FOR THOSE WHO ARE WISHING FOR AN OFF TOPIC POST

This isn't it, as this post pertains to the physical dynamics of a
round wooden cylindrical object (bat) making kinetic contact, with a
leather sphere (baseball) and the following gravitational dynamics
that determine the resulting trajectory of the sphere in
question.........enjoy


Physics: Albert Einstein's Theory of Relativity
Simplifying the Metaphysics of Einstein's Special and 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)

Physical objects are not in space, but these objects are spatially
extended (as fields). In this way the concept 'empty space' loses its
meaning. ... The field thus becomes an irreducible element of physical
description, irreducible in the same sense as the concept of matter
(particles) in the theory of Newton. ... The physical reality of space
is represented by a field whose components are continuous functions of
four independent variables - the co-ordinates of space and time. Since
the theory of general relativity implies the representation of
physical reality by a continuous field, the concept of particles or
material points cannot play a fundamental part, nor can the concept of
motion. The particle can only appear as a limited region in space in
which the field strength or the energy density are particularly high.
(Albert Einstein, Metaphysics of Relativity, 1950)

Physics constitutes a logical system of thought which is in a state
of evolution, whose basis (principles) cannot be distilled, as it
were, from experience by an inductive method, but can only be arrived
at by free invention. The justification (truth content) of the system
rests in the verification of the derived propositions (a priori/
logical truths) by sense experiences (a posteriori/empirical
truths). ... Evolution is proceeding in the direction of increasing
simplicity of the logical basis (principles). .. We must always be
ready to change these notions - that is to say, the axiomatic basis of
physics - in order to do justice to perceived facts in the most
perfect way logically. (Albert Einstein, Physics and Reality, 1936)


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Introduction to Albert Einstein's Theory of Relativity - Newton's
Mechanics - Newton / Time Particles Forces - Newton / Light - Newton's
Law of Inertia - Faraday EM Force Field - Maxwell's Equations -
Lorentz / Electron - Lorentz Transformations - Albert Einstein's
Theory of Relativity - Special Relativity - General Relativity -
Summary of Einstein's Relativity - Top of Page

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Introduction
Hi Everyone (June, 2007). I am currently re-writing all the main pages
on this website to simplify them / make them a bit more human
friendly. I realise this page is quite long - but it contains a very
good summary of the evolution of Physics and how this led to
Einstein's theory of relativity. Most importantly it shows how we can
simplify his foundations of representing matter as continuous fields
in space-time, to waves in continuous space. It is actually a very
simple obvious solution once realised - but like all things it takes a
while to adjust to new knowledge. It does lead to a very simple
sensible foundation for understanding physical reality, and thus how
you exist in the universe. So I think it is worth the effort!
Geoff Haselhurst

The development during the present century is characterized by two
theoretical systems essentially independent of each other: the theory
of relativity and the quantum theory. The two systems do not directly
contradict each other; but they seem little adapted to fusion into one
unified theory. For the time being we have to admit that we do not
possess any general theoretical basis for physics which can be
regarded as its logical foundation. (Albert Einstein, 1940)

As is well known, there are two fundamental theories which are the
pillars of modern Physics - Albert Einstein's Special and General
Relativity (1905, 1915) and Quantum Theory (1900-1930). Further,
Albert Einstein's General Relativity (on Gravitation and accelerated
motion) then laid the foundations for modern Cosmology (as gravity is
a phenomena that extends across the universe - though we now realise
that charge also plays a significant role in the evolution of the
universe).

Now it is also universally known that Albert Einstein's Relativity
Theory is famous for being incomprehensible. And it even seems that
some scientists enjoy this incomprehensibility of the universe.
However, philosophy teaches us that things become absurd when we have
errors in our language and metaphysical foundations. Thus the solution
is not to have endless arguments (and amusements) over these
absurdities, but rather, to go back to the foundations and ensure that
you have not made any errors.

Having done this, it is clear that there is in fact a more simple way
of describing reality than Einstein's assumption of Continuous Fields
in Space-Time. While Einstein was correct in rejecting the 'particle'
concept we now realise that the 'continuous field' concept (i.e.
Faraday, Maxwell, Lorentz, and which Einstein used in his Theory of
Relativity) is also incorrect.
Instead, it is simpler (and solves many problems) to describe reality
from One thing existing, Space, and its Properties as a Wave Medium
for Spherical Waves that form Matter. This is explained in the
articles listed at the top of this page.

So you will find our pages a little different than most, because we
are describing reality (and thus explaining Albert Einstein's Theory
of Relativity) from a slightly different foundation than the current
paradigm of 'particles' and 'fields' in 'Space-Time', to a more simple
foundation of Spherical Standing Waves in Space. And we are describing
a theory that can now be sensibly understood (so if you want absurdity
and its sensations that postmodern physics seems to enjoy, this is not
a good website for you.)

Though I am primarily a philosopher / metaphysicist I have read
Einstein a great deal, he is probably the philosopher / scientist whom
I have most affection for (and I do have great affection for many
philosophers). And one thing that Einstein understood well was the
importance of understanding the history and evolution of knowledge. As
a philosopher strongly influenced by evolution, I cannot agree more,
that it is critical (and now neglected) to study the history and
evolution of knowledge if we are to correctly understand it, and thus
have any hope of correcting the errors (and there are clearly many
errors in modern physics, as there are in philosophy and metaphysics).

Certainly, by understanding the foundation of knowledge in physics at
the time Einstein developed his theory of relativity, we can now
easily understand why he chose the path of representing matter as
Continuous Spherical 'Fields' in Space-Time. And of most significance
we can now also understand how there is a more simple solution, by
describing matter in terms of Spherical Waves in Continuous Space,
that clearly explains and solves the problems caused by Einstein's
failure to find a pure 'field theory of matter'.

Thus we must begin by considering the evolution of the main ideas and
concepts that lay at the metaphysical foundations of Albert Einstein's
Theory of Relativity. i.e. Newton's Mechanics (1687), Faraday's
Electromagnetic Field Theory (1832), Maxwell's Equations (1876) and
Lorentz's Theory of the Electron (1900). So this page follows their
knowledge, which makes for an interesting little journey to read
about! And most of the summary comes from Albert Einstein himself - so
it is a very good quality / astute history of physics! I hope you
enjoy the journey.

Geoff Haselhurst


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Introduction to Albert Einstein's Theory of Relativity - Newton's
Mechanics - Newton / Time Particles Forces - Newton / Light - Newton's
Law of Inertia - Faraday EM Force Field - Maxwell's Equations -
Lorentz / Electron - Lorentz Transformations - Albert Einstein's
Theory of Relativity - Special Relativity - General Relativity -
Summary of Einstein's Relativity - Top of Page

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The Particle/Space Duality of Newton's Mechanics (1687)
We begin with a very good summary of Atomism, as their ultimate
conclusion, that the 'particle' is a conceptual tool for the logical
positivist / mathematical physicist, but does not physically exist, is
absolutely correct. (As the Principles state, the 'particle' effect is
Caused by the Wave-Center of the Spherical Standing Wave.)

Atomism arose as an explanatory scheme with the ancient Greeks (around
400BC), Leucippus and Democritus, and Epicurus, and the Roman poet,
Lucretius. At the most fundamental level atomism is the belief that
all phenomena are explicable in terms of the properties and behaviour
of ultimate, elementary, localized entities (or 'fundamental
particles'). Thus it prescribes a strategy for the construction of
scientific theories in which the behaviour of complex bodies is to be
explained in terms of their component parts. That strategy has led to
many of the successes of modern physical science, though these do not
prove that there actually are 'ultimate entities' of the type
postulated by atomism.
Their (the atomists) analysis goes 'behind' the appearance of minute,
unchangeable and indestructible 'atoms' separated by the emptiness of
'the void'. It is the void which is said to make change and movement
possible. All apparent change is simply the result of rearrangements
of the atoms as a consequence of collisions between them. This seems
to lead to mechanical determinism, though, in an attempt to leave room
for freewill, Epicurus and Lucretius postulated that atoms might
'deviate' in their courses.

Read the article on Free Will

However if 'what exists' is 'atoms', what of the 'void'? In different
ways both Aristotle and Descartes denied that there could be such a
thing as literally 'empty space'. Physically therefore they saw the
world as a plenum. Atomism was also associated with atheism, since as
Lucretius put it, 'Nothing can ever be created out of nothing, even by
divine power.' Conversely no thing can ever become nothing - so the
atomists proposed a strict principle of conservation of matter.
The attempt of the ancient atomists to solve a metaphysical problem
about the nature of change resulted in a brilliantly fruitful strategy
for the construction of theories in the physical sciences. However
there are unanswered philosophical objections to atomism and the very
successes it has stimulated suggest that 'the stuff of the world'
cannot ultimately be understood in terms of atomism. A thoroughgoing
positivism will continue to hold that 'atomic theories' are simply
devices for talking about observable phenomena. (The Concise
Encyclopedia of Western Philosophy and Philosophers, 1991)

With this understanding of the 'particle' in mind, and with Albert
Einstein as our guide, we shall now explain and solve Newton's
Mechanics, and thus also appreciate how this theory profoundly (though
incorrectly) shaped the face of modern physics.


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Introduction to Albert Einstein's Theory of Relativity - Newton's
Mechanics - Newton / Time Particles Forces - Newton / Light - Newton's
Law of Inertia - Faraday EM Force Field - Maxwell's Equations -
Lorentz / Electron - Lorentz Transformations - Albert Einstein's
Theory of Relativity - Special Relativity - General Relativity -
Summary of Einstein's Relativity - Top of Page

--------------------------------------------------------------------------------

Sir Isaac Newton Concepts of Time, Particles, and Forces
(Instant Action-at-a-Distance)
We begin with two very famous quotes from Newton on Absolute Space and
Time. Let us first say that Newton's comments on Absolute Space being
the foundations of the Relative Motions of Matter in Space is
absolutely correct and very astute as Newton effectively predicts the
evolution of relativity (that it is easier to measure the motion of
matter relative to other matter, rather than to Space itself!)

Absolute Space, in its own nature, without regard to any thing
external, remains always similar and immovable. Relative Space is some
moveable dimension or measure of the absolute spaces; which our senses
determine, by its position to bodies; and which is vulgarly taken for
immovable space.

.... And so instead of absolute places and motions, we use relative
ones; and that without any inconvenience in common affairs; but in
Philosophical disquisitions, we ought to abstract from our senses, and
consider things themselves, distinct from what are only sensible
measures of them. For it may be that there is no body really at rest,
to which the places and motions of others may be referred.

.... Absolute, True, and Mathematical Time, of itself, and from its own
nature flows equably without regard to any thing external, and by
another name is called Duration: Relative, Apparent, and Common Time
is some sensible and external (whether accurate or unequable) measure
of Duration by the means of motion, which is commonly used instead of
True time; such as an Hour, a Day, a Month, a Year.

.... For the natural days are truly unequable, though they are commonly
consider'd as equal, and used for a measure of time: Astronomers
correct this inequality for their more accurate deducing of the
celestial motions. It may be, that there is no such thing as an
equable motion, whereby time may be accurately measured. All motions
may be accelerated and retarded, but the True, or equable progress, of
Absolute time is liable to no change. The duration or perseverance of
the existence of things remains the same, whether the motions are
swift or slow, or none at all. (Newton, 1687)

Newton is also largely correct that Time is intimately connected to
Motion, for Time is ultimately caused by the Wave-Motions of Space. It
is also correct to assume an absolute Time (like QT rather than
Relativity) such that we have a constant reference to measure the
changing velocity of wave-motion. (But Time does not exist as a 'thing
in itself' like Newton thought!)

Let us now consider Albert Einstein's analysis of Newton's Mechanics
(which is lucid and logical as reflects the greatness of Albert
Einstein).

The first attempt to lay a uniform theoretical foundation was the work
of Newton. In his system everything is reduced to the following
concepts:
i) Mass points with invariable mass
ii) Instant action-at-a-distance between any pair of mass points
iii) Law of motion for the mass point.
Physical events, in 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. There was not,
strictly speaking, any all-embracing foundation, because an explicit
law was only formulated for the actions-at-a-distance of gravitation;
while for other actions-at-a-distance nothing was established a priori
except the law of equality of actio and reactio. Moreover, Newton
himself fully realized that time and space were essential elements, as
physically effective factors, of his system. (Albert Einstein, 1940)

We now realise his obvious error was to introduce discrete 'particles'
with Motion, rather than the Motion of Space itself, i.e. Spherical
Standing Wave Motion, which creates the 'particle effect' at its Wave-
Center.

Newton's endeavours to represent his system as necessarily conditioned
by experience and to introduce the smallest possible number of
concepts not directly referable to empirical objects is everywhere
evident; in spite of this he set up the concept of absolute space and
absolute time. For this he has often been criticized in recent years.
Therefore, in addition to masses and temporally variable distances,
there must be something else that determines motion. That something he
takes to be relation to absolute space. He is aware that space must
possess a kind of physical reality if his laws of motion are to have
any meaning, a reality of the same sort as material points and their
distances. (Albert Einstein, 1954)

As stated in the first chapter, Albert Einstein considered matter to
be spatially extended (and represented by Spherical Force Fields) thus
he did not believe in the existence of a fundamental Space or Time
that was separate from Matter. As with Leibniz and Mach, Albert
Einstein believed that all motion of matter in Space could instead be
understood as motion of matter relative to other matter, thus the
concept of an absolute Space became unnecessary.

In Newtonian physics the elementary theoretical concept on which the
theoretical description of material bodies is based is the material
point, or particle. Thus matter is considered a priori to be
discontinuous. This makes it necessary to consider the action of
material points on one another as action-at-a-distance. Since the
latter concept seems quite contrary to everyday experience, it is only
natural that the contemporaries of Newton - and indeed Newton himself
- found it difficult to accept. Owing to the almost miraculous success
of the Newtonian system, however, the succeeding generations of
physicists became used to the idea of action-at-a-distance. Any doubt
was buried for a long time to come. (Albert Einstein, 1950)

The solution though is obvious once known - to discard the discrete
particle in Space and replace it with the Spherical Standing Wave
(SSW) in Space. Then instant action-at-a-distance between discrete
particles becomes action-at-a-distance between the In and Out-Waves of
the Wave-Centers 'particles' in Space.
This leads to a clear understanding of how matter interacts with other
matter at-a-distance in Space, as it is the interaction of the In-
Waves and Out-Waves with other SSWs (and particularly their Wave-
Centers) that explains all matter to matter interactions in Space.
These interactions are limited by the velocity of the In-Waves and Out-
Waves which is the velocity of light c. Thus actions-at-a-distance are
not instantaneous as Newton had assumed, but are limited by the
velocity of the In-Waves (velocity of light c, as Albert Einstein
realised).
On the other hand, with respect to an absolute Space, it is one
purpose of this article to show that in fact Newton was correct, there
does exist a fundamental physical Space which acts as a wave medium
and necessarily connects all things. Newton's error was to further
assume the existence of the motion of material particles in this
Space, rather than the (Spherical) Wave-Motion of Space itself.

Newton's error, of assuming too many existents, leads to two
insurmountable problems;

a) How does matter exist as a discrete particle in Space and move
through the Space around it?
As Born explains;

One obvious objection to the hypothesis of an elastic Aether (Space)
arises from the necessity of ascribing to it the great rigidity it
must have to account for the high velocity of Waves. Such a substance
would necessarily offer resistance to the motion of heavenly bodies,
particularly to that of planets. Astronomy has never detected
departures from Newton's Laws of Motion that would point to such a
resistance. (Born, 1924)

While Born is correct that Space is very rigid and this explains the
high Wave-Velocity, he (along with most physicists) mistakenly assumes
that separate 'particles' exist in this Space, and thus it is
inconceivable that Space itself can exist as it would resist the
motion of these particles. The obvious solution is to replace the
concept of matter existing as discrete particles with matter existing
as Spherical Standing Waves in this Space, thus the motion of the
particle becomes the apparent motion of successive Wave-Centers.

b) How do these discrete particles gravitationally act-at-a-distance
with other particles separate in Space?
Newton simply assumed that discrete particles could act instantly on
other particles at-a-distance in Space (Newton's instantaneous action-
at-a-distance) though he was well aware of this problem as he explains
in his famous letter to Bentley;

It is inconceivable that inanimate brute matter should, without
mediation of something else which is not matter, operate on and affect
other matter without mutual contact. ... That gravity should be
innate, inherent and essential to matter, so that one body may act
upon another at-a-distance, through a vacuum, without the mediation of
anything else by and through which their action may be conveyed from
one to another, is to me so great an absurdity that I believe no man,
who has in philosophical matters a competent faculty of thinking, can
ever fall into it.
So far I have explained the phenomena by the force of gravity, but I
have not yet ascertained the cause of gravity itself. ... and I do not
arbitrarily invent hypotheses. (Newton. Letter to Richard Bentley 25
Feb. 1693)

Action-at-a-distance has puzzled philosophers and physicists since
Newton first assumed instantaneous action-at-a-distance for
gravitational Mass. For if matter is assumed to be a tiny particle,
how could it interact (instantly!) with other matter at a distance in
Space (across the entire universe)?

For example, how do we, here on earth, sense the heat and light from
the sun so distant in Space? We now realize that matter is not small,
it is large. Indeed Albert Einstein was very close to the truth -
matter is spherically spatially extended, thus as we have said,
Newton's instant action-at-a-distance from a particle becomes action-
at-a-distance from the Wave-Center of Spherical Standing Waves in
Space, due to the interaction and change in velocity of their In and
Out-Waves.

(i.e. As a consequence of Principle Two, the In-Waves of the Spherical
Standing Wave in Space interact with other SSWs in Space (particularly
their high Wave-Amplitude/Density Wave-Centers) as they flow in
through them and change their velocity accordingly. This determines
where each successive In-Wave will ultimately meet at their respective
Wave-Center (i.e. the future position of the Wave-Center / 'particle')
which causes the apparent motion (acceleration) of the 'particle'.
This then explains action-at-a-distance (from the Wave-Center) and why
it is not instantaneous, but rather, is limited by the velocity of the
In-Waves / Velocity of light c.)


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Introduction to Albert Einstein's Theory of Relativity - Newton's
Mechanics - Newton / Time Particles Forces - Newton / Light - Newton's
Law of Inertia - Faraday EM Force Field - Maxwell's Equations -
Lorentz / Electron - Lorentz Transformations - Albert Einstein's
Theory of Relativity - Special Relativity - General Relativity -
Summary of Einstein's Relativity - Top of Page

--------------------------------------------------------------------------------

Sir Isaac Newton's Concept of Light as a Particle
It is true that Newton tried to reduced light to the motion of
material points in his corpuscular theory of light. Later on, however,
as the phenomena of finite velocity, polarization, diffraction, and
interference of light forced upon this theory more and more unnatural
modifications, Huygens' undulatory wave theory of light prevailed.
(Albert Einstein, 1936)

Albert Einstein clearly realized, as did physicists of the time, that
the particle concept of light is unable to explain experimental
phenomena like polarization, diffraction, and interference, which are
obviously explained by wave phenomena. This divide between Newton's
particle conception of light and Huygens' wave theory of light was
decided by Thomas Young's (1801) famous double slit experiment which
showed interference patterns that could only be explained by a wave
theory. For how could a single particle travel through two slits and
interfere with itself?
Further, as Albert Einstein argues, it is impossible to explain how
particles of matter emit and absorb particles of light.

What in that case becomes of the material points of which light is
composed when the light is absorbed? (Albert Einstein, 1931)

So while Newton's particle theory for light and matter had substantial
logical (mathematical) success at explaining certain phenomena,
particularly the orbits of planets, it clearly produced many paradoxes
due to its fundamental error of assuming the existence of discrete
particles.

Yet no serious doubt of the mechanical (particle) foundation of
physics arose, in the first place because nobody knew where to find a
foundation of another sort. Only slowly, under the irresistible
pressure of facts, there developed a new foundation of physics,
'Field' physics. (Albert Einstein, 1954)

We shall shortly consider the 'Field' physics, but before this we need
to finally explain Newton' famous Law of Inertia;
An object at rest will remain at rest and an object in motion will
continue in motion with a constant velocity unless it experiences a
net external force. (Serway, 1992)


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Introduction to Albert Einstein's Theory of Relativity - Newton's
Mechanics - Newton / Time Particles Forces - Newton / Light - Newton's
Law of Inertia - Faraday EM Force Field - Maxwell's Equations -
Lorentz / Electron - Lorentz Transformations - Albert Einstein's
Theory of Relativity - Special Relativity - General Relativity -
Summary of Einstein's Relativity - Top of Page

--------------------------------------------------------------------------------

Sir Isaac Newton's Law of Inertia F = m.a
Mass is caused by the Relationship between Change in Velocity c of the
In-Wave and the resultant Change in Location of the Wave-Center /
Acceleration of the 'Particle'.

By understanding the properties of space and how they effect the
velocity of waves we can now simply explain Newton's Law of Inertia
F=m.a which is at the very heart of Physics.

i) Any Change in Velocity of the Spherical In-Waves from One Direction
Changes where these In-Waves meet at their respective Wave-Center
which we see as the Accelerated Motion of the 'Particle'. (This is the
cause of matter interactions / forces / field effects, i.e. Newton's
Law of Inertia F=m.a)

ii) The Spherical In-Waves are formed from the Huygens' Combination of
Out-Waves from All other Matter in our Finite Spherical Universe.
(This is the Cause of Mach's Principle - the Mass (Wave-Density) of an
object is determined by all the other matter in the Universe.)

This explains how matter 'particles' (Wave-Centers) are 'Necessarily
Connected' to other Matter in the Space around them, and thus leads to
the explanation of 'Force' and Newton's famous Law of Inertia Force =
Mass * Acceleration (F=m.a)

Consider the Spherical In-Waves of One Electron / Spherical Standing
Wave (SSW).

If there is no change in the velocity of the Spherical In-Wave then
there can be no change in the apparent motion of the Wave-Center /
'particle'.
i.e. If the Spherical In-Waves comes in with the same velocity in all
directions then the Wave-Center / 'particle' will remain stationary in
the same place in Space.

Conversely, if there is a change in velocity of the Spherical In-Waves
in one direction then this will also cause a change in the location
where the wave center 'particle' forms in Space which we see as the
motion (acceleration) of the Wave-Center / 'particle'.

So when we consider the future motion of a particle we must actually
consider the velocity of the Spherical In-Waves only, for it is
logical that this alone determines where these In-Waves will meet at
their future Wave-Centers.

This is the underlying cause of the Law of Inertia and the concepts of
force, mass and acceleration. We can now translate the language of
physics into the language of the WSM. When we apply a Force to an
object we are in fact changing the velocity of their In-Waves, and
this causes the wave center to re-position. It is this relationship
between the change in velocity of In-Waves and the change in location
(apparent motion / acceleration) of the Wave-Center that causes the
concept of Mass and explains the necessary connection between
apparently discrete matter particles. (i.e. Action-at-a-distance).

Though this is perhaps a little confusing upon first reading, with
time it becomes more obvious that the Spherical Wave Structure of
Matter simplifies and solves the problems of Newton's Mechanics by
removing the concept of discrete 'particles' and replacing this with
Spherical Wave Motions of Space whose Wave-Center's Cause the
'Particle' Effect.

Let us now consider the next major evolution in the theoretical
foundation of Physics, Faraday's Electromagnetic Force Fields.


--------------------------------------------------------------------------------

Introduction to Albert Einstein's Theory of Relativity - Newton's
Mechanics - Newton / Time Particles Forces - Newton / Light - Newton's
Law of Inertia - Faraday EM Force Field - Maxwell's Equations -
Lorentz / Electron - Lorentz Transformations - Albert Einstein's
Theory of Relativity - Special Relativity - General Relativity -
Summary of Einstein's Relativity - Top of Page

--------------------------------------------------------------------------------

Faraday's Electromagnetic Force Field, Particle/Field Duality (1832)
Faraday's Continuous Electromagnetic Force Field is a Mathematical
Approximation of Many Discrete Standing Wave Interactions.

The greatest change in the axiomatic basis of physics - in other
words, of our conception of the structure of reality - since Newton
laid the foundation of theoretical physics was brought about by
Faraday's and Maxwell's work on electromagnetic field phenomena.
(Albert Einstein, 1931)

Faraday (1832) developed the mathematical concept of the 'electro-
magnetic force field' as a way of mathematically describing action-at-
a-distance for charged particles (i.e. electrons and protons). This is
a continuous mathematical 'plotting' of the effects (forces and thus
accelerated motions) that matter has on other matter in the Space
around it, thus it is a description of effects rather than causes
(Inductive / a posteriori rather than deductive / a priori. And this
becomes important when you read Hume and Kant, for they explain that
the ultimate Principles of Physics must be a priori, not a
posteriori!).

This field concept replaced Newton's instant action-at-a-distance
between discrete particles. Importantly, the electromagnetic (e-m)
field is a vector (directional) quantity that defines force and
direction of acceleration of many charged particles upon one another.
It is continuous in the sense that the distance and force between
particles can vary by infinitely small amounts.
For example, electrons near one another in Space experience a mutual
force of repulsion and this behaviour can be mathematically described
using Faraday's e-m field which quantifies this force and describes
how it varies with distance and direction. As Albert Einstein
explains;

Faraday must have grasped with unerring instinct the artificial nature
of all attempts to refer electromagnetic phenomena to actions-at-a-
distance between electric particles reacting on each other. How was
each single iron filing among a lot scattered on a piece of paper to
know of the single electric particles running round in a nearby
conductor?
All these electric particles together seemed to create in the
surrounding space a condition which in turn produced a certain order
in the filings. These spatial states, today called fields, would, he
was convinced, furnish the clue to the mysterious electromagnetic
interactions. He conceived these fields as states of mechanical stress
in an elastically distended body (ether/space). For at that time this
was the only way one could conceive of states that were apparently
continuously distributed in space. The peculiar type of mechanical
interpretation of these fields remained in the background - a sort of
placation of the scientific conscience in view of the mechanical
(Newtonian) tradition of Faraday's time. (Albert Einstein, 1940)

It seems that the 'electromagnetic force field' is a poorly understood
concept which causes considerable confusion. It is quite basic though,
as it is nothing more than a mathematical description of how matter
affects and moves other matter in the Space around it. This
mathematical 'force field' is a very powerful tool for mathematical
physicists (as is the particle) and as a consequence many physicists
(including Faraday, Maxwell, and Lorentz) imagined this 'field' to be
real and therefore assumed that an 'Aether' (made up of many smaller
particles!) must exist in Space as the medium for this 'field'. Born
describes the ether as follows;

The undulatory, or wave theory, on the other hand, sets up an analogy
between the propagation of light and the motion of waves on the
surface of water or sound waves in air. For this purpose it has to
assume the existence of an elastic medium that permeates all
transparent bodies; this is the luminiferous ether. The individual
particles of this substance merely oscillate about their positions of
equilibrium. That which moves on as the light wave is the state of
motion of the particles and not the particles themselves. (Born,
1924)

In fact there is no 'ether' simply because there are no 'force
fields'. Both are mathematical constructions (rather clumsy and
confusing ones at that) to try to explain how matter 'particles'
interacted with other 'particles' in the space around them. Once we
understand the Spherical Wave Structure of Matter in Space though,
then we no longer need these mathematical ideas, instead we realise
that Space itself is a continuous wave medium (which necessarily
connects all things) and there are no such things as discrete
particles.


--------------------------------------------------------------------------------

Introduction to Albert Einstein's Theory of Relativity - Newton's
Mechanics - Newton / Time Particles Forces - Newton / Light - Newton's
Law of Inertia - Faraday EM Force Field - Maxwell's Equations -
Lorentz / Electron - Lorentz Transformations - Albert Einstein's
Theory of Relativity - Special Relativity - General Relativity -
Summary of Einstein's Relativity - Top of Page

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Maxwell's Equations & the Finite Velocity of Light Waves (1876)
When Maxwell (1876) used this field theory to assume that light was an
Electromagnetic Wave, and then correctly deduced the finite velocity
of light, it was a powerful logical argument for the existence of the
electromagnetic force field, and that light was a wave like change in
the field (electromagnetic radiation) that propagated with the
velocity of light c through the ether.
In fact Maxwell was simply confirming that all Wave-Center to Wave-
Center (particle) interactions are not instantaneous as Newton
assumed, but are limited by the velocity of the In-Waves which is the
Velocity of Light c.
So while Maxwell misunderstood the true nature of the waves (which are
physical waves in Space rather than mathematical vector e-m waves), he
is largely correct. This new knowledge was significant as it
established the importance of the finite velocity of light c and
further enhanced the field theory, thus rejecting Newton's theory of
particles and instant action-at-a-distance.

The precise formulation of the time space laws of those fields was the
work of Maxwell (1870s). Imagine his feelings when the differential
equations he had formulated proved to him that the electromagnetic
fields spread in the form of polarized waves and with the speed of
light! To few men in the world has such an experience been
vouchsafed.
Only after Hertz (1888) had demonstrated experimentally the existence
of Maxwell's electromagnetic waves did resistance to the new theory
break down. And what was true for electrical action could not be
denied for gravitation. Everywhere Newton's (instant) actions-at-a-
distance gave way to fields spreading with finite velocity.
At that thrilling moment he surely never guessed that the riddling
nature of light, apparently so completely solved, would continue to
baffle succeeding generations. (Albert Einstein, 1954)

And this is true. Because they were using a mathematical construction
of a continuous e-m wave, rather than the true Spherical Standing
Wave, they were in for a rather disturbing discovery not long
thereafter. For standing wave interactions only occur at discrete
frequencies, like notes on the string of a guitar, thus while the true
Spherical Standing Wave Structure of Matter predicts that wave
interactions will be discrete, the continuous e-m wave does not
anticipate this.
Thus when Max Planck (1900) discovered that there are only certain
allowed discrete energy states for electrons in molecules and atoms,
and that light is only ever emitted and absorbed by electrons in
discrete amounts or 'quanta', contrary to Maxwell's formulation that
light is a continuous electromagnetic wave, then this caused a
fundamental problem for the field theory that was never resolved. It
is only now, with knowledge of the true foundations of physics and
reality, that we can understand, and thus anticipate and correct, the
errors of contemporary modern physics. (This is explained in more
detail in Quantum Theory)


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Introduction to Albert Einstein's Theory of Relativity - Newton's
Mechanics - Newton / Time Particles Forces - Newton / Light - Newton's
Law of Inertia - Faraday EM Force Field - Maxwell's Equations -
Lorentz / Electron - Lorentz Transformations - Albert Einstein's
Theory of Relativity - Special Relativity - General Relativity -
Summary of Einstein's Relativity - Top of Page

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Lorentz's Theory of the Electron (1900)
Hendrik Lorentz in The Theory of the Electron describes the electron
as a spherical spatially extended electromagnetic field about a
charged particle (electron) in the ether. Thus inadvertently he
continued this error of assuming the 'field' to be real, and described
the electron as a charged particle that somehow 'generated' a
spherical spatially extended 'field' in the ether around it. This was
profound simply because Albert Einstein used Lorentz's foundations to
develop his 'field' theory of matter which founds his theory of
Relativity. As Albert Einstein explains;

At the turn of the century the theoretical physicists of all nations
considered H.A. Lorentz as the leading mind among them, and rightly
so. The physicists of our time are mostly not fully aware of the
decisive part which H.A. Lorentz played in shaping the fundamental
ideas in theoretical physics. The reason for this strange fact is that
Lorentz's basic ideas have become so much a part of them that they are
hardly able to realize quite how daring these ideas have been and to
what extent they have simplified the foundations of physics.
Then came H.A. Lorentz's decisive simplification of the theory. He
based his investigations with unfaltering consistency upon the
following hypotheses:
The seat of the electromagnetic field is the empty space. In it there
are only one electric and one magnetic field vector. This field is
generated by atomistic electric charges upon which the field in turn
exerts ponderomotive forces. The only connection between the
electromagnetic field and ponderable matter arises from the fact that
elementary electric charges are rigidly attached to atomistic
particles of matter. For the latter Newton's law of motion holds.
Upon this simplified foundation Lorentz based a complete theory of all
electromagnetic phenomena known at the time, including those of the
electrodynamics of moving bodies. It is a work of such consistency,
lucidity, and beauty as has only rarely been attained in an empirical
science. (Albert Einstein, 1954)

Lorentz imagined that the ether exists throughout Space and that
matter/fields existed as a state of this ether.

Indeed one of the most important of our fundamental assumptions must
be that the ether not only occupies all space between molecules,
atoms, or electrons, but that it pervades all these particles. We
shall add the hypothesis that, though the particles may move, the
ether always remains at rest.
I cannot but regard the ether, which can be the seat of an
electromagnetic field with its energy and its vibrations, as endowed
with a certain degree of substantiality, however different it may be
from all ordinary matter. (Lorentz, The Theory of the Electron, 1906)

In fact Lorentz was very close to the truth, if he had just discarded
the old notions of 'particles' and 'fields' then his concept of
vibrations / wave motions of the ether, and the equivalence of the
ether with Space would have been correct and would then have led to
the correct conception of matter as the spherical wave motion of
Space.
As Max Born writes;

Lorentz proclaimed the very radical thesis which had never before been
asserted with such definiteness: The ether is at rest in absolute
space. In principle this identifies the ether with absolute space.
Absolute space is no vacuum, but something with definite properties
whose state is described with the help of two directed quantities, the
electrical field E and the magnetic field H, and, as such is called
the ether. (Born, 1924)

Thus we now realise that Lorentz's fundamental problem was believing
that the e-m field physically existed. The solution is to realize
that, yes, a fundamental Space does exist, as Faraday, Maxwell, and
Lorentz sensibly imagined, but it is a wave medium for real waves in a
physical medium, described by their Wave Amplitude only (Scalar
waves). Space does not exist as an 'ether' for mathematical e-m waves
of force (vector waves that must include both force and direction of
force for both Electric and Magnetic Fields).

To aid this understanding, let us now have Albert Einstein summarize
this confusing state of affairs that had arisen by the early 1900s.

It became clear that there existed in free space states which
propagated themselves in waves as well as localized fields which were
able to exert forces on electrical masses or magnetic poles brought to
the spot. Since it would have seemed utterly absurd to the physicists
of the nineteenth century to attribute physical functions or states to
space itself, they invented a medium pervading the whole of space, on
the model of ponderable matter (i.e. tiny particles that moved
backwards and forwards as they propagated waves) the ether, which was
supposed to act as a vehicle for electromagnetic phenomena, and hence
for those of light as well. The picture was, then, as follows: space
is filled by the ether, in which the material corpuscles or atoms of
ponderable matter swim around; the atomic structure of the latter had
been securely established by the turn of the century (1900). Thus the
introduction of the field as an elementary concept gave rise to an
inconsistency of the theory as a whole.
Maxwell's theory, although adequately describing the behaviour of
electrically charged particles in their interaction with one another,
does not explain the behaviour of electrical densities, i.e., it does
not provide a theory of the particles themselves. They must therefore
be treated as mass points on the basis of the old Newtonian theory.
The combination of the idea of a continuous field with that of
material points discontinuous in space appears inconsistent. Hence the
material particle has no place as a fundamental concept in a field
theory. Thus even apart from the fact that gravitation is not
included, Maxwell's electrodynamics cannot be considered a complete
theory. (Albert Einstein, 1950)

As Albert Einstein explains though, the particle was a necessary part
of the evolution of the field theory, for 'forces' must have
'particles' to act upon!

The participation of matter in electromagnetic phenomena has its
origin only in the fact that the elementary particles of matter carry
unalterable masses and electric charges and on this account are
subject on the one hand to the actions of ponderomotive (Newtonian /
Mass) forces and on the other hand possess the property of generating
a field (Charge). The elementary particles obey Newton's law of motion
for material points. This is the basis on which H. A. Lorentz obtained
his syntheses of Newton's mechanics and Maxwell's field theory.
The weakness of this theory lies in the fact that it tried to
determine the phenomena by a combination of partial differential
equations (Maxwell's field equations for empty space) and total
differential equations (equations of motion of point particles), which
procedure was obviously unnatural. The inadequacy of this point of
view manifested itself in the necessity of assuming finite dimensions
for the particles in order to prevent the electromagnetic field
existing at the surfaces from becoming infinitely large.
The Maxwell equations in their original form do not, however, allow
such a description of particles, because their corresponding solutions
contain a singularity. Theoretical physicists have tried for a long
time (1936), therefore, to reach the goal by a modification of
Maxwell's equations. These attempts have, however, not been crowned
with success.
Thus it happened that the goal of erecting a pure electromagnetic
field theory of matter remained unattained for the time being,
although in principle no objection could be raised against the
possibility of reaching such a goal. What appears certain to me,
however, is that, in the foundations of any consistent field theory
the particle concept must not appear in addition to the field concept.
The whole theory must by based solely on partial differential
equations and their singularity-free solutions. (Albert Einstein,
1936)

(Note: A singularity is where the radius of the particle tends to zero
thus the field strength tends to infinity and the mathematics to
describe it fails. And this led to Feynman's problems of
'renormalisation' as explained in the Article on Quantum Theory.)

This explains why Albert Einstein tried to develop a field theory of
matter (without the use/need of particles) though he never succeeded
in this venture, simply because matter, as a Spherical Standing Wave
Motion of Space cannot be described by continuous force fields. (i.e.
Standing Wave interactions are discrete, not continuous!) Thus he
writes;

Since the theory of general relativity implies the representation of
physical reality by a continuous field, the concept of particles or
material points cannot play a fundamental part, nor can the concept of
motion. The particle can only appear as a limited region in space in
which the field strength or the energy density are particularly high.
(Albert Einstein, 1954)

We now realise his error of working with 'spherical force fields'
rather than Spherical Wave Motions, whose changing velocities of In-
Waves cause the apparent motions of the particles and thus the
'forces' between these particles! Thus he was correct to discard the
concept of discrete particles, his error was to also discard the
concept of motion and work with 'forces' when a careful analysis leads
to the realisation that Motion is more fundamental than Force (i.e.
That Force requires the measurement of Motion).
We shall consider this in more detail shortly, but first let us
proceed with the further discoveries of Lorentz.


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Introduction to Albert Einstein's Theory of Relativity - Newton's
Mechanics - Newton / Time Particles Forces - Newton / Light - Newton's
Law of Inertia - Faraday EM Force Field - Maxwell's Equations -
Lorentz / Electron - Lorentz Transformations - Albert Einstein's
Theory of Relativity - Special Relativity - General Relativity -
Summary of Einstein's Relativity - Top of Page

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The Lorentz Transformations & How the Electron Changes Ellipsoidal
Shape With Motion
On How a Change in Velocity of the In-Wave (Vel. of Light c) Causes a
Change in Ellipsoidal Shape of the In-Wave, and also Causes a Change
in the Future Position and Thus the Apparent Motion (Acceleration) of
the Wave-Center.

Thus far we have largely considered a SSW stationary in Space, so let
us now consider a SSW where the Wave-Center appears to be moving
through Space, as this then leads to the Lorentz Transformations and
the foundations of Special Relativity.
As the particle does not exist, and instead we are considering the
behaviour of the Wave-Center of a SSW, we realize that the motion of
the particle through Space is actually the apparent motion of
successive Wave-Centers which are determined by where each successive
spherical (in reality ellipsoidal) In-Wave meets at its respective
Wave-Center.



Fig:1.6.1 The Ellipsoidal Shape of a Moving Wave-Center: If the In-
Waves on the right are slowed down as they travel in through Space of
higher Wave-Density (Principle II) then they are stretched back into
an ellipsoidal shape (rather than being exactly spherical) and have a
shorter Wavelength. It is this change in ellipsoidal shape and
Wavelength of the In-Wave which causes the apparent motion of the Wave-
Center and thus the Lorentz Transformations.

If a Wave-Center is to move through Space then it is clear that we
must change the velocity of the In-Waves from one side relative to the
other such that they no longer meet in the same place. Thus by
changing the velocity of the In-Waves we cause the Wave-Center to
change its position in Space. This is the cause of acceleration (and
in fact of all forces, as per Newton's Law of Inertia F=m.a).

This also explains the foundation of the Lorentz transformations and
how this was used by Albert Einstein to develop his special and
general relativity.

To begin, if we slow down the In-Wave on one side of the Wave-Center
then these In-Waves will meet more in the direction of the slower In-
Waves. Further, the spherical shape of the In-Waves will become
ellipsoidal and this change in shape will directly relate to the
apparent motion of the Wave-Center (particle). A convenient analogy is
to imagine the point (particle) where the In-Wave meets at its Wave-
Center as a footstep, and the motion of the particle through Space can
be imagined as a sequence of discrete steps corresponding to where
each successive In-Wave meets at its Wave-Center.

The Lorentz Transformations provide formulas for the change of
ellipsoidal shape of matter (as a spatially extended e-m field) with
motion of the Wave-Center (particle) and how this affects Mass, Time
and Length/Dimension. The motion (and change in ellipsoidal shape) is
simply relative between the source and observer, it makes no
difference as to who is moving. (This formula for change of mass and
dimension has been amply verified in particle accelerators and TV
tubes.)

As Born confirms;

Lorentz assumed that every moving electron contracts in the direction
of motion, so that from a sphere it becomes a flattened spheroid of
revolution, the amount of flattening depending in a definite way on
the velocity. This hypothesis seems at first sight strange. It
certainly gives a simpler formula for the way electromagnetic mass
depends on velocity than does Abraham's theory, but this in itself
does not justify it. (Born, 1924)

As the dimension of matter as Spherical Wave Motions is determined by
BOTH the wavelength and shape of the ellipsoidal standing waves about
the Wave-Centre of the electron (matter), which relates to the motion
of the centre, thus the moving electron's spatial dimensions must be
distorted into an ellipsoidal shape. This explains the true
foundations of the Lorentz Transformations and the 'null result' of
the Michelson-Morley experiment. And Lorentz was very close to the
truth in explaining this, he writes;

In order to explain this absence of any effect of the Earth's
translation (in the Michelson/Morley experiment), I have ventured the
hypothesis, that the dimensions of a solid body undergo slight change,
of the order of v2/c2, when it moves through the ether.
From this point of view it is natural to suppose that, just like the
electromagnetic forces, the molecular attractions and repulsions are
somewhat modified by a translation imparted to the body, and this may
very well result in a change of dimensions. ... The electrons
themselves become flattened ellipsoids. (Lorentz, 1906)



Fig: 1.6.2 The Michelson-Morley experiment with the center of an
ellipsoidal wave system as the observer. Due to our dimension being
determined by wavelength, we shall always measure arm 1 of an
interferometer, to be the same length as that of arm 2, irrespective
of which direction we may rotate the interferometer. The arms are both
7 wavelengths long. From this we can conclude that it will take the
same time for the ellipsoidal In-Waves to propagate in to the center
along arm 1 as it does along arm 2. (This must be true, as the
electron 'particle is caused by the Wave-Center of the ellipsoidal
wave system, and this is where the ellipsoidal wave meets, obviously
at the same time. As there is no time difference for the two paths, no
interference is observed.)
NOTE: This diagram is not exactly accurate, but it gives you the
general idea!

The Michelson Morley experiment confirms that this is true, and that
the light takes the same time to travel each path. This is a general
principle, and is the cause of Albert Einstein's principle of special
relativity.
This enables Albert Einstein to postulate that the velocity of light
is always measured to be the same, as this is true. Albert Einstein
writes;

The so called special or restricted relativity theory is based on the
fact that Maxwell's equations (and thus the law of propagation of
light in empty space) are converted into equations of the same form,
when they undergo a Lorentz transformation. (Albert Einstein, 1954)

So now let us briefly explain Albert Einstein's Relativity, which has
had such a profound, and yet ultimately confusing, impact on modern
physics.


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Introduction to Albert Einstein's Theory of Relativity - Newton's
Mechanics - Newton / Time Particles Forces - Newton / Light - Newton's
Law of Inertia - Faraday EM Force Field - Maxwell's Equations -
Lorentz / Electron - Lorentz Transformations - Albert Einstein's
Theory of Relativity - Special Relativity - General Relativity -
Summary of Einstein's Relativity - Top of Page

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Albert Einstein's Theory of Relativity (1905,1915)
The special theory, on which the general theory rests, applies to all
physical phenomena with the exception of gravitation; the general
theory provides the law of gravitation and its relation to the other
forces of nature. (Albert Einstein, 1919)

The theory of relativity may indeed be said to have put a sort of
finishing touch to the mighty intellectual edifice of Maxwell and
Lorentz, inasmuch as it seeks to extend field physics to all
phenomena, gravitation included. (Albert Einstein, 1934)

Albert Einstein's Special and General Relativity relate to the
Empirical (a posteriori) truth that the laws of nature, and thus the
velocity of light, are always measured to be the same for all
observers irrespective of their motion relative to one another.
(Principle of Relativity)
So for example, as the earth is orbiting the sun, classically one
would expect that we would measure different velocities for the light
we see from stars when we are moving towards them rather than away
from them, yet measurements always give the same value for the
velocity of light from the stars, irrespective of our motion.


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Introduction to Albert Einstein's Theory of Relativity - Newton's
Mechanics - Newton / Time Particles Forces - Newton / Light - Newton's
Law of Inertia - Faraday EM Force Field - Maxwell's Equations -
Lorentz / Electron - Lorentz Transformations - Albert Einstein's
Theory of Relativity - Special Relativity - General Relativity -
Summary of Einstein's Relativity - Top of Page

--------------------------------------------------------------------------------

Albert Einstein' Special Relativity (1905)
The Principle of Newtonian Relativity. The laws of Mechanics are the
same in all inertial (non-accelerated) reference frames.
Newton, amongst others, noticed that the laws of mechanics seemed to
be the same irrespective of the observer's (constant) motion through
Space. If you throw a ball vertically in the air it comes back down
vertically. It does not matter whether you are standing still on the
earth, or moving with a constant velocity (Newton used the example of
a ship) across the surface of the earth, it still goes straight up and
down relative to the person who throws it.

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)

This was an observational/empirical fact that has been known since the
seventeenth century. It was Albert Einstein who used this fact, but
applied it to Lorentz's Electromagnetic Theory of the Electron, rather
than simply to Newton's mechanics, to develop his theory of special
and general relativity which gave rise to his geometry of space-time,
his 'curvature of space' that explained the motion of bodies in a
gravitational field.
It is the purpose of this chapter to follow his logic, but for the
first time we can explain this from the true foundation of what
exists, from the foundation of the Spherical Standing Wave Structure
of Matter in a Three Dimensional Space.
While this truth of the Wave Structure of Matter greatly simplifies
Albert Einstein's Relativity, I again emphasize that some patience and
effort to re-read sections will be required, but that the reward for
this effort will be a clear understanding of the most famous theory
ever constructed. (And a certain exhilaration at understanding how
gravity works!)

Explaining the Two Postulates of Special Relativity (Albert Einstein,
1905)
1. ... the same laws of electrodynamics and optics will be valid for
all frames of reference for which the equations of mechanics hold
good. ... A co-ordinate system that is moved uniformly and in a
straight line relative to an inertial system is likewise an inertial
system. By the 'special principle of relativity' is meant the
generalization of this definition to include any natural event
whatever: thus, every universal law of nature which is valid in
relation to a co-ordinate system C must also be valid, as it stands,
in relation to a co-ordinate system C' which is in uniform translatory
motion relative to C. (Albert Einstein, 1954)

And therefore the Velocity of Light (as one of the laws of
electrodynamics) has the same measured value in all inertial (non-
accelerated) reference frames.

2. The second principle, on which the special theory of relativity
rests, is the 'principle of constant velocity of light in vacuo.' This
principle asserts that light in vacuo always has a definite velocity
of propagation (independent of the state of motion of the observer or
of the source of the light). The confidence which physicists place in
this principle springs from the successes achieved by the
electrodynamics of Maxwell and Lorentz. (Albert Einstein, 1954)

Albert Einstein (1905) cleverly combined the work of Faraday, Maxwell
and Lorentz to propose the 'Theory of Special Relativity' which
described the effects of relative Motion (inertial or non-accelerated)
on the properties of matter. His famous postulate being that the laws
of nature (mechanics and electrodynamics) are the same for all
observers irrespective of their motion (non-accelerated), which leads
to the further postulate that the velocity of light must always be
measured to be the same irrespective of motion.

What these two postulates logically say is that if you measure the
velocity of light c to have a particular value, then irrespective of
which inertial (non-accelerated) reference frame you are moving in,
you will always measure the velocity of light c to have the same
value. This same measurement for the velocity of light is an
experimental fact. But this does not mean that the velocity of light
in Space is constant. The velocity of light is not constant, but it is
always measured to be the same, and this fact has caused enormous
confusion within Modern Physics.
When a Wave-Center is moving through Space (See Fig: 1.7.1) then the
cause of this is a difference in velocity of the In-Waves from one
side to the other, but there is also a compensating change in
wavelength such that the velocity of the In-Waves is always measured
to be the same. Because Albert Einstein incorrectly assumed that the
velocity of light was constant and thus the same in all directions, he
had to adjust his rate of time to compensate for this difference in
the velocity of light which is the cause of motion. It is true though
that if the velocity of the In-Waves does not change, then the
resultant Wave-Center does not accelerate and must travel with a
constant velocity (i.e. non accelerated motion).



Fig: 1.7.1: Pythagoras' Theorem is Caused by the Spherical shape of
Matter as a Spherical Wave Motion of Space. Further, three dimensional
space and spherical space are equivalent, as it takes three variables
to describe the surface of a sphere. In fact the cause of three
dimensional space is simply that matter interacts spherically

Einstein correctly realized that matter was spherically spatially
extended, and thus interacted with other matter spherically (this
being the cause of Pythagoras' Theorem).

From the latest results of the theory of relativity it is probable
that our three dimensional space is also approximately spherical, that
is, that the laws of disposition of rigid bodies in it are not given
by Euclidean geometry, but approximately by spherical geometry.
(Einstein, 1954)

But Einstein did not actually know how matter existed in Space;

The theory of relativity leads to the same law of motion without
requiring any special hypothesis whatsoever as to the structure and
behavior of the electron. (Einstein, 1954)

His theory is empirically (a posteriori) founded from observation of
how matter 'pushes' other matter around, thus his 'representation' of
matter as spherical force fields.

Albert Einstein's Metric equation is simply Pythagoras' Theorem
applied to the three spatial co-ordinates, and equating them to the
displacement of a ray of light.

Special relativity is still based directly on an empirical law, that
of the constancy of the velocity of light.
dx2 + dy2 + dz2 =(cdt)2 where cdt is the distance traveled by light c
in time dt.
The fact that such a metric is called Euclidean is connected with the
following. The postulation of such a metric in a three dimensional
continuum is fully equivalent to the postulation of the axioms of
Euclidean Geometry. The defining equation of the metric is then
nothing but the Pythagorean theorem applied to the differentials of
the co-ordinates. (Albert Einstein, 1934)
In the special theory of relativity those co-ordinate changes (by
transformation) are permitted for which also in the new co-ordinate
system the quantity (cdt)2 (fundamental invariant dS2) equals the sum
of the squares of the co-ordinate differentials. Such transformations
are called Lorentz transformations. (Albert Einstein, 1934)

The reason why Special Relativity works mathematically is twofold:
i) Special relativity assumes that the velocity of light is constant,
and thus if there is no change in the velocity of the In-Wave then
there can be no acceleration of the Wave-Center. This explains why
special relativity is limited to relative motion between matter that
is non-accelerated. (Inertial reference frames)
ii) In Albert Einstein's Metric Equations the displacement of the
light beam is determined by cdt, thus it makes no difference,
mathematically speaking, if the velocity of light is assumed constant,
and thus time is changed to keep the metrical equation true (as Albert
Einstein did) or conversely, to assume a constant Time, and that the
velocity of In-Waves (Light) is changed. As it turns out, it is this
latter case which is true, and this differing velocity of the In-Waves
(from one side of the Wave-Center relative to the other) is the cause
of the apparent motion of Wave-Centers.
Significantly, Albert Einstein confirms this view, that the velocity
of light is not always constant, when he writes;

(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)

Most importantly though, despite these changes in the velocity of the
In-Waves, their velocity is always measured to be the same.
This curious phenomena occurs because for any relative difference in
the velocity of the In-Wave from one side of the Wave-Center to the
other, there is a corresponding change in wavelength (which determines
length), such that the same In-Wave always meets at its Wave-Center at
the same time. As velocity is length/time then the velocity of the In-
Wave (velocity of light c) is always measured to be the same, and the
difference in wave velocity from one side to the other causes the
apparent motion of the Wave-Center through Space. It seems that many
people mistakenly assume that the velocity of light is constant, it is
not, but is always measured to be the same (irrespective of motion) -
this fact has caused much confusion.
Because Albert Einstein misunderstood time (as his geometry of
relativity had no dynamic Wave Motion, which is the true cause of
time) this then partly explains why he disliked Quantum Theory (though
there are many reasons to dislike QT due to its absurd
interpretations!).

.... the methods introduced by quantum mechanics are not likely to give
a useful basis for the whole of physics. In the Schrodinger equation,
absolute time, and also the potential energy, play a decisive role,
while these two concepts have been recognized by the theory of
relativity as inadmissible in principle. (Albert Einstein, 1954)

Now it is this relationship about the change in wavelength and
ellipsoidal dimension with Motion that is at the heart of Relativity
so it is important to hear what Lorentz has to say on the subject;

....the simplest course is certainly to consider the electrons
themselves as wholly immutable, as perfectly rigid spheres, with a
constant uniformly distributed surface charge. .. But, unfortunately,
it is at variance with our theorem. ... It is for this reason that I
have examined what becomes of the theory, if the electrons themselves
are considered as liable to the same changes of dimensions as the
bodies in which they are contained. ... the explanation of Michelson's
experimental result, ... admit, for moving bodies, only a contraction,
determined by the coefficient in the direction of the line of motion.
The electrons themselves become flattened ellipsoids.
This would enable us to predict that no experiment made with a
terrestrial source of light will ever show us an influence of the
Earth's motion.
It is clear that, since the observer is unconscious of these changes,
( the contraction of a measuring rod in the direction of motion),
relying on his rod, he will not find the true shape of bodies. He will
take for a sphere what really is an ellipsoid,
Attention must now be drawn to a remarkable reciprocity that has been
pointed out by Albert Einstein. ... Let us now imagine that each
observer and (one is moving with constant velocity relative to the
other) is able to see the system to which the other belongs, ... It
will be clear by what has been said that the impressions received by
the two observers and would be alike in all respects. It would be
impossible to tell which of them moves or stands still with respect to
the ether. ... This is a point which Albert Einstein has laid
particular stress on, in a theory in which he starts from what he
calls the principle of relativity.
I cannot speak here of the many highly interesting applications which
Albert Einstein has made of this principle. His results concerning
electromagnetic and optical phenomena agree in the main with those
which we have obtained in the preceding pages, the chief difference
being that Albert Einstein simply postulates what we have deduced, ...
from the fundamental equations of the electromagnetic field. By doing
so, he may certainly take credit for making us see in the negative
result of experiments like those of Michelson, Rayleigh and Brace, not
a fortuitous compensation of opposing effects, but the manifestation
of a general and fundamental principle.
Yet, I think, something may also be claimed in the favour of the form
in which I have presented the theory. I cannot but regard the ether,
which can be the seat of an electromagnetic field with its energy and
its vibrations, as endowed with a certain degree of substantiality,
however different it may be from all ordinary matter. (Lorentz, 1906)

Thus Lorentz was correct;

In order to explain this absence of any effect of the Earth's
translation, I have ventured the hypothesis, that the dimensions of a
solid body undergo slight change when it moves through the ether.
(Lorentz, 1906)

Most profoundly, Lorentz first deduced the foundations of Albert
Einstein's Relativity from the assumption of a rigid Space (ether),
and that the cause of the electromagnetic field effect that he was
using was in fact vibrations in this Space/Ether.
Though Albert Einstein related relative motions of matter only to
other matter and not back to an absolute Space like Lorentz did,
(which is mathematically simpler I suppose) the important point is
that the Logic of Relativity is founded on, and completely consistent
with, an Absolute Space. (Contrary to current opinions)

From Lorentz's purely mathematical foundation Albert Einstein then
developed his Theory of Relativity, which assumed that matter existed
as a spherical spatially extended field which changes ellipsoidal
shape with motion and thus also with acceleration (which leads to the
ellipsoidal geometry which underpins General Relativity and
gravitation).

Albert Einstein took one further step than Lorentz though, and assumed
(like Leibniz and Mach) that all motion of matter was relative only to
other matter, he writes;

It has, of course, been known since the days of the ancient Greeks
that in order to describe the movement of a body, a second body is
needed to which the movement of the first is referred. (Albert
Einstein, 1919)

By doing this Albert Einstein effectively renounced the concept of a
fundamental Space separate from matter (as a field), as he explains
below;

Since the field exists even in a vacuum, should one conceive of the
field as state of a 'carrier', or should it rather be endowed with an
independent existence not reducible to anything else? In other words,
is there an 'aether' which carries the field; the aether being
considered in the undulatory state, for example, when it carries light
waves? The question has a natural answer: Because one cannot dispense
with the field concept, it is preferable not to introduce in addition
a carrier with hypothetical properties. (Albert Einstein, 1950)

Physical objects are not in space, but these objects are spatially
extended. In this way the concept 'empty space' loses its meaning.
The field thus becomes an irreducible element of physical description,
irreducible in the same sense as the concept of matter (particles) in
the theory of Newton. (Albert Einstein, 1954)

By using Albert Einstein's own words it is now possible to show that
his ideas need only a slight modification - from his foundation that
matter is a spherical spatially extended 'field', to a foundation
based upon Space rather than matter, and that matter is caused by
Spherical Standing Waves in Space.
Albert Einstein is correct in asserting that matter is spherically
spatially extended, and thus to reject the concept of the particle;

According to general relativity, the concept of space detached from
any physical content (matter, objects) does not exist. The physical
reality of space is represented by a field whose components are
continuous functions of four independent variables - the co-ordinates
of space and time. Since the theory of general relativity implies the
representation of physical reality by a continuous field, the concept
of particles or material points cannot play a fundamental part, nor
can the concept of motion. The particle can only appear as a limited
region in space in which the field strength or the energy density are
particularly high. (Albert Einstein, 1950)

Albert Einstein is nearly correct when he says that the particle can
only appear as a limited region in Space in which the field strength/
energy density is particularly high, for this is simply the high Wave-
Amplitude & Density of the Wave-Center of the Spherical Standing Wave.
This obviously explains why Matter can never exceed the Velocity of
Light. As the particle is in fact the Wave-Center of a Spherical
Standing Wave (SSW), it is impossible for this Wave-Center to ever
move faster than the velocity of the incoming waves, which is the
velocity of light.

Unfortunately Albert Einstein incorrectly assumed that a mathematical
description of effects, the spherical, spatially extended continuous
force field, was the best way of representing reality. In fact these
force field effects are caused by the changing velocity of the In-
Waves which determine the future position of the Wave-Center (and thus
the apparent force and accelerated motion of the particle). In essence
the field theory is a continuous mathematical approximation of effects
which are caused by many discrete (quantum) standing wave
interactions. Hence the Wave Structure of Matter (WSM) explains the
'cause' of both the 'field' and the 'particle effects'.

Though most of Albert Einstein's discussion of Space is in terms of
matter interactions described by fields, it is important to realise
that Albert Einstein actually knew that Space must somehow exist and
have properties that caused these force fields, he writes;

Recapitulating, we may say that according to the general theory of
relativity space is endowed with physical qualities; in this sense,
therefore, there exists an ether. According to the general theory of
relativity space without ether is unthinkable; for in such space there
not only would be no propagation of light, but also no possibility of
existence for standards of space and time (measuring-rods and clocks),
nor therefore any space-time intervals in the physical sense. (Albert
Einstein, Leiden Lecture, 1920)

In ending this summary of Special Relativity, it is important to
acknowledge the great power of this mathematical theory, as Albert
Einstein explains (for it leads directly to Albert Einstein's famous
E=mc2). But now we realise that this equivalence of Matter and Energy
is simply because they are both manifestations of the same thing, Wave-
Motion of Space.

The heuristic method of the special theory of relativity is
characterized by the following principle: only those equations are
admissible as an expression of natural laws which do not change their
form when the co-ordinates are changed by means of the Lorentz
transformation (covariance of equations with respect to the Lorentz
transformations). This method led to the discovery of the necessary
connection between momentum and energy, between electric and magnetic
field strength, electrostatic and electrodynamic forces, inert mass
and energy; thus the number of independent concepts and fundamental
equations was reduced. (Albert Einstein, 1934)


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Introduction to Albert Einstein's Theory of Relativity - Newton's
Mechanics - Newton / Time Particles Forces - Newton / Light - Newton's
Law of Inertia - Faraday EM Force Field - Maxwell's Equations -
Lorentz / Electron - Lorentz Transformations - Albert Einstein's
Theory of Relativity - Special Relativity - General Relativity -
Summary of Einstein's Relativity - Top of Page

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Albert Einstein's General Relativity
On Accelerated Motion and Gravitation. 1915
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)

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, as previously explained, 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
Wave-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 Wave-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 Wave-Density. 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 Wave-
Density Space resulting in a change in ellipsoidal shape or the SSW
and results in the Wave-Center (electron) moving towards the Space of
higher Wave-Density (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)


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Introduction to Albert Einstein's Theory of Relativity - Newton's
Mechanics - Newton / Time Particles Forces - Newton / Light - Newton's
Law of Inertia - Faraday EM Force Field - Maxwell's Equations -
Lorentz / Electron - Lorentz Transformations - Albert Einstein's
Theory of Relativity - Special Relativity - General Relativity -
Summary of Einstein's Relativity - Top of Page

--------------------------------------------------------------------------------

Summary of Einstein's Relativity
Explaining and Solving the Problems of Einstein's Relativity
Einstein (from Faraday, Maxwell, Lorentz) represented matter as a
continuous spherical electromagnetic force field in spacetime.
Einstein is correct that there is no 'particle' and matter is
spherically spatially extended. However, the spherical 'force field'
can be sensibly explained with the Spherical Standing Wave Structure
of Matter.
We realize that forces are caused by a change in the velocity of the
spherical In-wave (from one direction) as this changes where these In-
waves meet at the wave-center, which we observe as a 'force
accelerating a particle'.
The change in ellipsoidal shape of the In-waves is the cause of
Einstein's Metrics and the Riemannian geometry of General Relativity.
With this new understanding let us then briefly summarize the problems
of Einstein's Relativity, as their solutions become obvious once we
understand the Spherical Standing Wave Structure of Matter.

i) Einstein's Relativity is a Theory of a posteriori Effects not a
priori Causes, and is founded on Many things (Matter) rather than One
thing (Space).
Einstein did not know how matter existed in Space and his
electromagnetic field theory of matter is Inductive (empirical / a
posteriori) and describes effects (of relative motion).

The theory of relativity leads to the same law of motion without
requiring any special hypothesis whatsoever as to the structure and
behavior of the electron. (Einstein, 1954)

His theory is empirically (a posteriori) founded from observation of
how matter 'pushes' other matter around (thus his 'representation' of
matter as spherical force fields).

As Ernst Mach insistently pointed out, the Newtonian theory is
unsatisfactory in the following respect: if one considers motion from
the purely descriptive, not from the causal, point of view, it only
exists as relative motion of things with respect to one another.
It compelled Newton to invent a physical space in relation to which
acceleration was supposed to exist. This introduction ad hoc of the
concept of absolute space, while logically unacceptionable,
nevertheless seems unsatisfactory.

Considered logically, concepts are free creations of the human
intelligence, tools of thought, which are to serve the purpose of
bringing experiences into relation with each other, so that in this
way they can be better surveyed. The attempt to become conscious of
the empirical sources of these fundamental concepts should show to
what extent we are actually bound to these concepts. In this way we
become aware of our freedom to create new concepts.

Descartes argued somewhat on these lines: space is identical with
extension, but extension is connected with bodies; thus there is no
space without bodies and hence no empty space.

It appears to me, therefore, that the formation of the concept of the
material object must precede our concepts of time and space. (Albert
Einstein, 1954)

Metaphysics, as a true description of Reality, must be based on a
priori causes AND these must be united back to one common thing that
causes and connects the many things (matter). The Metaphysics of Space
and Motion is founded on the a priori existence of One thing, Space
and its properties as a wave-medium, that One thing, Space, must first
exist for Many things, matter to be able to exist and move about in an
interconnected manner (as reality shows).

ii) Continuous Fields do Not Explain the Discrete Energy Levels of
Matter and Light as Determined by Quantum Theory.
The Electric and Magnetic Force Fields were first founded on repeated
observations (Induction / a posteriori) of how many trillions of
charged 'particles' (electrons and protons) behaved. This explains why
the fields were continuous, as many trillions of discrete standing
wave interactions blend together into a continuous force. Thus the
continuous field can never describe the real standing wave
interactions of matter, as Einstein came to realize.

The great stumbling block for the field theory lies in the conception
of the atomic structure of matter and energy. For the theory is
fundamentally non-atomic in so far as it operates exclusively with
continuous functions of space, in contrast to classical mechanics
whose most important element, the material point, in itself does
justice to the atomic structure of matter. (Einstein, 1954)

iii) Einstein's 'Fields' require 'Particles'.
As Einstein used the empirical/theoretical foundations developed by
Faraday, Maxwell and Lorentz he required the existence of a 'Particle'
to somehow generate the 'Field' which in turn acted on other
'Particles'.

The special and general theories of relativity, which, though based
entirely on ideas connected with the field-theory, have so far been
unable to avoid the independent introduction of material points, … the
continuous field thus appeared side by side with the material point as
the representative of physical reality. This dualism remains even
today disturbing as it must be to every orderly mind. (Einstein, 1954)

iv) Einstein's Continuous Field Theory of Matter gives rise to
Singularities and Infinite Fields.
The Maxwell equations in their original form do not, however, allow
such a description of particles, because their corresponding solutions
contain a singularity. Theoretical physicists have tried for a long
time (1936), therefore, to reach the goal by a modification of
Maxwell's equations. These attempts have, however, not been crowned
with success. What appears certain to me, however, is that, in the
foundations of any consistent field theory the particle concept must
not appear in addition to the field concept. The whole theory must by
based solely on partial differential equations and their singularity-
free solutions. (Einstein, 1954)

As Wolff explains (see Quantum Theory), the equation for a scalar
spherical wave give rise to a finite wave-amplitude at the wave-center
(consistent with observation) whereas spherical vector electromagnetic
fields tend to infinity as the radius tends to zero (and there are no
vector e-m solutions in spherical coordinates!).

v) Einstein Rejects both 'Particles' and Motion.
While Einstein correctly rejected the point 'particle' concept of
matter, he assumed that Motion only applied to 'particles' (a common
error!) thus he also rejected the concept of Motion, and represented
matter as spherical force fields. The error is twofold; firstly, he
did not consider the (wave) Motion of Space itself, and secondly, he
should have realized that to measure forces we must first measure the
change in Motion of a particle, thus Motion is a priori to forces
(i.e. Force = dE/dx).

Since the theory of general relativity implies the representation of
physical reality by a continuous field, the concept of particles or
material points cannot play a fundamental part, nor can the concept of
motion. (Einstein, 1954)

We now realize that neither the 'Particle' nor the continuous
electromagnetic force 'Field' is a complete description of Reality
thus we must reject both the 'Particle' and the 'Field', and what
remains is Motion. Hence we can now clearly see both Einstein's error
and the true path left to explore - the study of Space as a wave
medium for wave Motion - and that the Spherical Wave Motion of Space
explains both the 'particle' (wave-center) and 'forces' (change in
velocity of In-Waves, which changes the location of the Wave-Center).

vi) Einstein Assumed Matter Caused Space Rather than the Wave-Motion
of Space Causing Matter.
Einstein was profoundly influenced by Mach;

Mach, in the nineteenth century, was the only one who thought
seriously of the elimination of the concept of space, in that he
sought to replace it by the notion of the totality of the
instantaneous distances between all material points. (He made this
attempt in order to arrive at a satisfactory understanding of
inertia.) (Einstein, 1954)

Because we only observe the motion of matter relative to all the other
matter in the universe, thus Einstein thought that matter, rather than
Space, must be the central perspective for representing Reality. Thus
Einstein's Relativity is empirically (a posteriori) founded from
observing the motion of matter relative to other matter.
The Metaphysics of Space and Motion is founded on the a priori fact
that Space is first necessary for matter to be able to exist and move
about. Einstein is empirically correct, and at the same time this was
his error because Metaphysics (and thus Reality) is not founded on
empirical observations.
In reality there is no motion of matter, there is only the spherical
wave-motion of Space, and the changing location of the wave-center
gives the 'illusion' of the motion of matter 'particles'. (Thus
Einstein's Relativity is founded on an illusion that matter moves,
when it is Space which is moving / vibrating.)

Newton was ultimately correct;

And so instead of absolute places and motions, we use relative ones;
and that without any inconvenience in common affairs; but in
Philosophical disquisitions, we ought to abstract from our senses, and
consider things themselves, distinct from what are only sensible
measures of them. (Newton, 1687)

Further, Lorentz's assumption of an Absolute Space is the foundation
for the Lorentz transformations and thus for Einstein's Relativity.

I cannot but regard the ether, which can be the seat of an
electromagnetic field with its energy and its vibrations, as endowed
with a certain degree of substantiality, however different it may be
from all ordinary matter. (Lorentz, The Theory of the Electron, 1906)

Einstein choose to ignore Space / Aether and work with relative
motions of matter to other matter, with matter being represented by
spherical fields.

The electromagnetic fields are not states of a medium, and are not
bound down to any bearer, but they are independent realities which are
not reducible to anything else. (Albert Einstein, Leiden Lecture,
1920)

In other words, is there an ether which carries the field; the ether
being considered in the undulatory state, for example, when it carries
light waves? The question has a natural answer: Because one cannot
dispense with the field concept, it is preferable not to introduce in
addition a carrier with hypothetical properties. (Albert Einstein,
1950)

Once we realise that the particle and the continuous electromagnetic
field it generates are both merely ideas, human approximations to
reality, then we solve these problems. We return to Lorentz's
foundation of One thing Space, and its properties as a wave medium
(vibrations) and replace the spherical particle & field with the
spherical wave Motion of Space. The idea of the field theory of matter
misled Einstein, and yet Einstein also realised that there must
somehow be a Space that interconnects matter.

Recapitulating, we may say that according to the general theory of
relativity space is endowed with physical qualities; in this sense,
therefore, there exists an ether. According to the general theory of
relativity space without ether is unthinkable; for in such space there
not only would be no propagation of light, but also no possibility of
existence for standards of space and time (measuring-rods and clocks),
nor therefore any space-time intervals in the physical sense. But this
ether may not be thought of as endowed with the quality characteristic
of ponderable media, as consisting of parts which may be tracked
through time. The idea of motion may not be applied to it. (Albert
Einstein, Leiden Lecture, 1920)

vii) Einstein Never United the Electromagnetic & Gravitational Fields
into a Unified Field Theory for Matter
Einstein's Relativity requires both an Electromagnetic Force Field to
explain Charge, and a Gravitational Field to explain Mass. He tried
and failed throughout his life to unite these two fields into one (and
to remove the 'particle' concept from them).

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)

We can now unite these two fields by demonstrating how they are both
caused by the properties of Space, i.e. that the wave velocity varies
with both wave-amplitude (charge) and wave-density (mass).

viii) Einstein's 'Curvature of the Four Dimensional Space-Time
Continuum'
The concept of the 'curvature of space' is a mathematical construction
of Einstein's general relativity. In reality Space is not 'curved',
instead (for gravitational forces) the wave-density of Space varies
dependent upon the nearby proximity of matter (SSWs), and this causes
a variation in the velocity of waves/light which changes the
ellipsoidal shape of matter and causes the curved path of matter and
light in Space. And this caused Einstein considerable problems (it
took him ten years to work out the ellipsoidal geometry for gravity/
general relativity!)

But the path (of general relativity) 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. (Albert Einstein,
1954)

Further, the four dimensional space-time continuum simply means that
three spatial dimensions and a time dimension are required to define
the motion of bodies and the path of light in three dimensional Space.

The non-mathematician is seized by a mysterious shuddering when he
hears of 'four-dimensional' things, by a feeling not unlike that
awakened by thoughts of the occult. And yet there is no more common-
place statement than that the world in which we live is a four-
dimensional space-time continuum. Space is a three-dimensional
continuum. ... Similarly, the world of physical phenomena is naturally
four dimensional in the space-time sense. For it is composed of
individual events, each of which is described by four numbers, namely,
three space co-ordinates x, y, z, and the time co-ordinate t. (Albert
Einstein, 1954)

The inseparability of time and space emerged in connection with
electrodynamics, or the law of propagation of light.
With the discovery of the relativity of simultaneity, space and time
were merged in a single continuum in a way similar to that in which
the three dimensions of space had previously merged into a single
continuum. Physical space was thus extended to a four dimensional
space which also included the dimension of time. The four dimensional
space of the special theory of relativity is just as rigid and
absolute as Newton's space. (Albert Einstein, 1954)

In fact the spherical wave Motion of Space requires three spatial
dimensions and a (wave) motion dimension (rather than a time
dimension, as motion causes time). Now this is very important, for it
is this 'curvature' that largely led to Einstein's early fame. It was
the prediction by Einstein that light curved as it grazed the sun
(subsequently confirmed by observation during a solar eclipse on the
29th May 1919) that resulted in his General Theory of Relativity
becoming widely accepted and very famous. His general principle is
correct though, matter does determine the geometric properties of
Space;

According to the general theory of relativity, the geometrical
properties of space are not independent, but they are determined by
matter. (Einstein, 1954)


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Concluding Remarks
Towards the end of his life Einstein was acutely aware that he had
failed to realize his dream of a unified field theory for matter and
that the continuous spherical spatially extended continuous field may
not truly represent the reality of matter. In 1954 Einstein wrote to
his friend Michael Besso expressing his frustration;

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. … I
consider it quite possible that physics cannot be based on the field
concept, i.e., on continuous structures. In that case, nothing remains
of my entire castle in the air, gravitation theory included, [and of]
the rest of modern physics.

Albert Einstein's General Theory of Relativity (GTR) has been
summarized as, 'The matter of the universe determines the properties
of Space, and the properties of Space determine the behaviour of
matter.'

The GTR is an experimentally correct description of the universe but
how or why it occurs was mysterious. With the Wave Structure of Matter
(WSM) we now see the existence of a universal symmetry and
interdependence of all matter in the universe. The Wave Structure of
Matter is the cause of this profound symmetry.
Principle Two of the WSM can be rephrased as, All waves from matter of
the universe determine the Wave-Density of Space which determines the
velocity of the waves c which then determines the behaviour of matter
in Space.
We can further shorten this to Matter affects Space affects Matter.
Thus the Wave Structure of Matter (WSM) explains the fundamental
origins of Albert Einstein's General Theory of Relativity (GTR) and
its application to the cosmic scale gravitational motion of the matter
of planets, stars, galaxies, etc.

Significantly though, the WSM also explains the Quantum realm, and how
Wave-Centers (particles) interact with other particles in the Space
around them, thus explaining Quantum Theory and the cause of the
discrete 'quanta' (photon) properties of light. Hence the Spherical
Standing Wave Structure of Matter explains both the large scale
(Cosmic realm) geometry of General Relativity (gravity) as well as the
small scale (Quantum realm) particle interactions of Quantum Theory
(light). (As a true description of reality must.)
All that needs to be done now is for some clever and curious
Mathematician to apply the Two Principles of the WSM to Albert
Einstein's Relativity and show that the two are mathematically
equivalent. This mathematics will be simpler, contain no infinities/
singularities, and will also be consistent with Quantum Theory and
Cosmology. Thus there now exists the opportunity for mathematical
physicists to explore a profound new logical language which should
provide many solutions to their current problems and in time lead to a
revolution of their subject.

Toodle-oo
.

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