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George Svetlichny

Publications and source records attributed to George Svetlichny.

31 records · Page 2Linked to original sources
arXiv2005

Amplification of Nonlocal Effects in Nonlinear Quantum Mechanics by Extreme Localization

Due to its connection to the diffeomorphism group, nonlinear quantum mechanics may play an important role in quantum geometry. The Doebner-Goldin nonlinearity (arising from representations of the diffeomorphism group) amplifies nonlocal signaling effects under extreme localization, suggesting that even if greatly suppressed at low energies, such effects may be significant at the Planck scale. This offers new perspectives on Planck-scale physics.

quant-ph↗
arXiv2004

Nonlinear Quantum Mechanics at the Planck Scale

I argue that the linearity of quantum mechanics is an emergent feature at the Planck scale, along with the manifold structure of space-time. In this regime the usual causality violation objections to nonlinearity do not apply, and nonlinear effects can be of comparable magnitude to the linear ones and still be highly suppressed at low energies. This can offer alternative approaches to quantum gravity and to the evolution of the early universe.

quant-ph↗
arXiv2003

Causality implies formal state collapse

A physical theory of experiments carried out in a space-time region can accommodate a detector localized in another space-like separated region, in three, not necessarily exclusive, ways: 1) the detector formally collapses physical states across space-like separations, 2) the detector enables superluminal signals, and 3) the theory becomes logically inconsistent. If such a theory admits autonomous evolving states, the space-like collapse must be instantaneous. Time-like separation does not allow such conclusions. We also prove some simple results on structural stability: within the set of all possible theories, under a weak empirical topology, the set of all theories with superluminal signals and the set of all theories with retrograde signals are both open and dense.

quant-ph↗
arXiv2002

Critique of "No-Signaling Condition and Quantum Dynamics"

We comment on the article of Ch. Simon, V. Buzek and N. Gisin: ``No-Signaling Condition and Quantum Dynamics'', Phys. Rev. Lett. 87 (2001) 170405, which argues that linearity of quantum mechanics follows from lack of superluminal signals and some usual hypotheses about measurements. We argue that such assumptions in the end are ineffective as an explanation of the linearity of quantum mechanics.

quant-ph↗
arXiv2002

Bell-type inequalities for partial separability in N-particle systems and quantum mechanical violations

We derive N-particle Bell-type inequalities under the assumption of partial separability, i.e. that the N-particle system is composed of subsystems which may be correlated in any way (e.g. entangled) but which are uncorrelated with respect to each other. These inequalities provide, upon violation, experimentally accessible sufficient conditions for full N-particle entanglement, i.e. for N-particle entanglement that cannot be reduced to mixtures of states in which a smaller number of particles are entangled. The inequalities are shown to be maximally violated by the N-particle Greenberger-Horne-Zeilinger (GHZ) states.

quant-ph↗
arXiv1999

The Space-time Origin of Quantum Mechanics: Covering Law

Lorentz covariance imposed upon a quantum logic of local propositions for which all observers can consistently maintain state collapse descriptions, implies a condition on space-like separated propositions that if imposed on generally commuting ones would lead to the covering law, and hence to a hilbert-space model for the logic. Such a generalization can be argued if state preparation can be conditioned to space-like separated events using EPR-type correlations. This suggests that the covering law is related to space-time structure, though a final understanding of it, through a self-consistency requirement, will probably require quantum space-time.

quant-ph↗
arXiv1999

Non-linear Schroedinger Equations, Separation and Symmetry

We investigate the symmetry properties of hierarchies of non-linear Schroedinger equations (introduced by Doebner and Goldin, and Goldin and Svetlichny), which describe non-interacting systems in which tensor product wave-functions evolve by independent evolution of the factors (the separation property). We show that there are obstructions to lifting symmetries existing at a certain number of particles to higher numbers. Such obstructions vanish for particles without internal degrees of freedom and the usual space-time symmetries. For particles with internal degrees of freedom, such as spin, these obstructions are present and their circumvention requires a choice of a new term in the equation for each particle number. A Lie-algebra approach for non-linear theories is developed.

quant-ph↗
arXiv1999

Preparation for Gauge Theory

Class lecture notes at a beginning graduate level on the mathematical background needed to understand classical gauge theory. Covers group actions, fiber bundles, principal bundles, connections, gauge transformations, parallel transport, curvature, covariant derivatives, pseudo-riemannian manifolds, lagrangians, clifford algebras, spin bundles, and the Dirac operator. Requires an elementary knowledge of groups, manifolds, lie groups and algebras, and mutlilinear algebra.

math-ph↗
arXiv1999

Long range correlations and relativity: metatheoretic considerations

Action-at-a-distance is a generic property of physical theories. As such, it is not a fruitful idea in theory building. Its absence confers a rigidity on a theory which we exemplify through analysis of long-range correlations of the EPR-type in relativistic theories. Rigidity is desirable for fundamental theories, and theory building should focus on structurally unstable properties, making action-at-a-distance a side issue. Though apparent superluminal effects seem to be present in many present-day physical theories, we maintain that they are not a basis for action-at-a-distance.

physics.gen-ph↗
arXiv1997

Quantum Formalism with State-Collapse and Superluminal Communication

Given the collapse hypothesis (CH) of quantum measurement, EPR-type correlations along with the hypothesis of the impossibility of superluminal communication (ISC) have the effect of globalizing gross features of the quantum formalism making them universally true. In particular, these hypotheses imply that state transformations of density matrices must be linear and that evolution which preserves purity of states must also be linear. A gedanken experiment shows that lorentz covariance along with the second law of thermodynamics imply a non-entropic version of ISC. Partial results using quantum logic suggest, given ISC and a version of CH, a connection between lorentz covariance and the covering law. These results show that standard quantum mechanics is structurally unstable, and suggest that viable relativistic alternatives must question CH. One may also speculate that some features of the hilbert-space model of quantum mechanics have their origin in space-time structure.

quant-ph↗
arXiv1995

Quantum Evoluton and Space-time Structure

The hilbert-space structure of quantum mechanics is related to the causal structure of space-time. The usual measurement hypotheses apparently preclude nonlinear or stochastic quantum evolution. By admitting a difference in the calculus of joint probabilities of events in space-time according to whether the separation is space-like or time-like, a relativistic nonlinear or stochastic quantum theory may be possible.

quant-ph↗