The Road to Reality - Roger Penrose (part 2)

It's been long enough that I decided it was worth reading a few more hundred pages. This bit covered physics up to the standard model (plus some basic general relativity), building on the first section's maths. Fortunately, I didn't need to remember all the details of the maths that was introduced previously, since as long as you can remember the gist of the maths, you can skim over the rest!

Shifting from the maths to the physics, it becomes clear that there's a gear change from Beauty to Truth - what matters is to match physical reality (or at least physics experiments), rather than have a beautiful theory. So, various bits of 'normalisation' (or throwing out unfortunate infinities) are accepted as long as the right results are reached. Mathematical tools and structures are still useful for providing constraints (such as various symmetries), but there's certainly a loss of elegance compared to the start of the book!

A couple of things jumped out at me. Having not done physics courses before, I hadn't previously come across Hamiltonians and Lagrangians. These functions describe the evolution of a system in terms of something like optimising paths in state space. They are core to quantum mechanics. However, it can also be used for Newtonian mechanics. When you do so, it does rather obfuscate the physical intuition, though. So, it's not surprising that quantum mechanical constructions tend not to lack a nice physical intuition! (Of course, on top of this, there is the linear evolution/probabilistic state collapse divide, which is still a big confusing fudge...)

The other thing is the importance and power of wrong ideas! This is more than the usual idea of, say, Newtonian mechanics providing an approximation to quantum mechanics. That's a bit like following a path of increasingly precise descriptions. In comparison, Dirac's view of positrons as holes in a sea of electrons explained some phenomena, but completely fails to account for others. It's not a more accurate description of physical reality. It's rather like taking a wrong turning. I can see no plausible reason why being wrong opens up so many interesting (and accurate!) insights.

By the end of this section we'd covered up to the standard model. It's fun to think that the book is already out of date - the Higgs boson is no longer an unconfirmed theory! I still don't feel terribly comfortable with it. Beyond the clear limitations of lots of mysterious numbers, and no integration with GR, I still prefer theories that I feel can easily be explained algorithmically. Partly QM is too computationally expensive, and partly the waveform evolution/collapse split is not clear. Ho hum.

Posted 2012-12-31.