Mathematical fumblings behind the campus bikeshed
The great physicist Roger Penrose has written:
‘…The standard model is clearly not the “ultimate answer”, with regard to particle physics, because it contains many unexplained features and “ragged edges”, despite its undoubted success. It involves about 17 unexplained parameters that simply need to be taken from observation.’
Then he talks about quantum field theory and the frequent need to ‘renormalize’ equations. ‘Renormalizing’ means, for example, when the maths yields an infinite negative mass or an infinite negative charge, arbitrarily to add infinite mass or infinite charge so that the problem goes away and you get values that meet experiments. Or to put it another way, the ‘twin criteria of agreement with observation’ and ‘mathematical consistency’ are ‘incompletely fufilled’ (p665) and ‘there is no accepted way of obtaining finite answers without such an “infinite rescaling” procedure applied not necessarily only to charge, or to mass, but to other quantities also’ (p678).
Physicists, possibly, can get away with much in the murky cellars of mathematics because the rest of us are ill-equipped to go down and supervise.
“What are you doing down there?’ we call.
‘Oh, I’m just renormalizing,’ they reply, amid the clink of bottles.
Those of us who are not unsupervised quantum physicists still live under tiresome restrictions: at GCSE, we can’t arbitrarily add numbers to make our equations come out right. In the bank, we find opposition to us renormalizing our overdrafts by suggesting the bank adds an infinite amount of positive-but-theoretical money. So tiresome!
Yet this is not to throw stones at physicists, who in my view have by their mathematical fluency made much more progress on paradoxical issues than (say) theologians (who are usually just restricted to human languages).
But it is to say that physics isn’t quite the purring engine, not quite the lonely pinnacle of rarefied human thought, that we might like to think.
And so, for example, when New Atheists claim that Quantum Field Theory and its like does away with the need for a Creator, since everything just pops spontaneously out of a quantum vacuum, we should remember these arguments are held together, at a fundamental level, by duct tape.
Quotes are from Roger Penrose’s magnificent The Road to Reality, which has sadly reminded me what three years of undergraduate study proved: in physics, I can hum the tunes but can’t do the lyrics.