6,796 research outputs found
Measuring the foaminess of space-time with gravity-wave interferometers
By analyzing a gedanken experiment designed to measure the distance
between two spatially separated points, we find that this distance cannot be
measured with uncertainty less than , considerably larger than
the Planck scale (or the string scale in string theories), the
conventional wisdom uncertainty in distance measurements. This limitation to
space-time measurements is interpreted as resulting from quantum fluctuations
of space-time itself. Thus, at very short distance scales, space-time is
"foamy." This intrinsic foaminess of space-time provides another source of
noise in the interferometers. The LIGO/VIRGO and LISA generations of
gravity-wave interferometers, through future refinements, are expected to reach
displacement noise levels low enough to test our proposed degree of foaminess
in the structure of space-time. We also point out a simple connection to the
holographic principle which asserts that the number of degrees of freedom of a
region of space is bounded by the area of the region in Planck units.Comment: 15 pages, TeX, A simple connection to the holographic principle is
added, minor changes in the text and abstract, and some changes in the
References; this new version will appear in the third "Haller" issue in
Foundations of Physic
An application of neutrix calculus to quantum field theory
Neutrices are additive groups of negligible functions that do not contain any
constants except 0. Their calculus was developed by van der Corput and Hadamard
in connection with asymptotic series and divergent integrals. We apply neutrix
calculus to quantum field theory, obtaining finite renormalizations in the loop
calculations. For renormalizable quantum field theories, we recover all the
usual physically observable results. One possible advantage of the neutrix
framework is that effective field theories can be accommodated. Quantum gravity
theories appear to be more manageable.Comment: LateX, 19 page
Projective Geometry and -Symmetric Dirac Hamiltonian
The -dimensional (generalized) Dirac equation is shown to have the
same form as the equation expressing the condition that a given point lies on a
given line in 3-dimensional projective space. The resulting Hamiltonian with a
mass term is not Hermitian, but is invariant under the combined
transformation of parity reflection and time reversal . When
the symmetry is unbroken, the energy spectrum of the free spin- theory is real, with an appropriately shifted mass.Comment: 7 pages, LaTeX; version accepted for publication in Phys. Lett. B;
revised version incorporates useful suggestions from an anonymous refere
A Generalization of Quantum Statistics
We propose a new fractional statistics for arbitrary dimensions, based on an
extension of Pauli's exclusion principle, to allow for finite multi-occupancies
of a single quantum state. By explicitly constructing the many-body Hilbert
space, we obtain a new algebra of operators and a new thermodynamics. The new
statistics is different from fractional exclusion statistics; and in a certain
limit, it reduces to the case of parafermi statistics.Comment: 11 pages, late
Anomalous particle-production thresholds through systematic and non-systematic quantum-gravity effects
A growing number of studies is being devoted to the identification of
plausible quantum properties of spacetime which might give rise to observably
large effects. The literature on this subject is now relatively large,
including studies in string theory, loop quantum gravity and noncommutative
geometry. It is useful to divide the various proposals into proposals involving
a systematic quantum-gravity effect (an effect that would shift the
main/average prediction for a given observable quantity) and proposals
involving a non-systematic quantum-gravity effect (an effect that would
introduce new fundamental uncertanties in some observable quantity). The case
of quantum-gravity-induced particle-production-threshold anomalies, a much
studied example of potentially observable quantum-gravity effect, is here used
as an example to illustrate the differences to be expected between systematic
and non-systematic effects.Comment: 10 pages, LaTe
Spacetime Foam, Holographic Principle, and Black Hole Quantum Computers
Spacetime foam, also known as quantum foam, has its origin in quantum
fluctuations of spacetime. Arguably it is the source of the holographic
principle, which severely limits how densely information can be packed in
space. Its physics is also intimately linked to that of black holes and
computation. In particular, the same underlying physics is shown to govern the
computational power of black hole quantum computers.Comment: 8 pages, LaTeX; Talk given by Jack Ng, in celebration of Paul
Frampton's 60th birthday, at the Coral Gables Conference (in Fort Lauderdale,
Florida on December 17, 2003). To appear in the Proceedings of the 2003 Coral
Gables Conferenc
Why 3 + 1 metric rather than 4 + 0 or 2 + 2?
Why does the physical 4-dimensional space have a 3 + 1 signature rather than a 4 + 0 or a 2 + 2 for its metric? We give a simple explanation based largely on a group-theoretic argument a la Wigner. Applied to flat spaces of higher dimensions the same approach indicates that metrics with more than one time dimension are physically unacceptable because the corresponding irreducible unitary representations are infinite dimensional (besides the trivial representation)
On Wigner's clock and the detectability of spacetime foam with gravitational-wave interferometers
A recent paper (gr-qc/9909017) criticizes our work on the structure of spacetime foam. Its authors argue that the quantum uncertainty limit for the position of the quantum clock in a gedanken timing experiment, obtained by Wigner and used by us, is based on unrealistic assumptions. Here we point out some flaws in their argument. We also discuss their other comments and some other issues related to our work. We see no reason to change our cautious optimism on the detectability of spacetime foam with modern gravitational-wave interferometers like LISA
Quantum algorithm for the Boolean hidden shift problem
The hidden shift problem is a natural place to look for new separations
between classical and quantum models of computation. One advantage of this
problem is its flexibility, since it can be defined for a whole range of
functions and a whole range of underlying groups. In a way, this distinguishes
it from the hidden subgroup problem where more stringent requirements about the
existence of a periodic subgroup have to be made. And yet, the hidden shift
problem proves to be rich enough to capture interesting features of problems of
algebraic, geometric, and combinatorial flavor. We present a quantum algorithm
to identify the hidden shift for any Boolean function. Using Fourier analysis
for Boolean functions we relate the time and query complexity of the algorithm
to an intrinsic property of the function, namely its minimum influence. We show
that for randomly chosen functions the time complexity of the algorithm is
polynomial. Based on this we show an average case exponential separation
between classical and quantum time complexity. A perhaps interesting aspect of
this work is that, while the extremal case of the Boolean hidden shift problem
over so-called bent functions can be reduced to a hidden subgroup problem over
an abelian group, the more general case studied here does not seem to allow
such a reduction.Comment: 10 pages, 1 figur
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