The main theories of fundamental physics died several decades ago, and have been wandering around like the undead ever since. General relativity, Einstein’s beloved theory of gravity, died in the 1980s, but this fact has still not been noticed by relativists, who still follow it like zombies, unable to smell the rotting flesh, or see the bones sticking out. The 1980s was the time when measurements of galaxies became accurate enough to demonstrate pretty conclusively that Einstein’s theory could not explain the observed structure of spiral galaxies. What did the theorists do, when faced with incontrovertible proof that the theory was wrong? They went into denial, and said the experiments must be wrong. And when the experimenters said, no, there’s nothing wrong with the experiments, the theorists said, well then, nature must be wrong. So they invented something called Dark Matter, to try and rescue their theory from certain death.
Of course, this strategy didn’t work, but it didn’t stop armies of zombies from believing in it. They “know” Dark Matter exists, despite the fact that 40 years of diligent searching has turned up precisely no evidence for it. Now, with the latest tests of gravity on widely-separated binary stars, even Dark Matter cannot rescue the theory. Now, everyone can see that the theory is well and truly dead. Well, you would think so, wouldn’t you? Unfortunately not. Believers in the magical properties of Dark Matter simply say it must be even more magical than we thought. Poppycock!
Why is GR wrong, and what can we do about it? The diagnosis I came up with ten years ago, and which still appears to be the correct diagnosis, is that there is no consistent definition of mass in physics. That is why I looked at all the experimental evidence for what mass really is, at all scales from a single neutrino to the entire visible universe. And then I looked at the theories, and analysed where the inconsistencies in the theories lie, buried deep in the mathematics.
So when I heard Basil Hiley, in his talk a few weeks ago, bemoan the fact that there is no (consistent) definition of mass in particle physics, and highlight this as one of the central problems, I pricked up my ears. And strangely enough, I found that he had given me the clue I needed, and that I had neglected, namely to look at the problem from a strictly Hamiltonian viewpoint. So to cut a long story short, after a few weeks’ work, I found a consistent definition of mass. It isn’t very difficult. Just take the symmetry group of Hamiltonian physics, as a group of 3×3 anti-Hermitian quaternion matrices, make it act on the Hermitian matrices, which represent fermions (matter) and form a Jordan algebra under the Poisson bracket {A,B}=AB+BA, and project onto the identity element of this algebra.
When I say I found a consistent definition of mass, what I really mean is that I found the consistent definition of mass – this is the only definition that is consistent with the Hamiltonian formulation of mechanics. In particular, it does not satisfy the Dirac equation. Which is hardly surprising, since the Dirac equation is based on Einstein’s mass equation, which is based on the theory of special relativity, which is inconsistent with the symmetries of Hamiltonian mechanics. Unfortunately, there is another herd of zombies following the undead Dirac equation, who will slaughter any messenger who has the temerity to deliver the long overdue message that the Dirac equation is dead.
It is hard to deliver a message that says the basic definition is wrong – zombies will say, it’s a definition, definitions can’t be wrong, calculations can be wrong, proofs can be wrong, theorems can be wrong, but definitions can’t be wrong because I can define mass however I like. Up to a point, that is true. But definitions can be useful, or they can be not useful. The Einstein/Dirac definition of mass has outlived its usefulness. It is no longer useful, and needs to be replaced.
There is no denying the inertia of the zombies who don’t want to change the definition, but I don’t think they appreciate the true gravity of the situation.