H. van Dam

Probing Spacetime Foam with Extragalactic Sources

Because of quantum fluctuations, spacetime is probably foamy on very small scales. We propose to detect this texture of spacetime foam by looking for halo structures in the images of distant quasars. We find that the Very Large Telescope interferometer will be on the verge of being able to probe the fabric of spacetime when it reaches its design performance. Our method also allows us to use spacetime foam physics and physics of computation to infer the existence of dark energy or matter, independent of the evidence from recent cosmological observations.

Unimodular theory of gravity and the cosmological constant

The unimodular theory of gravity with a constrained determinant gμν is equivalent to general relativity with an arbitrary cosmological constant Λ. Within this framework Λ appears as an integration constant unrelated to any parameters in the Lagrangian. In a quantum theory the state vector of the universe is thus expected to be a superposition of states with different values of Λ. Following Hawking’s argument one concludes that the fully renormalized Λ=0 completely dominates other contributions to the integral over Λ in the vacuum functional. In this scenario of the unimodular theory of gravity the cosmological constant problem is solved. Furthermore, this formulation naturally provides an external (cosmic) time for time ordering of measurements so that the quantum version of the unimodular theory can have a normal ‘‘Schrodinger’’ form of time development, giving a simpler interpretation to the equation of the universe.

Probing Planck-scale physics with extragalactic sources?

At Planck scale, spacetime is foamy because of quantum fluctuations predicted by quantum gravity. Here we consider the possibility of using spacetime foam-induced phase incoherence of light from distant galaxies and gamma-ray bursters to probe Planck-scale physics. In particular, we examine the cumulative effects of spacetime fluctuations over a huge distance. Our analysis shows that they are far below what is required in this approach to shed light on the foaminess of spacetime.

A small but nonzero cosmological constant

Recent astrophysical observations seem to indicate that the cosmological constant is small but nonzero and positive. The old cosmological constant problem asks why it is so small; we must now ask, in addition, why it is nonzero (and is in the range found by recent observations), and why it is positive. In this essay, we try to kill these three metaphorical birds with one stone. That stone is the unimodular theory of gravity, which is the ordinary theory of gravity, except for the way the cosmological constant arises in the theory. We argue that the cosmological constant becomes dynamical, and eventually, in terms of the cosmic scale factor R(t), it takes the form Λ(t)=Λ(t0)(R(t0)/R(t))2, but not before the epoch corresponding to the redshift parameter z~1.

Energy-momentum uncertainties as possible origin of threshold anomalies in UHECR and TeV-γ events

Abstract A threshold anomaly refers to a theoretically expected energy threshold that is not observed experimentally. Here we offer an explanation of the threshold anomalies encountered in the ultra-high energy cosmic ray events and the TeV- γ events, by arguing that energy–momentum uncertainties due to quantum gravity, too small to be detected in low-energy regime, can affect particle kinematics so as to raise or even eliminate the energy thresholds.

On Wigner's clock and the detectability of spacetime foam with gravitational-wave interferometers

Abstract 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, including a simple connection to the holographic principle. We see no reason to change our cautious optimism on the detectability of spacetime foam with future refinements of modern gravitational-wave interferometers like LIGO/VIRGO and LISA.

Neutrix calculus and finite quantum field theory

In general, quantum field theories (QFT) require regularizations and infinite renormalizations due to ultraviolet divergences in their loop calculations. Furthermore, perturbation series in theories like quantum electrodynamics are not convergent series, but are asymptotic series. We apply neutrix calculus, developed in connection with asymptotic series and divergent integrals, to QFT, obtaining finite renormalizations. While none of the physically measurable results in renormalizable QFT is changed, quantum gravity is rendered more manageable in the neutrix framework.

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 will then appear to be more manageable.

A comment on fermionic tachyons and poincaré representations

Abstract We extend Wigners work on the wave equations for integer-spin particles to the spinorial case. A recent suggestion that the neutrino might be a fermionic tachyon is examined. We point out that a four-component Dirac equation cannot describe a fermionic tachyon.

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.