Albert Einstein's Theory of General Relativity

When forced to summarize the general theory of relativity in one sentence:
Time and space and gravitation have no separate existence from matter. (Albert Einstein)


Introduction to Albert Einstein's General Relativity

On Accelerated Motion and Gravitation, 1915

General Relativity extends special Relativity to include accelerated Motion, and the relationship between Force, Mass and Acceleration (and Time and Dimension), thus it is important to first ask 'Why does Acceleration of Matter in Space Exist in our Universe?'
Only once we understand this can we possibly understand Albert Einstein's General Relativity.

The solution is quite simple. By understanding the Spherical In and Out Wave structure of Matter (SSWs) we deduce that any change in velocity of the In-Waves (Principle Two) causes a change in where the In-Waves meet at their Wave-Centers which we observe as the accelerated Motion of the particle. This is why acceleration exists and is defined as a change in velocity - because it is caused by a change in velocity of the In-Waves!
This change in the velocity of waves in Space is dependent upon the mass-energy density of space (for Gravitational Mass), and is the true physical cause of General Relativity and Albert Einstein's gravitational fields, thus explaining Albert Einstein's comment that;

(Special relativity is founded) on the basis of the law of the constancy of the velocity of light. But the general theory of relativity cannot retain this law. On the contrary, we arrived at the result that according to this latter theory the velocity of light must always depend on the co-ordinates when a gravitational field is present. (Albert Einstein)

Let us now consider the concept of Mass more closely.

On Inertial Mass and Gravitational Mass

Now for the principle of the conservation of mass. Mass is defined by the resistance that a body opposes to its acceleration (inert mass). It is also measured by the weight of the body (gravity mass). That these two radically different definitions lead to the same value for the mass of a body is in itself an astonishing fact. ... According to the principle - namely, that masses remain unchanged under any physical or chemical changes - the mass appeared to be the essential (because unvarying) quality of matter.

Physicists accepted this principle up to a few decades ago. But it proved inadequate in the face of the special theory of relativity. It was therefore merged with the energy principle. ... We might say that the principle of the conservation of energy, having preciously swallowed up that of the conservation of heat, now proceeded to swallow that of the conservation of mass - and holds the field alone. (Albert Einstein, 1946)

It is an unsatisfactory feature of classical mechanics that in its fundamental laws the same mass constant appears in two different roles, namely as 'inertial mass' in the law of motion, and as 'gravitational mass' in the law of gravitation. (Albert Einstein, 1936)

Let us then explain these two related forms of Mass, Inertial and Gravitational, as then we can clearly understand why they are equivalent

a) Inertial Mass

Imagine the Wave-Center (electron) of a Spherical Standing Wave (SSW) in free Space away from massive bodies. As the mass-energy density of space is the same in all directions, therefore the velocity of the In-Waves is the same from all directions and does not change, thus the In-Waves will always meet at the same point in Space (the Wave-Center). This is the physical foundation of inertial mass - a body remains stationary (it does not accelerate) if there is no change in the velocity of the In-Wave. (No forces act upon it.)

b) Gravitational Mass

Consider the same stationary Wave-Center (electron) of a SSW but now imagine a massive body, such as the Earth, placed to one side of the electron. What effect will this have?
We can consider this massive body, the earth, as a place of Space of very high mass-energy density of space. Therefore the velocity of In-Waves and Out-Waves (velocity of light) will be slower in this Space as Principle II states. This therefore causes a change in shape of the In-Waves (and Out-Waves) due to a slowing of their velocity in this high mass-energy density of Space resulting in a change in ellipsoidal shape or the SSW and results in the Wave-Center (electron) moving towards the Space of higher mass-energy density of space (the earth).

On the Equivalence of Inertial Mass and Gravitational Mass

And so we see that it is Principle Two which causes both gravitational mass and inertial mass. As it is the same principle that causes both, this explains their equivalence.
Let us now consider a simple example of this equivalence that will make it easier to understand.

Imagine standing in a room, the room existing in Space away from any stars or other massive bodies. We would be weightless in the Space as there would be no gravitational effect.

Now if we imagine the room being accelerated upwards, (relative to the floor), at 9.8m/s, as the occupant of the room, we would not be able to tell if we are being accelerated or if we are in the Earth's gravitational field.

Further, if there is a rope attached to an object hanging from the ceiling of the room, the tension in the rope could be due either to the inertia caused by accelerating the room, or to the object's weight due to its mass in a gravitational field. This is the empirical equivalence of gravitational and inertial mass.

The establishment of this general principle of relativity is made easier by a fact of experience that has long been known, namely, that the weight and the inertia of a body are controlled by the same constant (equality of inertial and gravitational mass). This hasty consideration suggests that a general theory of relativity must supply the laws of gravitation, and the consistent following up of the idea has justified our hopes. But the path was thornier than one might suppose, because it demanded the abandonment of Euclidean geometry. This is what we mean when we talk of the 'curvature of space'. The fundamental concepts of the 'straight line', the 'plane', etc., thereby lose their precise significance in physics.

In the general theory of relativity the doctrine of space and time, or kinematics, no longer figures as a fundamental independent of the rest of physics. The geometrical behaviour of bodies and the motion of clocks rather depend on gravitational fields which in their turn are produced by matter. (Albert Einstein, 1919)

The principle of the equivalence of inertial and gravitational mass could now be formulated quite clearly as follows: in a homogenous gravitation field all motions take place in the same way as in the absence of a gravitational field in relation to uniformly accelerated co-ordinate system. (Albert Einstein, 1934)

There is no reason to exclude the possibility of interpreting this behaviour as the effect of a 'true' gravitational field (principle of equivalence of inertial/gravitational mass). This interpretation implies that A is an 'inertial system', even though it is accelerated with respect to another inertial system. (Albert Einstein, 1950)

And so we see that Albert Einstein based his mathematics for gravitation, on the fact that Matter in an accelerated reference frame (Inertial Mass) behaved the same as Matter in a gravitational field (Gravitational Mass). (Principle of Equivalence.)
Thus if we know the Lorentz transformation for moving with a constant velocity, (which require linear transformations of the co-ordinate system) then we can calculate how the Lorentz transformation would change if the reference frame is now accelerated.

.. the theory of gravitation is based on the principle of equivalence discussed above and rests on the following consideration: according to the theory of special relativity, light has a constant velocity of propagation. If a light ray in a vacuum starts from a point, designated by the co-ordinates X1, X2, and X3 in a three dimensional co-ordinate system, at the time X4; it spreads as a spherical wave and reaches a neighbouring point (X1+dX1, X2+dX2, X3+dX3) at the time X4+dX4. Introducing the velocity of light, c, we write the expression:

dX12 + dX22 + dX32 = (c.dX4)2

This expression represents an objective relation between neighbouring space time points in four dimensions, and it holds for all inertial systems, provided the co-ordinate transformations are restricted to those of special relativity. The relation loses this form, however, if arbitrary continuous transformations of the co-ordinates are admitted in accordance with the principle of general relativity. (The equations expressing the laws of Nature must be covariant with respect to all continuous transformations of the co-ordinates. This is the principle of general relativity.) (Albert Einstein, 1954)

Albert Einstein is thus forced to use a curved (non-linear) co-ordinate system (rather than linear as per Special Relativity and the Lorentz Transformations), which he found from the work of Gauss and Riemann (called symmetrical tensors).

In order to account for the equality of inert and gravitational mass within the theory it necessary to admit non-linear transformations of the four co-ordinates. Mathematics suggests an answer which is based of the fundamental investigations of Gauss and Riemann. (Albert Einstein, 1954)

To introduce this non-linear transformation, it was necessary for Albert Einstein to adjust the velocity of light dependent upon the energy density (gravitational field) of Space. This is true, because it is this change in velocity of Wave Motion that is the cause of Gravity.
As Albert Einstein says; (and we know that we have repeated this quote - but it is important and misunderstood!)

(Special relativity is founded) on the basis of the law of the constancy of the velocity of light. But the general theory of relativity cannot retain this law. On the contrary, we arrived at the result that according to this latter theory the velocity of light must always depend on the co-ordinates when a gravitational field is present. (Albert Einstein, 1954)


Albert Einstein's Theory of General Relativity

Physics constitutes a logical system of thought which is in a state of evolution, whose basis (principles) cannot be distilled from experience by an inductive method, but can only be arrived at by free invention. (Albert Einstein, 1936)
Metaphysics of Relativity
Principles in Physics
Physical events, in Isaac Newton's view, are to be regarded as the motions, governed by fixed laws, of material points in space. This theoretical scheme is in essence an atomistic and mechanistic one. (Albert Einstein, 1940)
Einstein on Sir Isaac
Newton's Mechanics
The greatest change in the axiomatic basis of physics since Newton, was brought about by Michael Faraday's and James Clerk Maxwell's work on electromagnetic field phenomena. (Albert Einstein, 1954)
Michael Faraday's EM
Field, Maxwell Equation
Special relativity is based on the fact that Maxwell's equations (& thus the law of propagation of light in empty space) are converted into equations of the same form, when they undergo a Lorentz transformation. (Einstein)
Albert Einstein on the
Lorentz Transformations
 If, relative to K, K' is a uniformly moving co-ordinate system devoid of rotation, then natural phenomena run their course with respect to K' according to exactly the same general laws as with respect to K. This statement is called the principle of relativity. (Albert Einstein, 1954)
Albert Einstein's Theory
of Special Relativity
When forced to summarize the general theory of relativity in one sentence: Time and space and gravitation have no separate existence from matter. (Albert Einstein)
Albert Einstein's Theory
of General Relativity
But the idea that there exist two structures of space independent of each other, the metric-gravitational and the electromagnetic, was intolerable to the theoretical spirit. We are prompted to the belief that both sorts of field must correspond to a unified structure of space. (Einstein, 1954)
Solution to Problems
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Can we visualize a universe which is finite yet unbounded? ... The supreme task of the physicist is to arrive at those universal laws from which the cosmos can be built up by pure deduction. (Albert Einstein, 1954)
Einstein Cosmology
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All these fifty years of conscious brooding have brought me no nearer to the answer to the question, 'What are light quanta?' Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken. (Albert Einstein, 1954)
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I do not believe in a personal God and I have never denied this but have expressed it clearly. If something is in me which can be called religious then it is the unbounded admiration for the structure of the world so far as our science can reveal it. (Albert Einstein, 1954)
Einstein on Theology
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The true value of a human being is determined by the measure and sense in which they have obtained liberation from the self. We shall require a substantially new manner of thinking if humanity is to survive. (Einstein, 1954)
Albert Einstein Quotes
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The ideals which have lighted my way, and time after time have given me new courage to face life cheerfully, have been Kindness, Beauty and Truth. (Albert Einstein, 1954)
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Albert Einstein"When forced to summarize the general theory of relativity in one sentence: Time and space and gravitation have no separate existence from matter. ... Physical objects are not in space, but these objects are spatially extended. In this way the concept 'empty space' loses its meaning. ... The particle can only appear as a limited region in space in which the field strength or the energy density are particularly high. ...
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Biography: Geoffrey Haselhurst, Philosopher of Science, Theoretical Physics, Metaphysics, Evolution. Our world is in great trouble due to human behaviour founded on myths and customs that are causing the destruction of Nature and climate change. We can now deduce the most simple science theory of reality - the wave structure of matter in space. By understanding how we and everything around us are interconnected in Space we can then deduce solutions to the fundamental problems of human knowledge in physics, philosophy, metaphysics, theology, education, health, evolution and ecology, politics and society.

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