arXiv subjects
Publications and source records attributed to Tatsu Takeuchi.
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.
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.
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.
We propose a toy model of baryogenesis which applies the `ratchet mechanism,' used frequently in the theory of biological molecular motors, to a model proposed by Dimopoulos and Susskind.
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.
We use the Borexino 153.6 ton.year data to place constraints on non-standard neutrino-electron interactions, taking into account the uncertainty in the 7Be solar neutrino flux, and backgrounds due to 85Kr and 210Bi beta-decay. We find that the bounds are comparable to existing bounds from all other experiments. Further improvement can be expected in Phase II of Borexino due to the reduction in the 85Kr background.
We discuss a direct test of the relation of time and energy in the very long-lived decay of tritium (H3) (meanlife τ~ 18 yrs) with the width Γ~ 10^{-24} eV [set by the time-energy uncertainty (TEU)], using the newfound possibility of resonance reactions H3 \leftrightarrow He3 with ΔE/E ~ 5x10^{-29}. The TEU is a keystone of quantum mechanics, but probed for the first time in this extreme time-energy regime. Forestalling an apparent deviation from the TEU, we discuss the ramifications and a possible generalization of the TEU as ΔE Δt > (\hbar/2)[1+(Δt/T)^n] where Δt = τis the time of measurement (the lifetime of the state), T=L/c the time for light to cross the Universe ~ 3x10^{18} s, and n a parameter subject to future measurements. (by R. S. Raghavan.)
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.
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.
We analyze the position and momentum uncertainties of the energy eigenstates of the harmonic oscillator in the context of a deformed quantum mechanics, namely, that in which the commutator between the position and momentum operators is given by [x,p]=i\hbar(1+βp^2). This deformed commutation relation leads to the minimal length uncertainty relation Δx > (\hbar/2)(1/Δp +βΔp), which implies that Δx ~ 1/Δp at small Δp while Δx ~ Δp at large Δp. We find that the uncertainties of the energy eigenstates of the normal harmonic oscillator (m>0), derived in Ref. [1], only populate the Δx ~ 1/Δp branch. The other branch, Δx ~ Δp, is found to be populated by the energy eigenstates of the `inverted' harmonic oscillator (m<0). The Hilbert space in the 'inverted' case admits an infinite ladder of positive energy eigenstates provided that Δx_{min} = \hbar\sqrtβ > \sqrt{2} [\hbar^2/k|m|]^{1/4}. Correspondence with the classical limit is also discussed.
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.
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.
We update the single-coupling bounds on R-parity violating supersymmetry using the most up to date data as of October 2009. In addition to the data listed in the 2009 Review of Particle Properties, we utilize a new determination of the weak charge of cesium-133, and preliminary tau-decay branching fractions from Babar. Analysis of semileptonic D-decay is improved by the inclusion of experimentally measured form-factors into the calculation of the Standard Model predictions.
We discuss possible constraints on R-parity violation from recently announced Belle/Babar results on the B\toτνbranching fraction, and the bounds on τ^-\to\ell^- K_S^0 (\ell=e or μ) from Babar.
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.
New physics beyond the Standard Model can lead to extra matter effects on neutrino oscillation if the new interactions distinguish among the three flavors of neutrino. In a previous paper, we argued that a long-baseline neutrino oscillation experiment in which the Fermilab-NUMI beam in its high-energy mode is aimed at the planned Hyper-Kamiokande detector would be capable of constraining the size of those extra effects, provided the vacuum value of \sin^2 2θ_{23} is not too close to one. In this paper, we discuss how such a constraint would translate into limits on the coupling constants and masses of new particles in various models. The models we consider are: models with generation distinguishing Z's such as topcolor assisted technicolor, models containing various types of leptoquarks, R-parity violating SUSY, and extended Higgs sector models. In several cases, we find that the limits thus obtained could be competitive with those expected from direct searches at the LHC. In the event that any of the particles discussed here are discovered at the LHC, then the observation, or non-observation, of their matter effects could help in identifying what type of particle had been observed.
New physics beyond the Standard Model can lead to extra matter effects on neutrino oscillation if the new interactions distinguish among the three flavors of neutrino. In Ref.1, we argued that a long-baseline neutrino oscillation experiment in which the Fermilab-NUMI beam in its high-energy mode is aimed at the planned Hyper-Kamiokande detector would be capable of constraining the size of those extra matter effects, provided the vacuum value of \sin^2 2θ_{23} is not too close to one. In this talk, we discuss how such a constraint would translate into limits on the coupling constants and masses of new particles in models such as topcolor assisted technicolor.
We discuss whether constraints can be placed on new physics from a hypothetical Fermilab to Hyper-Kamiokande neutrino oscillation experiment.