Archive for quantum field theory

Matter and forces in quantum field theory – an attempt at a philosophical elucidation

Posted in Maynooth, The Universe and Stuff with tags , , , on March 16, 2021 by telescoper

I thought the following might be of general interest to readers of this blog. It’s a translation into English of an MSc thesis written by a certain Jon-Ivar Skullerud of the Department of Theoretical Physics at Maynooth University. I hasten to add that Dr Skullerud hasn’t just finished his MSc. It just appears that it has taken about 30 years to translate it from Norwegian into English!

Anyway, the English version is now available on the arXiv here. There isn’t really an abstract as such but the description on arXiv says:

This is a translation into English of my Masters thesis (hovedoppgave) from 1991. The main topic of the thesis is the relation between fundamental physics and philosophy, and a discussion of several possible ontologies of quantum field theory.

I note from here that hovedoppgave translates literally into English as “main task”.

I haven’t read this thesis from cover to cover yet – partly because it’s in digital form and doesn’t have any covers on it and partly because it’s 134 pages long –  but I’ve skimmed a few bits and it looks interesting.



Lectures by Video

Posted in Education, The Universe and Stuff with tags , , , , on October 2, 2012 by telescoper

I spent a short while this morning sitting in on a lecture from one of our fourth-year modules, on Quantum Field Theory. Nothing obviously remarkable about that, except that the lecture was in fact delivered by Prof. Graham Shore of Swansea University and I was sitting in the School of Physics & Astronomy at Cardiff University with a group of twenty or so Cardiff undergraduates.

This was the first lecture our students have received from Swansea as part of an arrangement to share some teaching. There was a plan to do it last year, but it fell apart owing to technical problems. When I took over as Director of Teaching and Learning earlier this year I was determined to make it work. I have long felt that many of our 4th-year students were losing out on some advanced topics, especially in particle physics, owing to the lack of expertise in that area here. Indeed, the lack of expertise in particle physics here in Cardiff is so extreme that our students have had to put up with being taught by me! Likewise Swansea’s undergraduates have missed out a bit on some topics we do here, especially astrophysics and gravitational physics. This division of labour dates back to the old federal University of Wales where it was decided for strategic reasons not to compete in these two areas of “big science” but to allow Cardiff to do astronomy, astrophysics and gravitational physics and Swansea the particle stuff. It was a sensible decision from a research point of view, but it meant that the two relatively small physics departments here in South Wales could offer their undergraduates more restricted choices of advanced topics  than at bigger universities.

Not for the first time, the web has furnished a solution. After a few technical problems – not entirely sorted out, to be honest – we’ve finally established a video link. The initial setup is temporary, but we will (hopefully by next week) have a permanent, high quality videoconferencing suite for future use. It will probably take some time for lecturers and students on both sides to get used to it, but sitting in this morning I found it more than satisfactory from the point of view of audibility and legibility. The only problem really is that the static camera shot makes it a bit claustrophobic. I’m not sure whether there’s a way around that without spending a fortune on multiple cameras.

Anyway, to mark this historic occasion I thought I post another video lecture on Quantum Field Theory just to give you a flavour of the content and the experience. This is by David Tong of Cambridge University as seen in a lecture recorded by the Perimeter Institute in Canada.


Anyway, in the spirit of openness, and because I couldn’t stay for the whole session,  I’d be interested to hear what any Cardiff students thought of the experience either in private or through the comments box..

Infinity or not Infinity?

Posted in The Universe and Stuff with tags , , , , , , on May 14, 2011 by telescoper

Most of us – whether scientists or not – have an uncomfortable time coping with the concept of infinity. Physicists have had a particularly difficult relationship with the notion of boundlessness, as various kinds of pesky infinities keep cropping up in calculations. In most cases this this symptomatic of deficiencies in the theoretical foundations of the subject. Think of the ‘ultraviolet catastrophe‘ of classical statistical mechanics, in which the electromagnetic radiation produced by a black body at a finite temperature is calculated to be infinitely intense at infinitely short wavelengths; this signalled the failure of classical statistical mechanics and ushered in the era of quantum mechanics about a hundred years ago. Quantum field theories have other forms of pathological behaviour, with mathematical components of the theory tending to run out of control to infinity unless they are healed using the technique of renormalization. The general theory of relativity predicts that singularities in which physical properties become infinite occur in the centre of black holes and in the Big Bang that kicked our Universe into existence. But even these are regarded as indications that we are missing a piece of the puzzle, rather than implying that somehow infinity is a part of nature itself.

The exception to this rule is the field of cosmology. Somehow it seems natural at least to consider the possibility that our cosmos might be infinite, either in extent or duration, or both, or perhaps even be a multiverse comprising an infinite collection of sub-universes. If the Universe is defined as everything that exists, why should it necessarily be finite? Why should there be some underlying principle that restricts it to a size our human brains can cope with?

On the other hand, there are cosmologists who won’t allow infinity into their view of the Universe. A prominent example is George Ellis, a strong critic of the multiverse idea in particular, who frequently quotes David Hilbert

The final result then is: nowhere is the infinite realized; it is neither present in nature nor admissible as a foundation in our rational thinking—a remarkable harmony between being and thought

But to every Hilbert there’s an equal and opposite Leibniz

I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author.

You see that it’s an argument with quite a long pedigree!

When I was at the National Astronomy Meeting in Llandudno a few weeks ago, I attended an excellent plenary session that featured this year’s Gerald Whitrow Lecture, by Alex Vilenkin, entitled The Principle of Mediocrity. This was a talk based on some ideas from his book Many Worlds in One: The Search for Other Universese, in which he discusses some of the consequences of the so-called eternal inflation scenario, which leads to a variation of the multiverse idea in which the universe comprises an infinite collection of causally-disconnected “bubbles” with different laws of low-energy physics applying in each. Indeed, in Vilenkin’s vision, all possible configurations of all possible things are realised somewhere in this ensemble of mini-universes. An infinite number of National Astronomy Meetings, each with the same or different programmes, an infinite number of Vilenkins, etc etc.

One of the features of this scenario is that it brings the anthropic principle into play as a potential “explanation” for the apparent fine-tuning of our Universe that enables life to be sustained within it. We can only live in a domain wherein the laws of physics are compatible with life so it should be no surprise that’s what we find. There is an infinity of dead universes, but we don’t live there.

I’m not going to go on about the anthropic principle here, although it’s a subject that’s quite fun to write or, better still, give a talk about, especially if you enjoy winding people up! What I did want to say mention, though, is that Vilenkin correctly pointed out that three ingredients are needed to make this work:

  1. An infinite ensemble of realizations
  2. A discretizer
  3. A randomizer

Item 2 involves some sort of principle that ensures that the number of possible states of the system we’re talking about  is not infinite. A very simple example from  quantum physics might be the two spin states of an electron, up (↑) or down(↓). No “in-between” states are allowed, according to our tried-and-tested theories of quantum physics, so the state space is discrete.  In the more general context required for cosmology, the states are the allowed “laws of physics” ( i.e. possible  false vacuum configurations). The space of possible states is very much larger here, of course, and the theory that makes it discrete much less secure. In string theory, the number of false vacua is estimated at 10500. That’s certainly a very big number, but it’s not infinite so will do the job needed.

Item 3 requires a process that realizes every possible configuration across the ensemble in a “random” fashion. The word “random” is a bit problematic for me because I don’t really know what it’s supposed to mean. It’s a word that far too many scientists are content to hide behind, in my opinion. In this context, however, “random” really means that the assigning of states to elements in the ensemble must be ergodic, meaning that it must visit the entire state space with some probability. This is the kind of process that’s needed if an infinite collection of monkeys is indeed to type the (large but finite) complete works of shakespeare. It’s not enough that there be an infinite number and that the works of shakespeare be finite. The process of typing must also be ergodic.

Now it’s by no means obvious that monkeys would type ergodically. If, for example, they always hit two adjoining keys at the same time then the process would not be ergodic. Likewise it is by no means clear to me that the process of realizing the ensemble is ergodic. In fact I’m not even sure that there’s any process at all that “realizes” the string landscape. There’s a long and dangerous road from the (hypothetical) ensembles that exist even in standard quantum field theory to an actually existing “random” collection of observed things…

More generally, the mere fact that a mathematical solution of an equation can be derived does not mean that that equation describes anything that actually exists in nature. In this respect I agree with Alfred North Whitehead:

There is no more common error than to assume that, because prolonged and accurate mathematical calculations have been made, the application of the result to some fact of nature is absolutely certain.

It’s a quote I think some string theorists might benefit from reading!

Items 1, 2 and 3 are all needed to ensure that each particular configuration of the system is actually realized in nature. If we had an infinite number of realizations but with either infinite number of possible configurations or a non-ergodic selection mechanism then there’s no guarantee each possibility would actually happen. The success of this explanation consequently rests on quite stringent assumptions.

I’m a sceptic about this whole scheme for many reasons. First, I’m uncomfortable with infinity – that’s what you get for working with George Ellis, I guess. Second, and more importantly, I don’t understand string theory and am in any case unsure of the ontological status of the string landscape. Finally, although a large number of prominent cosmologists have waved their hands with commendable vigour, I have never seen anything even approaching a rigorous proof that eternal inflation does lead to realized infinity of  false vacua. If such a thing exists, I’d really like to hear about!