Theorems in physics

From Euclid onwards, every theorem in mathematics has been of the form “hypothesis implies conclusion”. There is no exception to this rule, under any circumstances, anywhere, anywhen, anybody, anything. Mathematicians and philosophers generally have precisely two ways of interpreting such a theorem: (a) if hypothesis is true, then conclusion is true, and (b) if conclusion is false, then hypothesis is false. Most other people, and unfortunately this includes a lot of physicists, have only one interpretation: (c) hypothesis is true, therefore conclusion is true. This is usually abbreviated to (d) conclusion is true.

The pitfalls of this approach are obvious. As more and more such theorems are proved, one is forced to swallow more and more absurd conclusions. There are quite a number of theorems in which the hypothesis is something like the axioms of quantum field theory, and the conclusion is something like the existence of the multiverse, or many-worlds, or electrons have free will, or any number of other completely absurd conclusions. Many physicists refuse to question the hypotheses, and are therefore compelled to believe these outrageous conclusions. As a mathematician, and an amateur philosopher, my interpretation is the opposite: the conclusions are absurd, therefore the hypotheses are false.

This argument is so old and so well-known that it is called “reductio ad absurdum”. Why can I not get a single mainstream physicist to accept this obvious, even tautological, argument?

The axioms of quantum field theory are false. End of.

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Group theory and astronomy

You’ve probably noticed that the tools I have used to analyse and correct the standard model of particle physics are group theory and astronomy. It is probably not a coincidence that the School of Mathematical Sciences at QMUL was at one time almost a “School of Group Theory and Astronomy”. It still had some of that ethos when I joined in 2004, though by the time I took early retirement in 2016 there was not much group theory left, and the Astronomy Unit had moved into the School of Physics.

There was a weekly “Pure Mathematics Seminar” which was dominated by group theory, but which from time to time hosted talks on astronomy. I was exposed to regular updates from colleagues on the state of astronomy, and the latest exciting news. So I could not miss the announcement in 2007 of Garrett Lisi’s “Exceptionally simple theory of everything”, which claimed to show how the Lie group E_8 could explain everything about the universe. This claim unfortunately has not lived up to expectations, but I was hooked, because E_8 is without a doubt the most interesting Lie group of all.

There is a “proof” in the literature that E_8 cannot work because it is too small. It took me several years to realise that in fact E_8 cannot work because it is too big. It seemed to me that the correct dimension must be somewhere in the region of 15, while E_8 has dimension 248. So I tried SU(4), and I tried SL(2,H), and I tried G_2, but they didn’t work.

In the meantime, I realised that if the ultimate goal is to unify the theories of the very big and the very small, then some of the numbers that are used in particle physics must also appear in astronomy. So I looked for suspicious coincidences. When I’d found three, on 5th January 2015, I went round the corner to the pub and bought 2 or 3 bottles of their best champagne. I knew I was onto something. I had located the problem, or one of the problems: the standard model does not take account of the acceleration of the laboratory.

I looked for a physicist to work with, but no-one seemed to be interested. Even now, when I have found around 18 suspicious coincidences, and explained many of them, no-one seems to be interested. One reason for this may be that since Einstein’s general theory of relativity was launched in 1915, the foundations of physics have been dominated by geometry. Everyone thinks that the solution to the problems can be found by piling on more and more abstract geometry. But this approach has been tried for 100 years and has failed. As I have shown, the problem is in the group theory, and the solution is therefore also in the group theory. And the correct dimension is 15: the group is SL(4,R).

arXiv policies

This is the email I received from the arXiv after I asked them to reconsider their rejection of my papers.

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From: arXiv Moderation [moderation@arxiv.org]
Sent: 24 December 2019 17:08
To: R A Wilson
Subject: [moderation #296581] moderation 294873 and 295991

Dear Robert,

Our moderators noted the relationship between these papers when considering their contents. These submissions were removed because our moderators determined that they did not contain results that would be considered refereeable for publication in a conventional journal, and as a result were not of plausible interest for arXiv.

Resubmission of this content is not allowed. However, your moderators are willing to reconsider their decision if it is published in a conventional journal with a resolving DOI.

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All four papers are currently being refereed for publication in conventional journals. They may of course be rejected in due course, but they are being refereed. Thus it is hard to understand the position that the arxiv has taken. I am not interested in arguing with them about this, and it seems to me that they are likely to lose more credibility than I am in the end. This is the reply I sent them, which as far as I am concerned is the end of the story:

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Interesting. It is becoming more and more clear why the fundamental theory of physics has made no progress in 40 years, and why the errors in the theory that date back to the 1910s and 1920s have never been corrected, despite the accumulation of vast amounts of experimental evidence that was not available to the pioneers of those days, that makes it clear that the assumptions they quite reasonably made in those days are not in fact valid.
It is sad to see the arxiv, that I thought was an engine of progress, is in fact an enemy of progress. Ah well, you live and learn.

Robert Wilson.

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How much is 1/3?

Amazon has three reviews of my book “The finite simple groups”, one each with 3, 4 and 5 stars. They helpfully translate this into percentages for me, and tell me I have 34% at 5 star, 35% at 4 star, and 31% at 3 star. Now I wonder how they worked that out?

Letter to THE about USS

I wrote to THE two days ago about the proposed destructive changes to the Universities Supperannuation Scheme. This is the letter I actually wrote, before editing. The published version will appear on Thursday.

Dear Sir,
Have we learnt nothing in the past six years about the difference between mathematical models and the real world? If you put garbage into a mathematical model, you will get garbage out. If you model the long-term viability of the USS on the ludicrous assumption that all UK universities go out of business tomorrow, why should anyone listen to you? Unfortunately, this is exactly what the USS is doing. This is pure mathematics, not economics, and the USS should leave pure mathematics to us pure mathematicians.
As a Trustee for several years of the London Mathematical Society, which celebrates its 150th anniversary next year, and hopes to keep going for another 150 years, I learned something about long-term viability. Of course you have to keep the nightmare scenario in the back of your mind, but you do not build your entire business model on it. Your business model must be built on prudent but reasonable assumptions, or else your business will not survive in the long term.
Ironically, the proposed changes to USS might actually bring about the nightmare scenario that the USS seem so concerned about. If, as seems likely, the scheme becomes so unattractive to new members that it becomes viable to set up a rival scheme, then this will eventually happen, and the USS will have dug its own grave.

Credo

I believe in a university which

* teaches students by challenging them, not mollycoddling them;

* researches the fundamental questions about life, the universe and everything, not superficial questions about how to make money;

* administers itself to support teaching and research, not the other way around.

The real HE market

My attention has been drawn to this devastating article in the London Review of Books on the folly of the government’s move towards the marketization of HE.

http://www.lrb.co.uk/v33/n10/howard-hotson/dont-look-to-the-ivy-league

Graduate employability

In a time of rising unemployment, there has been much talk about what graduates need in order to get a (good) job, and what universities can do to help them. I leave aside the obvious impossibility of the task we are charged with, that is, getting more people into jobs, when the jobs simply don’t exist.

Talking to employers, it is clear that what they chiefly expect from graduates are an ability and willingness to learn, and flexibility. The actual topic of the degree is in most cases largely irrelevant, but a `difficult’ subject,  like mathematics, is generally preferred.

Unfortunately, pressures on universities from outside, and therefore pressures on academics from university managers, tend to push in the opposite direction from the real interests of the students. Directives to provide detailed printed lecture notes, model solutions to all exercises, sample exams, etc etc all militate against our aim to teach students how to learn.

If we bow to the pressure to spoon-feed our students in this way, we let both them and society down. We may improve some largely meaningless statistics, and thereby our position in league tables, by so doing, but we will produce graduates who cannot think for themsleves, who cannot deal with a new situation they have not seen before, and who therefore cannot get the job they want, and think they deserve.

So, a plea to university managers: please stop interfering in things you don’t understand, like how to teach mathematics, and let us, the professionals, get on with the job the way we know works best.