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Lay Nam Chang

Publications and source records attributed to Lay Nam Chang.

At least 19 recordsLinked to original sources
arXiv2019

Spekkens' Toy Model, Finite Field Quantum Mechanics, and the Role of Linearity

We map Spekkens' toy model to a quantum mechanics defined over the finite field $\mathbb{F}_5$. This allows us to define arbitrary linear combinations of the epistemic states in the model. For Spekkens' elementary system with only $2^2=4$ ontic states, the mapping is exact and the two models agree completely. However, for a pair of elementary systems there exist interesting differences between the entangled states of the two models.

quant-ph↗
arXiv2016

Observable Effects of Quantum Gravity

We discuss the generic phenomenology of quantum gravity and, in particular, argue that the observable effects of quantum gravity, associated with new, extended, non-local, non-particle-like quanta, and accompanied by a dynamical energy-momentum space, are not necessarily Planckian and that they could be observed at much lower and experimentally accessible energy scales.

gr-qc↗
arXiv2014

Quantum F_un: the q=1 Limit of Galois Field Quantum Mechanics, Projective Geometry, and the Field with One Element

We argue that the q=1 limit of Galois Field Quantum Mechanics, which was constructed on a vector space over the Galois Field F_q=GF(q), corresponds to its `classical limit,' where superposition of states is disallowed. The limit preserves the projective geometry nature of the state space, and can be understood as being constructed on an appropriately defined analogue of a `vector' space over the `field with one element' F_1.

quant-ph↗
arXiv2013

Quantum Systems based upon Galois Fields: from Sub-quantum to Super-quantum Correlations

In this talk we describe our recent work on discrete quantum theory based on Galois fields. In particular, we discuss how discrete quantum theory sheds new light on the foundations of quantum theory and we review an explicit model of super-quantum correlations we have constructed in this context. We also discuss the larger questions of the origins and foundations of quantum theory, as well as the relevance of super-quantum theory for the quantum theory of gravity.

quant-ph↗
arXiv2013

Is Quantum Gravity a Super-Quantum Theory?

We argue that quantum gravity should be a super-quantum theory, that is, a theory whose non-local correlations are stronger than those of canonical quantum theory. As a super-quantum theory, quantum gravity should display distinct experimentally observable super-correlations of entangled stringy states.

gr-qc↗
arXiv2013

Biorthogonal Quantum Mechanics: Super-Quantum Correlations and Expectation Values without Definite Probabilities

We propose mutant versions of quantum mechanics constructed on vector spaces over the finite Galois fields GF(3) and GF(9). The mutation we consider here is distinct from what we proposed in previous papers on Galois field quantum mechanics. In this new mutation, the canonical expression for expectation values is retained instead of that for probabilities. In fact, probabilities are indeterminate. Furthermore, it is shown that the mutant quantum mechanics over the finite field GF(9) exhibits super-quantum correlations (i.e. the Bell-Clauser-Horne-Shimony-Holt bound is 4). We comment on the fundamental physical importance of these results in the context of quantum gravity.

math-ph↗
arXiv2013

Spin and Rotations in Galois Field Quantum Mechanics

We discuss the properties of Galois Field Quantum Mechanics constructed on a vector space over the finite Galois field GF(q). In particular, we look at 2-level systems analogous to spin, and discuss how SO(3) rotations could be embodied in such a system. We also consider two-particle `spin' correlations and show that the Clauser-Horne-Shimony-Holt (CHSH) inequality is nonetheless not violated in this model.

quant-ph↗
arXiv2013

Galois Field Quantum Mechanics

We construct a discrete quantum mechanics using a vector space over the Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discrete quantum mechanics cannot be reproduced with any hidden variable theory.

quant-ph↗
arXiv2012

Some Mutant Forms of Quantum Mechanics

We construct a `mutant' form of quantum mechanics on a vector space over the finite Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discretized quantum mechanics cannot be reproduced with any hidden variable theory. An alternative `mutation' is also suggested.

quant-ph↗
arXiv2011

On the Minimal Length Uncertainty Relation and the Foundations of String Theory

We review our work on the minimal length uncertainty relation as suggested by perturbative string theory. We discuss simple phenomenological implications of the minimal length uncertainty relation and then argue that the combination of the principles of quantum theory and general relativity allow for a dynamical energy-momentum space. We discuss the implication of this for the problem of vacuum energy and the foundations of non-perturbative string theory.

hep-th↗
arXiv2011

Bell's Inequalities, Superquantum Correlations, and String Theory

We offer an interpretation of super-quantum correlations in terms of a "doubly" quantum theory. We argue that string theory, viewed as a quantum theory with two deformation parameters, the string tension α' and the string coupling constant g_s, is such a super-quantum theory, one that transgresses the usual quantum violations of Bell's inequalities. We also discuss the \hbar\to\infty limit of quantum mechanics in this context. As a super-quantum theory, string theory should display distinct experimentally observable super-correlations of entangled stringy states.

quant-ph↗
arXiv2010

Quantum Gravity, Dynamical Energy-Momentum Space and Vacuum Energy

We argue that the combination of the principles of quantum theory and general relativity allow for a dynamical energy-momentum space. We discuss the freezing of vacuum energy in such a dynamical energy-momentum space and present a phenomenologically viable seesaw formula for the cosmological constant in this context.

hep-th↗
arXiv2009

The Effect of the Minimal Length Uncertainty Relation on the Density of States and the Cosmological Constant Problem

We investigate the effect of the minimal length uncertainty relation, motivated by perturbative string theory, on the density of states in momentum space. The relation is implemented through the modified commutation relation [x_i,p_j]=i hbar[(1 + beta p^2) delta_{ij} + beta' p_i p_j]. We point out that this relation, which is an example of an UV/IR relation, implies the finiteness of the cosmological constant. While our result does not solve the cosmological constant problem, it does shed new light on the relation between this outstanding problem and UV/IR correspondence. We also point out that the blackbody radiation spectrum will be modified at higher frequencies, but the effect is too small to be observed in the cosmic microwave background spectrum.

hep-th↗
arXiv2005

Hydrogen-atom spectrum under a minimal-length hypothesis

The energy spectrum of the Coulomb potential with minimal length commutation relations $[X_i, P_j] = i\hbar\{δ_{ij}(1+βP^2) + β'P_iP_j\}$ is determined both numerically and perturbatively for arbitrary values of $β'/β$ and angular momenta $\ell$. The constraint on the minimal length scale from precision hydrogen spectroscopy data is of order of a few GeV$\null^{-1}$, weaker than previously claimed.

hep-th↗
arXiv2003

Massive torsion modes, chiral gravity, and the Adler-Bell-Jackiw anomaly

Regularization of quantum field theories introduces a mass scale which breaks axial rotational and scaling invariances. We demonstrate from first principles that axial torsion and torsion trace modes have non-transverse vacuum polarization tensors, and become massive as a result. The underlying reasons are similar to those responsible for the Adler-Bell-Jackiw (ABJ) and scaling anomalies. Since these are the only torsion components that can couple minimally to spin 1/2 particles, the anomalous generation of masses for these modes, naturally of the order of the regulator scale, may help to explain why torsion and its associated effects, including CPT violation in chiral gravity, have so far escaped detection. As a simpler manifestation of the reasons underpinning the ABJ anomaly than triangle diagrams, the vacuum polarization demonstration is also pedagogically useful. In addition it is shown that the teleparallel limit of a Weyl fermion theory coupled only to the left-handed spin connection leads to a counter term which is the Samuel-Jacobson-Smolin action of chiral gravity in four dimensions.

hep-th↗
arXiv2002

Classical Implications of the Minimal Length Uncertainty Relation

We study the phenomenological implications of the classical limit of the "stringy" commutation relations [x_i,p_j]=i hbar[(1+beta p^2) delta_{ij} + beta' p_i p_j]. In particular, we investigate the "deformation" of Kepler's third law and apply our result to the rotation curves of gas and stars in spiral galaxies.

hep-th↗