We present a generalized account of how one might achieve energy conservation violation with quantum coherence effects. The general setup involves a violation of energy conservation by means of a change to the preparation of a coherent quantum mechanical effect which causes a change to the probability distribution of the measurable statistics of an observable. We also present a simple theoretical account of why there is a violation of conservation occurring in this setup.
We present a generalized account of how one might achieve energy conservation violation with quantum coherence effects. The general setup involves a violation of energy conservation by means of a change to the preparation of a coherent quantum mechanical effect which causes a change to the probability distribution of the measurable statistics of an observable. We also present a simple theoretical account of why there is a violation of conservation occurring in this setup.
All measurable phenomena in physics are irreducibly particle like and the wave picture of physical systems only arises when explaining a statistically relevant set of measurements of individual systems as an average. The wave picture arises in the effects of interference which can always be explained in the context of the state description of the interfering system, interference necessitates that the measurement outcomes be calculated by squaring the amplitudes after adding and non-interference is calculated by squaring before adding. Even though the calculation for each is independently valid, the change in the statistics when one modulates between interference and noninterference, as in the quantum eraser, requires a violation of the law of conservation of energy. There is no “driving force ” in the change of statistics. It is always a change in preparation that leads to the change of interference statistics, whilst in the calculation there is only a change in the state description. The irreducibly particle like nature of the quanta requires that there be a causal “driving force ” in the change in statistics and a mere change in description is an insufficient explanation by the standards of energy conservation. We present the argument that indeed this has already all been proven in the historic 1991 study of the ZWM papers of quantum coherence. Wave Particle Duality by Statistical Correspondence The first conceptual argument to arise in the history of quantum mechanics is that which questions how the
In quantum mechanics, conservation laws are usually understood only statistically and only in the context of unitary evolution: during such evolution, if an observable commutes with the Hamiltonian, its expectation value and Born-rule probability distribution remain unchanged. Individual measurement outcomes, however, disrupt even this weak form of statistical conservation. Recently, though, it has been argued that a stronger, non-statistical form of conservation, valid at the level of individual measurement outcomes, can be recovered. The proposal relies on the claim that any superposition of eigenstates of a conserved quantity must ultimately be prepared relative to another physical system, which serves as the relevant reference frame and remains correlated with the system being prepared. On this enlarged description, the change observed in the measured system is claimed to be exactly compensated by an opposite change in the preparer, thereby restoring conservation at the level of individual measurement outcomes. We analyze this proposal and argue that it faces significant conceptual difficulties. We show that the proposed mechanism is not adequately justified and, moreover, does not establish conservation in individual measurement outcomes as claimed.
When a measurement is made on a system that is not in an eigenstate of the measured observable, it is often assumed that some conservation law has been violated. Discussions of the effect of measurements on conserved quantities often overlook the possibility of entanglement between the measured system and the preparation apparatus. The preparation of a system in any particular state necessarily involves interaction between the apparatus and the system. Since entanglement is a generic result of interaction, as shown by Gemmer and Mahler[1], and by Durt[2,3] one would expect some nonzero entanglement between apparatus and measured system, even though the amount of such entanglement is extremely small. Because the apparatus has an enormous number of degrees of freedom relative to the measured system, even a very tiny difference between the apparatus states that are correlated with the orthogonal states of the measured system can be sufficient to account for the perceived deviation from strict conservation of the quantity in question. Hence measurements need not violate conservation laws.
Abstract Fluctuation theorems (FT) reveal crucial properties about the nature of non-equilibrium dynamics by constraining the statistical distribution of quantities such as heat, work and entropy production. Here, we report theoretical and experimental results regarding two FT for a new quantity, named coherent energy, which is an energy form directly associated with the coherences of a quantum state. The FT are verified using the two-point measurement protocol with an all-optical setup in which the system information is encoded in the polarization of one photon of a pair. From the outcomes of our experiment we directly assess the energy probability distributions. We also demonstrate an universal bound on the energy of thermal states under the action of unitary operations, which could be the first step to establish an arrow of time for reversible processes.
In isolated quantum systems that have conserved quantities, such as energy and total magnetization, the conserved quantities cannot vary their values with their own dynamics.To violate conservation laws of the system keeping the unitary nature in the system's dynamics, quantum coherence must be supplied from the outer environment.This provides a general and abstract interpretation of the underlying mechanism of unitary operations on systems of interest.In this paper, we consider the amount of quantum coherence cost to realize the desired unitary operation.We derive upper and lower bounds for the coherence cost to implement arbitrary unitary operation within the desired error.These two bounds asymptotically match each other in a small error regime, and give an asymptotic equality.We present applications of our theories to several physical situations such as quantum heat engines and entanglement erasure.
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.