A 2020 VISION FOR A NEW THEORY OF PHYSICS ROBERT ARNOTT WILSON Abstract. I offer a vision for a possible unified model of fundamental physics, based on a rigorous examination of the underlying assumptions. Where the assumptions on which current theories are based are contradictory, I offer revised assumptions that are not. Much of this is necessarily speculative, but much is supported by the experimental evidence. I omit the detailed technical and mathematical arguments, that can be found elsewhere. 1. The fundamental problems 1.1. The status quo. The physical theory of the very small is based on quantum mechanics, which is a very successful theory that underpins almost all of modern technology. The physical theory of the very big is based on general relativity, which is a very successful theory that underpins our understanding of the universe and our place within it, and is also an essential ingredient in modern technology such as GPS. There is only one problem|these two theories are incompatible with each other. This problem has been known since the 1930s but we seem to be nowhere near a solution yet. A full discussion can be found in [1]. Part of the reason for this is that the two theories have been almost too success- ful. By the 1970s, quantum mechanics had developed into the `standard model of particle physics' which explains almost everything about the elementary particles of which the universe is made. Almost every experiment has confirmed the model in almost every detail, culminating in the discovery of the Higgs boson in 2012. 1.2. The neutrino mass problem. There is perhaps just one irritating gap, and that is that we do not understand the masses of the elementary particles. A par- ticular case of this is the neutrino mass problem. Neutrinos are produced in the interior of stars, in radioactive decays and in nuclear reactors. They are very hard to detect, as most of them pass right through the Earth without hitting anything on the way. The question is whether neutrinos have mass, or whether, like the photons that constitute light (and X-rays, and microwaves, and radio waves, and so on), they are massless. The standard model requires them to have non-zero mass in order to explain their experimentally observed properties. But no experiment has been able to measure this mass directly, and it must be very small|no more than about one-millionth of the mass of the electron, which is the next lightest particle. Therefore this (hypothetical) non-zero mass is a prediction of the standard model that has not yet been confirmed by experiment. While most physicists regard this prediction as a solid fact, I do not. There is simply not enough physical evidence to support this hypothesis, in my opinion. Date: February 23rd 2020; revised February 27th 2020. 1 2 ROBERT ARNOTT WILSON 1.3. The dark matter problem. Similarly, general relativity has developed into the `concordance model of cosmology' which explains almost everything about the structure of the universe on a large scale. But again there is a fly in the ointment, and again it is a problem of mass. According to our current understanding of normal matter, there is simply not enough mass inside galaxies for them to behave in the way that they obviously do. The structure of galaxies can only be explained by general relativity if there is a large amount of `dark matter', making up nearly 85% of the total matter in the universe. There is no direct evidence of this dark matter, and therefore its existence must be regarded as a prediction of general relativity that has not been confirmed by experiment. While most cosmologists regard this prediction as solid fact, I do not. I am not alone in this, but my opinion is definitely a minority opinion. 1.4. A possible way forward? In the light of these problems, I have been working on developing a mathematical model for fundamental physics in which • neutrinos have zero mass, and • there is no dark matter. If such a model can be built, then there is some possibility that it might eventually replace the existing models. Mathematical details are presented in [2]. 2. The basic assumptions 2.1. Lessons from history. There is a close analogy here with Einstein's de- velopment of the theory of special relativity in 1905. In the late 19th century explorations of the properties of light, electricity and magnetism had developed to the point where serious contradictions started to appear. There were experimental results that could not be reconciled with any commonsense view of the universe. The Michelson{Morley experiment produced the apparently absurd result that the speed of light in a vacuum is always the same, independently of how fast you are moving when you measure it. Einstein cut the Gordian knot by taking this result at face value, and making it his basic assumption. He was then able to develop a theory which not only explained the phenomena which had been seen, but also made predictions about new phenomena. These predictions, such as the one that moving clocks run slow, have been very well tested, and found to be correct. Now it turns out that, just as Einstein had to abandon the most basic assump- tions about the nature of space and time, so we have to abandon the most basic assumptions about the nature of mass and spin. 2.2. The concept of spin. Ordinary spinning objects return to their original state after rotating through 360◦. Quantum mechanics is based on the idea that certain fundamental particles, including the electron, proton and neutron that make up all of ordinary matter, `spin' in a different way: they have to rotate through two whole revolutions, that is 720◦, before they return to their original state. This is not as mysterious as it sounds, and can be visualised with an ordinary coffee mug: if you rotate it through 360◦ on a table it comes back to where it started. Now try to keep hold of the mug as you rotate it in the air in front of you: after 360◦ you will find your arm is uncomfortably twisted, but if you keep going through another 360◦ in the same direction, you will find your arm has somehow magically untwisted itself. A 2020 VISION FOR A NEW THEORY OF PHYSICS 3 That image provides a model for how electrons, protons and neutrons `spin'| something is `holding on' to them. That something, I maintain, is the rest of the universe, and the way it is holding on is by the various forces of nature, most im- portantly electromagnetism, but also including gravity. This means that ordinary space and time are sufficient to explain this initially surprising property of elec- trons, protons and neutrons. In quantum mechanics, for mainly historical reasons, an abstract space of `spinors' is used instead|but is not necessary, as this discus- sion proves. Occam's razor, that is the principle that the simplest explanation is the best, should therefore force us to remove the concept of a spinor from quan- tum mechanics altogether. Everything that can be explained with spinors can be explained with spacetime instead. In fact I have shown elsewhere that it is the concept of a spinor that is itself responsible for the contradiction between quantum mechanics and general relativity. Thus it is not only desirable, but almost certainly essential, to abandon the concept of a spinor altogether. A further benefit of avoiding spinors is that we avoid at least some of the problems of interpretation of quantum mechanics, which bedevil the subject. The basic question is `What is a spinor?' which is unanswerable, although many people have tried to answer it. A weaker version of the question is `How should we think about a spinor?' to which the traditional answer is `Shut up and calculate.' Questions of this type go away when spinors are replaced by spacetime. There are however other questions of interpretation that do not necessarily go away, which I will come back to later. 2.3. The concept of mass. A similar problem affects the concept of mass, in the foundations of general relativity. Einstein originally took as his starting point the `general principle of relativity', that is, the principle that the laws of physics are the same for all observers. But in the end his theory of general relativity was based instead on the `equivalence principle', that gravitational mass and inertial mass are the same thing. Gravitational mass measures how hard gravity pulls an object, and determines how heavy an object is. Inertial mass measures how difficult it is to move the object, and does this by seeing how hard the electromagnetic forces between atoms push and pull. The equivalence principle therefore states that the relative strength of gravity and electromagnetic forces is always the same. This principle has been tested to high accuracy both on the Earth and in satellites orbiting the Earth, and no discrepancy has yet been found. But it is known that the relative strengths of electromagnetism and the nuclear forces are not always the same, so why should gravity be any different? Cosmological evidence from the shapes and sizes of galaxies also casts doubt on the equivalence principle on very large scales. It is therefore desirable, if possible, to devise a more general theory that does not assume the equivalence principle. 2.4. Up the creek without a paddle. To summarise the conclusions at this point, we have found it necessary to abandon the basic assumptions of both quan- tum mechanics and general relativity, namely • the existence of spinors, and • the equivalence of gravity and inertia.