Towards Quantum Gravity: A Framework for Probabilistic Theories with Non-Fixed Causal Structure

General relativity is a deterministic theory with non-fixed causal structure. Quantum theory is a probabilistic theory with fixed causal structure. In this paper we build a framework for probabilistic theories with non-fixed causal structure. This combines the radical elements of general relativity and quantum theory. The key idea in the construction is physical compression. A physical theory relates quantities. Thus, if we specify a sufficiently large set of quantities (this is the compressed set), we can calculate all the others. We apply three levels of physical compression. First, we apply it locally to quantities (actually probabilities) that might be measured in a particular region of spacetime. Then we consider composite regions. We find that there is a second level of physical compression for the composite region over and above the first level physical compression for the component regions. Each application of first and second level physical compression is quantified by a matrix. We find that these matrices themselves are related by the physical theory and can therefore be subject to compression. This is the third level of physical compression. This third level of physical compression gives rise to a new mathematical object which we call the causaloid. From the causaloid for a particular physical theory we can calculate verything the physical theory can calculate. This approach allows us to set up a framework for calculating probabilistic correlations in data without imposing a fixed causal structure (such as a background time). We show how to put quantum theory in this framework (thus providing a new formulation of this theory). We indicate how general relativity might be put into this framework and how the framework might be used to construct a theory of quantum gravity.Comment: 23 pages. For special issue of Journal of Physics A entitled "The quantum universe" in honour of Giancarlo Ghirard

Quantum Mechanical Interaction-Free Measurements

A novel manifestation of nonlocality of quantum mechanics is presented. It is shown that it is possible to ascertain the existence of an object in a given region of space without interacting with it. The method might have practical applications for delicate quantum experiments.Comment: (revised file with no need for macro), 12, TAUP 1865-91

Quantum Locality?

Robert Griffiths has recently addressed, within the framework of a 'consistent quantum theory' that he has developed, the issue of whether, as is often claimed, quantum mechanics entails a need for faster-than-light transfers of information over long distances. He argues that the putative proofs of this property that involve hidden variables include in their premises some essentially classical-physics-type assumptions that are fundamentally incompatible with the precepts of quantum physics. One cannot logically prove properties of a system by establishing, instead, properties of a system modified by adding properties alien to the original system. Hence Griffiths' rejection of hidden-variable-based proofs is logically warranted. Griffiths mentions the existence of a certain alternative proof that does not involve hidden variables, and that uses only macroscopically described observable properties. He notes that he had examined in his book proofs of this general kind, and concluded that they provide no evidence for nonlocal influences. But he did not examine the particular proof that he cites. An examination of that particular proof by the method specified by his 'consistent quantum theory' shows that the cited proof is valid within that restrictive version of quantum theory. An added section responds to Griffiths' reply, which cites general possibilities of ambiguities that make what is to be proved ill-defined, and hence render the pertinent 'consistent framework' ill defined. But the vagaries that he cites do not upset the proof in question, which, both by its physical formulation and by explicit identification, specify the framework to be used. Griffiths confirms the validity of the proof insofar as that framework is used. The section also shows, in response to Griffiths' challenge, why a putative proof of locality that he has described is flawed.Comment: This version adds a response to Griffiths' reply to my original. It notes that Griffiths confirms the validity of my argument if one uses the framework that I use. Griffiths' objection that other frameworks exist is not germaine, because I use the unique one that satisfies the explicitly stated conditions that the choices be macroscopic choices of experiments and outcomes in a specified orde

Theoretical Study of the Structural Phase Transition in RbCaF\u3csub\u3e3\u3c/sub\u3e

We have made a first-principles study of the structural phase transition at Tc = 193 K in RbCaF3, using interionic potentials derived by the Gordon-Kim approach, and a new extension of the quasiharmonic approximation for the free energy. The transition is caused by instability of a triply degenerate R-point vibration which leads to a coordinated rotation of the CaF6 octahedra. We find that, as the lattice contracts, the quasiharmonic frequency of the R-point vibrations becomes imaginary at approximately 1280 K: Below this temperature the static lattice energy, as a function of CaF6 rotation, has a double minimum. However, the quasiharmonic free energy has no minimum for finite rotations until T ≤ 125 K. Thus the present theory predicts that Tc = 125 K (cf Tc = 193 K. experimental). In the region between 125 and about 1280 K nests of modes about the zone edges have imaginary quasiharmonic frequencies. By a simple extension of the quasiharmonic theory their contribution to the free energy has also been included. We also predict that the melting temperature is approximately 1350 K, which agrees very well with the measured value of 1382 K. However, the predicted thermal expansion of the perovskite phase at room temperature is ~17% lower than the observed value. This leads us to argue that the good agreement between theoretical and experimental melting temperatures is, in part, due to a cancellation between neglected anharmonic effects and certain deficiencies in the interionic potentials. We also find that, for the tetragonal phase, the calculated c / a ratio and rotation angle for the CaF6 octahedra which minimize the static energy are in good agreement with measured values at low temperature. We also discuss certain more general implications of the present work. Specifically, we suggest that our results indicate that it may be more natural to regard the structural phase transition as arising from the unfreezing of the distortion associated with the lower-symmetry phase. Our results also provide a natural explanation for the apparently universal tendency of transition temperatures for zone-boundary instabilities to be raised by hydrostatic stress

A Simple Algorithm for Local Conversion of Pure States

We describe an algorithm for converting one bipartite quantum state into another using only local operations and classical communication, which is much simpler than the original algorithm given by Nielsen [Phys. Rev. Lett. 83, 436 (1999)]. Our algorithm uses only a single measurement by one of the parties, followed by local unitary operations which are permutations in the local Schmidt bases.Comment: 5 pages, LaTeX, reference adde

On the theory of magnetic field dependence of heat conductivity in dielectric in isotropic model

Phonon polarization in a magnetic field is analyzed in isotropic model. It is shown, that at presence of spin-phonon interaction phonon possess circular polari-zation which causes the appearance of heat flux component perpendicular both to temperature gradient and magnetic field.Comment: 5 pages, 0 figure

On relativistic elements of reality

Several arguments have been proposed some years ago, attempting to prove the impossibility of defining Lorentz-invariant elements of reality. I find that a sufficient condition for the existence of elements of reality, introduced in these proofs, seems to be used also as a necessary condition. I argue that Lorentz-invariant elements of reality can be defined but, as Vaidman pointed out, they won't satisfy the so-called product rule. In so doing I obtain algebraic constraints on elements of reality associated with a maximal set of commuting Hermitian operators.Comment: Clarifications, reference added; published versio

Detection of moisture and moisture related phenomena from Skylab

The author had identified the following significant results. Soil moisture and precipitation variations were not detectable as tonal variations on the S19OA IR B and W photography. Some light tonal areas contained high precipitation .83 inches and high moisture content 21.1% while other light tonal areas contained only .02 inches precipitation and as little as 0.7% moisture. Similar variations were observed in dark tonal areas. This inconsistency may be caused by a lapse of 3 to 4 days from the time precipitation occurred until the photographs were taken and the fact that in the first inch of soil the measured soil moisture was generally less than 5.0%. For overall tonal contrast, the aerial color, color IR and aerial B and W appear to be the best. Cities stand out from the landscape best in the aerial color and color IR, however, to see major street patterns a combination of the two aerial B and W bands and the two IR B and W bands may be desirable. For mapping roads it is best use all 6 bands. For lake detection, the IR B and W bands would be the best but for streams the aerial B and W band would be better. The aerial color, color IR, and the two IR B and W bands are best for distinguishing cultivated and non-cultivated areas, whereas the two aerial B and W bands are better for seeing local relief. Clouds may be best seen in the aerial color and color IR bands

A toy model for quantum mechanics

The toy model used by Spekkens [R. Spekkens, Phys. Rev. A 75, 032110 (2007)] to argue in favor of an epistemic view of quantum mechanics is extended by generalizing his definition of pure states (i.e. states of maximal knowledge) and by associating measurements with all pure states. The new toy model does not allow signaling but, in contrast to the Spekkens model, does violate Bell-CHSH inequalities. Negative probabilities are found to arise naturally within the model, and can be used to explain the Bell-CHSH inequality violations.Comment: in which the author breaks his vow to never use the words "ontic" and "epistemic" in publi

Detection of moisture and moisture related phenomena from Skylab

There are no author-identified significant results in this report