## The Equivalence of Acceleration and Gravitation in General Relativity

nakayama
nakayama

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.

There is a picture with two small rockets. One is at a standstill on the ground and the other is accelerating upward vertically (in outer space). On the floor of each, acceleration 1g is acting. Now, an engine (the second engine) of each rocket starts. Propulsive force by jet downward is 1.2mg. Acceleration acting on the floor will be 1.2g in the first rocket and 2.2g in the second rocket. Gravity and inertial force will not be the same.

nakayama
nakayama

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.

There is a picture with two small rockets. One is at a standstill on the ground and the other is accelerating upward vertically (in outer space). On the floor of each, acceleration 1g is acting. Now, an engine (the second engine) of each rocket starts. Propulsive force by jet downward is 1.2mg. Acceleration acting on the floor will be 1.2g in the first rocket and 2.2g in the second rocket. Gravity and inertial force will not be the same.

nakayama
nakayama

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.

On the ground, g is acting. On the other side of the earth, it is the same. These two positions are not in accelerated motions that can explain this g. Gravity and inertial force will not be equivalent.

nakayama
nakayama

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.

Some books deny relativity of accelerated motions. Some books seem not to deny. The latter will mean the denial of inertial frames. But it is not mentioned. The counterattack will be afraid of. Inertial frames will deny a picture of a free fall. (local area will not be a refuge).

On a body, acceleration g is acting. From the circumstances, when cause is impossible to be gravity, it is inertial force and when cause is impossible to be inertial force, it is gravity. Namely, equivalence principle will be impossible (if there is only one case that shows the cause of g, equivalence principle will be impossible).

nakayama
nakayama

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.

Three elevator cabins start free fall. There is the interval of 0.1 seconds at the start time. How does relativity explain ?

nakayama
nakayama

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.

On three elevator cabins each lined up on the ground, acceleration 1 g, 2 g and 3 g acts. After certain time, the position from the starting line will be 0a, 1a, and 2a. If the starting line is accepted to be an inertial frame, the explanation will be possible only by gravity. By the way, position of a falling body (in free fall) is shown by formula 1/2gtt.

nakayama
nakayama

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.

Without conviction, I try to write a view. Apologize if it is wrong.

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 ?

Apology : In yesterday's post, a word "upward" was left out. Acceleration acts upward.

nakayama
nakayama

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.

P.S. (to Dec 18)

To grasp a free fall, position inside the cabin is not suitable. All can be grasped from the outside.

nakayama
nakayama

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.

On a plane, plural bodies are moving in uniform linear motions (inertial motions). It is possible to suppose that one of these bodies is at a standstill and is possible to rewrite motions of other bodies. But it will be impossible on plural bodies in moving in accelerated motions. Relativity of accelerated motions will be impossible. Free fall will not be inertial frame.

nakayama
nakayama

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.

Does principle of gravity and inertial force acting on a body differ according to the size of body ? Why infinite small area is specialized ?