Rafael Sorkin | Perimeter Institute for Theoretical Physics (original) (raw)

Papers by Rafael Sorkin

AIP Conference Proceedings, 2009

In Mod. Phys. Lett. A 9, 3119 (1994), one of us (R.D.S) investigated a formulation of quantum mec... more In Mod. Phys. Lett. A 9, 3119 (1994), one of us (R.D.S) investigated a formulation of quantum mechanics as a generalized measure theory. Quantum mechanics computes probabilities from the absolute squares of complex amplitudes, and the resulting interference violates the (Kolmogorov) sum rule expressing the additivity of probabilities of mutually exclusive events. However, there is a higher order sum rule that quantum mechanics does obey, involving the probabilities of three mutually exclusive possibilities. We could imagine a yet more general theory by assuming that it violates the next higher sum rule. In this paper, we report results from an ongoing experiment that sets out to test the validity of this second sum rule by measuring the interference patterns produced by three slits and all the possible combinations of those slits being open or closed. We use attenuated laser light combined with single photon counting to confirm the particle character of the measured light.

Classical and Quantum Gravity, 2012

Physical theories are developed to describe phenomena in particular regimes, and generally are va... more Physical theories are developed to describe phenomena in particular regimes, and generally are valid only within a limited range of scales. For example, general relativity provides an effective description of the Universe at large length scales, and has been tested from the cosmic scale down to distances as small as 10 meters [1, 2]. In contrast, quantum theory provides an effective description of physics at small length scales. Direct tests of quantum theory have been performed at the smallest probeable scales at the Large Hadron Collider, ∼10 −20 meters, up to that of hundreds of kilometers [3]. Yet, such tests fall short of the scales required to investigate potentially significant physics that arises at the intersection of quantum and relativistic regimes. We propose to push direct tests of quantum theory to larger and larger length scales, approaching that of the radius of curvature of spacetime, where we begin to probe the interaction between gravity and quantum phenomena. In particular, we review a wide variety of potential tests of fundamental physics that are conceivable with artificial satellites in Earth orbit and elsewhere in the solar system, and attempt to sketch the magnitudes of potentially observable effects. The tests have the potential to determine the applicability of quantum theory at larger length scales, eliminate various alternative physical theories, and place bounds on phenomenological models motivated by ideas about spacetime microstructure from quantum gravity. From a more pragmatic perspective, as quantum communication technologies such as quantum key distribution advance into Space towards large distances, some of the fundamental physical effects discussed here may need to be taken into account to make such schemes viable.

outcomes from the complex wavefunction of the system. It's quadratic nature entails that interfer... more outcomes from the complex wavefunction of the system. It's quadratic nature entails that interference occurs in pairs of paths. An experiment is in progress in our laboratory that sets out to test the correctness of Born's rule by testing for the presence or absence of genuine three-path interference [1]. This is done using single photons and a three slit aperture. Although the Born rule has been indirectly verified to high accuracy in other experiments, the consequences of a detection of even a small three-way interference in the Quantum mechanical null prediction are tremendous. If a non-zero result were to be obtained, it would mean that Quantum Mechanics is only approximate, in the same way that the double slit experiment proves that classical physics is only an approximation to the true law of nature. This would give us an important hint on how to generalize Quantum Mechanics and open a new window to the world. Some preliminary observations have been reported in reference [2]. In this talk, I will show results that bound the possible violation of the second sum rule and will point out ways to obtain a tighter experimental bound. [

I argue that the true quantum gravity scale cannot be much larger than the Planck length, because... more I argue that the true quantum gravity scale cannot be much larger than the Planck length, because if it were then the quantum gravity-induced fluctuations in Λ would be insufficient to produce the observed cosmic "dark energy". If one accepts this argument, it rules out scenarios of the "large extra dimensions" type. I also point out that the relation between the lower and higher dimensional gravitational constants in a Kaluza-Klein theory is precisely what is needed in order that a black hole's entropy admit a consistent higher dimensional interpretation in terms of an underlying spatio-temporal discreteness.

Monthly Notices of the Royal Astronomical Society: Letters, May 1, 2007

Using a variety of quantitative implementations of Occam's razor we examine the low quadrupole, t... more Using a variety of quantitative implementations of Occam's razor we examine the low quadrupole, the 'axis of evil' effect and other detections recently made appealing to the excellent Wilkinson Microwave Anisotropy Probe (WMAP) data. We find that some razors fully demolish the much lauded claims for departures from scale-invariance. They all reduce to pathetic levels the evidence for a low quadrupole (or any other low cutoff), both in the first and third year WMAP releases. The 'axis of evil' effect is the only anomaly examined here that survives the humiliations of Occam's razor, and even then in the category of 'strong' rather than 'decisive' evidence. Statistical considerations aside, differences between the various renditions of the data sets remain worrying.

arXiv (Cornell University), May 26, 2023

APS April Meeting Abstracts, Apr 1, 2003

ABSTRACT

arXiv (Cornell University), Apr 7, 2010

I will propose that the reality to which the quantum formalism implicitly refers is a kind of gen... more I will propose that the reality to which the quantum formalism implicitly refers is a kind of generalized history, the word history having here the same meaning as in the phrase sum-over-histories. This proposal confers a certain independence on the concept of event, and it modifies the rules of inference concerning events in order to resolve a contradiction between the idea of reality as a single history and the principle that events of zero measure cannot happen (the Kochen-Specker paradox being a classic expression of this contradiction). The so-called measurement problem is then solved if macroscopic events satisfy classical rules of inference, and this can in principle be decided by a calculation. The resulting conception of reality involves neither multiple worlds nor external observers. It is therefore suitable for quantum gravity in general and causal sets in particular.

International Journal of Modern Physics, Dec 1, 1989

In this paper, we explore the consequences of diffeomorphism invariance in generally covariant th... more In this paper, we explore the consequences of diffeomorphism invariance in generally covariant theories. Such theories in two and three dimensions are known to admit topological excitations called geons. It is shown by specific examples that a quantum state of two identical geons may not be an eigenstate of the geon exchange operator, which means that a geon may have no definite statistics. As shown before by Sorkin and as discussed further here, it may also happen, for instance, that in 3 + 1 dimensions a tensorial (spinorial) geon obeys Fermi (Bose) statistics, while in 2 + 1 dimensions an "integral-spin" geon can obey "fractional statistics". Thus ideas on spin and statistics borrowed from Poincaré invariant theories are not always valid in quantum gravity, at least without further physical inputs. Previously, it was shown by Friedman and Sorkin that pure gravity in three space dimensions may admit spinorial states. This result is extended to two dimensions where pure gravity is shown to admit "fractional spin" geons.

Nucleation and Atmospheric Aerosols, 1997

Quantum Gravity admits topological excitations of microscopic scale which can manifest themselves... more Quantum Gravity admits topological excitations of microscopic scale which can manifest themselves as particles-topological geons. Nontrivial spatial topology also brings into the theory free parameters analogous to the θ-angle of QCD. We show that these parameters can be interpreted in terms of geon properties. We also find that, for certain values of the parameters, the geons exhibit new patterns of particle identity together with new types of statistics. Geon indistinguishability in such a case is expressed by a proper subgroup of the permutation group and geon statistics by a (possibly projective) representation of the subgroup. This talk attempts to answer two questions concerning the effect of topology in generally covariant theories: "how many free parameters are there in quantum gravity?" and "do topological geons really act like particles?" By way of comparison, consider the standard model, which contains both continuous parameters (like the masses of the

Physical review, Jan 30, 2004

Physical review, Jan 15, 1992

It is customary, when discussing configuration spaces of identical particles in two or more dimen... more It is customary, when discussing configuration spaces of identical particles in two or more dimensions, to discard the configurations where two or more particles overlap, the justification being that the configuration space ceases to be a manifold at those points, and also to allow for nonbosonic statistics. We show that there is in general a loss of physical information in discarding these points by studying the simple system of two free particles moving in the plane and requiring that the Hamiltonian be selfadjoint. We find that the Hamiltonian for fermions is unique, but that in all other cases (i.e. , for particles obeying properly fractional or Bose statistics) there is a one-parameter family of possible self-adjoint extensions. We show how a plausible limiting procedure selects a unique extension from each family, the favored extension being the one for which the wave function remains finite at the points of overlap. We also test our procedure by applying it to the known case of the hydrogen atom.

General Relativity and Gravitation, Jul 1, 1989

Nucleation and Atmospheric Aerosols, 2000

We present a review of the spin and statistics of topological geons, particles in 3+1 quantum gra... more We present a review of the spin and statistics of topological geons, particles in 3+1 quantum gravity. They can have half-odd-integral spin and fermionic statistics and since the underlying gravitational field is tensorial and bosonic, this is an example of "emergent" non-trivial spin and statistics as displayed by familiar non-gravitating objects such as skyrmions. We give the topological background and show that in a "canonical" quantization of gravity there is no spin-statistics correlation for topological geons. Allowing the topology of space to change, for example in a sum-over-histories approach, raises the possibility that a spin-statistics correlation can be recovered for geons. We review a conjectured set of rules powerful enough to give such a spinstatistics correlation for all topological geons. These would appear to rule out the possibility of parastatistics and may rule out spinorial and fermionic geons altogether.

International Journal of Modern Physics, Oct 30, 1992

The first and second homology groups H for configuration spaces of framed two-dimensional particl... more The first and second homology groups H for configuration spaces of framed two-dimensional particles and antiparticles, with annihilation included, are computed when up to two particles and an antiparticle are present. The set of 'frames' considered are S 2 , SO(2) and SO(3). It is found that the H 1 groups are those of the 'frames' and are generated by a cycle corresponding to a 2ic frame rotation. This same cycle is homologous to the exchange paththe spinstatistics theorem. Furthermore for the frame space SO(2), H2 contains a Z subgroup which implies the existence of a nontrivial Wess Zumino term. A rotationally and translationally invariant, topologically nontrivial Wess Zumino term for a pair of anyons and an antianyon is exhibited for this case.

Modern Physics Letters A, Feb 1, 1989

There exists a class of particle-like topological excitations in generally covariant theories cal... more There exists a class of particle-like topological excitations in generally covariant theories called geons, discussed by Friedman and Sorkin, and by these authors, and others. Here, we show by specific examples that certain of these geons can be so quantized that they are characterized by no definite statistics. For instance, three-dimensional geons may be neither bosons nor fermions (nor paraparticles). It can also happen, as pointed out before by Sorkin, and as we briefly discuss here, that a tensorial (spinorial) goen obeys Fermi (Bose) statistics. Our usual conceptions about the statistics of particle species thus do not seem to be valid in generally covariant theories, at least without further physical inputs such as, perhaps, the possibility of topology change.

Modern Physics Letters A, Oct 30, 1994

The additivity of classical probabilities is only the first in a hierarchy of possible sum-rules,... more The additivity of classical probabilities is only the first in a hierarchy of possible sum-rules, each of which implies its successor. The first and most restrictive sum-rule of the hierarchy yields measure-theory in the Kolmogorov sense, which physically is appropriate for the description of stochastic processes such as Brownian motion. The next weaker sum-rule defines a generalized measure theory which includes quantum mechanics as a special case. The fact that quantum probabilities can be expressed "as the squares of quantum amplitudes" is thus derived in a natural manner, and a series of natural generalizations of the quantum formalism is delineated. Conversely, the mathematical sense in which classical physics is a special case of quantum physics is clarified. The present paper presents these relationships in the context of a "realistic" interpretation of quantum mechanics. An attitude toward Quantum Mechanics which is suitable for quantum gravity in general, and for its application to cosmology in particular, is not so easy to find. Understanding the early universe requires us to reason about a time in the distant past in which observers in the ordinary sense of the word can hardly have been present. For such a situation, a philosophically "realistic" attitude toward quantum mechanics would seem to be more effective than one based on operators which must find their physical meaning in terms of "measurements". If the reality in question

Canadian Journal of Physics, Apr 1, 2008

We consider the family of "Kerr-Bolt" solutions (characterized by three real parameters: a size, ... more We consider the family of "Kerr-Bolt" solutions (characterized by three real parameters: a size, a Newman-Unti-Tamburino (NUT) charge, and a spin rate) and evaluate their mass, angular momentum, and entropy according to the boundary counterterm prescription. Demanding the absence of any singularities reduces the number of free parameters and imposes some restrictions on the thermodynamics of solutions.