## The Higgs Boson

January 11, 2012

I am beginning to attract some religious conspiracy theorists…I think I’d better change the subject!

So…deep breath.  I’m going to attempt to explain this whole Higgs boson thing which the news keeps going on about, and which, seeing as it is supposedly one of the most important things ever, I’ve been meaning for a while to actually try to properly understand.  Usual disclaimers: I am not a physicist (in fact whether or not I’m even a proper mathematician is arguable) and I am writing this mainly as a motivation to increase my own understanding.  However, my theory is that, unless an expert is a supremely good communicator, it is often easier to gain a basic understanding of a complex subject from another interested layperson (as they know exactly how you feel).  Certainly I would have liked someone else to have written something like this to save me the effort!

I think we have all heard about the search for the Higgs boson by the people at CERN.  Probably, if you’re still reading this, you have also, like me, wondered exactly what this boson is, what it does, and why it matters so much.  And probably you have some vague notion that it is a particle which “gives other particles mass”.  That is the point I shall start from.

But first, a question – why are things the size they are?  Sounds a bit vague and philosophical, I know.  But the size of an object is determined by the size of the molecules which make it up, which are in turn determined by the size of their constituent atoms.  Atoms consist of a nucleus made up of protons and neutrons, surrounded by orbiting electrons.  And the size of an atom is determined by the sizes of the orbits of its electrons.  But the size of electrons’ orbits depends on the mass of the electron!  So in order to find an answer to why things are the size they are, we need to address the question of why an electron has the mass it does.  And while we’re at it, we may as well ask why other elementary particles have the mass they do…for example, why do photons have no mass at all?

## Schrödinger’s cat

November 8, 2011

I usually read novels in bed, as my brain tends to be too tired to take in any more information for the day.  So the fact that this is the third post I am starting with a reference to a popular science book makes me think that perhaps I have not been working hard enough…

The book in question is The Emperor’s New Mind, by Roger Penrose.  The main thesis of this wonderful book is, apparently (and in a very small nutshell), that the mind does not work like a computer*.  However, I am currently about 3/4 of the way through it, and this has not yet been touched upon!  Rather, over 400 pages or so, Penrose has valiantly attempted to explain Turing machines, classical mechanics, relativity, quantum theory and cosmology to the interested (and, one must assume, quite dedicated) layperson.  I can only assume that all this is going to coalesce into a grand theory of Mind, but it does so far seem like quite an ambitious project.  Having tried to achieve this kind of comprehensive introduction to even the smallest of mathematical subjects myself in previous posts (you might have noticed that I have long since given up trying to do this), I have great respect for Penrose’s tenacity.  I find that the problem with this type of enterprise lies in trying to tread the line between being impenetrable to non-mathematicians, and boring for mathematicians.   While The Emperor’s New Mind is a great book, I think it is safe to say that it probably falls on the former side of this line; it is perhaps not entirely suitable for bedtime reading.

Anyway, I have just been reading Penrose’s take on the maltreated feline of this post’s title, and it got me thinking, so I thought I would discuss it.  The cat in question is a paradox which Erwin Schrödinger came up with in order to show the absurdity of trying to apply quantum theory at the classical physical level (that is, the everyday world with which we interact, as opposed to the exceedingly odd quantum level of subatomic particles).   This is, of course, a massive and complex subject, and I will only provide the merest of scrapes of its surface!  If you happen to be a pedantic physicist, then please do comment on any inaccuracies in what follows.

## A year’s work, lessons learnt

October 11, 2010

I’m back!  And rather surprisingly, I seem to have gained a lot of readers in my absence.   Having not even logged on to WordPress for a few months, I have returned to see that my google reader subscription rate has doubled, and the number of people visiting the blog has increased by more than at any point since I started writing it.  I’m not really sure what lesson to take from this.  Probably it is just the natural result of a gradual snowballing effect: over time more people click on your site, the google rankings go up, causing more people to click on your site…

Then again it’s  possible that people just prefer it when I don’t write anything!  Well I’m sorry those people, but I intend to start again.  Although possibly even more erratically than before.

Anyway, I will explain the terrible sequence of events which led me to abandon blog shortly, but first, a shameless Rupert Murdoch-style using of one of my products to promote another! (I would do this at the end, but am rather doubtful as to how many people actually make it to the end of my posts).  Having been introduced to Vietnamese coffee by my father-in-law a while ago, I have utterly fallen in love with it, and realised that it is very difficult to find here in the UK.  So I have set up a (very) small business selling it.  The website is here.  Try it!  You won’t be disappointed.

Sorry about that.  Now, this is what happened.  Having struggled with the proof of a knotty mathematical problem for the better part of a year, I was advised by my supervisor to publish what I had.  So I put the paper on the arXiv (an online preprint archive), not really expecting to achieve anything, but generally wanting to share the knowledge out of a spirit of altruism (and self-promotion).  Within a few hours of it appearing, a certain Peter Mueller had read it, and proved the last part of the conjecture!  (So there you go doubters: people do read your preprints).  This was wonderful news; we invited him to be a co-author, and set about writing a final draft. I also wrote a whole long blog post about how great this was, and what it all meant.  But then a couple of days later Prof. Mueller sent me some rather less good news: he had found a  mistake in my work, which completely invalidated the whole thing…

## Random Matrices and the Riemann Hypothesis

January 15, 2010

I made it to my second post!  This is the greatest achievement of my blogging life so far.

Having never even heard of random matrix theory before last week, I have recently been hearing talk of it bandied about all over the place.  When I asked my supervisor why this might be, he replied that they were a “hot topic”, and went on to explain the recent connections that have been made between the distribution of zeros of the Riemann zeta function, and that of eigenvalues of large random matrices.  So I’m going to write a bit about it here.

Random matrices are intuitively exactly what you might first suspect they are: matrices with “random” entries.  Of course, it is technically meaningless to say that an element of a matrix is random (hence the inverted commas), but what we can do is to use probability theory to rigorously define an analogous concept.  Without going into in too much depth, we can think of a random matrix as being a matrix with elements that are random numbers from some probability distribution (that is, random variables).  So an $n\times n$ random matrix is actually a collection of all the possible $n\times n$ matrices, along with probability density functions telling us how likely each of these is to occur.