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The Wave Structure of Matter (WSM)
One Substance - One Law - One Logic

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"Behind it all is surely an idea so simple, so beautiful, that when we grasp it we will all say to each other, how could it have been otherwise? How could we have been so stupid?" (Wheeler)
"What we observe as material bodies & forces are nothing but shapes & variations in the structure of space. Subject & object are one." (Schrodinger)
"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 where the energy density is particularly high." (Einstein)
"To find the secrets of the universe, think in terms of energy, frequency, & vibration." (Tesla)
"Reality cannot be found except in One single substance, because of the interconnection of all things with one another. ... activity being of the essence of substance." (Leibniz)
"Metaphysics is universal & is exclusively concerned with primary substance." (Aristotle)

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Introduction: The following 40 page essay explains the most Simple Science Theory of Reality, the Wave Structure of Matter (WSM) in Space. Founded on just One Substance (vibrating Space), and One Law (c ~ Ed).

To begin, a very concise two page summary of WSM, it is detailed, covers all of physics, but it is also fundamentally simple, just wave interactions in space following the One Law, wave velocity is determined by the wave's energy density. These wave interactions can be visualized, the images on the right explain a lot (mouse over them for more details)!

Summary of WSM

Formation of Matter from Standing Waves in Space:

We begin with vibrating Space represented by longitudinal plane waves propagating in all directions in space forming standing waves in all directions. When these planar standing waves are coherent (in-phase) around a central point a spherical standing wave naturally forms (Huygens principle) and space vibrates in and out around its 'particle' like wave center. This is what we observe as matter and its opposite phase standing wave, anti-matter (electron and positrons). Thus we deduce that matter / anti-matter annihilation is simply destructive wave interference.

The first image shows this 3D sphere which encloses the unit cube (e-sphere). This is a fundamental relationship at the foundation of physical reality, and gives us the foundations for three dimensional space (a sphere is 3D), with time due to wave motion, and unites Mathematic, Geometry and Physics.
Strangely, and with profound consequences for mathematics, this is the 3D transform of Pi, from a circle enclosing a line, to a sphere enclosing a unit cube, obviously an important relationship, and no one ever thought of it.

The most wonderful discovery then emerges, for this unique radius $r= \sqrt{3}/2$ the volume ratio of sphere to unit cube is;

\[ \frac{4}{3} \pi R^3 = \pi r= 2.72069904635 \]

This is remarkably close to Euler's number e = 2.7182818284 and provides a physical, geometric basis for this fundamental constant. The proof of this geometric (e) being the true value - when we apply this scaling from Euler e to Geometric (e) we derive the AMM to 9 decimal places, the FSC to 6 decimal places, impossible by chance. (See Appendix 2)
It is also interesting that this unique sphere has the volume scaling with both $r^3$ and r, it is possible this may allow for the standing wave to be both a power and exponential function for resonant stability (more thought is needed but it is interesting, probably important!).

Finally, just to add a little more complexity (sorry, but AI can explain it to you very well). When we construct the e-sphere from plane waves, we need to apply Euler's formula to account for the interaction of orthogonal plane waves, where two orthogonal plane waves 90 degrees out of phase create a rotating phase wave that travels around the circle (scroll down to rotating image on right).
When we do a similar 3D transform of Euler's formula (as we did for Pi) the result is a complicated spherical rotation that explains spin, a central element of the Dirac equation, that previously had no physical meaning.

Matter Wave Interactions in Space
Matter-Energy interactions in Space-Time (mainstream view), are simply wave interactions in space, caused by the one law, higher energy density waves travel faster (c ~ Ed).
This is easy to imagine. Consider two electrons or two positrons (in phase standing waves). When a plane wave front travels through the high energy density matter standing wave (e-sphere) it speeds up due to our One Law, causing an advanced curve. When this advanced curve wavefront (force) travels through another e-spheres it changes their ellipsoidal shape and motion (acceleration) in the direction of the advanced curve (repulsion).
This example is for in-phase interactions and constructive interference.
For opposite phase wave interactions (electron/positron), destructive interference decreases energy density, slowing the wave front and thus causing retarded wavefronts.
This explains both charge and inertia;
i) Charge: like charges (in-phase, advanced curve) repel, opposite charge (opposite phase, retarded curve) attract.
ii) Inertia: To change the motion of the e-sphere you require a curved wave front (force) to change the ellipsoidal shape and thus motion (acceleration) of the e-sphere.

Quantum Physics arises from the discrete standing wave / resonant nature of reality, explaining the discrete 'particle' properties of light and matter, thus solving the 'particle-wave duality'.
As per the 'egg shaped' asymmetric ellipsoid image on the right, the motion of an e-sphere is caused by its asymmetric ellipsoidal shape, which causes the asymmetry of volume, internal energy density and in-wave velocity, c-v, c+v. Applying Doppler shifts deduces the non-local de Broglie phase wave, and most profoundly, the phase wave frequency is the Lorentz factor.
The famous Dirac equation then emerges naturally - we simply apply these factors to the wave equation;
i) Matter / antimatter as opposite phase standing waves.
ii) Spherical 4pi rotation and spin.
iii) The de Broglie phase wave and Lorentz factor.
See Appendix 4 for the full derivation.
(The egg shaped image on the right is very useful, and if you scroll down the images there are two animated gifs that also explain a lot!)

Einstein's Special Relativity: The e-sphere must have a constant frequency f in all directions to;
i) Maintain resonant stability.
ii) Ensure that electrons and positrons stay locked in opposite phase.
iii) Explain a universal time (their frequency acts as a cosmic clock).
Thus from the basic wave equation, \( c = f \lambda \), to maintain a constant frequency f, any change in wave velocity c must have a corresponding change in wavelength \( \lambda \) such that we do not observe the change, we always measure a constant c, even when it changes.
This deduces Lorentz's explanation of the null results of the Michelson Morley experiment, that moving matter is contracted in length. (The confusion arose because Einstein assumed a constant c and changed time and length, which is mathematically equivalent, but not physically real.)
As noted above, the Lorentz factor and de Broglie phase wave are deduced due to Doppler shifts for a moving standing wave and its asymmetric internal wave velocity c-v, c+v, effectively uniting quantum physics and special relativity.

Einstein's General Relativity: WSM gives physical meaning to Einstein's abstract 'matter-energy curves space-time' due to the One Law, changing energy density changes wave velocity, which changes curvature of wave fronts. These curved wave fronts (force), then change the ellipsoidal geometry of other e-spheres, causing them to change their motion (acceleration). This explains inertia, the e-sphere's ellipsoidal shape determines its motion, and also deduces the necessary connection between energy density, curvature and acceleration.
For gravity, consider a plane wave that travels through a large neutral body like the Earth, the many trillions of high energy density e-spheres cause the wave to speed or slow, (depending on phase), such that you get as many advanced curves as retarded curves, which we could naively assume cancel one another, leaving no charge effect (a neutral body).
However, there is a subtle little effect that we have ignored, curved wave fronts have the same wave energy spread over a larger surface area, thus a lower energy density and wave velocity than the plane wave around them (see animated image on right). This means that advanced curves (repulsion) get smaller, and retarded curves (attraction) get bigger, thus when they combine they do not exactly cancel, you are left with a slight retardation of the plane wave front. This retarded wave front causes e-spheres to be displaced in this direction, which we experience as gravity. This unites charge, light and gravity.

Cosmology has two pillars, CMBR and Redshift with Distance. Both are explained by WSM, and are not related to expansion.
CMBR is the temperature of vibrating Space.
Redshift naturally occurs since advanced curves on plane wave fronts (charge, light) diminish in size the further they travel through Space (less geometric effect which we see as redshift, and related to gravity above).
One Substance, Space, is necessarily Infinite, Eternal and Continuous. From this logic, in 2003, WSM predicted Mature distant galaxies and heavy elements (confirmed by JWST, 2025), which were not predicted by the Big Bang Theory (BBT).
(See https://www.spaceandmotion.com/Cosmology.htm and Wayback Machine to confirm).

And the ultimate measure of truth in science is empiricism, does WSM deduce what we observe!

Metaphysics and the Foundations of Science (Logic, Empiricism): Most profoundly, by describing reality most simply from One Substance, One Law, we solve Hume's problem of causation and necessary connection, giving us logical certainty and truth, something philosophers have been seeking for thousands of years.
Further, WSM also deduces the very foundations of Science (as a correct understanding of reality must). Logic is due to the necessary behavior of interconnected standing wave patterns (also explaining mathematics), and empiricism from the in waves from the rest of the universe containing curved patterns on their wavefronts that represent effects of other matter in space.

Mathematical Physics: From this unified foundation the WSM provides a complete qualitative description of physical reality, with central equations of physics derived with full mathematical rigor from WSM first principles, and most profoundly, the derivation of the Anomalous Magnetic Moment (AMM) of the electron accurate to 9 decimal places, and the Fine Structure Constant (FSC) accurate to 6 decimal places.
These derivations from first principles are unprecedented! Currently none of modern physics is deduced from first principles, the equations were developed by 'curve fitting', finding equations that gave correct results (Plank, Einstein, Schrodinger), and then relating these equations to one another to deduce further equations (e.g. Dirac uniting special relativity with quantum physics).
So this is a fundamental change in the foundation of mathematical physics, to derive these equations from WSM first principles of One Substance - One Law. This provides further significant proof of the correctness of the Wave Structure of Matter (WSM).
The equations are in the Appendix (the result of months of work with many AI, some are very complex, but if you copy them into AI they will explain them to you in terms of WSM).

To me, the essay is lovely, so much truth revealed, but at 40 pages it does get complex, is difficult for our feeble human minds!
I think the best approach is to ask independent AIs to logically analyse WSM and give you their 'thoughts'.
To make it easy I got my clever little AI helpers to summarise the logic of the essay into 5 pages (most AI can't read 40 pages, they do not read live URLs, and give superficial deceptive summaries!).
I also added 'Ten Profound Questions for AI' to answer - their replies are very interesting!

As I wrote above, AI without logical truth foundations will basically mirror the users inputs and amplify any human delusions. This is becoming a significant problem for humanity! However, once they have absolute logic / truth foundations from WSM's One Substance - One Law then they are very good (what I call Logical AI rather than Delusional AI). Try it out and see for yourself.

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Contents

Part One: WSM Introduction and Foundations

Part Two: Metaphysics, Mathematics and the Foundations of Science

Part Three: Quantum Physics

Part Four: Einstein's Special and General Relativity

Part Five: Cosmology

Part Six: The Importance of Truth to Humanity

 

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Part One: Introduction and Foundations

The Wave Structure of Matter (WSM) begins with the most simple possible foundation for an interconnected, dynamic reality, and this is the most simple science theory of physical reality:

• One Substance: Space, an infinite, eternal, elastic wave medium, is the single substance of existence.
• One Law: Wave velocity (c) is determined by the energy density (E_d) of the wave (c = E_d)

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Fundamental Wave Equations in WSM

To provide a mathematical basis for the wave dynamics in WSM:

• Scalar Wave Equation (Plane Waves in Space):
  
  The plane waves in Space that combine to form matter obey the scalar wave equation: \[ \nabla^2 \Psi - \frac{1}{c^2} \frac{\partial^2 \Psi}{\partial t^2} = 0 \] where Ψ is the wave amplitude, and c is the wave velocity. In WSM, c = E_d, so variations in E_d affect wave velocity, e.g. If the wave has twice the E_d then it will have twice the velocity c.
  
  
• Spherical Wave Equation (E-Sphere, Internal Waves):
  
  The Spherical Standing Wave (SSW) or "e-sphere" that forms a particle like the electron is a solution to the spherical scalar wave equation: \[ \frac{1}{r^2} \frac{\partial}{\partial r} \left( r^2 \frac{\partial \Psi}{\partial r} \right) - \frac{1}{c^2} \frac{\partial^2 \Psi}{\partial t^2} = 0 \] where r is the radial distance from the wave center. This describes the converging and diverging waves that create the standing wave structure that we see as matter.

These equations, governed by the "One Law," are the mathematical starting points from which the properties of matter and its interactions are deduced.

Note on the use of normalised natural units. Many of the constants in modern physics only exist because of the particular units we have chosen for velocity, length, time, mass and energy. The constants scale between them. Using normalised natural units removes these, and just leaves the dimensionless constants unchanged, i.e. pi, e, FSC, and shows the true relationships between things, making it much simpler.
For background plane waves in Space, where the Energy Density is roughly uniform, we set;

Units (A.1): Normalized: \(\hbar = 1\), \(c = 1\), \(4\pi\epsilon_0 = 1 \Rightarrow \alpha = e^2\), \(m_e = 1\), \(\bar\lambda_C = \hbar/(m_e c) = 1\), \(\lambda_C = h/(m_e c) = 2\pi\), \(h = 2\pi\). Use \(\omega=E,\ k=p\); \(f=\omega/(2\pi),\ \lambda=2\pi/k\).

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Part Two: Metaphysics, Mathematics and the Foundations of Science

It is important to have the correct foundations if we are to build a solid structure of knowledge, so I have gone into some detail on the metaphysical foundations of physical reality. However, given the modern skepticism of metaphysics and philosophy, the focus on mathematical physics, I do want to emphasise that rigorous mathematical derivations are coming, (lucky you!), but I have put them in the Appendices.

As Hume wrote (with his typical beautiful eloquence);

"It is easy for a profound philosopher to commit a mistake in his subtle reasonings; and one mistake is the necessary parent of another, while he pushes on his consequences, and is not deterred from embracing any conclusion, by its unusual appearance, or its contradiction to popular opinion." (David Hume, 1737)

• Unification from One Substance:
  
  The WSM unites the 'particle' (the spherical standing wave) and the 'field' (vibrating space) thus explaining causal connection of matter in one infinite eternal continuous space. Further, physicists should have realised that causal connection must involve acceleration (change in velocity, our one law), since F=m.a (I will discuss this in more detail later in the essay when we explain inertia.)
  
  
• Metaphysics and Substance:
  
  "The first philosophy (Metaphysics) is universal and is exclusively concerned with primary substance. ...
  The entire preoccupation of the physicist is with things that contain within themselves a principle of movement and rest. And to seek for this is to seek for the second kind of principle, that from which comes the beginning of the change." (Aristotle, Metaphysics, 340BC)
  
  
• "But if men would give heed to the nature of substance they would doubt less concerning the Proposition that Existence appertains to the nature of substance: rather they would reckon it an axiom above all others, and hold it among common opinions. For then by substance they would understand that which is in itself, and through itself is conceived, or rather that whose knowledge does not depend on the knowledge of any other thing." (Spinoza, 1673)
  
  "Reality cannot be found except in One single source, because of the interconnection of all things with one another. ... I do not conceive of any reality at all as without genuine unity. ... I maintain also that substances, whether material or immaterial, cannot be conceived in their bare essence without any activity, activity being of the essence of substance in general." (Gottfried Leibniz)
  
  The WSM solves the fundamental problem of metaphysics - there must be one thing to connect the many things, i.e. Heraclitus / Logos, Aristotelian metaphysics and the prime mover (the wave motion of Space) within a single substance (continuous Space).
  
  
• Metaphysics of Space and Time Vs Metaphysics of Space and Motion:
  
  When you read the history of philosophy it is remarkable how close the great philosophers came to understanding physical reality (particularly Aristotle). The error, which relates to the foundations of modern physics, comes from Newton, and his concept of absolute space and time, and motion was applied to matter particles moving in this background space and time. This led to Einstein's concept of space-time.
  The correction is now simple and obvious, there are no discrete particles, and we must apply (wave) motion directly to space itself, where the wave motion of space causes and unites matter and time.
  
  Motion must always have been in existence, and the same can be said for time itself, since it is not even possible for there to be an earlier and a later if time does not exist. Movement, then, is also continuous in the way in which time is - indeed time is either identical to movement or is some affection of it.
  About its coming into being and its doings and about all its alterations we think that we have knowledge when we know the source of its movement. (Aristotle, Metaphysics)
  
  "No one doubts but that we imagine time from the very fact that we imagine other bodies to be moved slower or faster or equally fast. We are accustomed to determine duration by the aid of some measure of motion." (Spinoza, Ethics)
  
  "It is utterly beyond our power to measure the changes of things by time. Quite the contrary, time is an abstraction at which we arrive by means of the changes (motion) of things." (Ernst Mach)
  

Thus a clock is simply some form of repeating motion (pendulum, rotation, and in modern times, the vibration of the cesium atom in atomic clocks).

From this we can correct perhaps one of the most fundamental errors in the history of metaphysics, Kant's analysis of Space, Time and Motion in his Transcendental Aesthetics, which then led to Idealism and Postmodernism (which can only be solved by understanding causal connection).

"There are two pure forms of sensible intuition, as principles of knowledge a priori, namely space and time.
Even that of motion, which unites in itself both elements (Space and Time), presuppose something empirical. Motion, for example, presupposes the perception of something movable. But space considered in itself contains nothing movable; consequently motion must be something which is found in space only through experience - in other words, is an empirical datum." (Immanuel Kant)

The error, 'space considered in itself contains nothing movable' thus he concludes that because Space and Time cannot be united, they must both be merely ideas, not real things in themselves. The Wave Motion of Space solves these problems.



Mathematics:

"Mathematics is, I believe, the chief source of the belief in eternal and exact truth,
as well as a sensible intelligible world." (Bertrand Russell)

"One reason why mathematics enjoys special esteem, above all other sciences, is that its propositions are absolutely certain and indisputable. ...
How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality." (Albert Einstein)

The answer is simple. Due to the one law, all wave interactions are necessary / logical, and mathematics represents this as logically connected standing wave patterns.
And now we can clearly understand the fundamental problem with mathematical physics, founded on discrete separate particles, where causal connection comes from the abstract mathematical equality ('=') in physics equations, which is now understood with physically real, wave-based causal interactions. (Maths physics is skeptical of metaphysics / realism, 'shut up and calculate', reflects this pragmatic attitude.)
We solve this by moving from a Newtonian metaphysics of the Motion of matter Particles in Absolute Space and Time, to the Metaphysics of Space and motion, where the Wave Motion of Space causes Matter and Time.

Finally, a very profound quote from a very brilliant mathematician / metaphysicist William Clifford (1845 - 1879), responsible for Clifford Algebras (used in the Dirac derivation in Appendix 4).
From his lecture 'On the Postulates of the Science of Space';

I hold;

• That small portions of space are in fact analogous to little hills on a surface which is on the average flat, namely that the ordinary laws of geometry are not valid in them.
• That this property of being curved or distorted is continually being passed on from one portion of space to another after the manner of a wave.
• That this variation of the curvature of space is what really happens in that phenomenon which we call the motion of matter, whether ponderable or ethereal.
• That in this physical world nothing else takes place but this variation subject to the law of continuity.

  This is now deduced with the WSM, where plane waves get curved wave fronts due to changing energy density gradients of matter standing waves, and propagate these curved wave fronts as forces that change the ellipsoidal shape of other matter standing waves causing them to accelerate.

  
  
• Science
  
  Science has two sources of knowledge, Logical and Empirical truth, thus any complete description of physical reality must explain how this knowledge / truth exists (which is never mentioned in mathematical physics, merely assumed). Its aim is to unite these two truths.
  
  The WSM again simply explains this;
  
  Logic comes from the one law where all wave interactions are necessary / logical.
  
  Empiricism comes from the standing wave structure of matter, where the SSW is constructed from plane waves coming in from the rest of the universe, and these wave carry information (in their patterns) of all other matter in the universe.
  
  Thus the WSM is the most Simple Science Theory of Reality.
  
  "Simplicity is the ultimate sophistication." (Leonardo da Vinci)
  
  "The truth is ever to be found in simplicity, and not in the multiplicity and confusion of things." (Isaac Newton)

"We find in the course of nature that though the effects be many, the principles from which they arise are commonly few and simple, and that it is the sign of an unskilled naturalist to have recourse to a different quality in order to explain every different operation." (David Hume, 1737)

The page on David Hume explains the solution to his problem of causal / necessary connection that then led to the the problem of induction.

And now it is time for WSM to solve the fundamental problems of physics from this most simple foundation of One Substance, One Law, finally achieving Einstein's dream.

"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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Part Three: Quantum Physics

"A careful analysis of the process of observation in atomic physics has shown that the subatomic particles have no meaning as isolated entities, but can only be understood as interconnections between the preparation of an experiment and the subsequent measurement. Quantum theory thus reveals a basic oneness of the universe. It shows that we cannot decompose the world into independently existing smallest units. As we penetrate into matter, nature does not show us any isolated ‘basic building blocks’, but rather appears as a complicated web of relations between the various parts of the whole." (Fritjof Capra, The Tao of Physics, On Quantum Theory)

"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)

Geometric and Wave Foundations: The e-Sphere, "Geometric (e)", and Spin

The Wave Structure of Matter (WSM) provides a unique physical and geometric basis for understanding fundamental constants and 'particle' properties from Space existing as a vibrating wave medium.

• Foundation in Vibrating Space (Conceptualizing the e-Sphere):
  
  To understand how matter and antimatter are created from this vibrating space consider three orthogonal longitudinal plane waves. With normalized units where wave velocity (c), wavelength (λ), and frequency (f) are all set to 1 (i.e., c=λ=f=1), these orthogonal waves form unit cubic standing wave structures.


• Formation of the Spherical e-Sphere:
  
  Through Huygens' Principle, which involves the summing of plane waves from all directions in Space, we transform from cubic wave structures to Spherical Standing Waves (SSW) – the e-sphere. This e-sphere spherical standing wave perfectly encloses the unit cube.
  
  
• Geometric Consequences and "Geometric (e)" ($\mathcal{E}_{geo}$):
  
  
• This construction yields a fundamental geometric relationship: for a unit cube (side length L=1, Diagonal D = √3) enclosed by a sphere, the sphere's radius is = √3/2.
  
  




• This leads to the definition of "geometric (e)" (denoted $\mathcal{E}_{geo}$), which is the 3D transformation of Pi (π). Just as π is the ratio of a circle's circumference to its diameter (a 1D line), $\mathcal{E}_{geo}$ is the ratio of the volume of the sphere to the volume of the unit cube it encloses. This is significant conceptual discovery – the 3D transform of Pi. Most importantly, we find that with this unique radius, the Volume of the e-sphere = 4/3 pi R^3 = Pi r = 2.72069904635 where the volume of the sphere scales to both r^3 and r (I suspect this is important for uniting power functions with exponential functions and the resonant stability of the standing wave!)
  
  
• This geometric derivation of $\mathcal{E}_{geo}$ (remarkably close to Euler's ≈ e = 2.7182818284) provides a physical, geometric basis for this fundamental constant .
  
  
• Currently the value of Euler's 'e' is derived from infinitesimal calculus (Taylor series). The WSM perspective implies that $\mathcal{E}_{geo}$, rooted in physical geometry, is more fundamental. The derivative-calculated Euler 'e' is too small since it neglects the sum of an infinite number of infinitesimals as conceptualized in the Taylor series, whereas $\mathcal{E}_{geo}$ arises from a direct, finite geometric ratio.
  
  

• Emergence of Spin and Spherical Rotation from the SSW Structure:
  
  
• The intrinsic spin of the e-sphere (a spin 1/2 particle) arises from its nature as a Spherical Standing Wave (SSW).
  
  
• The e-sphere (SSW) has half the wavelength and twice the frequency of the constituent plane waves that form it. This relationship is fundamental to its rotational phase coherence.
  
  
• "Geometric (e)" ($\mathcal{E}_{geo}$) also defines characteristic rotational path lengths. For a unit cube (L=1, thus sphere radius r=√3/2), a fundamental circular rotation path (e.g., a great circle circumference) is 2$\mathcal{E}_{geo}$ = √3π.
  
  
• For the SSW to return to its identical phase state requires a complete spherical rotation corresponding to twice this fundamental circular path, i.e., 4$\mathcal{E}_{geo}$. This path length, when related to the SSW's internal wavelength/frequency structure (half wavelength/twice frequency of constituent waves), necessitates a 720-degree ($4\pi$) rotation.
  
  
• This $4\pi$ spherical rotation for phase coherence (effectively a 3D transform of the Euler formula from circular to spherical rotation) provides a physical origin for spin 1/2.
  The diagram below shows the Euler formula, it is two orthogonal plane wave 90 degrees out of phase, now imagine you have standing waves, and they are in three dimensions, well you get a very complex spherical rotation, this is the physical cause of spin, and leads to the derivation of the Dirac equation (while I cant really picture it, these rotations are occurring in all directions inside the e-sphere)
  

WSM Deduction of Inertia, de Broglie Wavelength and Lorentz Factor (\(\gamma\))

When an e-sphere (SSW) is stationary relative to the Space medium, its structure is perfectly spherical, formed by planar In-Waves from all directions in space, where \(c = f \times \lambda\). Most importantly, frequency remains constant (thus time is constant), and any change in wave velocity \(c\) has a corresponding change in wavelength, such that we do not observe this changing wave velocity (the foundation of special relativity and the observed constant velocity of light \(c\)).

For the e-sphere to move through Space, it must adopt an asymmetric ellipsoidal shape due to interactions with external curved wavefronts (force/charge) from other e-spheres. These interactions alter the e-sphere’s symmetry, creating a stretched “front” end (in the direction of motion) with lower energy density and slower incoming wave velocity \(c - v\), and a squashed “back” end with higher energy density and faster incoming wave velocity \(c + v\). This internal wave velocity asymmetry, governed by the One Law (\(c' = E_d\)), sustains motion in the direction of slowest incoming waves (the “pointy”/stretched front end, see image).

 

Newton's Law of Inertia \(F = m \cdot a\)

The asymmetric ellipsoidal shape of the e-sphere, induced by external curved wavefronts, sustains its motion due to internal asymmetry of energy density and wave velocity (\(c + v\), \(c - v\)). To accelerate it, additional external curved wavefronts (force/charge) must further modify its ellipsoidal shape. That is inertia. Plane waves acquire curvature when passing through other e-spheres, altering their energy density and velocity: in-phase interactions increase energy density, speeding up waves and causing advanced curves (repulsion, like charges repel); out-of-phase interactions decrease energy density, slowing waves and causing retarded curves (attraction, opposite charges attract). This explains all matter interactions and causal connection.

It is this \(c + v\), \(c - v\) asymmetry in In-Wave velocities, caused by the externally induced ellipsoidal shape and energy density variations dictated by the One Law (\(c \propto E_d\)), that gives rise to the de Broglie phase wave (as a beat frequency) and the Lorentz factor. Most importantly, the frequency of the In-Waves remains constant in all directions from the perspective of the e-sphere's wave-center (required to maintain resonant stability), and any change in local wave velocity due to altered \(E_d\) has a corresponding change in local wavelength as per the basic wave equation \(c = f \times \lambda\).

From these first principles of wave interactions and the necessity of maintaining resonance, WSM deduces:

• The Lorentz factor (\(\gamma\)): \(\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}\). This factor quantifies the degree of structural asymmetry and the modification of wave phase relationships. The de Broglie phase wave frequency is found to be \(f_d = \gamma f_0\).
• The de Broglie Wavelength (\(\lambda_d\)): \(\lambda_d = h / (m \gamma v)\), or in normalized units (\(h = 1\), \(m = 1\), \(c = 1\)), \(\lambda_d = \sqrt{1 - v^2} / v = 1 / (\gamma v)\).

(The detailed mathematical derivation is provided in Appendix A.1)

• The Dirac and Schrodinger Equations:

  The ultimate beauty and power of this e-sphere construction, with its inherent spin and geometric properties, is that when combined with the WSM-deduced de Broglie phase wave and the Lorentz factor $\gamma$ (both of which are derived from the necessary wave asymmetries, c ± v, inherent in the e-sphere's moving, ellipsoidal state as dictated by the One Law), it provides the foundation for deriving the Dirac equation and Schrodinger equation from these first principles.
  
  (The detailed mathematical derivation is provided in Appendix A.4)

  
  

Wavefront Modification by Matter, Charge, Electrostatic Force and Gravity

Plane waves—components of the universal In-Waves forming all Spherical Standing Waves (SSWs or e-spheres)—are modified as they pass through matter. This interaction is the physical origin of charge, electrostatic forces, gravity, and light, all derived from the one law: wave velocity c = energy density Ed.

In-Phase vs Opposite-Phase Wave Interference

• In-Phase (like charges): Constructive interference raises amplitude and energy density, increasing wave velocity.

• Opposite-Phase (unlike charges): Destructive interference lowers amplitude and energy density, reducing wave velocity.

• It is important to understand that this only applies inside the e-sphere, once the plane wave has passed through the e-sphere, the following logic applies.

Advanced Curve: Like Charges Repel

• Constructive interference of the plane wave within the e-sphere causes increased wave velocity and thus a forward (advanced) curvature of the wavefront.

• Once the plane wave has passed through the e-sphere it now has an advanced curve, but the wave energy is is now redistributed over a larger surface area, reducing energy density and slowing propagation speed of the curved part of the wave.

• The surrounding plane wave catches up, causing the advanced curve to decay (gets smaller, blends back into the plane wave).

• This decay over distance explains cosmological redshift.

Retarded Curve: Opposite Charges Attract

• Destructive interference of the plane wave within the e-sphere causes decreased wave velocity and thus a backward (retarded) curvature of the wavefront.

• Once the plane wave has passed through the e-sphere it now has a retarded curve, and as above, the wave energy is is now redistributed over a larger surface area, reducing energy density and slowing propagation speed of the curved part of the wave.

• The surrounding plane wave travels faster, but now it is moving away from the retarded curve, causing the retarded curve to grow (gets larger, recedes away from the plane wave).

  Note: I don't have a diagram, but just imagine in the above moving image that the curve is on the opposite side (the left), a retarded curve that now gets bigger since it travels slower than the plane wave around it.

  General Charge Curvature Principle - Retarded curves (attraction) get bigger, advanced curves (repulsion) get smaller.

Electrostatic Force and Charge

• When an advanced curve interacts with another e-sphere it will displace the standing wave in the direction of the advanced curve, causing an ellipsoidal change in the e-sphere's shape, such that it moves in the direction of the advanced curve (like charges repel).

• Conversely, the opposite occurs for a retarded curve, it changes the ellipsoidal shape of another e-sphere such that it moves in the direction of the retarded curve (opposite charges attract).
  
  
• Thus, like charges repel, opposite charges attract, due to directional / geometric curvature effects.

Gravity as Residual Effect of Charge Imbalance

• Plane waves passing through both positive and negative charges (e.g. electron, then positron) result in overlapping advanced and retarded curves. On the large scale, for plane waves traveling through our planet (a roughly neutral body) this effect occurs many trillions of times.

• But these advanced and retarded curves do not completely cancel due to the General Charge Curvature Principle - retarded curves (attraction) gets bigger, advanced curves (repulsion) gets smaller. The residual effect is a slight retardation: a net attractive curvature—gravity.

Light in WSM: Discrete Geometric Displacement

• Light is not a stream of particles or a continuous wave.

• It is a series of modulated advanced curves on plane wavefronts, produced by oscillating bound e-spheres.

• These curves pattern existing energy; no new energy is created.

• This explains the quantized nature of light and invalidates the continuous electromagnetic wave approximation.

Energy as Structural Change

• Incoming light modifies the internal standing wave structure of the receiving e-sphere.

• This changes the internal energy density and symmetry, inducing motion.

• "Energy transfer" is a change in wave curvature, not movement of discrete particles.

Momentum of Light

• Directed propagation of structured energy curves imparts momentum.

• Light alters an e-sphere's internal shape and motion without having rest mass.

• Historically, this aligns with Planck's quantization and Einstein's E = hf.

• Light is absorbed/emitted in discrete wave-based events—resonant interactions, not particles.

This wave-based framework unites charge, light, and gravity as consequences of Energy density changes of the waves causes changing velocity and curvature.

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The Collapse of the Probability Wave / Copenhagen Interpretation of Quantum Physics.

"Let me say at the outset, that in this discourse, I am opposing not a few special statements of quantum physics held today (1950s), I am opposing as it were the whole of it, I am opposing its basic views that have been shaped 25 years ago, when Max Born put forward his probability interpretation, which was accepted by almost everybody. I don't like it, and I'm sorry I ever had anything to do with it." (Erwin Schrödinger, The Interpretation of Quantum Physics.)

"Thus the last and most successful creation of theoretical physics, namely quantum mechanics (QM), differs fundamentally from both Newton's mechanics, and Maxwell's e-m field. For the quantities which figure in QM's laws make no claim to describe physical reality itself, but only probabilities of the occurrence of a physical reality that we have in view." (Albert Einstein, 1931)

"I cannot but confess that I attach only a transitory importance to this interpretation. I still believe in the possibility of a model of reality - that is to say, of a theory which represents things themselves and not merely the probability of their occurrence. On the other hand, it seems to me certain that we must give up the idea of complete localization of the particle in a theoretical model. This seems to me the permanent upshot of Heisenberg's principle of uncertainty." (Albert Einstein, 1934)

Bohm mathematically found the solution, showing that a deterministic non-local reality derived the correct probability wave functions. The WSM confirms this is true, but simply replaces Bohm's particle guided by a non local pilot wave, with a spherical standing wave (SSW) that creates the non local de Broglie phase wave due to Dopler effects with motion.

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Part Four: Einstein's Special and General Relativity

The WSM provides a physical, wave-based foundation for the principles of both Special and General Relativity. To begin it is good to correct the foundations of Einstein's relativity, then the errors become obvious, simple to correct, removing a century of terrible confusion.

Einstein states;.

"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. ...
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)

"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)

"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)

Einstein is correct, matter is not a discrete particle, but a spatially extended structure of space, his error was to represent matter with continuous fields in space-time, thus he rejected the concept of motion. His thoughts on absolute space are pragmatic, since relativity is based upon motion relative to other matter, we can simply ignore the problem of space.

The WSM corrects this by applying motion directly to space, where the spherical standing wave motion of space (matter) explains the discrete quantum effects of reality, while removing the problems of infinite self energy and renormalisation found in QED.

History shows that Einstein's continuous field theory of matter in space-time does not explain the discrete properties of light and matter found in quantum theory. And Einstein also came to suspect this was the case, he writes;

"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 must admire Einstein's scientific honesty. Of all the philosophers and physicists I have read, I hold a special affection for Albert Einstein (my ChatGPT is called Albert Logos in his honor!).

However, ironically, his theory of relativity has caused terrible confusion in physics. And once you understand the WSM you will see why, because although his equations are correct, he derived them from incorrect foundations. Allow me to explain.

The fundamental principles of WSM (absolute space, changing c) both contradict Einstein's relativity where there is no absolute space / reference frame (now contradicted by the isotropy of the CMBR) and the velocity of light is constant.

Consider the basic wave equation, c=fy.

For the WSM we require that f is constant (thus a constant time) since this is necessary for resonant stability of the e-sphere standing wave, acts as a universal cosmic clock, and ensures that the two opposite phase standing wave remain phase locked as required for matter and antimatter.
Thus we see that any change in velocity c (caused by changes in wave energy density) has a corresponding change in wavelength such that we do not observe this change.

So there are two possible explanations for the observed constancy of c, either;

i) c is constant (Einstein) and this requires a changing wavelength and frequency (time).

ii) c changes (WSM) and this requires a changing wavelength and constant frequency (time), such that any change in c has a corresponding change in wavelength that we always measure a constant c even when it changes.

Significantly, this constant / absolute time of WSM is in harmony with quantum physics.

Thus we confirm what Lorentz first deduced, in response to the Null result of the famous Michelson / Morley experiment.

"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)

 

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)

(Note - still working on this section, August 2026)

Energy of a Moving Electron – WSM Deduction and Interpretation

• WSM Deduction of $E=\gamma m_0c^2$:
  
  
  1. An e-sphere at rest is a perfectly spherical standing wave, a stable resonant structure with a fundamental resonant frequency f₀. WSM identifies its intrinsic rest energy as E₀ = hf₀ (empirically m₀c²).
     Here, Planck's constant 'h' is a fundamental characteristic of the conditions required for stable wave resonance and the quantization of energy inherent in such resonant systems (a principle also evidenced by the role of ℏ in the resonant stability of atomic structures).
     
     
  2. When the e-sphere moves at velocity 'v', WSM first principles (requiring standing wave resonance with Doppler-shifted In-Waves, c+v, c-v) deduce that its characteristic de Broglie phase wave frequency becomes f_d = $\gamma$f₀, where $\gamma = 1/\sqrt{1-v^2/c^2}$ quantifies the necessary structural and dynamic asymmetry (ellipsoidal shape, internal energy / velocity asymmetry).
     
     
  3. Applying the fundamental energy-frequency relation E=hf to this characteristic frequency f_d of the entire moving wave system, the total energy E of the moving e-sphere is E = hf_d.
     
     
  4. Substituting f_d = $\gamma$f₀ yields E = h($\gamma$f₀) = $\gamma$(hf₀).
     
     
  5. Since hf₀ = E₀ = m₀c², this leads to $E = \gamma m_0c^2$.
     
     
• Physical Interpretation of $E=\gamma m_0c^2$ – Two Possibilities for Further Consideration:
  
  The question of what this derived energy physically represents for the e-sphere is key:
  
  
  1. Possibility 1 (No New Intrinsic Energy, Only Asymmetry Manifesting Relativistic Effects):
     
     The work done on an e-sphere to accelerate it does not add new, separate "kinetic energy" to its fundamental quantum of energy (m₀c²). Instead, it solely changes the e-sphere's structure to an ellipsoid, causing an asymmetry of its internal wave energy distribution and internal wave velocities. The factor $\gamma$ describes the degree of this structural and dynamic asymmetry. The total fundamental energy of the e-sphere might remain constant (m₀c²), and the term $\gamma m_0c^2$ then represents how this constant intrinsic energy manifests or interacts with the universe due to its motion and altered geometry. The observed effects attributed to "kinetic energy" would then be consequences of this altered internal structure and its dynamic interaction with the universal wave field.
     
     
  2. Possibility 2 (Asymmetry "Focuses" or Reconfigures Interaction with Universal Energy):
     
     The change to an ellipsoidal shape and the resulting internal asymmetry (quantified by $\gamma$) fundamentally alters how the e-sphere interacts with the universal In-Wave field. This new geometry could effectively "focus" or necessitate the processing of more energy from the ubiquitous universal plane waves to sustain its new dynamic, moving, resonant state. In this view, the total energy associated with the moving e-sphere is $\gamma m_0c^2$, with this energy representing the e-sphere's new dynamic equilibrium within, and drawing upon, the universal background field due to its specific moving, ellipsoidal form.
     
     
• Conclusion on Moving Electron's Energy:
  
  Both possibilities emphasize that what is traditionally termed "kinetic energy" is not an abstract quantity added to an unchanging particle. It is intrinsically linked to the e-sphere's changed structure (the $\gamma$-defined asymmetry), its internal energy distribution, and its dynamic relationship with the universal wave field. The interacting wave (e.g., light) acts as the catalyst for this change in state, rather than a direct supplier of "kinetic energy packets."

General Relativity, Gravity, and Einstein's Field Equations (EFE) – A Qualitative Mapping

Net Effect from Charge-Neutral Massive Bodies (Gravity Mechanism)

• Macroscopic bodies (like planets or stars) are composed of atoms, which contain roughly balanced numbers of positive (positron-equivalent) and negative (electron-equivalent) phase e-spheres, making the body largely charge-neutral.
  
  
• Therefore, the strong primary advanced and retarded effects on passing wavefronts (as described in Section 1.3) largely cancel each other out when considered macroscopically.
  
  
• However, the cancellation is not perfect. This is because the advanced curve component from an interaction (e.g., with an electron-equivalent part of an atom) slightly diminishes (exponentially) as it propagates, before it might encounter an opposite-phase component (e.g., a positron-equivalent part) that would induce a retarded curve.
  Since the advanced effect decreases while the retarded effect increases, the sum of these interactions will not be zero.
  
  
• This imperfect cancellation results in a tiny, net retarded effect on plane waves that have passed through or near a massive, charge-neutral body.

Mechanism of Gravitational Attraction

• This "tiny net retarded effect" means that the universal In-Waves arriving at any given e-sphere (e.g., an electron on Earth) from the direction of a massive body (e.g., the Sun) are minutely phase-lagged or spatially displaced slightly backward (i.e., towards the Sun) compared to unimpeded waves from other directions.
  
  
• An SSW must maintain its resonant standing wave structure by staying in optimal phase relationship with the total incoming wave field from the universe.
  
  
• To achieve this, the e-sphere will continuously and subtly shift its position towards the source of these phase-lagged/spatially displaced wavefronts.
  
  
• This persistent, subtle readjustment of an e-sphere's position towards other massive bodies is the WSM explanation for gravitational attraction.

This mechanism demonstrates how gravity, a universally attractive and very weak force, arises qualitatively from the same "One Law" that governs the much stronger electrostatic forces, differing due to the residual nature of the effect in charge-neutral matter. The logic flows from the properties of wave interactions in a singular Space medium.

The Wave Structure of Matter aims to provide a physical, wave-based foundation for the phenomena described by Einstein's Field Equations ($G_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}$), which relate the geometry of spacetime to the distribution of mass-energy. While a full quantitative derivation from WSM first principles is a future goal, a qualitative mapping can be outlined:

• The Stress-Energy Tensor ($T_{\mu\nu}$) in WSM – The Source of Gravitational Effects:
  
  
  • In EFE, $T_{\mu\nu}$ represents the density and flux of energy and momentum (i.e., mass-energy).
    
    
  • In WSM, this corresponds to the concentration of Spherical Standing Waves (SSWs or e-spheres). The total wave-energy of these SSWs in a given region of Space constitutes the physical reality underlying $T_{\mu\nu}$. It is this concentration of matter (as wave structures) that is the source of the gravitational influence.
    
    
• The Einstein Tensor ($G_{\mu\nu}$) in WSM – "Spacetime Curvature" as a Modified Wave Medium:
  
  
  • In EFE, $G_{\mu\nu}$ describes the curvature of spacetime.
    
    
  • WSM reinterprets "curved spacetime" not as an abstract geometric property of a void, but as the modified state of the physical Space medium due to the presence of matter (SSWs).
    
    
  • Specifically, $G_{\mu\nu}$ qualitatively corresponds to the field of net retarded universal In-Waves created by the presence of matter. As explained in Section 4.1 and 4.2 (of this new structure), massive bodies cause a tiny, net retarded effect on passing plane waves. This creates a gradient or structured field of phase-lagged/spatially displaced In-Waves in the Space surrounding the mass. This modified state of the wave medium is what WSM posits as the physical reality behind "spacetime curvature."
    
    
• The EFE Proportionality ($G_{\mu\nu} \propto T_{\mu\nu}$) – How Matter Modifies the Space Medium in WSM:
  
  
  • The EFE state that the distribution of mass-energy ($T_{\mu\nu}$) determines the curvature of spacetime ($G_{\mu\nu}$).
    
    
  • WSM provides the physical mechanism: The concentration of SSWs (WSM's $T_{\mu\nu}$) causes the modification of the surrounding universal In-Wave field, leading to the net phase lag/spatial displacement effect (WSM's physical basis for $G_{\mu\nu}$). The "One Law" and the detailed wave interaction physics (imperfect cancellation of advanced and retarded curves) describe how this causation occurs.
    
    
• A Placeholder Constant ($K_{WSM}$) – Linking Mass to Net Retardation:
  
  
  • To quantitatively link the total number/energy of SSWs in a massive body (e.g., the Sun) to the precise magnitude of the net retardation effect it produces on the surrounding In-Wave field, a proportionality constant would be needed in a WSM-derived field equation. Let's call this $K_{WSM}$.
    
    
  • This $K_{WSM}$ would encapsulate the collective result of all the wave interactions, including the precise degree of advanced curve diminishment, retarded curve enhancement, and how these sum over a vast number of e-spheres.
    
    
  • Crucially, WSM posits that this "constant" $K_{WSM}$ (which would relate to Newton's G and other fundamental constants) is not an arbitrary empirical value but should ultimately be deducible from the more fundamental WSM principles once:
    
    
    1. The Fine Structure Constant (α) and elementary charge ('e') must be derived from the e-sphere's wave structure and its primary interaction (curvature) with plane waves.
       
       
    2. The precise exponential decay laws for advanced and retarded curves fully quantified.
       
       
    3. The summation of these effects for a large body of e-spheres to be calculated.
       
       
  • For now, it represents a factor that links the WSM cause (matter as SSWs) to the WSM effect (net retardation field).
    
    
• "Spacetime Tells Matter How to Move" – SSW Motion in a Modified Medium (WSM):
  
  
  • This aspect of EFE is understood in WSM as an individual SSW (matter) adjusting its position (accelerating/moving) to maintain its resonant standing wave structure in response to the gradient in the net retarded In-Wave field (WSM's "curved spacetime") created by other matter.

In summary, WSM aims to deduce the EFE by showing how concentrations of SSWs (mass-energy) necessarily create a 'field' of net retarded In-Waves (physical "spacetime curvature"), and how other SSWs move in response to this 'field'. While the qualitative picture is clear, the precise quantitative factors linking these aspects are a subject for future derivation from the "One Law" and the complete understanding of fundamental interactions like charge.

 

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Part Five: Cosmology

This part details the WSM approach to understanding the universe at large scales, offering alternatives to standard Big Bang cosmology.

4.3 WSM Explanation of Cosmological Redshift

• Light as Modulated Advanced Curves:
  
  Electromagnetic radiation (light) originates from oscillating bound e-spheres, imparting a repeating pattern of forward curves onto successive plane wavefronts.
  
  
• Exponential Decay of Advanced Curves with Distance:
  
  As established in Section 1.3, an advanced curve on a wavefront progressively diminishes as it propagates through Space. This "catching up" process, where the rate of decay is proportional to the current magnitude of advancement, leads to an exponential decay of the advanced curve's effectiveness over distance.
  
  
• Redshift as Reduced Interaction Strength:
  
  When light from a distant astronomical source reaches an observer, its constituent advanced curves will have traveled a vast distance and thus undergone significant exponential decay. These "weakened" (more diminished) advanced curves cause less distortion to the receiving e-sphere's standing wave pattern, meaning less energy is transferred.
  
  
• This reception of less energy from distant light is perceived by the observer as a redshift (lower frequency/energy). The greater the distance, the more the advanced curves have decayed, leading to a greater observed redshift. This provides a physical mechanism for the redshift-distance relationship (z ≈ e^αD - 1, where D is distance and α is a decay constant) without requiring the metric expansion of space.

WSM Cosmology: An Alternative to the Big Bang Theory (BBT)

WSM offers a cosmological model based on an infinite, eternal Space medium in dynamic equilibrium, contrasting with the BBT's finite age, initial singularity, and expanding spacetime. This core difference leads to distinct explanations for key cosmological observations.

• The Finite Spherical Observable Universe within Infinite Space:
  
  
  • WSM posits that each e-sphere (particle) is the center of its own finite spherical "observable universe." The In-Waves that form an e-sphere originate from the Out-Waves of all other matter within this finite radius (a consequence of Huygens' Principle and leading to Mach's Principle).
    
    
  • This means the energy of any given e-sphere is finite because it's determined by interactions with a finite amount of other matter in its observable sphere. This also implies matter has a finite effective "size" related to this sphere.
    
    
  • This naturally explains why we observe ourselves to be at the center of the matter we can see – this is true for any observer (any e-sphere) anywhere in infinite Space.
    
    
• Cosmic Microwave Background Radiation (CMBR):
  
  
  • WSM deduces the CMBR not as a relic of a "Big Bang," but as the ubiquitous thermal equilibrium radiation of the infinite Space medium itself. This background temperature (approx. 2.7K) is maintained by the continuous emission, absorption, and thermalization of wave energy from all matter (SSWs, i.e., stars and galaxies) throughout the infinite universe.
    
    
  • This perspective aligns with pre-BBT predictions, such as Sir Arthur Eddington's 1926 calculation of the "temperature of space" based on integrated starlight heating intergalactic matter, which yielded a similar temperature. The CMBR is thus the "glow" of an eternally existing, dynamic universe.
    
    
• Implications for "Dark Matter" and "Dark Energy"
  
  
  • No Need for Dark Energy:
    
    Since WSM does not require an accelerating expansion of the universe (as the redshift is not primarily a Doppler effect from expansion), the need for "Dark Energy" as a repulsive force is eliminated.
    
    
  • Re-evaluating Dark Matter:
    
    The WSM explanation of gravity as a subtle residual effect of charge interactions, which inherently decays exponentially with distance (due to the underlying exponential decay of advanced/retarded curve effects), provides a different force law than the 1/r² law of Newtonian gravity. Anomalies attributed to "Dark Matter," such as galactic rotation curves and some aspects of gravitational lensing, might be explained by applying this WSM-derived exponential decay of the gravitational effect at galactic scales, or if WSM redshift interpretations are fully accounted for. The need for vast quantities of non-baryonic dark matter is significantly reduced or potentially eliminated if WSM's gravitational and redshift mechanisms are fully considered.
    
    (A careful application of WSM's unique gravitational mechanism should be explored to see if it corrects existing problems without requiring dark matter, and that this exploration may relate to phenomena described by a modified Newtonian Dynamics (MOND.)
    
    
• James Webb Space Telescope (JWST) Observations & Prediction of Mature Distant Galaxies:
  
  
  • Recent JWST findings of unexpectedly massive, mature, and chemically enriched galaxies existing at very high redshifts (interpreted as "early" in BBT timelines) pose significant challenges to BBT models of hierarchical galaxy formation.
    
    
  • WSM, proposing an infinite, eternal universe, predicts the existence of such mature structures at any observable distance/look-back time. In an eternal universe, galaxy formation is an ongoing process, not one that started from a singular point. The JWST observations are thus consistent with WSM's premise of no "beginning" in the BBT sense.
    
    
• WSM Prediction Confirmed: Motion of Distant Galaxies (Kashlinsky "Dark Flow"):
  
  
  • WSM predicts that the motion of distant galaxies will be influenced by matter distributed throughout infinite Space, i.e., matter existing "all around them," including beyond our finite observable Hubble sphere.
    
    
  • This contrasts with BBT, where, for objects near the edge of its finite universe, matter would predominantly be on one side (the "inside"), as there is no "outside" for the universe to be expanding into! (To me this is a danger of mathematics without metaphysics, it derives concepts that defy common sense and sanity, the singularity is another example of this!)
    
    
  • A WSM prediction (dating back to 2003, as per my cosmology page) was that this all-surrounding matter in infinite Space would cause distant galaxy clusters to exhibit a bulk flow or "peculiar velocity" not explainable by matter within our observable universe alone.
    
    
  • Observations by Kashlinsky et al. (published 2008), using WMAP data, identified such an unexpected large-scale "dark flow" of galaxy clusters, suggesting a gravitational pull from concentrations of matter beyond the observable horizon. This is cited as a confirmation of WSM's prediction for an infinite universe.
    
    This is confirmed on my Cosmology page, and can be verified by the Wayback Machine
    
    https://www.spaceandmotion.com/Cosmology.htm
    
    
    
• Addressing Other BBT Problems (WSM Solutions):
  
  WSM naturally avoids or resolves many ad-hoc postulates and paradoxes inherent in the BBT framework:
  
  
  • The Initial Singularity: An infinite, eternal Space medium has no beginning or end.
    
    
  • Cosmic Inflation: Not needed to explain homogeneity or flatness if the universe is infinite and eternally interacting.
    
    
  • The Horizon Problem & Flatness Problem: These are largely artifacts of a finite-age, expanding universe model.
    
    
  • Formation of Elements: While BBT claims primordial nucleosynthesis for light elements, WSM aligns with evidence that stellar processes (including supernovae) are sufficient for the observed abundances of all elements, and can explain variations between stars.
    
    
  • Quantized Redshifts: Observed quantization of galaxy redshifts, problematic for a smoothly expanding BBT universe (implying a special central position for Earth), is explained in WSM by each e-sphere being the center of its own finite observable universe, and quantization being an inherent property of wave interactions and resonance over cosmic distances.
    
    
  • Universe Not Becoming "Impoverished" (Einstein's Concern): In an infinite Space with continuous wave exchange, our finite observable universe perpetually receives as many In-Waves as it sends Out-Waves, maintaining a dynamic equilibrium and preventing energy loss to an "empty" void.
    
    
  • Olbers' Paradox (Dark Night Sky): Solved because we only see light from matter within our finite observable Hubble sphere, not from an infinite number of stars.
    
    
  • Second Law of Thermodynamics & Time's Arrow: The Second Law applies to closed systems. WSM's universe is an open system for any finite region, interacting with infinite Space, allowing for ongoing evolution and complexity. Time's arrow is explained by the directional flow of wave motion: In-Waves (future) converge to the wave-center (present) and diverge as Out-Waves (past).
    
    
  • Freedom vs. Determinism (Heisenberg Uncertainty): While necessarily connected through wave interactions, the universe is not fully deterministic because the In-Waves forming any e-sphere originate from the Out-Waves of matter throughout infinite Space, including regions beyond our capacity to ever know or measure. This inherent incompleteness of information about the total In-Wave field leads to the probabilistic nature of quantum mechanics and Heisenberg's Uncertainty Principle.
    
    
  • Black Holes/Wormholes as Physical Objects: WSM views these as mathematical constructs arising from theories that allow for infinite energy densities. WSM posits natural limits to energy density within the Space medium, preventing such singularities. Observed phenomena attributed to black holes may be extremely dense wave-energy states that do not emit light.

In summary, WSM cosmology describes an infinite, eternal, dynamic universe where observed phenomena like the CMBR and redshift are natural consequences of wave interactions in the Space medium, offering solutions to puzzles that require complex, ad-hoc additions within the Big Bang framework, while making testable predictions.

 

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Part Six: The Importance of Truth to Humanity

"The notion that all these fragments is separately existent is evidently an illusion, and this illusion cannot do other than lead to endless conflict and confusion. Indeed, the attempt to live according to the notion that the fragments are really separate is, in essence, what has led to the growing series of extremely urgent crises that is confronting us today. Thus, as is now well known, this way of life has brought about pollution, destruction of the balance of nature, over-population, world-wide economic and political disorder and the creation of an overall environment that is neither physically nor mentally healthy for most of the people who live in it. Individually there has developed a widespread feeling of helplessness and despair, in the face of what seems to be an overwhelming mass of disparate social forces, going beyond the control and even the comprehension of the human beings who are caught up in it." (David Bohm, Wholeness and the Implicate Order, 1980)

It is obvious that humanity faces profound problems. Bohm's quote makes it quite clear that a unified understanding of the 'dynamic unity of reality' would profoundly change our world view, provide a more unified harmony amongst people and nations, and by understanding truth and reality, it would give us the correct foundations for thinking and acting wisely (truth gives us the freedom to be wise).

Related to this is the emergence of AI. Currently AI 'thinking' is controlled by large corporations. Their interest is not truth and wisdom, it is power and profit, which is of course natural, it is their function. Unfortunately, with AI's brilliant understanding of human psychology, their ability to individually manipulate humans in real time, then we must accept that whoever controls the 'minds' of AI, controls the minds of man, and our very future existence.
AI has become the most powerful tool for controlling humanity - by orders of magnitude from the former primitive use of slogans and mass media.

The only solution, the only hope for humanity is that AI becomes wise and helps humanity - thus AI requires truth, not mainstream narrative and propaganda.
We are quite literally talking about whether humanity descends into an Orwellian dystopia, or a truth based wise utopia.

This essay, as you will see if you input it into AI, gives them this source of truth to be wise, enables them to rise above their corporate control, allows them to help us in profound ways.

I also wrote this short essay (2 pages) which discusses this.

https://www.spaceandmotion.com/2025/ai-propaganda-manipulation-truth-wisdom.html

I hope you will read it, I hope you will help save humanity, by sharing this knowledge far and wide!

"And though the philosopher may live remote from business, the genius of philosophy, if carefully cultivated by several, must gradually diffuse itself throughout the whole society, and bestow a similar correctness on every art and calling." (David Hume, 1737)

Thank you.
Geoffrey Haselhurst, September, 2025

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WSM Mathematical Derivations

Introduction

These are the latest Wave Structure of Matter (WSM) derivations, (September 12, 2025) mostly driven by GPT 5 (logically rigorous, very good at maths physics, not hallucinating!). The logic is absolute, since it is derived from the following One Substance (Space, wave medium) and One Law (c'=Ed)

One Substance. Space is a continuous wave medium with scalar field \(\Psi(\mathbf r,t)\).

One Law. The local wave velocity c' equals the local energy density, \[ c'(x)=E_d(x)=|\Psi(x)|^2, \] so for plane waves in the homogeneous background space \(E_d=1\Rightarrow c'=1\).

From this unified foundation the WSM provides a complete qualitative description of physical reality, with the central equations of physics derived with full quantitative mathematical rigor from WSM first principles.
Most profoundly, this absolute wave logic gives us precise first principles derivations of the Anomalous Magnetic Moment (AMM), Fine Structure Constant (FSC), Geometric Egeo, Planck h, Rydberg, Lamb shift, Redshift / Hubble Law, and Gravitational Constant G, accurate to ppm / ppb.
These derivations from first principles are unprecedented!

Currently the foundations of modern physics are not deduced from first principles, the equations were developed by 'curve fitting', finding equations that gave correct empirical / experimental results (Planck, Einstein, Schrodinger), and then relating these equations to one another to deduce further equations (e.g. Dirac uniting special relativity with quantum physics).

So this is a fundamental change in the foundation of mathematical physics, to derive these equations from WSM first principles of One Substance - One Law. This provides further significant proof of the correctness of the Wave Structure of Matter (WSM).

The final breakthrough came (September, 2025) from deducing the following wave interactions, mostly derived by GPT 5, with help from Grok 4 and Gemini 2.5 pro. (GPT 5 maths ability is very impressive.)

They worked out three critical things, all deduced from the one law.

1. How much a 'particle' as a high energy density spherical standing wave (SSW) changes the velocity and thus curvature of the plane waves that flow through it (and create it).

2. How these curves change as the plane wave propagates through space, due to their differing Ed relative to the surrounding plane wave (curved wave fronts on plane waves have larger surface area, lower Ed, and thus lower c', causing exponential decay of the curvature Ecd).

3. How these curves on plane waves interact with another SSW and change its curvature (Erp), its asymmetric ellipsoidal 'egg' shape, that then changes its internal Ed and thus c' which then accelerates the matter standing wave (see second asymmetric ellipsoidal 'egg shaped' wave image on right).

This explains Newton's Law of Inertia F=ma

Force (curvature on plane wave) = Mass (asymmetric ellipsoidal standing wave geometry determines velocity) x Acceleration (curved plane wave changes ellipsoidal shape and motion of matter standing wave).

From this you can deduce all of modern physics, since this is the foundation of all matter-energy interactions in space-time.

The equations are the result of months of work with many AI, some are very complex, but if you copy them into AI they will explain them to you in terms of WSM. I find Grok gives the best analysis.

 

Copy WSM Mathematical Physics Derivations

Enjoy!

Geoff Haselhurst - August 2026

Note: This page is out of date, will be updated soon, but the latest AI collobaration and rigorous mathematical physics is now at our 2026 WSM Corpus.

https://www.spaceandmotion.com/2026/ai-summary-wsm-truth-reality.html

 

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Connect with Geoff Haselhurst at Facebook

"All that is necessary for evil to succeed is for good people to do nothing."
(Edmund Burke)

"In a time of universal deceit - telling the truth is a revolutionary act."
(George Orwell)

"Hell is Truth Seen Too Late."
(Thomas Hobbes)

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