This work asserts that quantum theory runs into a fundamental conflict with the principles of energy conservation inferred from the statistical evolution of interacting systems. The gist is the energy of systems by the principles of Lagrangian mechanics leaves out of account their energy associated with the phase flows of non-invariant phase volume. The quantum theory takes this fact into account, but does that improperly. We show it by presenting insoluble inconsistencies and a case study.
This work asserts that quantum theory runs into a fundamental conflict with the principles of energy conservation inferred from the statistical evolution of interacting systems. The gist is the energy of systems by the principles of Lagrangian mechanics leaves out of account their energy associated with the phase flows of non-invariant phase volume. The quantum theory takes this fact into account, but does that improperly. We show it by presenting insoluble inconsistencies and a case study.
In this article, we discuss through a principle of action the quantum information in relation to the information paradox.The information paradox, which arises in black hole physics, suggests that information can be lost when matter falls into a black hole, which contradicts the principle of information conservation in physics.We propose that the principle of action, which asserts that the action of a physical system is conserved, can be applied to information, showing that information is conserved in a similar way to energy and momentum.Through mathematical models and theoretical analysis, we show that the conservation of information can be understood as a result of the evolution of a system and probability amplitudes in quantum mechanics.
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 statistical formulations of quantum mechanics correctly describe energy and momentum exchange with remarkable accuracy there are individual cases, paradoxically, that violate the conservation laws. A recent study finds that in order to account for observed violations frames of reference involved in preparation of the initial state must be explicitly taken into account [1]. We show here that the same conclusion was arrived at in a much simpler way by Einstein over 100 years ago. Deficiencies in the foundations of non-relativistic theory are corrected by introducing Hamilton’s principle and deriving relativistic equations of motion. This allows quantum mechanical formalism in abstract space to be replaced by the superposition of particle field geometries in real space. Applying the calculus of variations to the Schrödinger wave equation reveals that the wave function is incomplete because it requires twice the allowable action minimum.
Classical statistical equilibrium appears to be based on a no-flow situation with a balance of pressure (including -dV/dx in the case of a potential present). It may be noted, however, that like quantum mechanics, a single particle has different probabilities of being at one x versus another. Furthermore, the Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein distributions may be obtained using reaction balance which is linked to conservation of energy i.e. g(f(ei))g(f(ej)) = g(f(el))g(f(ek)) where ei+ej=el+ei=e. Taking ln of the former expression and linking to the latter yields f(ei), the probability distribution. g=1 for the MB case, f(e)/(1-f(ei)) for the FD and f(e)/(1+f(ei)) for the BE. In classical mechanics, one has the conservation equation: p(x)*p(x)/2m + V(x) = E. In quantum bound systems one has: KE(ave)(x) + V(x) = E which appears to be very similar, although it is based on ensemble averages and there is a momentum distribution P(p/x) at each x. A question which arises is: What is the “conservation of energy” equation for a particular p of the P(p/x) distribution? In this note, we argue the “potential” term associated with a component p*p/2m is related to the part of the potential which contributes to the “creation” of p. In particular, we consider V(x)= Sum over k V(k) exp(ikx) where each k term renders a kick of momentum k. One may create a momentum p using k and p-k for each value of k. We further argue that: p*p/2m P(p/x) + contributing portion of V(x) = E P(p/x) ((1)) for all p. Thus, in quantum equilibrium, which involves a flow, there is a “constant E” type of equation i.e. ((1)), different in form but similar in idea, to that of classical statistical mechanical equilibrium. In previous notes, we referred to this as cycling, but in this note we wish to consider it in terms of dynamics. We further note that in both classical statistical mechanics and quantum mechanics, the energy-probability p equation makes use of the overall average energy which is bT for the classical case and E for the quantum. (b is constant)
Conservation of energy and momentum are fundamental ideas of physics which appear in Newtonian mechanics and as such are considered to be deterministic. One may follow the center-of-masses of two particles r1(t), r2(t) up to an interaction and pinpoint energy and momentum at a specific x,t. Special relativity is also deterministic (based on x=vt) and one would expect that conservation of energy and momentum should be enforced in a deterministic manner there as well. In every frame, one could write: Kronecker delta (E1-E2) Kronecker delta (p1x-p2x) … Kronecker delta (p1z-p2z). Such determinism would bypass quantum mechanics completely because quantum mechanics involves a non-deterministic approach to conservation of E,p. We argue, however, that it is actually deterministic special relativity which gives rise to non-deterministic conservation of E,p for a specific reason. We suggest that in a rest frame, a particle with rest mass mo is associated with a running time t, but no notion of x space or momentum. One might be tempted to set p=0, but in principle we argue that there is no notion of momentum for a rest particle and no notion of space because it is simply sitting at one point. Momentum only arises if one views the particle at rest from a frame moving at -v, leading to p = mov/sqrt(1-vv/cc). It is only in Newtonian mechanics that one introduces a priori a momentum which may then be applied in any frame. Such is not the case in special relativity. If one takes this idea seriously, it has strong consequences because one cannot have a set of Kronecker deltas in each frame as listed above. One Kronecker delta in the rest frame (mo1-m2), would have to transform into Kronecker(E1-E2) Kronecker (p1x-p2x) for motion in the x direction alone. Mathematically a single Kronecker delta does not transform into two Kronecker deltas. One requires a mathematical function which describes energy conservation in the rest frame and then transforms naturally to describe both energy and momentum conservation in a moving frame. Given that mocc and t are the only variables in the rest frame, we suggest a function based on the Lorentz invariant -Et+px. If this is the case, then t and x must act as independent variables which at first seems like a problem because it is understood that x=vt. One may show, however, as we do in detail, that this invariant allows for fluctuations to t and x and so one may in fact create the function exp(-iEt+ipx) (which is like a probability) and enforces non-deterministic conservation of energy and momentum. Non-deterministic conservation means that one must interact exp(-ip1x) exp(ip2x) over some space to obtain 0. Physically, this is linked to the notion that p hits occur probabilistically in space (2-slit experiment) and so this same probabilistic notion applies to conservation. Deterministic conservation at only one x,t is at odds with 2-slit interference which shows that one may interact probabilistically at two points in space. Thus, one must account for conservation of p at both.
The overriding problem in theoretical physics is the inability to determine the nature of physical reality [1]. We show in the following discussion that the source of the problem lies at the very beginning of quantum mechanics a hundred years ago when its founding principles were derived. The use of mathematical equations as a substitute for physical reality caused a premature, hastily conceived disassociation from classical models. Using methods accessible to all, irrespective of educational background, we restore a connection to classical physics by demonstrating that quantum mechanics as currently interpreted violates the conservation of energy. References may be found in first year university physics textbooks or by conducting internet searches of individual terms throughout the manuscript.
This paper introduces the Entropic I-Field Theory, a fundamental framework that establishes irreversibility as a physical principle rather than an emergent property. We propose a universal scalar field—the I-field—that couples dissipatively to all matter and radiation. By breaking time-reversal symmetry at the fundamental level through an extended Euler-Lagrange-Rayleigh variational principle, the theory preserves causality and conservation laws while introducing intrinsic directionality to physical evolution.The framework replaces purely unitary quantum evolution with non-conservative dynamics in which the I-field coupling introduces dissipative terms into the equations of motion. Through numerical validation across quantum, chaotic, and thermodynamic systems, we demonstrate that the theory provides unified solutions to foundational paradoxes: the quantum measurement problem is resolved through objective I-field-mediated collapse, thermodynamic irreversibility arises from fundamental symmetry breaking rather than statistical coarse-graining, and the arrow of time emerges from field dynamics rather than initial conditions. The theory makes testable predictions accessible with current technology: temperatureindependent decoherence at ultralow temperatures, universal noise floors violatingfluctuation-dissipation relations, modified atomic energy levels proportional to I-field strength, and measurable time variation of fundamental constants. These predictionsdistinguish the framework from standard physics and provide experimental pathways for falsification. If confirmed, this would establish irreversibility as a fundamental interaction encoded in the Lagrangian rather than an emergent statistical phenomenon.