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 (September 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
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
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
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.
Quantum Theory: Werner Heisenberg Quotes
This page on Werner Heisenberg is in three parts (links go to headings lower on page);
1. The Heisenberg Uncertainty Principle
3. A discussion of some important quotes from his book on the Philosophy of Physics
The aim is to show that Heisenberg's conclusions were not correct simply because he (nor any other physicist) realised that Dirac worked out physical reality (mathematically) in 1928 when he factorized Schrodinger's relativistic wave equation for matter into plane wave solutions. We now know that all of modern physics can be deduced from this foundation, where the three dimensional space we all experience exists and has complex (transverse) plane waves flowing through it in all directions. There are four unique phase solutions for these intersecting plane waves where all the complex components cancel and you are left with scalar (longitudinal) spherical standing waves, two pairs with opposite phase that exactly match the properties of the two spin states of the electron and positron (antimatter is just the opposite phase standing wave to matter, thus why they annihilate). You can read more on this on the home page.
1. The Heisenberg Uncertainty Principle
Heisenberg's uncertainty principle states that we cannot know both the position and momentum of a particle. If we know the momentum then we do not know the position, and visa versa, if we know the position then we do not know the momentum. This discovery has had profound consequences for the evolution of physics as it supported the emerging postmodern philosophical view that all knowledge was uncertain (which is not correct).
Werner Heisenberg discovered his famous Heisenberg Uncertainty Principle in March 1926, working with his matrix mechanics (1925). This was at the same time that Schrodinger independently discovered his wave equations. In May 1926 Schrodinger showed that his wave mechanics was mathematically equivalent to Heisenberg's matrix mechanics. And as history shows, Schrodinger's wave equations proved to be most useful and now dominate the foundations of quantum physics.
The importance of this is that Schrodinger was convinced the waves were real and detested Born's probability wave interpretation (1928) which also became universally accepted because it is mathematically true (the problem of physics being dominated by mathematicians who are generally poor philosophers / metaphysicists.)
For the deduction of the uncertainty principle from wave foundations please see the Heisenberg Uncertainty Principle page.
2. A critique of his philosophical / metaphysical essay 'ORDNUNG DER WIRKLICHKEIT' (REALITY AND ITS ORDER)
If the word "reality" means nothing other than the totality of the connections that pervade and carry our life, then it is probably true that there must exist very different areas or layers of reality. We simply wish to comprehend the whole world as a single, coherent nexus of related phenomena.
However, it was in this very question that the scientific exploration of nature during the last decades compelled a change of perception. For us the predictable course of natural phenomena in space and time is no longer the firm skeleton of the world but only one nexus among others that becomes separated from the web of relations that we call the world by the way we examine it, by the questions we pose to nature. This view resulted from the insight into the laws of nature, gained with the advances of natural science, according to which phenomena can no longer be reduced to processes in space and time.
Thus, finally, we must persist until we gain an understanding of reality that comprehends the diverse coherent relationships as part of a single meaningfully ordered world.Of course, it is not only as a result of recent scientific developments that reality came to be described as a web of diverse relations.
However, it was in this very question that the scientific exploration of nature during the last decades compelled a change of perception. For us the predictable course of natural phenomena in space and time is no longer the firm skeleton of the world but only one nexus among others that becomes separated from the web of relations that we call the world by the way we examine it, by the questions we pose to nature. This view resulted from the insight into the laws of nature, gained with the advances of natural science, according to which phenomena can no longer be reduced to processes in space and time.
That imposes anew the task of ordering, understanding and determining the diverse connections or "areas of reality" in their mutual relations. They need to be related anew to the separation of the world into an "objective" and a "subjective" reality. The boundaries of those areas have to be determined and it must be discovered how the one conditions the other. Thus, finally, we must persist until we gain an understanding of reality that comprehends the diverse coherent relationships as part of a single meaningfully ordered world.
Of course, it is not only as a result of recent scientific developments that reality came to be described as a web of diverse relations. On the contrary, what we have here is the renewed consideration of ancient, often explored chains of ideas. The justification to repeat what had been said often before is based only in the fact that the development of natural science in the past decades has thrown a unique new light on this view.
Perhaps this development justifies the hope that it must be possible to determine more accurately than before the mutual relations of the diverse areas of reality. It is likely that much of the confusion in the thinking about reality results from the fact that every single thing participates simultaneously in diverse webs of connection, just as every word relates simultaneously to diverse contexts. We need proof that a clear separation is at all possible, given these circumstances. Only an example that can demonstrate with mathematical clarity the mutual relations of two areas of reality will convince the reader that it is possible to order the various layers of reality clearly and to depict their boundaries.
A complete and exact depiction of reality can never be achieved.
Generally speaking, every attempt to speak about reality will have both "static" and "dynamic" features at one and the same time. Clear, purely static thinking is in danger of deteriorating into form without content. Dynamic thinking can become vague and incomprehensible.Here, a sentence can, generally speaking, not be "right" or "wrong". But one may call a sentence "true" when it fruitfully leads to an abundance of other ideas. The opposite of a "right" sentence is a "false" one. But the opposite of a "true" sentence will often be another "true" one. The most famous systematic formulation of this "dynamic" representation of reality is Hegel's dialectics.
A complete and exact depiction of reality can never be achieved.
Every domain of reality can finally be depicted in language. The abyss that separates different domains cannot be bridged by logical reasoning or coherent linear development of language.
The ability of human beings to understand is without limit. About the ultimate things we cannot speak.The Pythagoreans' studies of the rational relations of harmonic vibrations of musical strings, Plato's ideas about symmetrical bodies, testify to the significance assigned to the mathematical form in the understanding of nature. Exact natural science since Newton is based on the silent presupposition that it must always be possible to order the areas of nature accessible to our experience according to strict laws that can be expressed mathematically. Even if one carefully analyzes other representations of reality as well, such as music or the creative arts, which are far removed from the natural sciences, they will reveal internal orders that are very closely related to mathematical laws. Those orders can be as clearly discerned as in a Bach fugue, for example, or in a symmetrical ribbon ornament; they might be noticed initially through a unique balanced quality, through the immediately evident beauty of a melody line such as that of the famous sub-theme in the first movement of Beethoven's D major violin concerto. Closer examination always shows simple mathematical symmetries comparable to those mathematics deals with in group theory. Thus, mathematics is order par excellence, in its purest form, freed from all content.The Pythagoreans' studies of the rational relations of harmonic vibrations of musical strings, Plato's ideas about symmetrical bodies, testify to the significance assigned to the mathematical form in the understanding of nature. Exact natural science since Newton is based on the silent presupposition that it must always be possible to order the areas of nature accessible to our experience according to strict laws that can be expressed mathematically. Even if one carefully analyzes other representations of reality as well, such as music or the creative arts, which are far removed from the natural sciences, they will reveal internal orders that are very closely related to mathematical laws. Those orders can be as clearly discerned as in a Bach fugue, for example, or in a symmetrical ribbon ornament; they might be noticed initially through a unique balanced quality, through the immediately evident beauty of a melody line such as that of the famous sub-theme in the first movement of Beethoven's D major violin concerto. Closer examination always shows simple mathematical symmetries comparable to those mathematics deals with in group theory. Thus, mathematics is order par excellence, in its purest form, freed from all content.The core domain from which we create reality ourselves constitutes for scientific language the infinitely remote singularity that even though it is indeed decisive for order in the finite sphere it can never be reached. Conversely, the language of faith cannot do justice to the domain of reality that is objectifiable and detached from us. For the words of that language have obtained their meaning precisely through their relation to us.
Religion alone can speak of the meaning of life. For "meaning" signifies that it is we who are addressed here, - this is the point to which science cannot advance. That is why in science's language about the meaning of life one can only say with Bohr: "The meaning of life consists in that it is meaningless to assert that life has no meaning". Science offers so little comfort for that reason. But exactly that insight offers enough comfort to the wise person who has come to know that all ideas through which we seek to fathom life's meaning circle back to the point where they started.
The concepts "objective" and "subjective" designate two poles from which an order of reality can take its beginning. They also describe two sides of reality itself. Still, it would be a crude oversimplification to divide the world into an objective and a subjective reality. This merely black and white representation created much inflexibility in philosophy of the last few centuries. The evaluation of these two sides of reality also differed a great deal at different times. At times, one side would have only been regarded almost as a deceptive appearance. To our age it seems more natural not to raise the issue of evaluation at all here and, instead, to strive for a more refined and clearer classification of reality. Since that classification is to be scientific, it will proceed step by step from the objective to the subjective. The description and delimitation of the individual domains of reality is carried out with the greatest of care, as is appropriate to the natural science as it has developed over many centuries.
"All effects we become aware of through experience, in whatever form they are, are connected in the most coherent fashion; they flow one into the other and undulate from the first to the last like waves. That people separate them from and contrast them with one another and mix them together is unavoidable. But this had to give rise to an endless conflict in science. Rigid, divisive pedantry and blurry mysticism both bring about the same disastrous results. But those activities, from the most basic to the noblest, from that of the brick falling off the roof to the radiant insight of the spirit that dawns on you or that you share with others: they are linked together." (Goethe)
From the point of view of recent natural science, it is not possible in general to dissociate the concept of substance from that of the rules of nature. If one follows the development of the concept of matter in modern physics, matter, just like force, finally appears to be a kind of structure of space. That structure is subject to the laws of nature and, as a result of certain features of "invariance" in those laws, the word "matter" may be used in the description of processes. However, it is not matter but the law that remains constant as phenomena evolve.
Only when this step has been taken and it has been recognized that there is no "substance" that follows specific laws, but only complexes of connections which we can experience and that when we describe them we also occasionally use words like substance or matter - only then we may correctly understand the sentence that the sought-for classification is one that orders reality according to those connections.
By "domain of reality" - if the word domain is used in the special sense of classification - we mean a totality of complexes of configurations governed by laws. On the one hand, such a totality must present a solid unity, otherwise one could not justifiably speak of a "domain". On the other, that totality must be capable of being exactly delimited from totalities so that a classification of reality actually becomes possible. This raises the question how a totality of laws can become complete in itself and exactly delimited from laws of a different kind.
But, in the end, we must always bear in mind that the reality of which we can speak is never reality "per se" but a perceived reality even, in many cases, one we ourselves have shaped. It may be objected that this last statement concedes that there still is, after all, an objective world wholly independent of us and of our thinking, a world that runs or can run without our help, which we really envisage in our research. One must reply to this at first so plausible objection that the phrase "there is" itself already derives from human language, for which reason it cannot properly signify something that would not be related to our ability to comprehend. For us, "there is" simply only the world in which the phrase "there is" has meaning.
2. (Classical) Physics
a) Newton's Mechanics
Mechanics presupposes further that every body (or its individual parts) is assigned a specific position. Space and time are seen as two firm, mutually independent patterns of order into which the world's processes can be arranged. Newtonian theory renounces from the outset the idea, already proposed in the days of Greek philosophy, that space and matter might be connected with each other. For example, in this sense, one might see space as upheld by matter's structure, or hold that matter is to be considered as a structure of space. Newtonian theory was instead content to objectify space and time in the form we know simply because experience teaches us that such an objectification is possible in a wide range of experiences.
b) Electricity and Magnetism
The development of the theory of electricity was responsible for the first decisive step forward in classical physics beyond Newtonian mechanics. The particular forces that are present between electrically charged or magnetic bodies are the object of this discipline. At the same time, it enables a quite general analysis of the concept of force which was still somewhat alien to Newtonian physics. In the theory of electricity, force is objectified and fixed in space and time by the concept of the "force field" in a manner similar to the way matter is objectified and fixed in mechanics. Force appears not only as an effect of one body on another, but is itself a process in space and time that can detach itself completely from all matter. Understanding the autonomy of force helps clarify the intrinsic relationship between force and matter which were eventually most clearly articulated in the natural laws that were discovered only at the beginning of the twentieth century in connection with the special theory of relativity. From the perspective of what we know today, it does not appear anomalous, for example, to speak of radiation, that is, the electromagnetic force field, as a special form of matter. Matter can change into radiation and radiation into matter. The principle about the conservation of matter is expanded into one about the conservation of energy, and energy can present itself in the most diverse forms: as radiation, motion, weight.
This development from mechanics to the theory of electricity met initially with resistance from many natural scientists because the idea of an autonomous force field apparently leads to the dissolution of the primitive concept of substance in Newtonian physics. Thus, there was no lack of experiments to reinstate the original concept of substance by introducing a hypothetical ether which was to be perceived as a carrier of the electromagnetic fields that appeared to be autonomous in space. But a substance that cannot be localized in space, that we can neither feel, weigh nor see, like ether, deserves this name even less than the electromagnetic force field. As a result, researchers had to decide to drop the primitive concept of matter. After all, the language we use to speak about nature is created in the interplay between action and experience and is not dependent on our often historically conditioned desires.
The discovery of matter-waves by de Broglie may serve as an example; they may be understood as objective wave processes in space-time if one ignores the corpuscular nature of matter. If one does not ignore the existence of elemental particles, then the patterns of the laws relevant here cease to be part of the domain of classical physics but belong to what falls under the comprehensive concept of quantum theory. This example demonstrates that it is not things but the complexes of connections that can be ordered according to different domains.
c) The Infinite
Einstein was the first person courageous enough to articulate the dependence
of space and time and he articulated it in mathematical terms. Later experiments
confirmed over and over again the conclusions of this new view of the space-time
structure with greatest precision so that its accuracy can hardly be doubted
any more.
For the experiences of astronomers suggest that the world's space is finite.
This is not meant, of course, to be true in the simple sense of that earlier
view of the world; - we will not arrive eventually at a boundary somewhere
far away from our earth but, as with travels on our globe, as we proceed
in a straight line into ever greater distances, we should eventually return
to our starting point. The road traveled that way is said to be finite and
can provide a basis for determining the size of the universe. From what
we know thus far, one can conclude that it may be a journey of several billion
light years. Other observations in astronomy lead to the conclusion that
the condition of the universe some five billion years ago must have been
very different from now; the world's matter then was apparently compressed
in a much narrower space under extremely high temperatures. Only much later
did stars and stellar constellations come into existence. This perception
has occasionally been expressed as follows: The universe has only existed
for five billion years.
Since this development occurred, the words "matter", "force", "structure of space and time" seem to represent only different sides of the same event.
Behind the world describable in statistical concepts would presumably lie
an objective reality, namely the position and motion of atoms. Mechanical
concepts would, therefore, have pre-eminence over properties since they
were thought to describe the actual events of the real world.
But that supposition has proven to be incorrect in light of what has been discovered over the past decades about the connections between chemical properties and atomic motion. Before addressing those discoveries, we must stress, by the way, how unsatisfying it would be to think that amidst the great wealth of human language the concepts of mechanics alone would be appropriate to describe the "actual" behavior of the world.
3. Chemistry
a) Heat
As described, the situation in theory of heat could possibly lead one to
the following supposition, namely that concepts like "temperature",
formed to describe properties, should apply only in a limited sense - for
example, only to systems of innumerable atoms, under suitable conditions
- but that they would not really describe the real behavior of bodies. They
might be thought to be much more statistical concepts (like "the age
of humans" ) that could be used in accordance with their original determination
only under suitable conditions. Behind the world describable in statistical
concepts would presumably lie an objective reality, namely the position
and motion of atoms. Mechanical concepts would, therefore, have pre-eminence
over properties since they were thought to describe the actual events of
the real world.
But that supposition has proven to be incorrect in light of what has been discovered over the past decades about the connections between chemical properties and atomic motion. Before addressing those discoveries, we must stress, by the way, how unsatisfying it would be to think that amidst the great wealth of human language the concepts of mechanics alone would be appropriate to describe the "actual" behavior of the world.
b) The Laws of Chemistry
The hypothesis of the atom proved itself to be the most natural method for ordering the discovered connections. The atom has to be ascribed specific forces, the so-called valences, by means of which it can attract neighboring atoms. Together, the concepts of atom and valence provide the primary framework with the help of which the house of chemistry can be erected.
Experiences in electro-chemistry gave rise to the assumption that atoms are capable of taking on certain electrical charges. The most natural geometrical extrapolation from this situation was once again the hypothesis that atoms are structured from electrically charged elementary building blocks. The development of chemistry thus automatically led research to examine the relations between chemical properties and the mechanical and electrical behavior of elementary particles. It was not absolutely necessary for the advance of chemistry to take the hypothesis of the atom literally in this way. Since the size of atoms does not play a role in most of the laws of chemistry, the concept of the atom could be viewed strictly as a working hypothesis. The chemical forces were accepted as such and not explained further. But increasing refinement of the tools of observation brought atoms and elementary particles directly into the accessible field of experience so that it became impossible to avoid the question any longer of the connection between the laws of chemistry and the mechanical behavior of elementary particles.
The laws of quantum theory may be presented as follows: The "state" of an atomic system is describable in terms of certain "quantities of state" or "functions of state". But those quantities do not directly represent a process or situation in space and time, like those of classical mechanics; they are not simply the locations and velocities of the particles that characterize a state. Rather, they have a certain relationship to the concept of temperature insofar as they generally provide us only with information regarding the probability with which we might anticipate certain locations and velocities of elementary particles if we undertake to observe them.
Two features of this situation are particularly important. One is that the quantity of state and everything it expresses does not in itself represent an objective fact in space and time. The other is that it is necessary through observation to analyze the quantity of state that establishes its connection to reality.
In relation to the first point, the impossibility to objectify these quantities of state in the ordinary sense is due most clearly to the abstract, mathematical character of those quantities. They are frequently represented formally in terms of functions in multidimensional abstract spaces that, as a result, cannot directly signify a process in space and time as we perceive them.
It is only through the act of observation that something objective is created from these possibilities. It follows that this act of observation and the intervention necessitated by observation are a decisive feature of quantum theory and its subject matter. Observation generally alters the state of the system. It does so, on the one hand, through the very intervention that makes the observation possible. In addition, in the area dealing with the discontinuous changes of the smallest units of matter, this intervention can no longer be minimized at will nor its repercussions accurately determined. On the other hand, every observation similarly alters our knowledge of the system. As the content that can rationally be associated with the concept "quantity of system" is, after all, knowledge of possible or probable behavior, observation discontinuously alters what we must call "state".
The intervention made by the act of observation causes, furthermore, that not all of the system's properties can be simultaneously objectified. Rather, the individual properties are frequently in "complementary" relationships. What this means is that objectifications, that is, the observation of a specific property, excludes knowledge of certain other properties. The observation of a specific property of the system so alters the state that something learned in earlier observations about the value, or the probable value, of another property is lost in the process.
d) Chance
For without that solid chain of cause and effect, we could not draw inferences from a "perception" to a specific "process" and every agreed upon explanation of what is taking place would be without foundation.
Classical physics does justice to this situation to the extent that from the outset it combines the representation of objective space-time processes with the presupposition that those processes are completely determined. Its model pictures spatial-material systems that are sealed off from the external world and whose temporal course is determined by their present state for all time.
Contrary to this idealization, quantum physics' concept of state creates an entirely new situation in relation to the question of determinacy of natural processes. In place of the closed system as something that happens in space and time, there is the totality of possible space-time processes that take place when a system is under observation, that is to say, when it is in connection with the external world. Here one could expect complete determinacy at best only when, in addition to the state of the system, the details of the intervention necessary for the observation could also be taken as given. But then accurate knowledge of those details could itself be attained only by precisely observing the means of observation that cause the intervention if the procedure of observing were itself not again dependent on an intervention that cannot be monitored. In other words, one is drawn into an unending regression which precludes meaningfully raising the issue of the determinacy of the processes of nature.
Nor can we assume that that the events seemingly left here to the play of chance were themselves fixed by natural laws of a different kind or of a higher order. For that would mean that the frequency of space-time processes would, under given conditions of quantum theory, be different in certain circumstances from what one would expect according to the rules of quantum theory and that would suggest that these rules do not yet represent the correct laws of nature. But this is improbable given the many accurate confirmations of those rules. And yet, even this question also is seen in a different light when one considers that perhaps there are systems or more accurately: that there is knowledge of systems to which quantum theory's concept of state can no longer be applied. Obviously, such systems would no longer be bound by what quantum theory declares regarding probability and could, therefore, be subsumed under quite different sets of connections. In this sense, and in this sense only, one may say that today physics leaves open the possibility that certain processes that appear to follow the play of chance in light of nature's laws known to us, are perhaps determined by connections of a higher order.
4. Organic Life
3. A discussion of some important quotes from Heisenberg's book on the Philosophy of Physics
The following quotes from Heisenberg are based upon the particle-wave duality
interpretation of quantum physics - where the waves are treated as 'probability
waves' for finding the 'particle'. While this is mathematically correct,
the reason for it is because matter 'particles' are really wave structures
(spherical standing waves) where the 'particle' is formed at the wave center.
Thus it turns out Einstein was correct, the uncertainty comes from the fact
that matter is a spatially extended structure of space, connected to all
other matter in the universe, and it is this lack of knowledge of a connected
system that causes the uncertainty.
I have added comments to the quotes (below) to explain the errors.
Both matter and radiation possess a remarkable duality of character, as they sometimes exhibit the properties of waves, at other times those of particles. Now it is obvious that a thing cannot be a form of wave motion and composed of particles at the same time - the two concepts are too different. (Werner Heisenberg, on Quantum Theory, 1930)
The
solution of the difficulty is that the two mental pictures which experiment
lead us to form - the one of the particles, the other of the waves - are
both incomplete and have only the validity of analogies which are accurate
only in limiting cases. (Werner Heisenberg, on Quantum
Theory, 1930)
This is not correct, the particle properties of light and matter are perfectly explained with a pure Wave Structure of Matter. The wave center of the spherical standing wave forms the particle, and the discrete (particle) properties of light are due to discrete resonant wave interactions.
Light and matter are both single entities, and the apparent
duality arises in the limitations of our language.
It is not surprising that our language should be incapable of describing
the processes occurring within the atoms, for, as has been remarked, it
was invented to describe the experiences of daily life, and these consist
only of processes involving exceedingly large numbers of atoms. Furthermore,
it is very difficult to modify our language so that it will be able to describe
these atomic processes, for words can only describe things of which we can
form mental pictures, and this ability, too, is a result of daily experience.
Fortunately, mathematics is not subject to this limitation, and it has been
possible to invent a mathematical scheme - the quantum theory - which seems
entirely adequate for the treatment of atomic processes; for visualization,
however, we must content ourselves with two incomplete analogies - the wave
picture and the corpuscular picture. (Quantum Theory, Werner Heisenberg,
1930)
We can picture the spherical standing wave structure of matter quite easily in fact. See the wave diagrams page. And because reality is based upon wave motions of space we find wave phenomena all around us, thus explaining why our minds have evolved the ability to understand this.
This
application of the concept of statistical laws was finally formulated in
the second half of the last century as the so-called statistical mechanics.
In this theory, which is based on Newton's mechanics, the consequences that
spring from an incomplete knowledge of a complicated mechanical system are
investigated. Thus in principle it is not a renunciation of determinism.
The incomplete knowledge of a system must be an essential part of every
formulation in quantum theory. Quantum theoretical laws must be of a statistical
kind. .. This state of affairs is best described by saying that all particles
are basically nothing but different stationary states of one and the same
stuff. Thus even the three basic building-stones have become reduced to
a single one. There is only one kind of matter but it can exist in different
discrete stationary conditions. (Atomic Physics and Causal Law, from The
Physicist’s Conception of Nature, Werner Heisenberg, 1958)
Every
word or concept, clear as it may seem to be, has only a limited range of
applicability. (Heisenberg, Physics and Philosophy, 1963)
The problems of language here are really serious. We wish to speak in some way about the structure of the atoms… But we cannot speak about atoms in ordinary language. (Heisenberg, Physics and Philosophy, 1963)
The most difficult problem… concerning the use of the language arises in quantum theory. Here we have at first no simple guide for correlating the mathematical symbols with concepts of ordinary language: and the only thing we know from the start is the fact that our common concepts cannot be applied o the structure of the atoms. (Heisenberg, Physics and Philosophy, 1963)
The violent reaction on the recent development of modern physics can only be understood when one realizes that here the foundations of physics have started moving; and that this motion has caused the feeling that the ground would be cut from science. (Heisenberg, Physics and Philosophy, 1963)
Correct. But they started with a particle conception of matter and then found that both Einstein's relativity and quantum physics contradicted this. The error was to move to a particle / probability wave duality, rather than to a Wave Structure of Matter (WSM) that deduces the particle properties of light and matter (as Schrodinger realised).
Natural science, does not simply describe and explain nature; it is part of the interplay between nature and ourselves. (Heisenberg, Physics and Philosophy, 1963)
What we observe is not nature itself, but nature exposed to our method of questioning. (Heisenberg, Physics and Philosophy, 1963)
I
remember discussions with Bohr which went through many hours till very late
at night an ended almost in despair; and when at the end of the discussion
I went alone for a walk in the neighbouring park I repeated to myself again
and again the question: Can nature possibly be so absurd as it seemed to
us in these atomic experiments? (Heisenberg, Physics and
Philosophy, 1963)
The world thus appears as a complicated tissue of events, in which connections of different kinds alternate or overlap or combine and thereby determine the texture of the whole. (Heisenberg, Physics and Philosophy, 1963)
Matter, as a spherical wave structure of space, is interconnected with all other matter in the observable universe. We humans along with all other matter are wave structures of the universe - and it is this spatially extended structure of matter that both enables us to see and interact with the things around us, and gives rise to the statistical aspects of quantum physics due to lack of knowledge of the ensemble. This confirms Einstein's explanation of the statistical foundations of quantum theory, though Einstein made the mistake of working from continuous fields in space-time rather than real waves in space, as continuous fields do not explain discrete quantum phenomena.
Help Humanity
"You must be the change you wish to see in the world."
(Mohandas Gandhi)
"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)
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.
It is Easy to Help!
Just click on the Social Network links at top of page, or copy a nice image or quote you like and share it. We have a wonderful collection of knowledge from the greatest minds in human history, so people will appreciate your contributions. In doing this you will help a new generation of scientists see that there is a simple sensible explanation of physical reality (One Substance, One Law) - the source of truth and wisdom, the only cure for the madness of man! Thanks! Geoff Haselhurst (Updated May, 2025)
A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it. (Max Planck, 1920)
"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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