In fact, the first law of conservation (that of mass) was found in chemistry and generalized to the conservation of energy in physics by means of Einstein’s famous “E=mc2”. Energy conservation is implied by the principle of least action from a variational viewpoint as in Emmy Noether’s theorems (1918): any chemical change in a conservative (i.e. “closed”) system can be accomplished only in the way conserving its total energy. Bohr’s innovation to found Mendeleev’s periodic table by quantum mechanics implies a certain generalization referring to the quantum leaps as if accomplished in all possible trajectories (according to Feynman’s interpretation) and therefore generalizing the principle of least action and needing a certain generalization of energy conservation as to any quantum change. The transition from the first to the second theorem of Emmy Noether represents well the necessary generalization: its chemical meaning is the generalization of any chemical reaction to be accomplished as if any possible course of time rather than in the standard evenly running time (and equivalent to energy conservation according to the first theorem).The problem: If any quantum change is accomplished in all possible “variations (i.e. “violations) of energy conservation” (by different probabilities), what (if any) is conserved?An answer: quantum information is what is conserved. Indeed, it can be particularly defined as the counterpart (e.g. in the sense of Emmy Noether’s theorems) to the physical quantity of action (e.g. as energy is the counterpart of time in them). It is valid in any course of time rather than in the evenly running one. That generalization implies a generalization of the periodic table including any continuous and smooth transformation between two chemical elements.
In fact, the first law of conservation (that of mass) was found in chemistry and generalized to the conservation of energy in physics by means of Einstein’s famous “E=mc2”. Energy conservation is implied by the principle of least action from a variational viewpoint as in Emmy Noether’s theorems (1918): any chemical change in a conservative (i.e. “closed”) system can be accomplished only in the way conserving its total energy. Bohr’s innovation to found Mendeleev’s periodic table by quantum mechanics implies a certain generalization referring to the quantum leaps as if accomplished in all possible trajectories (according to Feynman’s interpretation) and therefore generalizing the principle of least action and needing a certain generalization of energy conservation as to any quantum change. The transition from the first to the second theorem of Emmy Noether represents well the necessary generalization: its chemical meaning is the generalization of any chemical reaction to be accomplished as if any possible course of time rather than in the standard evenly running time (and equivalent to energy conservation according to the first theorem).The problem: If any quantum change is accomplished in all possible “variations (i.e. “violations) of energy conservation” (by different probabilities), what (if any) is conserved?An answer: quantum information is what is conserved. Indeed, it can be particularly defined as the counterpart (e.g. in the sense of Emmy Noether’s theorems) to the physical quantity of action (e.g. as energy is the counterpart of time in them). It is valid in any course of time rather than in the evenly running one. That generalization implies a generalization of the periodic table including any continuous and smooth transformation between two chemical elements.
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.
The principle of least action, which has so successfully been applied to diverse fields of physics looks back at three centuries of philosophical and mathematical discussions and controversies. They could not explain why nature is applying the principle and why scalar energy quantities succeed in describing dynamic motion. When the least action integral is subdivided into infinitesimal small sections each one has to maintain the ability to minimize. This however has the mathematical consequence that the Lagrange function at a given point of the trajectory, the dynamic, available energy generating motion, must itself have a fundamental property to minimize. Since a scalar quantity, a pure number, cannot do that, energy must fundamentally be dynamic and time oriented for a consistent understanding. It must have vectorial properties in aiming at a decrease of free energy per state (which would also allow derivation of the second law of thermodynamics). Present physics is ignoring that and applying variation calculus as a formal mathematical tool to impose a minimization of scalar assumed energy quantities for obtaining dynamic motion. When, however, the dynamic property of energy is taken seriously it is fundamental and has also to be applied to quantum processes. A consequence is that particle and wave are not equivalent, but the wave (distributed energy) follows from the first (concentrated energy). Information, provided from the beginning, an information self-image of matter, is additionally needed to recreate the particle from the wave, shaping a “dynamic” particle-wave duality. It is shown that this new concept of a “dynamic” quantum state rationally explains quantization, the double slit experiment and quantum correlation, which has not been possible before. Some more general considerations on the link between quantum processes, gravitation and cosmological phenomena are also advanced.
The explicit history of the “hidden variables” problem is well-known and established. The main events of its chronology are traced. An implicit context of that history is suggested. It links the problem with the “conservation of energy conservation” in quantum mechanics. Bohr, Kramers, and Slaters (1924) admitted its violation being due to the “fourth Heisenberg uncertainty”, that of energy in relation to time. Wolfgang Pauli rejected the conjecture and even forecast the existence of a new and unknown then elementary particle, neutrino, on the ground of energy conservation in quantum mechanics, afterwards confirmed experimentally. Bohr recognized his defeat and Pauli’s truth: the paradigm of elementary particles (furthermore underlying the Standard model) dominates nowadays. However, the reason of energy conservation in quantum mechanics is quite different from that in classical mechanics (the Lie group of all translations in time). Even more, if the reason was the latter, Bohr, Cramers, and Slatters’s argument would be valid. The link between the “conservation of energy conservation” and the problem of hidden variables is the following: the former is equivalent to their absence. The same can be verified historically by the unification of Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics in the contemporary quantum mechanics by means of the separable complex Hilbert space. The Heisenberg version relies on the vector interpretation of Hilbert space, and the Schrödinger one, on the wave-function interpretation. However the both are equivalent to each other only under the additional condition that a certain well-ordering is equivalent to the corresponding ordinal number (as in Neumann’s definition of “ordinal number”). The same condition interpreted in the proper terms of quantum mechanics means its “unitarity”, therefore the “conservation of energy conservation”. In other words, the “conservation of energy conservation” is postulated in the foundations of quantum mechanics by means of the concept of the separable complex Hilbert space, which furthermore is equivalent to postulating the absence of hidden variables in quantum mechanics (directly deducible from the properties of that Hilbert space). Further, the lesson of that unification (of Heisenberg’s approach and Schrödinger’s version) can be directly interpreted in terms of the unification of general relativity and quantum mechanics in the cherished “quantum gravity” as well as a “manual” of how one can do this considering them as isomorphic to each other in a new mathematical structure corresponding to quantum information. Even more, the condition of the unification is analogical to that in the historical precedent of the unifying mathematical structure (namely the separable complex Hilbert space of quantum mechanics) and consists in the class of equivalence of any smooth deformations of the pseudo-Riemannian space of general relativity: each element of that class is a wave function and vice versa as well. Thus, quantum mechanics can be considered as a “thermodynamic version” of general relativity, after which the universe is observed as if “outside” (similarly to a phenomenological thermodynamic system observable only “outside” as a whole). The statistical approach to that “phenomenological thermodynamics” of quantum mechanics implies Gibbs classes of equivalence of all states of the universe, furthermore re-presentable in Boltzmann’s manner implying general relativity properly … The meta-lesson is that the historical lesson can serve for future discoveries.
Quantum mechanics was reformulated as an information theory involving a generalized kind of information, namely quantum information, in the end of the last century. Quantum mechanics is the most fundamental physical theory referring to all claiming to be physical. Any physical entity turns out to be quantum information in the final analysis. A quantum bit is the unit of quantum information, and it is a generalization of the unit of classical information, a bit, as well as the quantum information itself is a generalization of classical information. Classical information refers to finite series or sets while quantum information, to infinite ones. Quantum information as well as classical information is a dimensionless quantity. Quantum information can be considered as a “bridge” between the mathematical and physical. The standard and common scientific epistemology grants the gap between the mathematical models and physical reality. The conception of truth as adequacy is what is able to transfer “over” that gap. One should explain how quantum information being a continuous transition between the physical and mathematical may refer to truth as adequacy and thus to the usual scientific epistemology and methodology. If it is the overall substance of anything claiming to be physical, one can question how different and dimensional physical quantities appear. Quantum information can be discussed as the counterpart of action. Quantum information is what is conserved, action is what is changed in virtue of the fundamental theorems of Emmy Noether (1918). The gap between mathematical models and physical reality, needing truth as adequacy to be overcome, is substituted by the openness of choice. That openness in turn can be interpreted as the openness of the present as a different concept of truth recollecting Heidegger’s one as “unconcealment” (ἀλήθεια). Quantum information as what is conserved can be thought as the conservation of that openness
The problem of indeterminism in quantum mechanics usually being considered as a generalization determinism of classical mechanics and physics for the case of discrete (quantum) changes is interpreted as an only mathematical problem referring to the relation of a set of independent choices to a well-ordered series therefore regulated by the equivalence of the axiom of choice and the well-ordering “theorem”. The former corresponds to quantum indeterminism, and the latter, to classical determinism. No other premises (besides the above only mathematical equivalence) are necessary to explain how the probabilistic causation of quantum mechanics refers to the unambiguous determinism of classical physics. The same equivalence underlies the mathematical formalism of quantum mechanics. It merged the well-ordered components of the vectors of Heisenberg’s matrix mechanics and the non-ordered members of the wave functions of Schrödinger’s undulatory mechanics. The mathematical condition of that merging is just the equivalence of the axiom of choice and the well-ordering theorem implying in turn Max Born’s probabilistic interpretation of quantum mechanics. Particularly, energy conservation is justified differently than classical physics. It is due to the equivalence at issue rather than to the principle of least action. One may involve two forms of energy conservation corresponding whether to the smooth changes of classical physics or to the discrete changes of quantum mechanics. Further both kinds of changes can be equated to each other under the unified energy conservation as well as the conditions for the violation of energy conservation to be investigated therefore directing to a certain generalization of energy conservation.