This short note proposes that the conserved substance of physics is action, not energy. Energy conservation is, by Noether's theorem, the exact statement of a uniform flow of time — an assumption that fails, even if only slightly, in a relativistic universe where clocks run at different rates in different places. Read the other way, Planck's relation becomes a conservation law rather than an empirical input: Eτ = h, one quantum of action processed per cycle of a local resonance, with ordinary energy conservation recovered as the special case in which the period τ is held fixed. The note carries exactly one assumption beyond the algebra, stated plainly rather than smuggled in: the vacuum is a medium of such resonances, and a particle is a persistent, self-closing cycle within it. Angle and capacity The invariant has two faces. The law pins the magnitude at h — the capacity — leaving the accumulated phase φ as the only freedom: dS = ℏ dφ. Every familiar conjugate pair is this one statement read along a different axis of advance — energy against time, momentum against position, angular momentum against orientation — three orthogonal accounts of one accumulating phase, each closing one unit of capacity per cycle: Eτ = h, pλ = h, L·2π = h. This split is where classical and quantum mechanics part ways. An open trajectory reads the phase continuously, and its stationary-phase condition is the principle of least action; a closed resonance can only count whole turns, and closure quantises. Quantisation is a property of closure, not a property of the phase — the boundary between classical and quantum is a change of topology, not a change of law. What follows mechanically From the capacity law alone, with no further postulate, three familiar structures are recovered. A resonance at rest turns at the Compton frequency ωC = mc²/ℏ, so that one full turn spends exactly one quantum, EτC = h: mass is nothing but a resonance's cycling rate. Driven through the medium, a resonance meets an increased flux that scales as the Lorentz factor; conserving its fixed action budget under that load forces its geometry to yield — contraction along the direction of motion, dilation of its internal period — recovering special relativity as mechanical equilibration rather than a postulate about coordinates, with no rest frame ever exposed because the same yielding that would reveal one also defines the observer's own rulers and clocks. Requiring the accumulated phase along a worldline to stay coherent, expanded in the weak-field limit, returns the classical Lagrangian directly, −Mc²dτ = (T − V − Mc²)dt: least action is not minimised as a primitive rule, it is what capacity conservation looks like when a resonance crosses a gradient of the medium. And the Heisenberg relation σxσp ≥ ℏ/2 is read as the ordinary bandwidth (Gabor) theorem for a wave and its Fourier transform — a floor on occupancy for a phase-locked resonance, not a ceiling on knowledge. Gravity, without a graviton The most interpretive claim in the note, flagged as such throughout: if the metric's invariant is Eτ = h rather than a fixed energy, the metric carries no absolute clock, and the phase-lock condition forces its temporal and spatial responses to be reciprocal, giving the bipolar exponential line element ds² = −e−2ξc²dt² + e+2ξdx². The conceptual point is what this reframes: the decades-long search for a quantum theory of gravity has sought a graviton by quantising the metric on a fixed background, when gravity is the background. On this reading there is no separate field to quantise — the medium's deformation is already quantised at h per cycle, and gravity is simply the shape of phase accumulation across its gradient. The problem is not solved so much as dissolved: relocated from “how do we quantise the metric” to “the metric was never a separate thing to quantise.” Scope The note is deliberately bounded, and says so explicitly rather than leaving the boundary implicit. It derives special relativity, the principle of least action, and the bandwidth reading of the uncertainty relation from the capacity law alone; it advances the gravitational reading as a stance to be tested against its consequences, not a completed theory. It does not derive the particle spectrum, specific masses, electric charge, colour, or the numerical values of G or α, and makes no cosmological claim. This separation is intentional: a conservation principle should be judged on its own terms. A companion note reports a closed-form numerical identity for the proton mass as a separate, independent empirical fact; the two are meant to be read, and to stand or fall, apart.
This short note proposes that the conserved substance of physics is action, not energy. Energy conservation is, by Noether's theorem, the exact statement of a uniform flow of time — an assumption that fails, even if only slightly, in a relativistic universe where clocks run at different rates in different places. Read the other way, Planck's relation becomes a conservation law rather than an empirical input: Eτ = h, one quantum of action processed per cycle of a local resonance, with ordinary energy conservation recovered as the special case in which the period τ is held fixed. The note carries exactly one assumption beyond the algebra, stated plainly rather than smuggled in: the vacuum is a medium of such resonances, and a particle is a persistent, self-closing cycle within it. Angle and capacity The invariant has two faces. The law pins the magnitude at h — the capacity — leaving the accumulated phase φ as the only freedom: dS = ℏ dφ. Every familiar conjugate pair is this one statement read along a different axis of advance — energy against time, momentum against position, angular momentum against orientation — three orthogonal accounts of one accumulating phase, each closing one unit of capacity per cycle: Eτ = h, pλ = h, L·2π = h. This split is where classical and quantum mechanics part ways. An open trajectory reads the phase continuously, and its stationary-phase condition is the principle of least action; a closed resonance can only count whole turns, and closure quantises. Quantisation is a property of closure, not a property of the phase — the boundary between classical and quantum is a change of topology, not a change of law. What follows mechanically From the capacity law alone, with no further postulate, three familiar structures are recovered. A resonance at rest turns at the Compton frequency ωC = mc²/ℏ, so that one full turn spends exactly one quantum, EτC = h: mass is nothing but a resonance's cycling rate. Driven through the medium, a resonance meets an increased flux that scales as the Lorentz factor; conserving its fixed action budget under that load forces its geometry to yield — contraction along the direction of motion, dilation of its internal period — recovering special relativity as mechanical equilibration rather than a postulate about coordinates, with no rest frame ever exposed because the same yielding that would reveal one also defines the observer's own rulers and clocks. Requiring the accumulated phase along a worldline to stay coherent, expanded in the weak-field limit, returns the classical Lagrangian directly, −Mc²dτ = (T − V − Mc²)dt: least action is not minimised as a primitive rule, it is what capacity conservation looks like when a resonance crosses a gradient of the medium. And the Heisenberg relation σxσp ≥ ℏ/2 is read as the ordinary bandwidth (Gabor) theorem for a wave and its Fourier transform — a floor on occupancy for a phase-locked resonance, not a ceiling on knowledge. Gravity, without a graviton The most interpretive claim in the note, flagged as such throughout: if the metric's invariant is Eτ = h rather than a fixed energy, the metric carries no absolute clock, and the phase-lock condition forces its temporal and spatial responses to be reciprocal, giving the bipolar exponential line element ds² = −e−2ξc²dt² + e+2ξdx². The conceptual point is what this reframes: the decades-long search for a quantum theory of gravity has sought a graviton by quantising the metric on a fixed background, when gravity is the background. On this reading there is no separate field to quantise — the medium's deformation is already quantised at h per cycle, and gravity is simply the shape of phase accumulation across its gradient. The problem is not solved so much as dissolved: relocated from “how do we quantise the metric” to “the metric was never a separate thing to quantise.” Scope The note is deliberately bounded, and says so explicitly rather than leaving the boundary implicit. It derives special relativity, the principle of least action, and the bandwidth reading of the uncertainty relation from the capacity law alone; it advances the gravitational reading as a stance to be tested against its consequences, not a completed theory. It does not derive the particle spectrum, specific masses, electric charge, colour, or the numerical values of G or α, and makes no cosmological claim. This separation is intentional: a conservation principle should be judged on its own terms. A companion note reports a closed-form numerical identity for the proton mass as a separate, independent empirical fact; the two are meant to be read, and to stand or fall, apart.
This short note proposes that the conserved substance of physics is action, not energy. Energy conservation is, by Noether's theorem, the exact statement of a uniform flow of time — an assumption that fails, even if only slightly, in a relativistic universe where clocks run at different rates in different places. Read the other way, Planck's relation becomes a conservation law rather than an empirical input: Eτ = h, one quantum of action processed per cycle of a local resonance, with ordinary energy conservation recovered as the special case in which the period τ is held fixed. The note carries exactly one assumption beyond the algebra, stated plainly rather than smuggled in: the vacuum is a medium of such resonances, and a particle is a persistent, self-closing cycle within it. Angle and capacity The invariant has two faces. The law pins the magnitude at h — the capacity — leaving the accumulated phase φ as the only freedom: dS = ℏ dφ. Every familiar conjugate pair is this one statement read along a different axis of advance — energy against time, momentum against position, angular momentum against orientation — three orthogonal accounts of one accumulating phase, each closing one unit of capacity per cycle: Eτ = h, pλ = h, L·2π = h. This split is where classical and quantum mechanics part ways. An open trajectory reads the phase continuously, and its stationary-phase condition is the principle of least action; a closed resonance can only count whole turns, and closure quantises. Quantisation is a property of closure, not a property of the phase — the boundary between classical and quantum is a change of topology, not a change of law. What follows mechanically From the capacity law alone, with no further postulate, three familiar structures are recovered. A resonance at rest turns at the Compton frequency ωC = mc²/ℏ, so that one full turn spends exactly one quantum, EτC = h: mass is nothing but a resonance's cycling rate. Driven through the medium, a resonance meets an increased flux that scales as the Lorentz factor; conserving its fixed action budget under that load forces its geometry to yield — contraction along the direction of motion, dilation of its internal period — recovering special relativity as mechanical equilibration rather than a postulate about coordinates, with no rest frame ever exposed because the same yielding that would reveal one also defines the observer's own rulers and clocks. Requiring the accumulated phase along a worldline to stay coherent, expanded in the weak-field limit, returns the classical Lagrangian directly, −Mc²dτ = (T − V − Mc²)dt: least action is not minimised as a primitive rule, it is what capacity conservation looks like when a resonance crosses a gradient of the medium. And the Heisenberg relation σxσp ≥ ℏ/2 is read as the ordinary bandwidth (Gabor) theorem for a wave and its Fourier transform — a floor on occupancy for a phase-locked resonance, not a ceiling on knowledge. Gravity, without a graviton The most interpretive claim in the note, flagged as such throughout: if the metric's invariant is Eτ = h rather than a fixed energy, the metric carries no absolute clock, and the phase-lock condition forces its temporal and spatial responses to be reciprocal, giving the bipolar exponential line element ds² = −e−2ξc²dt² + e+2ξdx². The conceptual point is what this reframes: the decades-long search for a quantum theory of gravity has sought a graviton by quantising the metric on a fixed background, when gravity is the background. On this reading there is no separate field to quantise — the medium's deformation is already quantised at h per cycle, and gravity is simply the shape of phase accumulation across its gradient. The problem is not solved so much as dissolved: relocated from “how do we quantise the metric” to “the metric was never a separate thing to quantise.” Scope The note is deliberately bounded, and says so explicitly rather than leaving the boundary implicit. It derives special relativity, the principle of least action, and the bandwidth reading of the uncertainty relation from the capacity law alone; it advances the gravitational reading as a stance to be tested against its consequences, not a completed theory. It does not derive the particle spectrum, specific masses, electric charge, colour, or the numerical values of G or α, and makes no cosmological claim. This separation is intentional: a conservation principle should be judged on its own terms. A companion note reports a closed-form numerical identity for the proton mass as a separate, independent empirical fact; the two are meant to be read, and to stand or fall, apart.
It is often claimed that Einstein is wrong about quantum mechanics. However, when comparisons are made with respect to theoretical foundations rather than experimental results Einstein’s theories are found to be superior. Although quantum mechanics correctly predicts what it is possible to observe (the emissions) with remarkable accuracy it ignores the other half of natural phenomena, that which cannot be observed (the absorptions), thereby violating the conservation of energy. Similarly, the conservation of momentum is violated by disregarding unobservable molecular impulses. Despite irrefutable proof that molecular impulses transfer momentum asymmetrically as shown by Einstein’s derivation of the A and B coefficients, the wave function is assumed to apply symmetrically in time. The deficiencies are corrected by introducing Hamilton’s principle and deriving relativistic equations of motion. This allows non-relativistic quantum mechanics to be described with a physical model and wave function behavior to be interpreted as the combined action of a particle and its associated quantized field. The calculus of variations is applied to the wave function to show that it is an incomplete equation of motion because it yields twice the allowable action minimum. The concept of reality is redefined by showing that reductionism applies to classical phenomena, but not quantum phenomena.
Physics is written in mathematics, and at the base of mathematics lies distinction: yes or no, identical or different, one or zero. A bit is the minimal written form of such a distinction. Physics can therefore measure only what can become distinguishable. What cannot be distinguished cannot yet appear as a physical record. From distinguishability comes information; from the registration of information comes physical time. Unified informational Theory (UiT) presents a unified physical framework in which time, mass, force, thermodynamic directionality, electromagnetic coupling, nuclear structure, and horizon physics are expressed through one informational registration mechanism: closed phase becoming physical record. The central object is a closed-light phase carrier: a closed photon-like phase structure carrying informational increments of ℏ, rotating on a complex phase surface at the Compton frequency, with a Planck-scale phase radius. It is not treated as a point mechanically moving through ordinary three-dimensional space. Before measurement, its structure exists in the complex phase domain as physical distinguishability: real, active, and capable of producing measurable effects, but not yet written as an ordinary 3+1 record such as position, trajectory, detector event, clock reading, or linear-time history. Measurement is the operation that projects and registers part of this complex phase structure into ordinary record-space, using energy and carrying a thermodynamic cost. In UiT, linear physical time is the ordered registration of physical change into record. A record may be a clock reading, track, pointer state, detector click, environmental correlation, thermodynamic trace, or any stable physical mark. Time is not a passive background parameter. It is the informational order produced when phase structure becomes registered reality. The same principle also defines force. All forces are gradients of one underlying registration object, read under different load conditions, geometries, and coupling branches. A force appears where an invariant closed phase carrier is placed in a field whose time-registration rate varies across record-space. The carrier cannot change its own invariant Compton phase throughput, so the mismatch between invariant internal phase and local registration capacity becomes a physical force. Inertia and gravity are therefore not separate mysteries at the deepest level: both are responses of the same closed phase throughput to different ways of limiting temporal registration. Special relativity arises when recorded motion consumes part of the available registration bandwidth. Motion requires information about position and change of position, and this cost enters quadratically. The carrier phase itself never stops moving; what changes is how much of its invariant phase throughput can be written as linear time rather than as recorded motion. Lorentz time dilation is therefore read as a registration-budget partition: motion spends part of the time-writing capacity. Gravity arises from the same Compton throughput read radially. A mass is not merely an object placed inside space. It is closed-light Compton sampling of a Planck registration-stiffness update. Around it, record-space has reduced capacity to write distinguishable temporal information. Less capacity remains for writing time, and the radial gradient of that capacity is read as gravity. In this view, space is not a rubber sheet that literally bends. Space is the local capacity to register distinguishable physical alternatives. Changing the time-registration capacity also changes the spatial registration structure, so the same geodesics are obtained, but their ontology changes: curvature is the metric bookkeeping of variable registration capacity. This same capacity logic leads directly to thermodynamics and entropy. Entropy counts the available or dispersed ways in which distinctions can be written, stabilized, erased, hidden, or made inaccessible. Thermodynamic directionality is not added from outside. It is the cost and irreversibility of registering physical distinction into stable record. Horizon entropy is the saturated boundary count of the same closed phase surface: the point where ordinary exterior registration reaches its limiting boundary. Electromagnetism is read as a phase-connection branch of the same object. Charge is not introduced as an unrelated primitive substance, but as a coupling orientation of phase registration. Electric and magnetic effects are different record-space readouts of this phase connection under different motion and registration conditions. The weak sector gives UiT its primary empirical handle. Radioactive decay is treated as a finite identity-rewrite process. In order for a decay path to be environmentally perturbable, the environment must couple to degrees of freedom required for reverse daughter-to-parent reconstruction. This requires local reverse temporal registration: a limited branch in which identity is locally unwritten and rewritten. From this postulate, UiT produces a taxonomy of radioactive-decay perturbability, functioning like a periodic table of decay influence. The table does not merely classify known decays by name; it identifies which decay channels can be perturbed and why, according to the informational variables required by the reverse reconstruction path. The strong sector is expressed through closed multi-carrier phase geometry. Three phase carriers form a zero-sum closure in the complex plane. What appears outwardly as fractional charge is a projection of a deeper internal closure: one-third is externally read, while two-thirds remain internally locked within the phase structure. This gives a geometric and numerical account of fractional charge weights, confinement architecture, and the Cornell-potential structure, while leaving full QCD dynamics and detailed coefficients as completion targets. UiT is not presented as a theory of everything, and it does not discard established physics. It proposes a deeper informational primitive from which quantum phase, relativistic time, gravitational distortion, thermodynamic irreversibility, electromagnetic coupling, weak decay, strong closure, and horizon counting arise as different expressions of one closed phase-registration object. The empirical content is twofold. The primary tested layer is the weak-sector perturbability table, which organizes radioactive decay channels according to the informational degrees of freedom required for reverse daughter-to-parent reconstruction. A second prospective discriminant predicts photon arrival-time delay with no linear Planck-energy term and leading quadratic Planck suppression. The compact unification principle is this: physical law is the geometry of informational registration. Time is the written order of phase registration; mass is closed-light Compton throughput; force is the gradient of registration mismatch; entropy is the count and cost of distinguishable writing; and the apparent separation between relativity, thermodynamics, electromagnetism, nuclear structure, and horizon physics reflects different readout conditions of the same underlying closed phase surface.
Special relativity at eleven parameters (SR11) defines a frame by a body: a frame has a mass M , a momentum P , a spin and a position, the transformation to it is the boost L(P ) built from its momentum, and the composition law of the theory says how a second body looks from it. A frame is therefore a physical system with a quantum state, which is what the programme of quantum reference frames has been building; what the eleven add is a kinematics in which the frame body's mass appears explicitly as the scale of its rapidity and fixes its resolution. This paper takes the composition law of the eleven, with the frame body in a superposition of momenta, as the transformation law between quantum reference frames. The transformation is the composition law controlled by the frame's momentum; it carries the momentum of the body it describes linearly, and all its non-linearity sits in the Wigner rotation, which is the only place where the frame's momentum and the body's spin are correlated: the Wigner rotation is the entangler of spin with momentum, and the reduced spin of a body relative to a frame in a superposition of momenta has the purity , the result of Giacomini, Castro-Ruiz and Brukner with the frame's mass as the scale of its rapidity. The one number of the mixing is that mass. A frame body localised to ∆x has a transverse rapidity spread of at least ℏ/(2M c ∆x), so that the product of a frame's position and rapidity resolutions is bounded below by half its reduced Compton length, and the spin purity of a body of rapidity θ seen from it is 1 2 (1 + e -s 2 ) with s = (σ P /(M c)) tanh(θ/2), the small-angle Wigner rotation; the floor ∆x ≳ ℏ/(M c) below which the frame body is no longer one body is the length c 2 /a max on which the acceleration bound of SR11 is built, one scale read once as a resolution and once as a ceiling. Because the transformation is diagonal in the frame's momentum, the frame's pointer basis is its momentum, and it decoheres, when the bodies it frames are traced out, by the overlap of their relative momenta and spins; the thermal blur of a frame defined by a body in a Jüttner ensemble, computed in the thermal monograph, is that decoherence already done, 0.997, 0.992, 0.977, 0.964 at k B T /(mc 2 ) = 0.05, 0.135, 0.5, 1, and a frame defined by a conserved charge does not decohere at all. A clock is a body: its time, its energy and its dilatation charge close on an sl(2, R), the energy-time sector of the dilatation block, so that a body of the eleven is a Page-Wootters clock whose reading is a self-adjoint operator, Pauli's obstruction not applying to a commutator that is an operator; the price is that the reading is positive and its flow quadratic, x 0 -τ D + τ 2 p 0 when the clock is driven by its own energy, at the initial rate of its dilatation charge, which is Planck's constant in the Heisenberg contraction, so that the clock is covariant on neither the full line nor the full flow; and the compact conformal Hamiltonian, whose spectrum is E 0 + n, gives the clock a period, the time circle of the reverse paradigm; de Alfaro, Fubini and Furlan's conformal quantum mechanics is its model. The eleven are then placed among the kinematics that put the Planck scale into relativity, Snyder's and Yang's quantised spacetimes, doubly special relativity, κ-Poincaré, relative locality and triply special relativity, and among the quantum-reference-frame formalisms: they agree with the former on a bounded momentum, in the compact sector, and differ by the acceleration bound, the spin as one of the primary quantities, the reciprocity as an automorphism, and the linear frame composition and undeformed addition of momenta of the ordinary reading; they agree with 1 the latter that a frame is a quantum system and make explicit, in its mass, a parameter those formalisms carry and do not use. What the theory does not do is interpret: its quantum step is the Poisson bracket of the sixteen made a commutator, and it takes no position on measurement.
It is often claimed that Einstein is wrong about quantum mechanics. However, when comparisons are made with respect to theoretical foundations rather than experimental results Einstein’s theories are found to be superior. Although quantum mechanics correctly describes energy exchange due to emissions with remarkable accuracy it ignores momentum exchange (the absorptions), thereby failing to recognize their causal relationship due to the conservation laws. The deficiencies in non-relativistic theory are corrected by introducing Hamilton’s principle and deriving relativistic equations of motion. This allows wave function behavior to be described as the combined action of a particle and an associated localized field. The calculus of variations is applied to the Schrödinger wave equation to show that it is incomplete because it yields twice the allowable action minimum.
As in classical physics, also in quantum mechanics: physical processes are bound to obey conservation laws. However, there is an important difference. While in classical physics we can suppose that all variables have definite values (irrespective of whether we know them or not), quantum mechanics allows them to be intrinsically uncertain. In those cases conservation laws apply only to ensemble averages (expectation values), and hence are less informative. They show their full strength in measurement processes. Then the measured values satisfy the respective conservation laws in any individual experiment. Let me remind you of spin measurements on a system of two spin-½ particles, being in a state with zero total spin, which we used in Section 5.5 to illustrate the EPR paradox. The spin components, with respect to an arbitrarily chosen direction, of the two particles are indefinite; however, measuring them yields definite values (+½ or −½) that add up to zero, thus confirming the angular conservation law. In the following, we will consider some realistic experiments for which conservation laws provide a simple explanation. Energy and momentum conservation For an understanding of the interaction between matter and radiation, Einstein's photon concept (actually, he spoke of ‘light quanta’) proved to be very helpful. He assumed photons to be particle-like constituents of electromagnetic radiation, in particular light. They have the energy h ν, where ν is the frequency of the radiation field. (Since the electromagnetic spectrum extends over an extremely wide range, there is a huge number of different sorts of photons.) The crucial point is that photons are generated or annihilated only as a whole. This property gives rise to typical quantum effects.