Sidney Coleman, Harvard University

"Past-Future Asymmetry of the Gravitational Field of a Point Particle" (1958)

The analytic extension of the Schwarzschild exterior solution is given in a closed form valid throughout empty space-time and possessing no irregularities except that at the origin. The gravitational field of a spherical point particle is then seen not to be invariant under time reversal for any admissible choice of time coordinate. The Schwarzschild surface r=2m is not a singularity but acts as a perfect unidirectional membrane: causal influences can cross it but only in one direction. The apparent violation of the principle of sufficient reason seems similar to that which is associated with instabilities in other nonlinear phenomena.

"Some New Conservation Laws" (with Charles Misner, 1959)

It is shown that field theories possessing a certain type of nonlinearity, termed intrinsic, also possess a new type of conservation law in which the conserved quantity is an integer even in the unquantized theory. For the example of general relativity the conserved quantity is shown to assume the values M = 0, ±1, ±2, …. This conservation law ("conservation of metricity") is valid regardless of any interaction of the metric field with other fields and regardless even of the equation of motion assumed for the metric field itself. The basis of the work is the principle that a quantity which is unchanged in value by an arbitrary continuous deformation is a fortiori unchanged in value by the passage of time. Some properties of metricity and of its carrier are given.

Space-Time Code Series

(See papers for full abstracts and text)

"Space-Time Code" (1969)

"Space-Time Code II" (1972)

"Space-Time Code III" (1972)

"Space-Time Code IV" (1974)

"Space-Time Code V" (with Graham Frye and Leonard Susskind, 1974)

"Quantum Relativity" (with J. Michael Gibbs, 1993)

We propose a unified description of the known forces. We formulate a quantum relativistic spacetime as a (directed) graph of causal arrows with indefinite Hilbert metric, whose physical meaning is given. The simplest graph whose quantum relativity supports conservation of energy-momentum also supports a semidirect product of the cyclic groups2 and3 and the four-group22. We call these lattice degrees of freedom (permutational) twain, trine, and spin. Quantized22 becomes LorentzSpin(4). Gauged, the energy-momentum and spin groups lead to gravity and torsion, and twain and trine lead toSU2 andSU3. We infer that color is actually trine, and thez component of isospin is twain.

"Spin, Statistics and Space-Time" (1999)

A statistics may be regarded as a functor from individuals to composites. Each of the classical groups generates a unique natural quantum statistics. The A groups generate Fermi-Dirac, the C Bose-Einstein, and the B and D, the newer Schur-Wilczek statistics, where the individual is described in a quadratic space and the composite in its spinor space. S-W is intermediate between F-D and E-B in the sense that swaps, which are +1 for E-B statistics and -1 for F-D, have eigenvalues ±1 or ±i for S-W. Of these statistics only the S-W is 2-valued and gives rise to spinors. Space-time points are therefore likely to be S-W, with spin arising from more fundamental swap. We argue that below the quark scale but far above the Planck scale, space-time, matter, measurement and the dynamical law are no longer distinct but fuse into one variable, the dynamic of the system; a localized refinement of the S matrix theory of Heisenberg. S-W statistics then implies a Clifford-algebraic language for physics, connecting the spinorial chessboard to the four-dimensionality of space-time.

"Clifford Algebra as Quantum Language" (with James Baugh, Andrei Galiautdinov, and Heinrich Saller, 2001)

We suggest Clifford algebra as a useful simplifying language for present quantum dynamics. Clifford algebras arise from representations of the permutation groups as they arise from representations of the rotation groups. Aggregates using such representations for their permutations obey Clifford statistics. The vectors supporting the Clifford algebras of permutations and rotations are plexors and spinors respectively. Physical spinors may actually be plexors describing quantum ensembles, not simple individuals. We use Clifford statistics to define quantum fields on a quantum space-time, and to formulate a quantum dynamics-field-spacetime unity that evades the compactification problem. The quantum bits of history regarded as a quantum computation seem to obey a Clifford statistics

"Nature as a Quantum Computer" (contributed to memorial volume for Jack Schwartz, 2012)

Set theory reduces all processes to assembly and disassembly. A similar architecture is proposed for nature as quantum computer. It resolves the classical space-time underlying Feynman diagrams into a quantum network of creation and annihilation processes, reducing kinematics to quantum statistics, and regularizing the Lie algebra of the Einstein diffeomorphism group. The usually separate and singular Lie algebras of kinematics, statistics, and conserved currents merge into one regular statistics Lie algebra.

"Unitary Quantum Relativity" (in progress, published posthumously, 2017)

A quantum universe is expressed as a finite unitary relativistic quantum computer network. Its addresses are subject to quantum superposition as well as its memory. It has no exact mathematical model. It Its Hilbert space of input processes is also a Clifford algebra with a modular architecture of many ranks. A fundamental fermion is a quantum computer element whose quantum address belongs to the rank below. The least significant figures of its address define its spin and flavor. The most significant figures of it adress define its orbital variables. Gauging arises from the same quantification as space-time. This blurs star images only slightly, but perhaps measurably. General relativity is an approximation that splits nature into an emptiness with a high symmetry that is broken by a filling of lower symmetry. Action principles result from self-organization pf the vacuum.

The author presents a simple algebraic quantum language sharpening and deepening that of Bohr, Heisenberg, and von Neumann, with its own epistemology, modal structure, and connectives. The core of the language is semigroup of physical actions. The work extends quantum algebra from first-order to high-order propositions, classes, and actions; from positive to indefinite metrics; and from quantum systems to quantum sets, quantum semigroups, and quantum groups. The reader learns the theory by applying it to simple quantum problems at gradually higher levels. The author applies the extended quantum theory to a spacetime structure, which was taken as a fixed part of the classical framework of the original quantum theory. This leads to a simple proposal connecting the internal variables of spin, color, and isospin with the fine structure of spacetime.

For a more complete list of Finkelstein's publications, visit his author page at the High Energy Physics Project.

Visit Finkelstein's faculty page at the Georgia Tech School of Physics