Bernard M. Diaz

Bernard M. Diaz
Bernard M. Diaz
Nationality	British
Known for	The four-vector Dirac bispinor, QED derived from a two-body interaction, the "versatile method" of quantisation, the Rowlands–Diaz universal rewrite system
	Scientific career
Fields	Computer science, Foundations of physics
Institutions	University of Liverpool

Bernard M. Diaz is a British computer scientist at the University of Liverpool who has spent two decades working on the foundations of physics from outside the physics establishment. He is listed in The Worldwide List of Dissident Scientists.

His work divides into two programmes, both of which begin by questioning something that professional physics treats as settled:

With Sarah B. M. Bell and John P. Cullerne he argued that the Dirac bispinor can be made to transform as a four-vector, that quantum electrodynamics can be derived from a simple two-body interaction, and — the culminating claim — that general relativity quantised by their method is renormalizable, and indeed isomorphic to QED.
With Peter Rowlands he developed the universal rewrite system, a generative scheme in which the whole structure of physics is unfolded from the conservation of zero.

That a computer scientist should arrive at both is not incidental. Both programmes treat physics as a matter of generative rules — what can be produced, step by step, from a minimal starting point — rather than of equations to be solved, and that is a computational instinct applied to a physical subject.

The Liverpool I.Q. Group

Diaz worked in the Department of Computer Science at the University of Liverpool, where the collaboration with Bell and Cullerne was based in what their papers name the I. Q. Group. Cullerne was simultaneously working with Peter Rowlands of Liverpool's Department of Physics on the nilpotent formulation of the Dirac equation, and the two efforts share both personnel and a common conviction: that the standard formalism of relativistic quantum mechanics contains avoidable assumptions, and that removing them changes what the theory can reach.

The four-vector Dirac bispinor

The programme's foundation is a 1998–2000 paper in Foundations of Physics, and its claim is precise:

It is usually supposed that the Dirac and radiation equations predict that the phase of a fermion will rotate through half the angle through which the fermion is rotated, which means, via the measured dynamical and geometrical phase factors, that the fermion must have a half-integral spin. We demonstrate that this is not the case and that the identical relativistic quantum mechanics can also be derived with the phase of the fermion rotating through the same angle as does the fermion itself. Under spatial rotation and Lorentz transformation the bispinor transforms as a four-vector like the potential and Dirac current.
— Bell, Cullerne & Diaz, Classical behaviour of the Dirac bispinor (2000)

The point deserves stating plainly. The half-angle behaviour of the fermion phase — the fact that a spin-½ particle must be turned through 720°, not 360°, to return to its original state — is one of the celebrated strangenesses of quantum mechanics, routinely presented as forced on us by the Dirac equation and confirmed by measurement. Bell, Cullerne and Diaz do not dispute the measurements. They dispute that the mathematics requires that reading, and claim to produce the identical relativistic quantum mechanics with a bispinor that rotates through the same angle as the particle and transforms as an ordinary four-vector, like the potential and the current.

Their own paper notes that earlier attempts at four-vector behaviour "foundered because a satisfactory current could not be derived" — the obstacle they claim to have removed.

QED from a two-body interaction

The four-vector bispinor is a means rather than an end. In a two-part paper of 2001 they mapped the theory into what they call M-space, an alternative space in which QED with the same transformational behaviour also holds, and used it to argue that QED reduces to two simple rules for a two-body interaction.

They completed the argument in The two-body interaction with a circle in time (2001), published in Foundations of Physics in 2004, which analyses a bound state equivalent to the attraction between a charged point particle and a second at rest. The test they set themselves is the right one: the solution yields energy and angular momentum eigenvalues identical to those obtained by the usual method of solving the Dirac equation, including fine structure. Their conclusion is that "QED may be decomposed into a two-body interaction at every point in spacetime."

The versatile method and quantum gravity

The purpose of re-deriving a theory that already worked becomes clear at the last step. The obstacle to quantum gravity is well known and was stated by the group in the standard terms:

Quantum Electrodynamics (QED) has been so successful a theory that it is taken as a model for the production of further quantum theories. However, when the prescription for quantising electromagnetic interactions that so successfully resulted in QED is applied to General Relativity the theory obtained is not renormalizable. We derive a different method of quantising classical electromagnetism which also results in QED. We call the method the versatile method.
— Bell, Cullerne & Diaz, A new approach to quantum gravity: a summary (2000)

The strategy is neat, and it is worth appreciating on its own terms. If two different quantisation procedures both reproduce QED — a theory whose predictions are the most accurately confirmed in physics — then QED cannot discriminate between them. But they need not agree elsewhere. Applied to the Einstein equation, the versatile method yields, they claim, a theory that is renormalizable, and which turns out to be isomorphic to QED "provided that the temporal and a spatial co-ordinate are exchanged."

The method carries a restriction they state openly: it applies to simple matter tensors — those reducible, in some frame that may vary with place and time, to a mass density with all other elements zero — so that the tensor can be put in one-to-one correspondence with the Dirac current. This is a real limitation on the class of physical situations covered, and they do not conceal it.

A later paper with Bell, Quantising general relativity using QED theory (2002), runs the argument in the other direction, applying QED theory to quantum gravity and finding "it leads to general relativity in the classical limit."

The universal rewrite system

Diaz's other collaboration is with Peter Rowlands, whose own page on this wiki lists among his research "a universal rewrite system derived from the concept zero, in collaboration with computer scientist Bernard Diaz."

Their 2002 paper A universal alphabet and rewrite system presents a scheme generating an infinite alphabet by a rule that conserves zero at every step:

We present two ways in which an infinite universal alphabet may be generated using a novel rewrite system that conserves zero (a special character of the alphabet and the symbol for that character) at every step. … The subset alphabets in addition to having mathematical interpretation as algebra can also be constrained to emerge in a minimal way which then has application as a foundational physical system.
— Rowlands & Diaz, A universal alphabet and rewrite system (2002)

The idea, developed since as the nilpotent universal computational rewrite system and the doctrine of zero totality, is that the universe sums to nothing at every stage, and that its structure — the parameters of space, time, mass and charge, and the algebras built on them — is what necessarily emerges when that constraint is applied recursively. It is a foundational proposal of the most ambitious kind: not a model of some phenomenon, but an attempt to say why physics has the shape it has. Rowlands has since extended the system to formal language theory, computation and biology.

Place in this wiki's tradition

Diaz belongs to the strand of researchers here who challenge orthodoxy not by rejecting its successful predictions but by disputing that the standard derivation is the only one available. He does not claim QED is wrong — he claims to have derived it twice, and to have shown that the second route reaches further.

The dissident affiliation is documented rather than inferred. A new approach to quantum gravity was presented at Physical Interpretations of Relativity Theory VII at Imperial College, London, in September 2000 — the conference series long organised by Michael C Duffy and central to the work catalogued on this wiki. Related work was presented at the 16th International Conference on Few-Body Problems in Physics in Taipei the same year, and appeared in the volume Gravitation and Cosmology: From the Hubble Radius to the Planck Scale.

Compare the broader questioning of the standard quantum formalism at Quantum Theory, and the nilpotent programme pursued in the neighbouring Liverpool department.

Assessment

Diaz's work is unusual among the material on this wiki in one important respect: it was refereed and published in mainstream venues. Foundations of Physics is a genuine peer-reviewed journal, and several of the group's papers appeared there. This is not self-published or conference-only work, and the claims are stated in the technical language of the field with their restrictions attached.

What it has not attracted is uptake. The programme has been very little cited, and the central claim — a renormalizable quantum gravity isomorphic to QED — has not been taken up, checked in print, or refuted in print by the quantum-gravity community, which has continued along the string-theoretic and loop-quantum-gravity routes. The papers themselves note that the earlier arXiv preprints were superseded by later ones, and after 2002 the quantum-gravity line appears to stop.

Two fair reservations should be recorded. The simple matter tensor restriction excludes a great deal of the physically interesting content of general relativity, so that even granting the result, the class of situations quantised is narrower than "general relativity" unqualified suggests. And an isomorphism to QED obtained by exchanging a temporal for a spatial coordinate is a strong structural claim that would need independent examination before its physical meaning were clear.

Neither reservation has been pressed in print, because essentially no one has engaged with the work at all — which is the more telling fact, and the reason it is catalogued here.

Papers

2002 – "Quantising general relativity using QED theory" (with S. B. M. Bell) — arXiv:physics/0211108
2002 – "A universal alphabet and rewrite system" (with Peter Rowlands) — arXiv:cs/0209026
2001 – "The two-body interaction with a circle in time" — Foundations of Physics 34(2), Feb. 2004; arXiv:quant-ph/0110162
2001 – "QED derived from the two-body interaction (2) The derivation" — Foundations of Physics 34(2), Feb. 2004; arXiv:quant-ph/0104018
2001 – "QED derived from the two-body interaction (1) Mapping to M-space" — Foundations of Physics 34(2), Feb. 2004; arXiv:quant-ph/0104017
2000 – "Classical behaviour of the Dirac bispinor" — Foundations of Physics 30(1), 35–57; arXiv:quant-ph/0011026
2000 – "A new approach to quantum gravity: a summary" — PIRT VII, Imperial College London; arXiv:gr-qc/0011008
2000 – "A new approach to quantum gravity: an overview" — 16th Int. Conf. on Few-Body Problems in Physics, Taipei; arXiv:gr-qc/0010106

All papers above are with Sarah B. M. Bell and John P. Cullerne except where noted.