The Equivalence of Acceleration and Gravitation in General Relativity

The Equivalence of Acceleration and Gravitation in General Relativity

Stanley16
Stanley16

February 21st, 2008, 11:18 pm #1



The Equivalence of Acceleration and Gravitation in General Relativity



So far, you've demonstrated nothing and debunked nothing.
You just keep saying the 'accelerated & non-accelerated' frames of reference are not equivalent' over and over without really demonstrating anything.

So let me give you a head start to enlighten you!

When a system of reference undergoes uniform acceleration, distant masses in the front of it must appear to accelerate towards it at the same uniform acceleration. By contrast, distant masses behind this same system of reference must appear to accelerate away from it at the same uniform acceleration.

Since there is no privileged system of reference in general relativity, an observer at rest with respect to this accelerated system is entitled to consider his system at rest and that the distant masses are undergoing the acceleration in question. And hence, he must conclude that the entire "space-time territory in question is under the sway of a gravitational field".

Look more closely at the profile of this equivalent gravitational field. All distant masses in the forward direction are accelerating towards the system of reference at the same uniform rate; while all distant masses in the backward direction are accelerating away from this same system at the same uniform rate. And this means that the source of this gravitational field must be located somewhere beyond the accelerating-away masses.

I hope, now, you're enlightened, and can see very clearly that acceleration and gravitation are indeed equivalent in every respect and exactly as Einstein concludes in his 1916-groundbreaking paper.


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AAF
AAF

February 22nd, 2008, 9:44 pm #2



Not bad, not bad at all; the above head start of yours is informing; but two or three important pieces of information are missing or left 'wittingly or unwittingly' out of it; please, allow me, now, to go there and retrieve them!

The main method employed in those hypothetical measurements ought to be and must be based upon the principle of Doppler effect.

Measurements obtained by the Doppler method, not only include the instantaneous acceleration, but also include the cumulative result we call 'velocity' due to this operating acceleration over time.

It follows, therefore, that when a system of reference undergoes acceleration (uniform or otherwise), the apparent velocity must be the same for all distant masses. That is in the case of actual acceleration on the part of the reference system in question.

By contrast, in the case of free-falling masses under the 'sway of a uniform gravitational field', the velocity profile as obtained by the Doppler method is quite different. The direction of this velocity is the same, but its magnitude must vary with position and depend entirely on how long the distant mass in question has been traversing this specific gravitational field. For instance, in your 'head start' above, the speed of all accelerating-away masses must be, by the physical necessity of free fall, greater by a large margin than the speed of all 'accelerating-toward-the-observer' masses.

In short, the velocity profile of masses in free fall is vastly different from the velocity profile of truly accelerated system of reference. The accelerated system and the non-accelerated system, therefore, are not equivalent. Einstein got it all wrong.


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Stanley16
Stanley16

February 23rd, 2008, 7:58 pm #3


The Equivalence of Acceleration and Gravitation in General Relativity



So far, you've demonstrated nothing and debunked nothing.
You just keep saying the 'accelerated & non-accelerated' frames of reference are not equivalent' over and over without really demonstrating anything.

So let me give you a head start to enlighten you!

When a system of reference undergoes uniform acceleration, distant masses in the front of it must appear to accelerate towards it at the same uniform acceleration. By contrast, distant masses behind this same system of reference must appear to accelerate away from it at the same uniform acceleration.

Since there is no privileged system of reference in general relativity, an observer at rest with respect to this accelerated system is entitled to consider his system at rest and that the distant masses are undergoing the acceleration in question. And hence, he must conclude that the entire "space-time territory in question is under the sway of a gravitational field".

Look more closely at the profile of this equivalent gravitational field. All distant masses in the forward direction are accelerating towards the system of reference at the same uniform rate; while all distant masses in the backward direction are accelerating away from this same system at the same uniform rate. And this means that the source of this gravitational field must be located somewhere beyond the accelerating-away masses.

I hope, now, you're enlightened, and can see very clearly that acceleration and gravitation are indeed equivalent in every respect and exactly as Einstein concludes in his 1916-groundbreaking paper.

I don't buy the velocity-profile hypothesis you invented above.

First of all, we have only two systems in this experiment: the system labeled K and the system labeled K'. The observer at K' has only two ways to interpret the measured amount of acceleration. It's either K' is accelerating or is at rest and the other system is under the sway of a uniform gravitational field. These two interpretations are exactly equivalent just as Einstein concluded. And so there is nothing for your 'velocity-profile hypothesis' but to "collapse in deepest humiliation".

Even if several systems of reference are given, this velocity-profile thing is still useless.

Remember that this type of gravitational fields appears only the moment we assume it. In other words, it wasn't there in the past to work the way you want it to work. Because of this, it's possible to make the time scale for taking measurements as short as desired to show only the given rate of acceleration and the equivalent rate of free fall. This method has been so successful in establishing the validity of special relativity within the framework of general relativity. It's so successful in the treatment of multiple systems of reference. And it's successful in the case of this thought experiment.

Thus I can say that your trouble here is the same as that of the fabled astronomer who was so busy looking at the wide sky only to have his leg broken by falling nose first into a small pit!

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Stanley16
Stanley16

February 24th, 2008, 3:25 am #4


The Equivalence of Acceleration and Gravitation in General Relativity



So far, you've demonstrated nothing and debunked nothing.
You just keep saying the 'accelerated & non-accelerated' frames of reference are not equivalent' over and over without really demonstrating anything.

So let me give you a head start to enlighten you!

When a system of reference undergoes uniform acceleration, distant masses in the front of it must appear to accelerate towards it at the same uniform acceleration. By contrast, distant masses behind this same system of reference must appear to accelerate away from it at the same uniform acceleration.

Since there is no privileged system of reference in general relativity, an observer at rest with respect to this accelerated system is entitled to consider his system at rest and that the distant masses are undergoing the acceleration in question. And hence, he must conclude that the entire "space-time territory in question is under the sway of a gravitational field".

Look more closely at the profile of this equivalent gravitational field. All distant masses in the forward direction are accelerating towards the system of reference at the same uniform rate; while all distant masses in the backward direction are accelerating away from this same system at the same uniform rate. And this means that the source of this gravitational field must be located somewhere beyond the accelerating-away masses.

I hope, now, you're enlightened, and can see very clearly that acceleration and gravitation are indeed equivalent in every respect and exactly as Einstein concludes in his 1916-groundbreaking paper.

A reply to bobs' objection:
http://www.network54.com/Forum/304711/m ... Relativity


No way!

In Einstein's thought experiment, the equivalent gravitational field is assumed to be uniform and its strength does not vary with the square of distance. And that means the space-time territory under consideration is very far from the gravitational center. For example, the gravitational field of the sun, at about one light year away, is essentially uniform and varies only with extremely minute amount with the square of distance. Your friend, here, knows very well this fact; that is why he went ahead and invented his useless 'velocity-profile' hypothesis.

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M.F. Yagan
M.F. Yagan

February 24th, 2008, 7:51 am #5


The Equivalence of Acceleration and Gravitation in General Relativity



So far, you've demonstrated nothing and debunked nothing.
You just keep saying the 'accelerated & non-accelerated' frames of reference are not equivalent' over and over without really demonstrating anything.

So let me give you a head start to enlighten you!

When a system of reference undergoes uniform acceleration, distant masses in the front of it must appear to accelerate towards it at the same uniform acceleration. By contrast, distant masses behind this same system of reference must appear to accelerate away from it at the same uniform acceleration.

Since there is no privileged system of reference in general relativity, an observer at rest with respect to this accelerated system is entitled to consider his system at rest and that the distant masses are undergoing the acceleration in question. And hence, he must conclude that the entire "space-time territory in question is under the sway of a gravitational field".

Look more closely at the profile of this equivalent gravitational field. All distant masses in the forward direction are accelerating towards the system of reference at the same uniform rate; while all distant masses in the backward direction are accelerating away from this same system at the same uniform rate. And this means that the source of this gravitational field must be located somewhere beyond the accelerating-away masses.

I hope, now, you're enlightened, and can see very clearly that acceleration and gravitation are indeed equivalent in every respect and exactly as Einstein concludes in his 1916-groundbreaking paper.

How can an observer be at rest relative to the accelerating frame since he himself is accelerating? imagine what happins to the passinger in a car coming to a sudden stop. An accelerating object is not at rest relative to anything he is in absolute motion
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Joined: February 22nd, 2008, 2:40 pm

February 24th, 2008, 1:53 pm #6


The Equivalence of Acceleration and Gravitation in General Relativity



So far, you've demonstrated nothing and debunked nothing.
You just keep saying the 'accelerated & non-accelerated' frames of reference are not equivalent' over and over without really demonstrating anything.

So let me give you a head start to enlighten you!

When a system of reference undergoes uniform acceleration, distant masses in the front of it must appear to accelerate towards it at the same uniform acceleration. By contrast, distant masses behind this same system of reference must appear to accelerate away from it at the same uniform acceleration.

Since there is no privileged system of reference in general relativity, an observer at rest with respect to this accelerated system is entitled to consider his system at rest and that the distant masses are undergoing the acceleration in question. And hence, he must conclude that the entire "space-time territory in question is under the sway of a gravitational field".

Look more closely at the profile of this equivalent gravitational field. All distant masses in the forward direction are accelerating towards the system of reference at the same uniform rate; while all distant masses in the backward direction are accelerating away from this same system at the same uniform rate. And this means that the source of this gravitational field must be located somewhere beyond the accelerating-away masses.

I hope, now, you're enlightened, and can see very clearly that acceleration and gravitation are indeed equivalent in every respect and exactly as Einstein concludes in his 1916-groundbreaking paper.

“No way!
In Einstein's thought experiment, the equivalent gravitational field is assumed to be uniform and its strength does not vary with the square of distance.”
“Your friend, here, knows very well this fact; that is why he went ahead and invented his useless 'velocity-profile' hypothesis.“
“ And that means the space-time territory under consideration is very far from the gravitational center.” emphasis added

Stanley 16,
First off, my mistake, my name should be bob s not “bobs”; I shudder to think there might be two of me.

Second, Einstein et al are free to think and assume as they see fit but thought experiments are a dime a dozen, so to speak. I do agree that a gravitational field is uniform radially from its source but I do not agree that it is uniform lineally. So here is what you should do to verify your friend; first leap off of a two foot wall then leap off of a twenty foot wall and tell me that your speed is the same for both leaps at the point of impact and I will become a believer.

Third, are you saying my friend Newton (invented) the “velocity-profile”? I’ll have you know that Newton spent his years experimenting not riding a bike. Einstein spent the last 30 years of his life trying to validate GR and SR...so, how did that turn out?

Next, could that “very far” be somewhere over the rainbow?

Finally, my original objection stands. Thank you.

bob s
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Stanley16
Stanley16

February 24th, 2008, 9:26 pm #7


The Equivalence of Acceleration and Gravitation in General Relativity



So far, you've demonstrated nothing and debunked nothing.
You just keep saying the 'accelerated & non-accelerated' frames of reference are not equivalent' over and over without really demonstrating anything.

So let me give you a head start to enlighten you!

When a system of reference undergoes uniform acceleration, distant masses in the front of it must appear to accelerate towards it at the same uniform acceleration. By contrast, distant masses behind this same system of reference must appear to accelerate away from it at the same uniform acceleration.

Since there is no privileged system of reference in general relativity, an observer at rest with respect to this accelerated system is entitled to consider his system at rest and that the distant masses are undergoing the acceleration in question. And hence, he must conclude that the entire "space-time territory in question is under the sway of a gravitational field".

Look more closely at the profile of this equivalent gravitational field. All distant masses in the forward direction are accelerating towards the system of reference at the same uniform rate; while all distant masses in the backward direction are accelerating away from this same system at the same uniform rate. And this means that the source of this gravitational field must be located somewhere beyond the accelerating-away masses.

I hope, now, you're enlightened, and can see very clearly that acceleration and gravitation are indeed equivalent in every respect and exactly as Einstein concludes in his 1916-groundbreaking paper.

To M.F. Yagan:

It's well established that, in every case of free fall, observers feel no acceleration at all.
In fact, this was Einstein's original insight, which eventually led him to the development of the general theory of relativity:

"There are several ways to formulate the Principle of Equivalence, but one of the simplest is Einstein's original insight: he suddenly realized, while sitting in his office in Bern, Switzerland, in 1907, that if he were to fall freely in a gravitational field (think of a sky diver before she opens her parachute, or an unfortunate elevator if its cable breaks), he would be unable to feel his own weight. Einstein later recounted that this realization was the "happiest moment in his life", for he understood that this idea was the key to how to extend the Special Theory of Relativity to include the effect of gravitation. We are used to seeing astronauts in free fall as their spacecraft circles the Earth these days, but we should appreciate that in 1907 this was a rather remarkable insight".

http://csep10.phys.utk.edu/astr162/lect ... lence.html

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Stanley16
Stanley16

February 24th, 2008, 10:04 pm #8


The Equivalence of Acceleration and Gravitation in General Relativity



So far, you've demonstrated nothing and debunked nothing.
You just keep saying the 'accelerated & non-accelerated' frames of reference are not equivalent' over and over without really demonstrating anything.

So let me give you a head start to enlighten you!

When a system of reference undergoes uniform acceleration, distant masses in the front of it must appear to accelerate towards it at the same uniform acceleration. By contrast, distant masses behind this same system of reference must appear to accelerate away from it at the same uniform acceleration.

Since there is no privileged system of reference in general relativity, an observer at rest with respect to this accelerated system is entitled to consider his system at rest and that the distant masses are undergoing the acceleration in question. And hence, he must conclude that the entire "space-time territory in question is under the sway of a gravitational field".

Look more closely at the profile of this equivalent gravitational field. All distant masses in the forward direction are accelerating towards the system of reference at the same uniform rate; while all distant masses in the backward direction are accelerating away from this same system at the same uniform rate. And this means that the source of this gravitational field must be located somewhere beyond the accelerating-away masses.

I hope, now, you're enlightened, and can see very clearly that acceleration and gravitation are indeed equivalent in every respect and exactly as Einstein concludes in his 1916-groundbreaking paper.

To bob s:

Leaping off walls would not verify the uniformity of gravitational fields.

How to explain this simple observation of Einstein to you and to that AAF?

Okay!

Let us consider the space-time region of the inner solar system, i.e. from the center of the sun to the orbit of the planet Mars.

Within this region, the strength of the solar gravitational field varies considerably with each distance of one astronomical unit; why? That is because this space-time region is very close to the source of this gravitational field, which in this case is the sun.

Now, let's consider a space-time region of the same size as that of the space-time region of the inner solar system, but located at one light year way from the sun.

Within this second region, the strength of the solar gravitational field is practically uniform and shows very little variation with each distance of one astronomical unit; why? That is because this space-time region is very distant from the source of this gravitational field, which in this case is still the sun.


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Joined: February 22nd, 2008, 2:40 pm

February 25th, 2008, 2:20 pm #9


The Equivalence of Acceleration and Gravitation in General Relativity



So far, you've demonstrated nothing and debunked nothing.
You just keep saying the 'accelerated & non-accelerated' frames of reference are not equivalent' over and over without really demonstrating anything.

So let me give you a head start to enlighten you!

When a system of reference undergoes uniform acceleration, distant masses in the front of it must appear to accelerate towards it at the same uniform acceleration. By contrast, distant masses behind this same system of reference must appear to accelerate away from it at the same uniform acceleration.

Since there is no privileged system of reference in general relativity, an observer at rest with respect to this accelerated system is entitled to consider his system at rest and that the distant masses are undergoing the acceleration in question. And hence, he must conclude that the entire "space-time territory in question is under the sway of a gravitational field".

Look more closely at the profile of this equivalent gravitational field. All distant masses in the forward direction are accelerating towards the system of reference at the same uniform rate; while all distant masses in the backward direction are accelerating away from this same system at the same uniform rate. And this means that the source of this gravitational field must be located somewhere beyond the accelerating-away masses.

I hope, now, you're enlightened, and can see very clearly that acceleration and gravitation are indeed equivalent in every respect and exactly as Einstein concludes in his 1916-groundbreaking paper.

In re: "To bob s:
Leaping off walls would not verify the uniformity of gravitational fields."

No way Stanley 16. No way am I going to respond to your misdirecting the original experiment you posted. You described two bodies in "free flight" and concluded two bodies in "free fall"; you "assumed" a gravitational field. Admit that point and we can move on from there. Thank you.

bob s
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AAF
AAF

February 25th, 2008, 11:48 pm #10


The Equivalence of Acceleration and Gravitation in General Relativity



So far, you've demonstrated nothing and debunked nothing.
You just keep saying the 'accelerated & non-accelerated' frames of reference are not equivalent' over and over without really demonstrating anything.

So let me give you a head start to enlighten you!

When a system of reference undergoes uniform acceleration, distant masses in the front of it must appear to accelerate towards it at the same uniform acceleration. By contrast, distant masses behind this same system of reference must appear to accelerate away from it at the same uniform acceleration.

Since there is no privileged system of reference in general relativity, an observer at rest with respect to this accelerated system is entitled to consider his system at rest and that the distant masses are undergoing the acceleration in question. And hence, he must conclude that the entire "space-time territory in question is under the sway of a gravitational field".

Look more closely at the profile of this equivalent gravitational field. All distant masses in the forward direction are accelerating towards the system of reference at the same uniform rate; while all distant masses in the backward direction are accelerating away from this same system at the same uniform rate. And this means that the source of this gravitational field must be located somewhere beyond the accelerating-away masses.

I hope, now, you're enlightened, and can see very clearly that acceleration and gravitation are indeed equivalent in every respect and exactly as Einstein concludes in his 1916-groundbreaking paper.

Buy it or not, that velocity profile for defining gravitational fields is nature's most devastating blow to Einstein's General Relativity and Einstein's new physics. His theory of gravitation, quite simply, has been born dead; and no amount of sophistry in the world can revive it or make it viable or reasonable or suitable for doing physics.

In any case, the above defensive argument would not work for the following reasons:

{1} Einstein, in his gedanken experiment, can reduce the number of available co-ordinate systems as he wishes; but he cannot reduce or limit or control the number of falling distant masses. He knew this; thus he wrote in his 1916 Paper: "the above-mentioned relation of freely movable masses to K' may be interpreted equally well in the following way. The system of reference K' is unaccelerated, but the space-time territory in question is under the sway of a gravitational field, which generates the accelerated motion of the bodies relatively to K'."

{2} The idea of 'It-Just-Has-Been-Born-Now ' Field of Gravity is absurd and in direct contradiction with the whole notion of gravitation and the notion of physical reality in general. You can't build viable physical theories upon absurdities of this kind.

{3} No shortening in the time of measurements can make the velocity component and the velocity profile disappear or go away. The changes of the coming light always form the same integrated package regardless of how the measurements are performed.

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