Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userWave Function Collapse, Decoherence, and Conservation Laws
49
0
0.0
(
0
)
Authors
Edward J. Gillis
Ask ChatGPT about the research
No Arabic abstract
The assumption that wave function collapse is induced by the interactions that generate decoherence leads to a stochastic collapse equation that does not require the introduction of any new physical constants and that is consistent with conservation laws. The collapse operator is based on the interaction energy, with a variable timing parameter related to the rate at which individual interactions generate the branching process. The approximate localization of physical systems follows from the distance-dependent nature of the interactions. The equation is consistent with strict conservation of momentum and orbital angular momentum, and it is also consistent with energy conservation within the accuracy allowed by the limited forms of energy that can be described within nonrelativistic theory. A relativistic extension of the proposal is outlined.
rate research
Read More
We formulate symmetries in semiclassical Gaussian wave packet dynamics and find the corresponding conserved quantities, particularly the semiclassical angular momentum, via Noethers theorem. We consider two slightly different formulations of Gaussian wave packet dynamics; one is based on earlier works of Heller and Hagedorn, and the other based on the symplectic-geometric approach by Lubich and others. In either case, we reveal the symplectic and Hamiltonian nature of the dynamics and formulate natural symmetry group actions in the setting to derive the corresponding conserved quantities (momentum maps). The semiclassical angular momentum inherits the essential properties of the classical angular momentum as well as naturally corresponds to the quantum picture.
The Transactional Interpretation of quantum mechanics exploits the intrinsic time-symmetry of wave mechanics to interpret the $psi$ and $psi$* wave functions present in all wave mechanics calculations as representing retarded and advanced waves moving in opposite time directions that form a quantum handshake or transaction. This handshake is a 4D standing-wave that builds up across space-time to transfer the conserved quantities of energy, momentum, and angular momentum in an interaction. Here we derive a two-atom quantum formalism describing a transaction. We show that the bi-directional electromagnetic coupling between atoms can be factored into a matched pair of vector potential Greens functions: one retarded and one advanced, and that this combination uniquely enforces the conservation of energy in a transaction. Thus factored, the single-electron wave functions of electromagnetically-coupled atoms can be analyzed using Schrodingers original wave mechanics. The technique generalizes to any number of electromagnetically coupled single-electron states---no higher-dimensional space is needed. Using this technique, we show a worked example of the transfer of energy from a hydrogen atom in an excited state to a nearby hydrogen atom in its ground state. It is seen that the initial exchange creates a dynamically unstable situation that avalanches to the completed transaction, demonstrating that wave function collapse, considered mysterious in the literature, can be implemented with solutions of Schrodingers original wave mechanics, coupled by this unique combination of retarded/advanced vector potentials, without the introduction of any additional mechanism or formalism. We also analyse a simplified version of the photon-splitting and Freedman-Clauser three-electron experiments and show that their results can be predicted by this formalism.
Nature imposes many restrictions on the operations that we perform. Many of these restrictions can be interpreted in terms of {it resource} required to realize the operations. Classifying required resource for different types of operations and determining the amount of resource are the crucial subjects in physics. Among many types of operations, a unitary operation is one of the most fundamental operation that has been studied for long time in terms of the resource implicitly and explicitly. Yet, it is a long standing open problem to identify the resource and to clarify the necessary and sufficient amount of resource for implementing a general unitary operation under conservation laws. In this paper, we provide a solution to this open problem. We derive an asymptotically exact equality that clarifies the necessary and sufficient amount of quantum coherence as a resource to implement arbitrary unitary operation within a desired error. In this equality, the required coherence cost is asymptotically expressed with the implementation error and the degree of violation of conservation law in the desired unitary operation. We also discuss the underlying physics in several physical situations from the viewpoint of coherence cost based on the equality. This work does not only provide a solution to a long-standing problem on the unitary control, but also clarifies the key question of the resource theory of the quantum channels in the region of resource theory of asymmetry, for the case of unitary channels.
We prove that potential conservation laws have characteristics depending only on local variables if and only if they are induced by local conservation laws. Therefore, characteristics of pure potential conservation laws have to essentially depend on potential variables. This statement provides a significant generalization of results of the recent paper by Bluman, Cheviakov and Ivanova [J. Math. Phys., 2006, V.47, 113505]. Moreover, we present extensions to gauged potential systems, Abelian and general coverings and general foliated systems of differential equations. An example illustrating possible applications of proved statements is considered. A special version of the Hadamard lemma for fiber bundles and the notions of weighted jet spaces are proposed as new tools for the investigation of potential conservation laws.
A single-particle multi-branched wave-function is studied. Usual which-path tests show that if the detector placed on one branch clicks, the detectors on the other branches remain silent. By the collapse postulate, after this click, the state of the particle is reduced to a single branch, the branch on which the detector clicked. The present article challenges the collapse postulate, claiming that when one branch of the wave-function produces a click in a detector, the other branches dont disappear. They cant produce clicks in detectors, but they are still there. An experiment different from which-path test is proposed, which shows that detectors are responsible for strongly decohering the wave-function, but not for making parts of it disappear. Moreover, one of the branches supposed to disappear may produce an interference pattern with a wave-packet of another particle.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
