## 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.

Two elevator cabins are falling. One is in a free fall and the other is falling on rails that are set on a face of steep slope (no friction). Each instrument shows value 0g and 0.1g (0.1g is not the value shown in the vertical direction). Equivalence principle is difficult to accept. By the way, value shown on the rails is 1g.

At everywhere of space, a surveillance network on acceleration, deceleration is spread. None can avoid.

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.

My conclusion

When a position of bodies is the same, gravity acts with the same g. At this position, gravity acts independently of the motion of bodies. In free fall also.
Inertial force is caused by acceleration (including deceleration) of bodies. At everywhere of space, a homogeneous mesh of net is spread and all follows (qualitatively, quantitatively). There is no exception. The net is sure. Yes, the same acceleration brings the same g and about it, gravity does not act at all. In free fall also.

Anonymous
Anonymous

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.

1 ”a position of bodies is the same” means ”a position of bodies in a gravitational field is the same”.
2 In free fall, the role of gravity is confusing, at a glance. But inertial force, acceleration both show concrete values. Gravity is only one of causes of acceleration. It’s role is secondary. Other forces can cause the same acceleration and inertial force.

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.

An elevator cabin that was hung with a rope is now falling in free fall. Tension of the rope is 0mg. Well, it is possible to control (in principle) this tension. Tension is controlled to be 0.2mg, 0.4mg, 0.6mg and 0.8mg. It will be natural to see that in all, the same gravity g is acting.

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.

An elevator cabin is hung by a crane. At the side of it, the second elevator cabin is passing in free fall. Passing speed is measured. This value is different from the value that was measured when the moon was just above. This difference can be explained with the gravity of the moon. On falling elevator cabin, gravity of the earth is acting also.

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.

It is said that gravity is waves and the speed is light speed. Then, in an elevator cabin in free fall, how about these ?

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.

Allow me to write frankly.

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.

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, an elevator cabin is accelerated with a rope to the left. Tension of the rope is 1.2mg. Next, this cabin is accelerated upward with a rope. Tension is the same 1.2mg. In this cabin, the same 1.2g is measured also. But, length of rope that was winded onto a reel will be different.

makayama
makayama

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 a space ship windowless, acceleration downward g is measured. The crew can vary the direction of the space ship (direction of center line relative to the celestial sphere). The crew will be able to show whether g is caused by gravity or by jet of the space ship.

But, the thing of this level will be written somewhere. Or, is it my misunderstanding ?

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). But, as shown in free fall, accelerated rocket is possible to draw parabola (If a condition of uniform linear motion of an observer is satisfied). A rocket on the ground is impossible.

Suppose that in gravitational sphere of the earth, the second rocket is in accelerated motion in various direction and at various g. Equivalence principle will be wrong.