In these posts I have emphasized ideas on the cutting edge of fundamental science which have testable predictions or other contact with experiment, rather than being merely fashionable. Now, up until recently it was widely assumed that ideas for the ‘Mount Everest’ challenge of quantum gravity, as Martin Rees puts it in his review of the multiauthored book On Space and Time, could never be tested experimentally.
Accordingly, theoretical physicists in the last two decades have often given up on serious experimental contact and based their ideas on fashion or ‘elegance’. This, unfortunately, is not by itself a reliable indicator as it rather depends on what maths you are familiar with, something which tends to be rather hit and miss in the theoretical physics community. I consequently agree with Martin Rees that we are nowhere near the ’summit’ as it were.
For example, I remember at the turn of the millennium waking up to a respectable BBC radio chat show, I believe it was In Our Time, in which a string theorist explained that string theory tries to unify quantum theory and gravity. When asked what was the evidence for string theory, the individual replied “well, there is evidence for quantum theory and there is evidence for gravity, so there is evidence for string theory.”
This was pretty shocking for me and for most of my colleagues (including my string theory colleagues) because a theory has to be judged by how it goes beyond what is known, not by the mere wish to succeed. It’s no doubt tough being on the radio and probably the interviewee was trying too hard to oversimplify, but it illustrates the problem. I should say that I am not against string theory per se, though I do agree with those who say that it should be judged in perspective and not to the exclusion of other approaches.
How can we return to experiment, as we surely must to make genuine progress in quantum gravity? In my own chapter of On Space and Time, I explain that one can make certain quantum gravity predictions without knowing quantum gravity and without pretending to have a theory of everything at all.
Comments
x, y, z should not commute if t does not
October 22, 2008 by Halliday, 1 year 2 weeks ago
Comment id: 32501
The primary problem I have with the non-commutativity relation expressed in the article is it's lack of general invariance (transform x, y, z, and t in any general way and you get something that doesn't match). What I would expect would be something like
xμ xν - xν xμ = xσ Cσμν
where Cσμν = -Cσνμ is some appropriate tensor field (with appropriate characteristics with regards to complex conjugation).
This still indicates that determining the location and time simultaneously is impossible (due to the non-commutativity, for non-vanishing C), though it also means that one cannot determine all three components of position either. This seems more realistic to me.
David
P.S. Thankfully, we can now use <sup> and <sub>!!!! :-)
Reply to David
November 21, 2008 by Anonymous, 50 weeks 1 day ago
Comment id: 33002
Hi David,
came across your comment. In fact the example is of the `lie algebra' type
that you suggest just that many of the components of the tensor C are
zero. The idea that classically you can rotate among the x,y,z,t is
expressed as a symmetry of the Lorentz group SO(3,1) and that there is
no preferred origin (point 0,0,0,0) combines with this as the statement of invariance under the Poincare group.All of this seems to be lost but is still there in the model but now as a quantum Poincare symmetry. For that, see a later
post on quantum symmetry. Its perfectly possible to have models with
x,y,z noncommuting but the simplest ones have t commuting with x,y,z; sort of complementary. Its possible to have `fully mixed up' examples but I dont know a good one which keeps Poincare symmetry as a group or quantum group. At the moment most attention is just on the simplest models for practical reasons.