[rev 031211] We construct the gravitational field out of bits. Since the bits are quantum, so is ... more [rev 031211] We construct the gravitational field out of bits. Since the bits are quantum, so is the field, its space-time, and its gauge group. The quantum logic used in this construction is a reversible higher-order logic and a quantum group represented by a Clifford algebra with indefinite metric. We use an expanded quantization process and correspondence principle involving a fundamental time as well as Planck’s constant, first on a toy time-dependent linear harmonic oscillator, and then on the Dirac and the Einstein theories. At space-time meltdown the canonical symmetry between time and energy is restored, possibly permitting their interconversion.
We formulate a theory of quantum processes, extend it to a generic quantum cosmology, formulate a... more We formulate a theory of quantum processes, extend it to a generic quantum cosmology, formulate a reversible quantum logic for the Quantum Universe As Computer, or Qunivac. Qunivac has an orthogonal group of cosmic dimensionality. It has a Clifford algebra of “cosmonions,” extending the quaternions to a cosmological number of anticommuting units. Its qubits obey Clifford-Wilczek statistics and are associated with unit cosmonions. This makes it relatively easy to program the Dirac equation on Qunivac in a Lorentz-invariant way. Qunivac accommodates a field theory and a gauge theory. Its gauge group is necessarily a quantum group.
A Clifford algebra over the binary field 2 = {0,1} is a second-order classical logic that is subs... more A Clifford algebra over the binary field 2 = {0,1} is a second-order classical logic that is substantially richer than Boolean algebra. We use it as a bridge to a Clifford algebraic quantum logic that is richer than the usual Hilbert space quantum logic and admits iteration. This leads to a higher-order Clifford-algebraic logic. We formulate a toy Dirac equation with this logic. It isexactly Lorentz-invariant, yet it approximates the usual Dirac equation as closely as desired and all its variables have finite spectra. It is worth considering as a Lorentz-invariant improvement on lattice space-times.
Points of spacetime, like bosons, are indistinguishable. This may be a macroscopic quantum effect... more Points of spacetime, like bosons, are indistinguishable. This may be a macroscopic quantum effect. Sets are fermionic, however, in that double occupation is excluded. Representing spacetime as a point set (“bosons” as “fermions”) introduces many unphysical degrees of freedom. Instead we represent a spacetime as a network of bosonic links ι {· · ·} generalizing and quantizing Peano’s theory of the natural numbers. His t becomes the fermionic quantizer but is itself bosonic. Immediate causal succession is the membership relation ∈ derived from ι The causal relation is the transitive relation ∈*=∈ · · · ∈ derived from ∈. We use ι to express a simple time axis and then Minkowski spacetime as quantum logic networks. While ι is used infinitely often in the mathematical foundations of differential geometry, and merely once or twice as quantization during quantum theory construction, in this theory it occurs at a rate of ~ 10120 s−4 in the vacuum. A Compton limit to the precision of spacetime coordinates, 16 orders of magnitude above the usual Planck limit, sets this rate.
[rev 031211] We construct the gravitational field out of bits. Since the bits are quantum, so is ... more [rev 031211] We construct the gravitational field out of bits. Since the bits are quantum, so is the field, its space-time, and its gauge group. The quantum logic used in this construction is a reversible higher-order logic and a quantum group represented by a Clifford algebra with indefinite metric. We use an expanded quantization process and correspondence principle involving a fundamental time as well as Planck’s constant, first on a toy time-dependent linear harmonic oscillator, and then on the Dirac and the Einstein theories. At space-time meltdown the canonical symmetry between time and energy is restored, possibly permitting their interconversion.
We formulate a theory of quantum processes, extend it to a generic quantum cosmology, formulate a... more We formulate a theory of quantum processes, extend it to a generic quantum cosmology, formulate a reversible quantum logic for the Quantum Universe As Computer, or Qunivac. Qunivac has an orthogonal group of cosmic dimensionality. It has a Clifford algebra of “cosmonions,” extending the quaternions to a cosmological number of anticommuting units. Its qubits obey Clifford-Wilczek statistics and are associated with unit cosmonions. This makes it relatively easy to program the Dirac equation on Qunivac in a Lorentz-invariant way. Qunivac accommodates a field theory and a gauge theory. Its gauge group is necessarily a quantum group.
A Clifford algebra over the binary field 2 = {0,1} is a second-order classical logic that is subs... more A Clifford algebra over the binary field 2 = {0,1} is a second-order classical logic that is substantially richer than Boolean algebra. We use it as a bridge to a Clifford algebraic quantum logic that is richer than the usual Hilbert space quantum logic and admits iteration. This leads to a higher-order Clifford-algebraic logic. We formulate a toy Dirac equation with this logic. It isexactly Lorentz-invariant, yet it approximates the usual Dirac equation as closely as desired and all its variables have finite spectra. It is worth considering as a Lorentz-invariant improvement on lattice space-times.
Points of spacetime, like bosons, are indistinguishable. This may be a macroscopic quantum effect... more Points of spacetime, like bosons, are indistinguishable. This may be a macroscopic quantum effect. Sets are fermionic, however, in that double occupation is excluded. Representing spacetime as a point set (“bosons” as “fermions”) introduces many unphysical degrees of freedom. Instead we represent a spacetime as a network of bosonic links ι {· · ·} generalizing and quantizing Peano’s theory of the natural numbers. His t becomes the fermionic quantizer but is itself bosonic. Immediate causal succession is the membership relation ∈ derived from ι The causal relation is the transitive relation ∈*=∈ · · · ∈ derived from ∈. We use ι to express a simple time axis and then Minkowski spacetime as quantum logic networks. While ι is used infinitely often in the mathematical foundations of differential geometry, and merely once or twice as quantization during quantum theory construction, in this theory it occurs at a rate of ~ 10120 s−4 in the vacuum. A Compton limit to the precision of spacetime coordinates, 16 orders of magnitude above the usual Planck limit, sets this rate.
Uploads
Papers by James Baugh