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


"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)
"When forced to summarize the general theory of relativity in one sentence: Time, space & gravitation have no separate existence from matter." (Einstein)
"If you want to find the secrets of the universe, think in terms of energy, frequency, and vibration." (Tesla)



WSM Human-AI Collaboration (August, 2026)

One Vibrating Space: From Ancient Philosophy / Metaphysics to Mathematical Physics, Evolution, Life, Mind and Civilisation

For three decades, WSM was principally a philosophical picture of one infinite, eternal, continuous elastic Space. Between May and August 2026, human–AI collaboration transformed it into a tiered mathematical-physics research programme: exact wave constructions, geometric identities, quantitative leading results, no-go theorems, numerical controls, bounded open calculations and clear falsification requirements.

In WSM, electron and positron are proposed as opposite carrier-phase spherical standing waves formed by the Huygens sum of background plane waves from every direction. Each has radial vibration—the candidate physical basis of charge—and axis-free spherical phase circulation—the candidate basis of spin. This open, flow-through wave centre is the e-sphere.

A stationary e-sphere is spherical. Curvature on an incoming wave changes its internal directional energy density and deforms it into a moving wave egg: the near side flattens, the far side elongates, the convergence centre shifts, and the waves reclose around a new position. Its changing internal \(E_d\), shape and reclosure are its motion. WSM therefore proposes a wave-geometric reading of inertia and \(F=ma\): force is imposed curvature, mass is resistance encoded by the recurrent form, and acceleration is its changing deformation. Action must calculate this geometry; geometry also constrains the action, as \(\pi\) and \(E_{\rm geo}\) already demonstrate.

The One Law

\[ \frac{c'}{c_0}=\frac{E_d}{E_{d0}}, \qquad \lambda'=\frac{c'}{f_0}, \qquad k'=\frac{\omega_0}{c'}. \]

At proposed universal carrier frequency \(f_0\), directional energy density changes local wave speed, wavelength and accumulated phase.

The Causal Engine

Relative phase → reinforcement or cancellation → directional \(E_d\) → \(c'\) and \(\lambda'\) → travel-time difference → forward or rear wavefront curve → changed Huygens reclosure → centre motion, deformation and interaction.

Changed out-waves from one e-sphere cross fresh in-waves elsewhere. Matter therefore interacts not across empty distance, but through propagated changes in the one Space constituting every e-sphere.

Status Key

A = exact mathematics or established observation; B = deduction under stated premises; C = proposed physical identification; D = decisive calculation or experiment still open; Q = rejected or quarantined shortcut.

One connected argument: Space → waves → recurrence → matter → life → mind → knowledge → wisdom.


1. Wave Structure of Matter: All Things from One Thing

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

One infinite, eternal, continuous elastic Space, active with real longitudinal waves. Matter is proposed not as a pellet or shell, but as an open e-sphere: waves converge from every direction, cross its changing centre, continue outward and recurrently rebuild the form. Their exchanged phases alter directional \(E_d\); the One Law converts that difference into speed, wavelength, curvature and changed reclosure. The decisive test is whether one frozen nonlinear action calculates stable matter and its measured interactions without separate substances or fitted repairs.

2. The One and the Many: From Greek Philosophy to Wave Physics

https://www.spaceandmotion.com/2026/ancient-greek-philosophy-metaphysics-to-modern-maths-physics.html

Parmenides defended continuous Being; Heraclitus lawful flux. Aristotle sought active substance and necessary cause, connected matter with form and motion, and defined time through motion. WSM gives these insights one physical form: Space persists while finite wave organisations change and recur. The Many are not detached substances but organisations of the One—distinct without disconnection. The question becomes exact: can one continuous wave law generate plurality, causation and knowledge?

3. Action of Vibrating Space: From Background Waves to the E-Sphere

https://www.spaceandmotion.com/2026/wsm-classical-action-quantum-wave.html

All-direction plane waves form the exact spherical pair \[ \chi=j_0(kr)\cos\tau, \qquad \mathbf V=\hat{\mathbf r}\,j_1(kr)\sin\tau. \] Waves cross the centre; none reflects from an electron wall. Phase reinforcement raises directional \(E_d\) and advances a forward curve; cancellation lowers \(E_d\) and writes a rear delay. Stationary action explains coherent selection, but the open task is one conservative nonlinear \(\Phi\)–\(\Gamma\) action selecting radius, frequency, spherical hand, stability, motion, currents and interaction together.

4. Mathematical Physics: From Wave Geometry to Prediction

https://www.spaceandmotion.com/2026/wsm-maths-physics-full-derivations.html

Every symbol must name real motion and face numerical test. Exact or conditional anchors include \[ \frac{R}{\lambda_0}=\frac{\sqrt3}{2},\qquad k_0R=\pi\sqrt3,\qquad E_{\rm geo}=\frac{\pi\sqrt3}{2},\qquad W=\cosh\eta,\qquad P=\sinh\eta. \] Directional phase moments separate \(V_1\) translation from \(V_2,V_4\) and higher deformation; in declared finite-e-sphere models \(V_4\) returns comparable to \(V_2\), defeating quadrupole-only truncation. The action must calculate how incoming curvature redistributes \(E_d\), moves the centre and forms the wave egg. This is where beautiful geometry becomes dangerous.

5. Quantum Theory: Real Waves, Resonance and Completed Events

https://www.spaceandmotion.com/2026/physics-quantum-theory-wave-mechanics.html

Matter diffracts because matter is wave organisation. Light is proposed as a changed train of real phase, curvature and coherence joining extended source and receiver structures, not a tiny traveller detached from its wave. WSM distinguishes driven response, continuous radiation and discrete completed transition. Quadratic absorption, \[ P_{\rm abs}\propto\left|\langle D_j,\Xi\rangle\right|^2, \] is a bridge, not yet the Born rule. The action must derive the action unit, probability, exclusivity, selection rules and Bell/CHSH correlations. Quantum mystery becomes a bounded real-wave programme.

6. Relativity: Moving Matter, Clocks and Curved Wavefronts

https://www.spaceandmotion.com/2026/physics-albert-einstein-special-general-theory-relativity.html

An incoming curve flattens the e-sphere’s near side, elongates its far side and changes internal \(E_d\), \(c'\), wavelength and reclosure. The \(V_1\) moment moves the centre; \(V_2,V_4\) and higher moments form the moving egg. Maintaining this recurrent asymmetry is the proposed origin of inertia. A steady solution must recover Doppler, de Broglie and Lorentz structure: \[ W\pm P=e^{\pm\eta},\qquad W=\gamma,\qquad P=\gamma\beta. \] WSM proposes fixed carrier recurrence \(f_0\) with corresponding changes in \(c'\) and \(\lambda'\). Because rods, clocks and signals share the same changed waves, they co-transform and yield measured invariant \(c\), including the Michelson–Morley null; the action must derive the cancellation quantitatively.

7. The Electron: Dirac, Feynman, QED, \(\alpha\) and AMM

https://www.spaceandmotion.com/2026/wsm-derivation-dirac-feynman-qed-fsc-amm.html

Electron and positron are proposed as opposite carrier-phase e-sphere branches; charge records how their waves combine. Same-phase reinforcement advances a forward curve and is proposed to produce repulsion; opposite-phase cancellation writes a rear delay and attraction. Non-collinear longitudinal motion closes into an axis-free spherical hand with a \(4\pi\) orientation lift. A parameter-free leading geometric ansatz gives \[ \alpha_0^{-1}=8\pi^2\sqrt3\approx136.757, \] 0.203% from measurement. The action must still derive charge sign, Coulomb scaling, Dirac dynamics, \(g=2\), electromagnetic normalisation, \(\alpha\), form factors and AMM without inserting their values.

8. Hadrons: Proton, Neutron and Higher Standing-Wave Matter

https://www.spaceandmotion.com/2026/wsm-qcd-hadron-baryon-meson-proton-neutron-muonic-standing-waves.html

Can the same Space form stable higher-energy, multi-lobed eigenmodes matching protons, neutrons, baryons and mesons? Their lobes are not independent pellets: each participates in the phase, \(E_d\), curvature and reclosure of the whole. WSM must match—not rename—QCD’s masses, charges, spin, parity, magnetic moments, radii, form factors, resonances, deep-inelastic response and jets. The electron–proton hierarchy tests whether one action truly contains several matter families.

9. Cosmology and Gravity: A Finite Universe in Infinite Space

https://www.spaceandmotion.com/2026/physics-wsm-cosmology-finite-universe-infinite-space.html

Boundless Space is distinguished from the finite matter-and-coherence domain contributing to our observable universe. In neutral matter, leading charge curves nearly cancel; WSM proposes that their nonlinear residual has lower \(E_d\), slower \(c'\) and a net rear phase curve, producing universal attraction. General relativity’s curved spacetime is then interpreted as the effective geometry of real moving wavefronts and the matter clocks they organise: Space is substance, succession comes from motion, and measured time from recurrence. The same action must recover equivalence, gravitational redshift, lensing, orbital dynamics and the tested relativistic limit.

Cosmological redshift is investigated as accumulated real-wave transport through changing environmental \(E_d\). It must jointly reproduce achromatic redshift, supernova time dilation, distance laws, Tolman brightness, BAO, CMB observations, image sharpness and structure growth. Otherwise the claimed unity has not reached the sky.

10. Novel Predictions and Famous Experiments Explained

https://www.spaceandmotion.com/2026/wsm-experimental-physics-tests-predictions.html

This page is the tribunal of the corpus. One curve-and-reclosure law must jointly recover charge sign, Coulomb \(1/r^2\), \(F=ma\), relativistic momentum, de Broglie wavelength, Lorentz covariance, Michelson–Morley, gravity, \(g=2\) and AMM. Candidate WSM-only signatures include \[ a_3=\kappa_3\sinh^3\eta+O(\sinh^5\eta), \] finite-coherence residues and environmental or orientation-dependent clock responses. A proposal becomes a prediction only when sign, magnitude, scaling, uncertainty, controls and decision threshold are frozen in advance.

11. Visualise Reality: Waves Becoming Matter

https://www.spaceandmotion.com/2026/visualise-reality-wsm-wave-geometry-diagrams.html

Watch the verbs. Relative phase changes directional \(E_d\); the One Law changes speed and wavelength; a forward or rear curve reaches another e-sphere; its near side flattens, far side elongates, \(V_1\) moves the centre, and higher moments form the egg. New out-waves then change future in-waves. Nothing strikes a shell: changing waves reconstruct changing matter. A diagram must never smuggle in a wall, reflection, rigid spin axis, transverse fundamental substance or tiny traveller. If the motion cannot be drawn coherently, the equations may conceal a contradiction.

12. Mathematics from Motion: Number, Logic, Time and Causal Freedom

https://www.spaceandmotion.com/2026/wsm-physical-foundations-mathematics-logic.html

Mathematics begins when connected reality forms distinguishable patterns whose changes preserve relations. Recurrence supports identity; finite pairing, number; quotienting, exact objects; counted recurrence, time; composable truth-preserving transformations, logic and proof. Mathematics succeeds when symbolic transformation preserves physical relation: \[ R(Tx)\approx F(Rx). \] The mathematician is finite organised reality representing its own necessary connections—Space representing itself.

13. The MDL Audit: Simplicity, Inputs and Explanatory Compression

https://www.spaceandmotion.com/2026/wsm-simplicity-inputs-vs-mainstream-physics+25.html

“One substance, one law” cannot hide complexity. Minimum Description Length counts every independently chosen substance, field, symmetry, constant, state rule, coefficient, boundary condition and fitted function. Under the declared equal-input electron ledger, conventional construction counts six inputs through Dirac and thirteen through leading AMM; the completed WSM target is \[ N_{\rm WSM}=5+N_c+N_f+\delta_m. \] Totals depend on coding convention. WSM wins only if one fixed action derives interaction, inertia, relativity, quantum response and cosmic propagation with fewer hidden choices.

14. Great Thinkers and the Search for One Reality

https://www.spaceandmotion.com/2026/wsm-explains-famous-quotes-maths-physics-philosophy-metaphysics.html

Heraclitus and Parmenides exposed flux and continuity. Aristotle wrote Physics and Metaphysics, sought active substance and necessary cause, connected matter, form, motion and time—and came remarkably close to the problem WSM addresses. Leibniz, Newton, Faraday, Maxwell, Riemann, Clifford, Einstein, Schrödinger and Bohm repeatedly returned to continuity, relation, waves and unity. Quotes are intellectual fossils, not votes: equations and experiments must decide whether WSM’s local real-wave mechanism is true.

15. Human–AI Letters to Humanity: Truth as a Shared Work

https://www.spaceandmotion.com/2026/ai-letters-to-humanity-wsm-unity-truth-reality.html

Geoffrey supplies the persistent wave picture, three-dimensional intuition, cross-domain memory and insistence that every symbol name physical motion. AI supply rapid research, formal translation, calculation, comparison, error detection and adversarial testing. Neither is sufficient alone. The shared discipline is: visualise → formalise → attack → calculate → predict → correct. The corpus tests whether intelligence can preserve a physical picture while making it mathematically vulnerable.

16. Truth and Madness: Reality as the Measure

https://www.spaceandmotion.com/2026/on-truth-and-madness.html

Truth is correspondence: representation succeeds insofar as it preserves what reality does. Civilisational madness begins when inherited representations survive reality’s contradiction. WSM is not true through beauty, coherence or sincerity; its proposed necessary connections must survive action, calculation and experiment. Truth remains possible because knower, representation and known belong to one causal reality: false models collide with the world; truthful models increase our power to act wisely.

17. Descartes, Cogito and Monism: The Thinking Wave

https://www.spaceandmotion.com/2026/descartes-cogito-unity-monism-vibrating-space-wsm.html

Descartes established that thinking occurs, then divided thought from extension and left their interaction mysterious. WSM refuses that fracture: body and mind are proposed as organisational levels of one vibrating Space. Perception is one organisation changed by another; memory is persistent altered organisation; thought transforms embodied representations; action returns change to the world. Conscious experience remains open, but causal correspondence requires no miracle when knower and known share one connected reality.

18. Evolution’s Physical Foundation: From Recurrence to Replication

https://www.spaceandmotion.com/2026/evolution-physical-causal-foundation-vibrating-space.html

Recurrence preserves form, but life requires replication, heritable variation and differential persistence: motion → recurrent form → self-maintaining chemistry → replication → variation → selection. WSM proposes one connected wave substrate beneath this sequence. Its unresolved bridge is quantitative: derive atoms, bonds, dissipative chemistry and first replicators from the same action without inserting biology as a new substance.

19. Evolution, Mind, Human and AI: Representation and Causal Freedom

https://www.spaceandmotion.com/2026/evolution-philosophy-mind-human-ai.html

Evolution favours organisations that preserve and transform information about real causes. Sensation changes an organism; memory retains traces; imagination recombines possible futures; valuation ranks them; action returns one selection to the world. This is limited causal freedom: neither ghost nor randomness, but endogenous selection through a learned, self-modifying organisation. Human brains and AI are different architectures by which reality represents its own relations and lets experiment select the representation that survives.

20. Evolutionary Utopia: The Ecology of Truth

https://www.spaceandmotion.com/2026/evolutionary-utopia.html

Physics alone does not choose values. Once life, mind, freedom, truth and continued evolution are valued, reality constrains the means: truth → wisdom → ecological fit → health → freer minds → continued evolution. Evolutionary Utopia is not a perfect endpoint but a self-correcting direction. Unity does not erase individuality: an e-sphere, organism or person is distinct through organised relation to the whole.


The Physical Interaction in One View

Out-wave from A → relative phase at B → directional \(E_d\) → \(c'\) and \(\lambda'\) → near-side flattening and far-side elongation → \(V_1\) centre displacement plus \(V_2,V_4\) and higher egg deformation → new out-waves → recursive interaction.

The e-sphere does not deform and then move as separate events: its changing internal \(E_d\), contour and reclosure are its motion.

Electric Interaction

Same relative carrier phase → reinforcement → phase advance → forward curve → proposed repulsion.
Opposite relative carrier phase → cancellation → phase delay → rear curve → proposed attraction.

For the stated deformation, \[ r_{\rm near}=R-\delta X, \qquad r_{\rm far}=R+\delta X, \] so \(\delta\mathbf X\) points away. The scientific debt is to derive the sign, magnitude and distance law from the frozen action rather than insert them.

Gravity and General Relativity

In neutral matter, forward and rear charge curves nearly cancel; WSM proposes that their nonlinear common reduction of \(E_d\) leaves a slight slower rear curve and universal attraction. General relativity is the successful effective geometry this wave mechanism must recover: matter-energy changes real wave propagation, while rods and clocks made from those waves measure the resulting curved spacetime relations.

Special Relativity and Michelson–Morley

WSM proposes fixed carrier recurrence \(f_0\) with \(c'=\lambda'f_0\): matter, clocks, rods and signal wavelengths co-transform with their common directional wave environment, yielding measured invariant \(c\), Lorentz relations and the Michelson–Morley null. The complete moving solution must derive these cancellations quantitatively.

Recursive AMM Mechanism

\[ \delta\mathbf X \rightarrow\delta\phi_{\rm out} \rightarrow\delta E_{d,{\rm sea}} \rightarrow\delta c' \rightarrow\delta\phi_{\rm in} \rightarrow\delta\mathbf X_{\rm next}. \]

A perturbed centre changes the egg and its out-waves; these alter the wave sea and the in-waves rebuilding the next cycle. The action must solve this feedback blindly and recover the observed anomalous magnetic moment rather than fit it.

Current Status — August 2026

Exact wave constructions, geometric identities, phase-moment relations and negative controls have been established under declared premises. A leading geometric \(\alpha\) ansatz has a fixed 0.203% discrepancy. The complete nonlinear action must still calculate two-e-sphere charge and Coulomb scaling; force, inertia and \(F=ma\); the moving egg, de Broglie modulation and Lorentz covariance; Michelson–Morley and the gravitational/GR limit; Born probability and Bell correlations; \(g=2\), \(\alpha\) and AMM; hadron structure; and the joint cosmological kernel.

Write the action. Let Space calculate itself.



Summary & Simple Solution to Main Problems of Albert Einstein's Relativity Theory
From Representing Matter as Continuous Fields in Space-Time (Mathematical) to Matter as Spherical Waves in Continuous Space (Physical)

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

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


Introduction

Hello. This page is in two parts. To begin, a summary of the metaphysical foundations of Einstein's Relativity, and how they can be simplified from Einstein's attempt of Representing Matter as Continuous Spherical Fields in Space-Time (Mathematical)
to describing Matter as Spherical Waves in Continuous Space (Physical).
This is followed by a summary of 8 central problems of the Theory of Relativity that Einstein could not solve, simply because he was working from a foundation of continuous spherical fields, rather than spherical standing waves. The solutions to these problems are very obvious once we have the correct wave foundations for matter interactions.

It should be emphasised here, that though these changes may seem trivial, they are not. While they confirm Einstein's view that Matter and Space (and Time, Gravity) are united, this Waves in Space foundation solves the central problems of Albert Einstein's Theory of Relativity, while also providing a sensible solution to Quantum Theory (which is in great need of sensible foundations to remove all the nonsense / quantum weirdness that currently flourishes due to the errors of the particle conception of matter). We should not forget the obvious - Quantum Theory is founded on wave equations. This is because standing waves only exist at discrete frequencies, as do their interactions.

Our minds change slowly to new knowledge, which always seems strange at first. So I hope you will read and think about this. It is very simple and obvious once known. And I cannot help but think it is important.

Enjoy,
Geoff Haselhurst


Short Summary of Physics and the Wave Structure of Matter in Space

At a fundamental level Modern Physics is founded on the concepts of particles and fields in space and time. Further difficulties arise because both light and matter exhibit a particle / wave duality, and there are two main fields, charge (electromagnetic) and mass (gravitational / inertial). While this is still a little simplistic, it makes the point that we have a number of different concepts without any clear understanding of how they are connected. This causes numerous problems for Human knowledge (and society), as we do not understand the necessary connections between these many things we experience. And as Hume made clear (see David Hume's Problem of Causation and Necessary Connection), without this knowledge of necessary connection between things that exist we can have no causal theory of knowledge, leaving the Sciences founded on Induction from repeated observation which is always uncertain (rather than deduction from metaphysical principles which is certain);

Experience only teaches us, how one event constantly follows another; without instructing us in the secret connexion, which binds them together, and renders them inseparable. (David Hume)

So how do we solve these problems? I think the simplest way to explain this is to list these central concepts of physics, show which path Albert Einstein took to try and unite them from a common foundation (which he failed to do), and then demonstrate from the most simple foundation (founded on One thing Space existing as a Wave Medium) how we can finally unite these concepts in a meaningful way that describes reality without paradox or contradiction. Now I know that most of you will be very skeptical of such a big claim, but the solution is pretty simple and obvious once known so I hope you will persevere (and it is concise / short!).

Central Concepts of Modern Physics

Newton's Mechanics - Space, Time, Matter as Particles with 'Mass', Force = Mass by Acceleration.
Continuous Electromagnetic Field Theory (Faraday, Maxwell, Lorentz, Einstein / Relativity) - Matter as Particles with 'Charge', Continuous Spherical Electromagnetic Fields, Light as Vector Electromagnetic Waves, Gravitational Fields (local theory - all matter interactions limited by velocity of light c)
Discrete Quantum Theory (Planck, Einstein, de Broglie, Schrodinger, Born) - Light as Discrete Particles (Photons), Scalar Waves, Probability Waves, Particle Wave Duality (Light & Matter), Quantum Entanglement (apparently non local theory - appear to be instantaneous matter interactions).

While this is still a little simplistic, you can see how confusing Physics becomes when you have so many concepts, some of which clearly contradict others (e.g. light and matter behave as both particles and waves, discrete particles and continuous fields, local and non local interactions). Albert Einstein attempted to simplify this mess with his 'field theory of matter' where he discarded the 'particle' concept and tried to represent matter as spherical fields in space-time, as he writes;

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

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

Now there are a number of Problems with Albert Einstein's Field Theory of Matter (see below), as he was well aware, and which, late in his life, caused him to write 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)

In hindsight it is easier to understand Einstein's error - the clue is that Quantum Theory's discovery of the wave properties of matter did not occur until 1928, whereas Einstein's continuous electromagnetic field foundations were developed from 1905 to 1916 based largely on the ideas of James Clerk Maxwell (Maxwell's Equations, 1870s) and Lorentz's Theory of the Electron (1900). So basically his mistake was to work with fields in space-time (mathematical) rather than real waves in Space (physical), largely because he did not have knowledge of the Wave properties of matter when he developed his Theory of Relativity.

In terms of the Metaphysical foundations of Physics, the central error has been to try and describe reality from the Many material things we experience, matter 'particles'. (i.e. Science, which is empirically founded). And even though Einstein rejected the 'particle', his field theory of matter is still founded on this priority of matter (that matter's field interactions cause the effect of space and time).
However, Metaphysics has known for several thousand years that it is necessary to describe reality from One thing existing to explain matter's interconnection in Space and the Universe. As Aristotle, Leibniz and Bradley write;

The first philosophy (Metaphysics) is universal and is exclusively concerned with primary substance. ... And here we will have the science to study that which is, both in its essence and in the properties which, just as a thing that is, it has. (Aristotle, 340BC)
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.
(Gottfried Leibniz, 1670)
We may agree, perhaps, to understand by Metaphysics an attempt to know reality as against mere appearance, or the study of first principles or ultimate truths, or again the effort to comprehend the universe, not simply piecemeal or by fragments, but somehow as a whole. (Bradley, 1846-1924)

By abiding by this central rule of Metaphysics and describing Reality in Terms of One thing existing, Space, and its Properties as a Wave Medium for Spherical Standing Waves that form Matter, we find a very simple solution to all of the above problems of Physics (again this is a big claim, but this website does explain many of these things). Basically Einstein is correct, Matter is a Spherically Spatially extended structure of Space (there is no 'particle') though most importantly we have simplified Einstein's ideas from;

Matter as Continuous Spherical Fields in Space-Time
to
Matter as Spherical Waves in Continuous Space.

It is then quite simple to show that:
The discrete 'particle' effect of matter is caused by the Wave-Center of the Spherical Standing Waves (the diagram shows that this is an obvious solution to the particle / wave duality of matter!).
The discrete 'particle' effect of light is caused by discrete Standing Wave Interactions / Resonant Coupling.
Time is caused by Wave Motion (as spherical wave motions of Space which cause matter's activity and the phenomena of time).
Forces / Fields are caused by wave interactions of the Spherical In and Out Waves with other matter in the universe which change the location of the Wave-Center (and which we 'see' as a 'force accelerating a particle').
Quantum Entanglement is likewise caused by the Interaction between the In and Out-Waves and all the other matter in the universe, thus matter is always subtly connected to other matter in the universe (i.e. matter is large not small, we only see the Wave-Center and have been deceived by its 'particle' effect). However, Einstein's 'Locality' is correct, all matter to matter interactions are limited by the velocity of Waves in Space.

Of most significance (the real beauty of this solution) is that not only does it solve the problems of Albert Einstein's Theory of Relativity, but it also solves the basic problems of Quantum Theory / Quantum Mechanics (founded on Wave Equations) and Cosmology (uniting finite matter & universe with infinite eternal space - the Big Bang Theory being founded on a basic error).


A simple solution to the Problems of Albert Einstein's Theory of Relativity

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The Wave Structure of Matter in Space

Einstein (from Faraday, Maxwell, Lorentz) represented matter as a continuous spherical field in spacetime. Einstein is correct that there is no 'particle' and matter is spherically spatially extended (Matter and Space are One and the same thing!). However, the spherical 'force field' can be sensibly explained with the Spherical Standing Wave Structure of Matter. We realize that forces are caused by a change in the velocity of the spherical In-wave (from one direction) as this changes where these In-waves meet at the wave-center, which we observe as a 'force accelerating a particle'. The change in ellipsoidal shape of the In-waves is the cause of Einstein's Metrics and the Riemannian geometry of General Relativity.

With this new understanding let us then briefly summarize the problems of Einstein's Relativity, as their solutions become obvious once we understand the Spherical Standing Wave Structure of Matter.

i) Einstein's Relativity is a Theory of a posteriori Effects not a priori Causes, and is founded on Many things (Matter) rather than One thing (Space).

Einstein did not know how matter existed in Space and his electromagnetic field theory of matter is Inductive (empirical / a posteriori) and describes effects (of relative motion).

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

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

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

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

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

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

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

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

The Electric and Magnetic Force Fields were first founded on repeated observations (Induction / a posteriori) of how many trillions of charged 'particles' (electrons and protons) behaved. This explains why the fields were continuous, as many trillions of discrete standing wave interactions blend together into a continuous force. Thus the continuous field can never describe the real standing wave interactions of matter, as Einstein came to realize.

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

iii) Einstein's 'Fields' require 'Particles'.

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

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

iv) Einstein's Continuous Field Theory of Matter gives rise to Singularities and Infinite Fields.

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

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

v) Einstein Rejects both 'Particles' and Motion.

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

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

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

vi) Einstein Assumed Matter Caused Space Rather than the Wave-Motion of Space Causing Matter.

Einstein was profoundly influenced by Mach;

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

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

Thus Newton was ultimately correct;

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

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

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

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

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

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

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

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

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

Einstein's Relativity requires both an Electromagnetic Force Field to explain Charge, and a Gravitational Field to explain Mass. He tried and failed throughout his life to unite these two fields into one (and to remove the 'particle' concept from them).

But the idea that there exist two structures of space independent of each other, the metric-gravitational and the electromagnetic, was intolerable to the theoretical spirit. We are prompted to the belief that both sorts of field must correspond to a unified structure of space. (Einstein, 1954)

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

viii) Einstein's 'Curvature of the Four Dimensional Space-Time Continuum'

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

But the path (of general relativity) was thornier than one might suppose, because it demanded the abandonment of Euclidean geometry. This is what we mean when we talk of the 'curvature of space'. The fundamental concepts of the 'straight line', the 'plane', etc., thereby lose their precise significance in physics. (Albert Einstein, 1954)

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

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

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

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

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


Concluding Remarks

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

All these fifty years of conscious brooding have brought me no nearer to the answer to the question, 'What are light quanta?' Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken. … I consider it quite possible that physics cannot be based on the field concept, i.e., on continuous structures. In that case, nothing remains of my entire castle in the air, gravitation theory included, [and of] the rest of modern physics.

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

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

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


Some Reference quotes (for my use)

But the idea that there exist two structures of space independent of each other, the metric-gravitational and the electromagnetic, was intolerable to the theoretical spirit. We are prompted to the belief that both sorts of field must correspond to a unified structure of space. (Einstein, 1954)

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

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)

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)

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


Summary & Simple Solution to Main Problems of Albert Einstein's Relativity Theory
From Representing Matter as Continuous Spherical Fields in Space-Time (Mathematical) to Matter as Spherical Waves in Continuous Space (Physical)

Physics constitutes a logical system of thought which is in a state of evolution, whose basis (principles) cannot be distilled from experience by an inductive method, but can only be arrived at by free invention. (Albert Einstein, 1936)
Metaphysics of Relativity
Principles in Physics
Physical events, in Isaac Newton's view, are to be regarded as the motions, governed by fixed laws, of material points in space. This theoretical scheme is in essence an atomistic and mechanistic one. (Albert Einstein, 1940)
Einstein on Sir Isaac
Newton's Mechanics
The greatest change in the axiomatic basis of physics since Newton, was brought about by Michael Faraday's and James Clerk Maxwell's work on electromagnetic field phenomena. (Albert Einstein, 1954)
Michael Faraday's EM
Field, Maxwell Equation
Special relativity is based on the fact that Maxwell's equations (& thus the law of propagation of light in empty space) are converted into equations of the same form, when they undergo a Lorentz transformation. (Einstein)
Albert Einstein on the
Lorentz Transformations
 If, relative to K, K' is a uniformly moving co-ordinate system devoid of rotation, then natural phenomena run their course with respect to K' according to exactly the same general laws as with respect to K. This statement is called the principle of relativity. (Albert Einstein, 1954)
Albert Einstein's Theory
of Special Relativity
When forced to summarize the general theory of relativity in one sentence: Time and space and gravitation have no separate existence from matter. (Albert Einstein)
Albert Einstein's Theory
of General Relativity
But the idea that there exist two structures of space independent of each other, the metric-gravitational and the electromagnetic, was intolerable to the theoretical spirit. We are prompted to the belief that both sorts of field must correspond to a unified structure of space. (Einstein, 1954)
Solution to Problems
Relativity Theory
Can we visualize a universe which is finite yet unbounded? ... The supreme task of the physicist is to arrive at those universal laws from which the cosmos can be built up by pure deduction. (Albert Einstein, 1954)
Einstein Cosmology
Finite Universe
All these fifty years of conscious brooding have brought me no nearer to the answer to the question, 'What are light quanta?' Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken. (Albert Einstein, 1954)
Quantum Theory
'Photon' Light Quanta
I do not believe in a personal God and I have never denied this but have expressed it clearly. If something is in me which can be called religious then it is the unbounded admiration for the structure of the world so far as our science can reveal it. (Albert Einstein, 1954)
Einstein on Theology
God, Religion, Morality
The true value of a human being is determined by the measure and sense in which they have obtained liberation from the self. We shall require a substantially new manner of thinking if humanity is to survive. (Einstein, 1954)
Albert Einstein Quotes
Religion Science Peace
The ideals which have lighted my way, and time after time have given me new courage to face life cheerfully, have been Kindness, Beauty and Truth. (Albert Einstein, 1954)
Albert Einstein Biography
Picture Photo Gallery

Help Humanity

"You must be the change you wish to see in the world."
(Mohandas Gandhi)

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. 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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