My attention was drawn to an attempt by an outsider to come up with (yet another) Grand Unified theory.

http://www.guardian.co.uk/science/2013/may/23/eric-weinstein-answer-physics-problems

http://www.guardian.co.uk/science/blog/2013/may/23/roll-over-einstein-meet-weinstein

What is unsual about this is that Mr Weinstein hasn't even published a paper describing his theory not even on ArXiv so that other people can examine it and test it's credibility. It would seem that his friendship with Marcus du Sautoy enabled him to give a highly prestigious lecture. I'm sure the guy has come up with some clever maths but like say the current state of superstrings or the multiverse the fact that the theory can't make any predictions and hasn't even been written down means it's definitely in the not even wrong theory.

It does make one question the credibility of Marcus du Sautoy who seems to be latching onto every possible break through in physics (not that Weinstein's attempt could be seen as a breakthrough) and over egg the pudding to say the least. He claimed in a Horizon programme last year that the alleged violation of the speed of light by neutrino's proved superstring theory and M theory. When in fact the result was shown to be due to a faulty cable. I did not see him eating his boxer shorts as Jim Al Khalili offered to if the result was shown to be correct. Marcus du Sautoy righthly has come in for some intense criticism in the way he has handled this issues some links to which can be seen here

http://blogs.scientificamerican.com/cocktail-party-physics/2013/05/24/dear-guardian-youve-been-played/

Anyway this is not the main point of this post. I want to examine what seems to be a misconception by the likes of Marcus du Sautoy about how physics works. People like him seem to think there is a one-one correspondence betweem mathematical structures and the natural world. However any mathematical construction when applied to the real world can only be an approximation not the real thing.

Hume put the dilemma quite precisely in his Fork. Humans use two types of reasoning deductive and inductive. Deductive reasoning such as mathematics applies to the realm of ideas whereas we use inductive reasoning to apply to matters of fact.

As I pointed out a couple of years back

http://www.blogger.com/blogger.g?blogID=7897235423812277683#editor/target=post;postID=7025597943261709647;onPublishedMenu=allposts;onClosedMenu=allposts;postNum=59;src=postname

Hume points out that although we use inductive reasoning all the time there can be no rational justification for it as it involves a circular argument. How do I know that if confronted with a glass of claret it will taste the same as another one by an appeal to experience. How do I ground my experiences by an appeal to the uniformity of nature. How do I know that nature is uniform by an appeal to experience. Reasoning based on induction requires many observations to establish a truth and again not every glass of claret will taste exactly the same. On the other hand inductive reasoning is used all the time.

In contrast in the realm of ideas mathematical and logical deductions once proven are true for all time it only needs one demonstration that eg the gap between two prime numbers is less than 7.5 billion to show that this is the case.

When it comes to applying mathematical ideas to the natural world although the laws of physics can be expressed mathematically they are only approximations albeit really good ones for a lot of cases. In what Hume calls mixed maths which we nowadays call Applied maths the laws are grounded in empirical observation. To test a theory requires a lot of hard work in relating the general principles to a concerte prediction. For example the predicition of the properties of the Higg's boson required many calculations by whole teams of people based on reasonable approximations from the Standard model using the techniques of quantum field theory and even more people to test the predctions by measuring the decay rates and scattering cross sections. This involves calculatiing Hundreds of Feynman diagrams and summing up their individual contributions to the given decay rate or scattering cross-section. Messy, tedious prone to error but thats how real calculations are made in physics even then the actual value of the given parameter will only be an approximation albeit a good one.

Another point is that the laws of phyiscs when expressed mathematically will always have an empirical constant associated with it. The accuracy of the application of say Schrodinger's equation which involves the masses and charges of the particles involved will only be as good as the measured values. Even if one day we do reduce everything to 1 coupling constant, that coupling constant will have to be measured and one measurement will not suffice. . All this points to a degree of approximation associated with the laws of physics expressed mathematically and far removed from the pristine unmessy platonic world that du Sautoy and Weinstein live in.

The symmetries of the Standard model are only approximate to take an example the masses of the quarks in each generation are only approximately the same, indeed as I pointed out it here

http://www.blogger.com/blogger.g?blogID=7897235423812277683#editor/target=post;postID=3500862736577281127;onPublishedMenu=allposts;onClosedMenu=allposts;postNum=3;src=postname

It stretches credulity to suggest that the top quark has the same mass as the bottom quark. Or that neutrino's are massless. Nevertheless as an empirical summary of the current status of particle physics the Standard model is probably the most empirically adequate theory we have. Even if trying to predict results from it is quite a messy busimess.

Such a world is far removed from the Pristine Platonic world of Marcus du Sautoy and Weinstein. It is not enough to come up with some elegant mathematics one has to show how it applies to the real world and acknowledge that at best it will be an ideal approximation. What people like Weinstein and Marcus du Sautoy do is confuse two quite separate areas and types of reasoning. Seduced by the elegance of their mathematics they think they have found the ultimate secret of reality. Unfortunately for them the natural world will always end up blowing a great raspberry at their naive idealism as the approximation will sooner or later breakdown.

Yours is one of the most interesting and clear article I've read about the connection between mathematical models and the reality they are designed to describe.

ReplyDeleteGood job.

Daniel L. Burnstein

Why thank you, It's all in Hume's Enquiry concerning Human understanding Chapter 4. I am surprised that most of the books on philosophy of science that I've read make absolutely no mention of Hume's Fork it really clarifies the situation.

ReplyDeleteBest wishes Chris