30,887 research outputs found
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
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
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
Limitation to Quantum Measurements of Space‐Time Distances
Inspired by the work of Wheeler among others, we have studied the problem of quantum measurements of space-time distances by applying the general principles of quantum mechanics as well as those of general relativity. Contrary to folklore, the mimimum error in the measurement of a length is shown to be proportional to the one-third power of the length itself. This uncertainty in space-time measurements implies an uncertainty of the space-time metric and yields quantum decoherence for particles heavier than the Planck mass. There is also a corresponding minimum error in energy-momentum measurements
From computation to black holes and space-time foam
We show that quantum mechanics and general relativity limit the speed
of a simple computer (such as a black hole) and its memory space
to \tilde{\nu}^2 I^{-1} \lsim t_P^{-2}, where is the Planck time.
We also show that the life-time of a simple clock and its precision are
similarly limited. These bounds and the holographic bound originate from the
same physics that governs the quantum fluctuations of space-time. We further
show that these physical bounds are realized for black holes, yielding the
correct Hawking black hole lifetime, and that space-time undergoes much larger
quantum fluctuations than conventional wisdom claims -- almost within range of
detection with modern gravitational-wave interferometers.Comment: A misidentification of computer speeds is corrected. Our results for
black hole computation now agree with those given by S. Lloyd. All other
conclusions remain unchange
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