Euclidian Geometry
Euclid the Mathematician

Geometry, Euclid, Physics: Wave Structure of Matter explains the Metaphysical Foundations of Euclid's Geometry.

The Spherical Wave Structure of Matter (WSM) Explains the Metaphysical Foundations of Euclid's Geometry and Einstein's Non-Euclidean Geometry

Geometry Euclid - 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. (Albert Einstein, 1954) 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. (Albert Einstein, 1954)


The Wave Structure of Matter explains Albert Einstein's General Relativity which is founded on 'Non-Euclidean' Geometry

Firstly, because of this slight 'elasticity' of Space, there can be no absolutely rigid bodies in Space, as Albert Einstein confirms;

There are no really rigid bodies in nature, therefore the properties predicated of rigid bodies do not apply to physical reality.
... The subtlety of the concept of space was enhanced by the discovery that there exist no completely rigid bodies. All bodies are elastically deformable and alter in volume with change in temperature.

Thus Euclid's Geometry of straight lines, perfect spheres, etc. is axiomatic rather than real.

Albert Einstein Confirms that Matter is Spherically Spatially Extended (not a ‘Particle’) and is the Size of the Universe.

Is it possible to imagine a spherical space? To imagine a space means nothing else than that we imagine an epitome of our space experience, i.e. of experience that we can have in the movement of rigid bodies. In this sense we can imagine a spherical space. (Albert Einstein, 1954)

This is absolutely correct, Matter as a Spherical Standing Wave is obviously Spherical and interacts with other matter in Space Spherically. But we should be more precise, for we use the word Spherical here to mean approximately 'Spherical' (actually ellipsoidal), as Albert Einstein confirms;

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. (Albert Einstein, 1954)

This is also true, three dimensional Space and Spherical Space are Equivalent (both require three variables/dimensions to describe their Structure). Further, 'Non-Euclidean' Space simply means that perfect / exact spheres (and perfectly straight lines) only exist in the axioms of Euclid's Geometry, and in the real world the 'Spherical' In-waves are not exactly Spherical and actually change shape (like stretched or squashed ellipsoids) with a change in velocity of the In-Wave (from one direction, i.e. when a 'force accelerates a particle') with the resultant change in location of the Wave-Center. (This explains the Lorentz Transformations, and leads to the ellipsoidal Geometry of General Relativity and Gravity / Acceleration. See below)

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. … 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 equals the sum of the squares of the co-ordinate differentials. Such transformations are called Lorentz transformations. (Einstein, 1954)

The defining equation of the metric is then nothing but the Pythagorean theorem applied to the differentials of the co-ordinates. (Albert Einstein, 1954)

In Albert Einstein's Relativity we show that Pythagoras' Theorem is a fundamental physical truth that both confirms that matter interacts spherically with other matter at-a-distance in Space, and explains why Albert Einstein was able to use Pythagoras' Theorem as the foundation (metric equations) for his Theory of Relativity.

Albert Einstein writes;

According to the general theory of relativity, the geometrical properties of space are not independent, but they are determined by matter.
The particle can only appear as a limited region in space in which the field strength or the energy density are particularly high.
This is also correct and profoundly important. The 'Particle' is a region of Space (the Wave-Center/Focal Point) where the Wave energy density (or if you prefer wave field strength) is very high.
Further, Principle Two tells us that as the mass-energy density of Space increases (where there are many Wave-Centers/’Particles’) then the Wave-Velocity decreases. e.g. The Space of the Moon and Earth have a high mass-energy density of space, thus the Spherical/Ellipsoidal In-Waves of the Moon are slowed by the Space of the Earth (and vice versa) and this changes the ellipsoidal shape/geometry of the In-Waves and causes the Wave-Centers to move towards one another (which is of course what we call gravity, and in the case of the moon/earth causes the ellipsoidal/curved orbital path of the moon's many trillions of Wave-Centers).
'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.'
'Physical objects are not in space, but these objects are spatially extended. In this way the concept 'empty space' loses its meaning.'

Another way of saying this is that it is impossible for Space (as a Wave-Medium) to Exist without Wave-Motion (Content/Matter) and thus Space and Matter (as a Spherical Standing Wave in Space) are interconnected and cannot be separated. Further, the field actually measures the change in velocity of the Spherical In-Waves and how this changes their ellipsoidal shape and the resultant motion (acceleration) of the Wave-Center (due to these changes in the In-Waves which determine the future position (Motion) of the Wave-Center). This explains why Space-Time is bound together, for it is caused by the Wave-Motion of Space which is obviously bound together!

See also: The Philosophy and Metaphysics of Mathematics and the Mathematical treatment of the Wave Structure of Matter (WSM)

Most Simple Science Theory of Reality


Explaining Albert Einstein's Three Dimensional Space and How Matter Exists as a Field in a Four Dimensional Space-Time Continuum

As is common (and tragic) with great minds, their ideas are incompletely / incorrectly understood and this leads to future errors and extravagances. Most modern physicists, and indeed, most physics text books, present the argument that Relativity is not an Aether/Space theory. In fact Relativity is an 'Aether/Space' Theory as Albert Einstein explains;

'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.'
'The aether of the general theory of relativity is a medium without mechanical (‘Particles’) and kinematic (Motion) properties, but which codetermines mechanical and electromagnetic events.' (Albert Einstein, 1920, Leiden Lecture)

The difference, and this is profound, is that Albert Einstein rejects the existence of ‘Particles’, and with it he rejects the existence of the Motion of ‘Particles’, thus he develops a field theory based upon Force (change in Motion and Ellipsoidal shape of Matter, i.e. Gravitational Mass) and thus renounces both Motion and ‘Particles’. Thus his Aether of Relativity must be devoid of both ‘Particles’ and Motion.

'Generalizing we must say this: There may be supposed to be extended physical objects to which the idea of motion cannot be applied. They may not be thought of as consisting of particles which allow themselves to be separately tracked through time.' (Albert Einstein, 1954)

Instead he describes Matter as being a Spherically Spatially Extended Field (in Space) which is Changing (in Time) and thus he effectively unites Space, Time and Matter into One thing, the 'Spherical Fields in a Four Dimensional Space-Time Continuum'.

'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.'

'I wished to show that space time is not necessarily something to which one can ascribe to a separate existence, independently of the actual objects of physical reality. Physical objects are not in space, but these objects are spatially extended. In this way the concept 'empty space' loses its meaning.'

'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)

Thus he agrees that the 'ether' or Space physically exists but that Matter, Space, and Time are intimately interconnected (rigidly interconnected by Space), which is true.
Albert Einstein (from Lorentz) does not say what Space/Matter/Time is, rather he explains how it behaves, thus Matter is 'represented' by a spherically extended Force Field (in Space), and this Field is changing: (both the forces (i.e. Charge / Light), and the Spherical / Ellipsoidal Shape (Mass / Gravity), in Time. (His Four Dimensional Space-Time Continuum).
His error is to remove the concept of Motion with the Concept of the ‘Particle’, and thus to attempt (though he failed) to explain both ‘Particles’ and Motion with a changing Force Field (this was perhaps possible, as Force determines accelerated Motion thus the concept of Motion exists in the concept of Force, though it requires the further existence of ‘Particles’ with Mass!). As it turns out though, the Electromagnetic Fields Albert Einstein used were continuous and vector, whereas the true (Wave) Motion is scalar (described by Wave-Amplitude only, see Point vi below) and form discrete standing Waves, thus his task was ultimately impossible (which of course explains his failure).

In fact Lorentz, whose work founded Albert Einstein's Relativity, (though he was also misled by the electromagnetic field and thus argued for an 'ether' for the vector field (Electromagnetic Waves) to exist in) was closest to the truth when he wrote;

' 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, 1900)


On the Curvature of Albert Einstein's 'Four Dimensional Space-Time Continuum'

Now it seems that many people do not correctly understand the meaning of the four dimensional space-time continuum, but it 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 which was briefly called 'world' by Minkowski 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)

Albert Einstein is absolutely correct, if we wish to define the successive Focal-Points (motion of ‘Particle’) of the In-Waves of a Spherical Standing Wave in Space then we require Three Dimensions for the Spherical Wave Structure in Space, and One Dimension for the Motion of the Waves. Thus we could number the Spherical In-Waves 1,2,3,4 ... counting out from the center, and thus plot successive Focal-Points for each successive In-Wave (e.g. (x1,y1,z1,1) (x2,y2,z2,2)) and these four dimensional plots would describe the motion of the Focal-Point (‘Particle’) through Three Dimensional Space. (Thus we see how Time is caused by Wave Motion).

It is important to realize though, that Matter's Curvature of the 'Four Dimensional Space-Time Continuum' is Only Mathematically True. For Matter moving past a massive body in Three Dimensional Space (e.g. an asteroid moving past the Earth) then it is the relationship between the high mass-energy density of space of the Earth, which slows the In-Wave-Velocity (and shortens the Wavelength and stretches the Spherical In-Waves into an Ellipsoidal Shape) that causes the Resultant Wave-Center's of the asteroid to Move in a Curved (Accelerated) Path (which Albert Einstein Mathematically and correctly describes using Four Dimensions of Space and Time, as is necessarily required to determine the Motion of an object in Three Dimensional Space!).

'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.
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 behavior of bodies and the motion of clocks rather depend on gravitational fields which in their turn are produced by matter.' (Albert Einstein, 1919)

Now this is very important, for it is this 'curvature' that largely led to Albert Einstein's early fame. As we have explained, the measurable properties affected by the presence of spherically spatially extended Matter in Space is that the path of nearby light and matter is caused to be curved.
It was the prediction by Albert 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! Just like an asteroid, the curved path of light is simply caused by the higher mass-energy density of space near Matter and the resultant slower Wave-Velocity. As Albert Einstein rightly says;

'The particle can only appear as a limited region in space in which the field strength / energy density is particularly high.'

But we now understand his error of using the e-m (Charge) and geometric / Ellipsoidal (Mass/Gravity) fields and realize that it is actually the mass-energy density of Spherical Standing Waves in Space which is particularly high at the Wave-Center/’Particle’. 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.'

Thus very tiny differences of Wave-Medium Density occur near very large masses such as the Sun due to this cumulative effect of many trillions of high mass-energy density of space Wave-Centers. This increasing mass-energy density of Space slows the velocity of the wave fronts and causes them to curve slightly when passing massive bodies like our sun.


Summary: Explaining Albert Einstein's Spherical Field Theory of Matter in Terms of the Spherical Wave Structure of Matter

Albert Einstein is correct that Matter, Time and Space are not separate (like ‘Particles’) but are somehow united by One thing (the Space of Our Universe).
His error was to develop his Metaphysics from the perspective of Matter (as changing Fields in Space-Time) rather than from Space and that Matter and Time are caused by the Spherical Standing Wave Motion of Space.
Thus he describes matter in Space as a 4D space-time continuum using the changing vector force field (direction and quantity of Force). Instead it is a Spherical Standing Wavemotion in Three Dimensional Space, and the fourth Dimension is Motion. (A standing wave MOTION field that describes a Scalar Quantity only - Wave Amplitude.)

Note: Scalar Waves are defined by ONE non directional quantity (Wave Amplitude), Vector Electromagnetic Waves are defined by TWO quantities representing Direction of Force (for both the electric and magnetic fields).
The continuous 'force field' is actually an approximation of many discrete standing Wave interactions and ultimately any force and resultant acceleration on a 'Particle' is caused by the change in velocity of their In-Waves. (The vector directional component is not fundamental (like in Albert Einstein's force field) but is caused by the slowing down (i.e. for gravity) of the In-Waves in one particular direction. (e.g. Our In-Waves coming in through the Space of the Earth.)

Thus Albert Einstein founded Relativity on a Continuous Vector Spherically Spatially Extended Force Field which changes in a Four Dimensional 'Space-Time' Continuum rather than a Discrete Scalar Spherically Spatially Extended Standing WaveMotion Field in Three Dimensional Space. (If we are to be precise with our language, but it is not really as complicated as it sounds!)
We replace Time with Wave Motion, and Matter, rather than being a continuous changing Spherical Force Field in Space-Time, is replaced with a discrete Spherical Standing Wave Motion 'Field' in Three Dimensional Space. (It is true though, that four dimensions are required to describe the Motion of Spherical Waves, and their resultant Wave-Center ‘Particle’ effect in Space.)


On the Solutions to the Major Problems of Albert Einstein's Relativity

But it cannot be claimed that those parts of the general relativity theory which can today (1940) be regarded as final have furnished physics with a complete and satisfactory foundation. In the first place, the total field appears in it to be composed of two logically unconnected parts, the gravitational and the electromagnetic. And in the second place, this theory, like the earlier field theories, has not up till now supplied an explanation of the atomistic structure of mater. This failure has probably some connection with the fact that so far it has contributed nothing to the understanding of quantum phenomena. (Albert Einstein, 1940)

i) Albert Einstein did not Know How Matter Existed in Space

The Electromagnetic Field Theory of Relativity is Inductive and describes Effects not Causes, and thus cannot describe Reality as Aristotle well knew.

Rather, they start this, displaying it to the senses, .... and go on to offer more or less rigorous demonstrations of the per se attributes of their proprietary genera. This sort of procedure is inductive and it is as plain as a pikestaff that it does not amount to a demonstration of essence or of what it is to be a thing. (Aristotle, Metaphysics)

The Electric and Magnetic Force Fields were first founded on repeated observations of how many trillions of Electrons and Protons behaved (how magnets and electrically charged objects attracted and repelled one another, and how moving magnets produced electrical currents in wires, and vice versa... etc.). This explains why the fields were continuous, as many trillions of discrete standing wave interactions blend together into a continuous force. It was only around 1900 (Planck) that Physicists discovered that energy exchanges were in discrete amounts, and by then the continuous field theory was well established by Faraday, Maxwell and Lorentz (and soon by Albert Einstein!)

The Electromagnetic Force Field Theory was always Empirical and Inductive though, and never described the actual Structure of the Electron. Thus Albert Einstein did not know what Matter was, he just knew certain Inductive Laws (from repeated observation) about how it behaves (by measuring the forces that matter has on the matter around it).

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)

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. ... I wished to show that space time is not necessarily something to which one can ascribe to a separate existence, independently of the actual objects of physical reality.' (Albert Einstein, 1934)

ii) Continuous Fields do Not Explain the Discrete Energy Levels of Matter as Determined by Quantum Theory

Albert Einstein limited his description of Reality to mathematically describing the effects (forces/acceleration) of Matter on other Matter in the Space around it using a Spherical Spatially Extended Continuous Force Field. He did not Understand the true Cause of this Effect which is a discrete Spherical Standing Wave and thus he was unable to unite the Continuous Fields of Relativity with the discrete (‘Particle’) Standing Wave (and Wave-Center) aspects of Reality as discovered by Quantum Theory.

The great stumbling block for a field theory of this kind 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. (Albert Einstein, 1934)

iii) Albert Einstein's Fields need ‘Particles’ to act Upon

Albert Einstein used the theoretical foundations developed by Faraday and Lorentz and thus required the Existence of a ‘Particle’ to somehow generate the ‘Field’ which in turn acted on other ‘Particles’. While Albert Einstein rejected the concept of a ‘Particle’, he was nonetheless stuck with the ‘Particle’ concept in his Field Theory of Matter as found in Relativity.

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 and total differential equations.... 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. (Albert Einstein, 1931)

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) forces and on the other hand possess the property of generating a field. 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. (Albert Einstein, 1936)

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. As Dr Milo Wolff explains, the Wave Structure of Matter solves these problems of Infinite Field Strengths.)

iv) Albert Einstein Believed Matter Caused Space Rather than Waves in Space Causing Matter

A body in motion or at rest must be determined for motion or rest by some other body, which, likewise, was determined for motion or rest by some other body, and this by a third and so on to infinity. (Spinoza, 1673)

Albert Einstein believed that the Motion of Matter could only be described relative to all the other Matter in the universe (like Leibniz, Spinoza and Mach), thus Matter, rather than Space must be the central perspective for describing the Motion of Matter (Reality). In a sense Albert Einstein assumes that Spatially extended Matter causes Space and Time (thus he renounced the Concept of an Absolute Space and Time somehow separate from Matter).

In the same way persons (human observers), who had to be introduced for the formation of an objective concept of time, also play the role of material objects in this connection. 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)

In fact Space, Matter, and Time are all united, none precedes any of the others. The material substance which exists is Space, so this is the primary existent, but it has always been vibrating, has always contained Spherical Standing Wave (Motion) which causes both Matter and Time, thus Space, Matter and Time are interconnected and have always existed together.

The difference between Albert Einstein’s Relativity and the Metaphysics of Space and Motion and the Wave Structure of Matter is that his fundamental perspective was from Matter, whereas our fundamental perspective is from Space (but both exist interconnected together so we should not get caught up by which one precedes the other!).

This view complements Spinoza's (which philosophically founds Relativity), that in a finite spherical universe within an infinite Space then the obvious way to measure the motion of one Wave-Center 'Particle' is to compare it to the Motion of all the others in the Universe. But this does not mean that Matter is primary (like Albert Einstein argues), in fact the better argument is that while there are many ‘Particles’ in the Universe, they all exist in One Space which must connect the ‘Particles’, thus the One Space is more fundamental (as we have explained earlier in this Metaphysic).

v) Albert Einstein Never United the Electromagnetic & Gravitational Fields into a Unified Field Theory for Matter

Einstein required both an Electromagnetic Force Field to explain Charge, and a Gravitational Field to explain Mass, thus he requires a ‘Particle’ that can be acted on by two fields and thus the ‘Particle’ must somehow possess properties of both Mass and Charge. He tried and failed throughout his life to unite these two fields into one (and to remove the ‘Particle’ concept from them).

Gravitation had indeed been deduced from the structure of space, but besides the gravitational field there is also the electromagnetic field. This had, to begin with, to be introduced into the theory as an entity entirely independent from gravitation. Terms which took account of the electromagnetic field had to be added to the fundamental field equations. 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. (Albert Einstein, 1934)

vi) Albert Einstein Rejects both ‘Particles’ and Motion

What Albert Einstein did though, was to not only reject the point ‘Particle’ concept of Matter (which it is correct to reject!), but also to reject the Motion of ‘Particles’, and thus to reject (incorrectly) the very concept of Motion and replace it with Force Fields.

In Newtonian mechanics, space and time play a dual role.
First, they play the part of carrier or frame for things that happen in physics, (e.g. motion of a ‘particle’) in reference to which events are described by the space co-ordinates and time.
The second role of space and time was that of being an 'inertial system'.
Thus physical reality was conceived as consisting, at least in principle, of space and time on one hand, and of permanently existing material points moving with respect to space and time on the other. The idea of the independent existence of space and time can be expressed drastically in this way: if matter were to disappear, space and time alone would remain behind (as a kind of stage for physical happening).
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.)
This standpoint was overcome ... with the 'concept of field' and its final claim to replace, in principle, the idea of a particle (material point).
The inseparability of time and space emerged in connection with electrodynamics, or the law of propagation of light. (Albert Einstein)

By removing the error of Time and Electrodynamics we can re-write this as;
'The inseparability of Wave Motion (not Time) and Space emerged in connection with the Wave Structure of Matter, or the law of propagation of light (finite velocity of Wave Motion).

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)

While he was correct to reject the Motion of ‘Particles’, his error was to reject the (wave) Motion of Space itself, and to describe matter as a spatially extended field which changes with Time.
But we now know that neither the ‘Particle’ nor the Continuous Electromagnetic Force Field is a complete description of Reality thus we must reject both the Field and the ‘Particle’, and what remains is Motion. Hence we can now clearly see both Albert Einstein's error and the true path left to explore - the study of Space as a Wave Medium for Wave Motion.

In fact Albert Einstein himself agreed that Quantum Theory, founded on the Wave Properties of matter in Space, is remarkably supported by factual observation;

Experiments on interference made with particle rays have given brilliant proof that the wave character of the phenomena of motion as assumed by the theory does, really, correspond to the facts.
The de Broglie-Schrodinger method, which has in a certain sense the character of a field theory, does indeed deduce the existence of only discrete states, in surprising agreement with empirical facts. It does so on the basis of differential equations applying a kind of resonance argument. (Albert Einstein, 1927)

If he had just considered the Spherical Standing Wave Structure of Matter, he would have found his unified field theory for matter. Instead we had to wait another seventy years and endure the agony of confusion and absurdity that creeps into human affairs when truth remains hidden. Remarkably, Stephen Hawking was very close to the truth when he wrote;

But maybe that is our mistake: maybe there are no particle positions and velocities, but only waves. It is just that we try to fit the waves to our preconceived ideas of positions and velocities. The resulting mismatch is the cause of the apparent unpredictability. (Hawking, 1988)

vii) Ockham's Razor - The Wave Structure of Matter requires less 'Existents' than the Field Theory of Matter

Albert Einstein's Relativity requires;
1.Spherical Fields in Space (Three Dimensional Space/ether)
2. Time (Fourth Dimension)
3. Electric Fields
4. Magnetic Fields
5. Gravitational Fields
6. ‘Particles’ with Mass and Charge
7. Finite Universe

The Metaphysics of Space and Motion and the Wave Structure of Matter (WSM) requires;
1. Spherical Waves in Space (Three Dimensional Space)
2. Wave Motion (Fourth Dimension)
and as per Principle Two, change in velocity of Wave-Motion determined by;
3. Wave-Amplitude (Charge, Light, Electricity)
The higher the combined Wave-Amplitudes the Faster the Velocity of the Wavemotion (and vice versa).
4. mass-energy density of space (Gravitational Mass)
The Higher the mass-energy density of Space, the Slower the Wave-Velocity (and vice versa)

The Metaphysics of Space and Motion and the WSM then explains the further existence of ‘Particles’, Time, Fields, and a Finite Universe in an Infinite Space. (And it is the assumption that these things physically existed that has deceived us.)
i) Discrete ‘Particles’ - Wave-Center of Spherical Standing Waves (and resonant coupling for light photons)
ii) Time - It takes Time for a Wave to flow from place to place. (i.e. The finite velocity of waves causes time)
iii) Force Fields - Force is caused by a change in velocity of the Spherical In-Waves which determines the future location of the Wave-Center (which we see as the accelerated Motion of the ‘Particle’.)
iv) Finite Spherical Universe - Exists perpetually in an Infinite Space where distant Matter's Out-Waves become our Matter's In-Waves (Huygens' Theory)

Thus once physicists satisfy themselves as to the truth of the WSM they are required to accept this Metaphysic simply because of the Principle of Simplicity (Ockham's Razor), that the theory which explains more things with less assumptions is the better theory. But this is a negative way to look at it. We should I think accept that this Metaphysics has explained enough to be taken seriously, perhaps even with some anticipation and sense of excitement, for it describes a very logical sensible spatial world that we can all imagine. And thus it requires mathematical analysis, and it requires experimental testing, and those that do take this seriously, well to me, it is logical that they shall have great success with their intellectual inquiries and shall make many startling discoveries which shall be exactly confirmed by experiment. Such is the power of truth...
But I am ahead of myself, I have not explained nearly enough to sound so bold and certain, we shall carry on with this argument later, for now we must continue with the serious business of slowly but surely presenting more evidence, for there are many things yet to explain.

Concluding Remarks On Albert Einstein

Albert Einstein (1879 - 1955) was a wise and intelligent man whose logical and moral writing remains to this day profoundly important to humanity. Any thoughtful person will find pleasure and great personal benefit from reading the ideas of this wonderful man who lived an extraordinary life. Famous for his mathematical theories, he experienced two world wars, fled his country and the persecution of Jews, and was a passionate pacifist who saw his knowledge being used for atomic warfare. Sadly, history shows that Albert Einstein failed in his attempts to unify the continuous force field theory for matter, light, and gravity (Relativity) with the discrete quantum ‘Particle’/Wave duality of matter and light (Quantum Theory).

At the present time (1954), the main question is whether a field theory of the kind here contemplated can lead to the goal at all. By this is meant a theory which describes exhaustively physical reality, including four dimensional space, by a field. The present day generation of physicists is inclined to answer this question in the negative. In conformity with the present form of the quantum theory, it believes that the state of a system cannot be specified directly, but only in an indirect way by a statement of the statistics of the results of measurements attainable on the system. The conviction prevails that the experimentally assured duality (particle and wave structure) can be realized only by such a weakening of the concept of realty. I think that such a far reaching theoretical renunciation is not for the present justified by our actual knowledge, and that one should not desist from pursuing to the end the path of the relativistic field theory.
Some physicists, among them myself, cannot believe that we must abandon, actually and forever, the idea of direct representation of physical reality in space and time; or that we must accept the view that events in nature are analogous to a game of chance. (Albert Einstein)

It now seems certain to us that physical reality cannot be explained in terms of changing ‘Electromagnetic Fields’ in Space and Time, but only in terms of Space and Wave Motion. Further, Quantum Theory is correct, a perpetual finite spherical universe in an infinite Space, though all matter is necessarily connected, can never be pre-determined, and this lack of knowledge means that Chance and probability exist as fundamental limitations on how precisely we can determine the future motions and positions of matter within our universe. (see Cosmology)

Towards the end of his life Albert 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 force field may not truly represent the reality of matter.
In 1954 Albert 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, 1954)

One cannot help but feel great sympathy for Albert Einstein and the dilemmas that he faced in his later years. On the one hand he clearly understood that matter was spherically spatially extended and was not a discrete ‘Particle’. But he also knew that the discrete nature of light and matter were incompatible with his conception of the continuous field and his wonderful logical construction of relativity, which had brought him such fame in his youth. How could he possibly abandon such success and begin again from new foundations?

Unfortunately for Albert Einstein, it has now become clear that Faraday's invention of the continuous electromagnetic force field to explain action-at-a-distance, while useful, is no more than a mathematical construction, a continuous approximation of many discrete Spherical Standing Wave 'quantum' events. It is a logical (mathematical) truth but not a physical truth of reality - the field does not exist as an actual physical entity or 'structure' of Space.

Albert Einstein's great work does survive though, but on a slightly different foundation than the e-m field. His 'castles' are instead founded on the Spherical Standing Wave Structure of Matter in Space. Indeed, they are extended because the origins of Relativity are now identified and understood as being caused by the Wave Structure of Matter (WSM). And certainly with no Albert Einstein (my friend who I have read so often for help and guidance) there would have been no Metaphysics of Space and Motion.

What is most remarkable though, is that from this very simple and sensible foundation of the Metaphysics of Space and Motion and the Spherical Standing Wave (SSW) Structure of Matter in Space we can now mathematically unite Relativity and Quantum Theory, and also Solve most of the perplexing puzzles and problems of Cosmology. (See Most Simple Science Theory) Further, we believe that, given time and scientific study, this knowledge will be able to explain ALL things that exist.
(In fundamental philosophical terms of Space and Wave Motion, and ultimately back to one absolute thing, Space! e.g. relations, processes, subjects and objects, a priori and a posteriori knowledge, species, identity, consciousness, etc. etc., which is exactly what one must necessarily be able to do if they know reality.)





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Albert Einstein"When forced to summarize the general theory of relativity in one sentence: Time and space and gravitation have no separate existence from matter. ... Physical objects are not in space, but these objects are spatially extended. In this way the concept 'empty space' loses its meaning. ... The particle can only appear as a limited region in space in which the field strength or the energy density are particularly high. ...
The free, unhampered exchange of ideas and scientific conclusions is necessary for the sound development of science, as it is in all spheres of cultural life. ... We must not conceal from ourselves that no improvement in the present depressing situation is possible without a severe struggle; for the handful of those who are really determined to do something is minute in comparison with the mass of the lukewarm and the misguided. ...
Humanity is going to need a substantially new way of thinking if it is to survive!" (Albert Einstein)


Biography: Geoffrey Haselhurst, Philosopher of Science, Theoretical Physics, Metaphysics, Evolution. Our world is in great trouble due to human behaviour founded on myths and customs that are causing the destruction of Nature and climate change. We can now deduce the most simple science theory of reality - the wave structure of matter in space. By understanding how we and everything around us are interconnected in Space we can then deduce solutions to the fundamental problems of human knowledge in physics, philosophy, metaphysics, theology, education, health, evolution and ecology, politics and society.

This is the profound new way of thinking that Einstein realised, that we exist as spatially extended structures of the universe - the discrete and separate body an illusion. This simply confirms the intuitions of the ancient philosophers and mystics.

Given the current censorship in physics / philosophy of science journals (based on the standard model of particle physics / big bang cosmology) the internet is the best hope for getting new knowledge known to the world. But that depends on you, the people who care about science and society, realise the importance of truth and reality.

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