Physics Unification founded on disintegrating foundations (New Scientist mag. 4th June)
Einstein sought a Unified Field Theory, but those who claim to follow him in chasing a field-free Theory Of Everything should beware the disintegrating basis.
Duff accepts the Standard Model representing gravity by particles (gravitons) is in trouble, so plumps for the Kaluza-Klein 5-D (5 dimension) equations that found no favour with Einstein. The PDEs (partial differential eqns) of physics have problems of completeness; The Einstein-Hibert equations need additional equations as only recently clarified [Fields tell matter how to move]. Second, multi-D equations are a mathematical trick needing a strong health warning, eg. treating time as a 4th dimension does not make it equivalent and interchangeable with the three space dimensions. They are still special, defining the space in which electromagnetic (and gravitational) fields exist. In this context, the 10 or 11 dimensions of superstrings or supersymmetry have to be seen as mathematical playthings.
Duff goes for M-theory, but like these it is no “theory” but a series of conjectures with no empirical evidence (Hawking’s faith in M-theory). Justification by “ability to absorb quantum mechanics and general relativity” is like much pseudo-science, so at most let’s allow a renaming as the M-hypothesis. The modern theory of gravitation – Fock, Weinberg, Logunov, Grishchuk – challenges the representation of gravity as geometry, which is valid only for uniformly accelerated and non-rotating frames.
Nor does the representation work for the fields of classical physics. Radiation from an accelerating charged particle is a travelling wave field whose energy has a mass-equivalent that acts as a gravitating source in the Einstein-Hilbert (E-H) equations. The gravitational fields, both quasi-static and as waves, likewise have mass-equivalents that serve as E-H sources. This non-linearity is crucial in high gravity situations near the Schwarzschild limit, as shown by the discovery of solutions without a ‘black hole’ (contracting increasingly slowly onto a mass-shell around a high-gravity core)
Conservation of energy and momentum (or ‘4-momentum’) is fundamental in physics’s inheritance from Maxwell and Einstein, covering field energy and including synchrotron emissions plus gravitational waves. Once Duff recognised these are not contained within superstrings or M-theory, if only because gravity from field-energy-as-mass is not represented in ‘gravity equals geometry’, he’d be forced to accept TOE’s disintegration.