For 100 years the problem of unification of quantum mechanics with gravity has haunted the theory of physics, with no prospect in sight of exorcising these ghosts any time soon. But perhaps the concept of unification is not well enough understood? Those of us who live in the British Isles understand a wide range of concepts of unification between the various countries of England, Wales and Scotland (which I will use as analogues of Electromagnetism and the Weak and Strong nuclear forces on account of the unaccountable coincidence of their initial letters) and Ireland (Inertia), often identified with the language Gaeilge (Gravity). The Weak Equivalence Principle that equates Inertia with Gravity, or Ireland with Gaeilge, is hotly contested, and MOND, in both forms of Modified Ireland (MI) and Modified Gaeilge (MG) are promoted as solutions to the very deep problems that undoubtedly remain.
Of course, this is not a blog about politics, and I am not going to make any political points about the problems of unification of Ireland, beyond pointing out that until Brexit was forced on us by a bunch of eejits, the problem was essentially solved by embedding in a Theory of Everything (Treaty of Europe), that meant the differences between Inertia/Gravity theory on the West of the Irish Sea, and Electro-Weak-Strong on the East no longer had any practical effect. The un-solving of this problem by red-tape-and-string theorists is something I will never forgive them for.
OK, rant over, now I will get back to the serious point of distinguishing between unification and synthesis. Electro-weak unification is a unification, not a synthesis. England and Wales are (legally) unified, without prejudice to our differences. E-W and Scotland are united, but not unified (please note the legal distinction – laws in Scotland are not the same as laws in England and Wales). E-W-S and G-I are not united at all, and have contradictory views of the nature of the universe. This is just the same as the Electro-Weak-Strong (particle physics) view of the universe being completely different from the Gravity-Inertia (relativistic) view of the universe. Not to mention the (artificial) border between Newtonian Inertia (Northern Ireland) and Einstein Gravity (Eire/Gaeilge).
Electroweak unification is just that – the electromagnetic U(1) and the weak SU(2) are unified into a (four-dimensional) group U(2). The letter U used here stands for “unitary” (in mathematics) or “unified” (in my analogies). But they are not synthesised, they are just forced together. My model synthesises them, into an (eight-dimensional) group SU(3). The letter S used here stands for “special” (in mathematics) or “synthesis” (in my analogies).
There is a movement in alternative theories of physics that points out parallels between the strong force (Scotland) and gravity (Gaeilge). They speak the same language (to some extent). The third foreign language I began to learn (after Norwegian and French) was Scottish Gaelic. Strong/Gravity unification is therefore in my blood. But Scottish Gaidhlig and Irish Gaeilge are not the same. They split apart some centuries ago. The strong SU(3) is not the same as the Inertia/Gravity SU(1,2). But apart from a few differences in signs (spelling) and pronunciation, not to mention vocabulary, they are still recognisably the same mathematical language.
Where were we? Synthesis? Yes. Synthesis of Electromagnetism and the Weak force using SU(3). Synthesis of the Weak and Strong forces using SU(5) – the Georgi-Glashow model – or was that Lloyd George? – my political history is Weak, I’m afraid. You see, Georgi and Glashow attempted a synthesis, not just a unification. Never mind that it failed, at least they tried. Instead of just unifying U(1) and SU(2) and SU(3) into the “standard model” (U(1) x SU(2) x SU(3))/Z_6, they synthesised them into SU(5).
Let’s take another example. The unification of space and time by Einstein/Lorentz/Minkowski was not just a unification, but a synthesis. The unification of spacetime with mass, however, was a mere unification, not a synthesis. Penrose converted it into a synthesis – or at least, he had the tools to do so, with his conformal group SU(2,2).
Last year, or the year before, I tried to unify Georgi-Glashow with Penrose. But it told me nothing, until I converted the unification into a synthesis, using SU(7,2). Now I can see the Synthesis and Unification of Everything (SUE). Most physicists know her as SUSY (supersymmetry), but She told me her real name. Only the camel knows the real name of God. Because She told me herself.