity is unrelated to the motion of body. In free fall also.

 
 
 
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