Sunday, June 7, 2015

Veracity and Verifiability

A crisp, concise op-ed, in this morning’s NYTimes, “A Crisis at the Edge of Physics” by Adam Frank and Marcelo Gleiser (both professors of physics), states the case against (over-cantilevered or under-buttressed) speculation, not only for string theory (which has notoriously come in from a lot of pushback;  see Lee Smolin, The Trouble with Physics), but for supersymmetry generally.  The authors note that, as of even date, “no supersymmetric particles have been found” (perhaps they are hiding out in a back room, playing poker with the Higgs boson).  So far as that goes, not a problem;  plenty of propositions in math and science took centuries or even millennia to settle.  What disturbs the authors is that some champions of supersymmetry -- the jusqu’au-boutistes, we might call them -- may simply move the verificationist goalposts.

Some may choose to simply retune their models to predict supersymmetric particles at masses beyond the reach of the Large Hadron Collider’s power of detection -- and that of any foreseeable substitute.

If that were only a problem for one avenue at the forward fringes of physics, that would not be a problem for most of us  as we bustle about our daily chores.  Yet the authors further suggest that certain well-traveled avenues  are actually cul-de-sacs:

The standard model, despite the glory of its vindication, is also a dead end.  It offers no path forward to unite its vision of nature’s tiny building-blocks with … gravity.

What really bothers the authors is something that goes well beyond physics:  “the specter of an evidence-independent science”.   And that specter has been haunting the West for some time, and increasingly reaches into the headlines, as witness the countermovements to the theses of natural selection or of global climate change.

Not being a physicist, I have no right to comment;  but, at the margins, this:

(1) The larger cultural worry, is the dissociation of the notion of Truth überhaupt  from that of Evidence and Argument. In that perspective, we would deplore the demand to dissociate theory from experiment.
(2)  Yet -- Do not forget  Einstein’s classic crack in 1919, anent the possible negative results of an experiment purporting to validate or refute General Relativity:  “Da könnt’ mir halt der liebe Gott leid tun.  Die Theorie stimmt doch.”  (Informal translation:  "I'm right.  Bite me.")

Die Theorie stimmt doch!

The consensus of scientific history (for right reasons or wrong)  has been to applaud  those cheeky remarks .

Compare, re Feynman and Gell-mann’s joint article “Theory of the Fermi Interaction” (written in 1957, and subsequently published in Physical Review):

The V - A theory was in disagreement with more than a half dozen experimental results on beta-decay,  but it was so beautiful  that the authors proposed it anyway, suggesting that all those results were wrong.
-- Harald Fritzsch, introduction to Murray Gell-Mann: Selected Papers (2010), p. 5


Einstein was speaking of his theory of gravitation.  But similarly for particle physics:

The Standard Model … has been driven largely by certain powerful consistency requirements, hard to satisfy in such theories.  In order to appreciate something of the force behind these consistency requirements (which continue to drive the more modern speculative theories, such as string theory), we shall need to look at the structure of quantum field theory. … The theoretical requirements appear to be so tight  that it might seem almost incidental that these answers are actually in excellent agreement with experiment!
-- Roger Penrose,  The Road to Reality (2004), p. 655-6


Working the equations of physics to their long-reaching logical conclusions, continually leads to apparent absurdities:  negative energies or frequencies, unobserved particles, particles moving backwards in time, a Hobson’s choice between acausality or indefinitely-proliferating alternate universes, and miscellaneous infinities.  Some physicists shudder at such;  others grin and say “Bring ‘em on.”  (Unfortunately, the latter are the ones favored in the popular media -- the problem of Physics Porn.)  The problem is deciding when that is just the way Nature (inscrutably) actually works (in which case you have made a major discovery), and when it is merely absurd.  Will the Higgs boson turn out to have been more like the positron (born from the forehead of Dirac’s mathematics) and the pion (brain-born from Yukawa), eventually found in everyday space, or like the cute-sounding but still-missing photinos, squarks, and pentaquarks?

So here is the larger temptation -- the intellectual Occasion of Sin:
Beginning several decades ago, comparing the results of experimentally well-verified physics  with the predictions of the equations, scientists marveled at what was memorably dubbed “the unreasonable effectiveness of mathematics”, summed up by the epigram “the equations seem to give us more than we put into them;  they seem to be wiser than ourselves”.   But The Edge beckons when we start to conclude, that if our favorite equations predict something, it must be so (if only in the Multiverse) -- even if, to the guys in the lab, it doesn’t seem physically reasonable.

As Penrose puts it:

What is the physical justification in allowing oneself to be carried along by the elegance of some mathematical description  and then trying to regard that description as describing a ‘reality’?
-- Roger Penrose,  The Road to Reality (2004), p. 670

That question takes us back  to a very old debate -- as old as poetry :  What is the relation between Beauty and Truth?

In that essay, we concluded that, in a sense, ‘beauty’ (in a rather austere sense of crisp symmetric elegance, having more to do with the Parthenon than a Miss America pageant or a Rosebowl parade) does characterize any deep theory in the mathematicized sciences -- but only in retroscpect, after years and decades of its practitioners coming to appreciate its depth; the theory does not wear its beauty on its sleeve.

Thus, even in the case of the (relatively) well-behaved, now-long-familiar poster child of particle physics, QED:  Paul Dirac, the pioneer of QFT, wasn’t buying it.   In response to a 1936 experiment (by Shankland) which suggested (incorrectly, as it turns out) that energy need not be microscopically preserved,

Dirac immediately jumped at this opportunity to disown QED, claiming “because of its extreme complexity, most physicists will be glad to see the end of it.
-- Matthew Schwartz, Quantum Field Theory and the Standard Model (2014), p. 247


Taking physics on faith

Penrose again, concerning a couple of signature contributions by Richard Feynman -- probably the educated public’s favorite hip physicist since Einstein:

The path-integral approach is, it seems, almost wholly dependent upon a faith that the wildly divergent expressions that we are presented with (like the divergent series above) actually have a deeper ‘Platonic’ meaning  that we may not yet properly perceive.
-- Roger Penrose,  The Road to Reality (2004), p. 670

Even that archetypal renormalizable theory, QED, is not actually a finite theory, even after renormalization.  How can this be?  Renormalization refers to the removal of infinities from finite collections of Feynman graphs.  It does not tell us that the summation of all these resulting finite quantities is actually convertent. … In fact it is not finite, but has a ‘logarithmic divergence’.
-- Roger Penrose,  The Road to Reality (2004), p. 680

As for the next step beyond QED (which is part of the Standard Model), QFT:

Strictly speaking, quantum field theory … is mathematically inconsistent.
-- Roger Penrose,  The Road to Reality (2004), p. 610


But let us set aside quantum mechanics, that known maze of paradox, along with its ever-more-speculative successors.  Surely matters stand better in the case of classical mechanics and electromagnetism, along with their tool-of-all-work, the venerable Lagrangian, which dates back to the eighteenth century. 

Yet even here, Penrose demurs:

In modern attempts at fundamental physics, when some suggested new theory is put forward, it is almost invariably given in the form of some Lagrangian functional. … However, I must confess my unease … The choice of Lagrangian is often not unique, and sometimes rather contrived … Even the Lagrangian for free Maxwell theory … has no obvious physical significance. … Moreover, the ‘Maxwell Lagrangian’ does not work as a Lagrangian unless it is expressed in terms of a potential, although the actual value of the potential, A, is not a directly observable quantity. … In most situations, the Lagrangian density does not itself seem to have clear physical meaning.
-- Roger Penrose,  The Road to Reality (2004), p. 491

Nor is Penrose a professional maverick or skeptic.   After all, the book we’ve been quoting from clocks in at over a thousand pages, and is subtitled “A Complete Guide to the Laws of the Universe”;  you wouldn’t do that if you thought physics was a crock.


Simply as an assertion, the Weyl curvature hypothesis  is perhaps more like a claim for ‘an act of God’  than a physical theory.
-- Roger Penrose,  The Road to Reality (2004), p. 769

Rule of Thumb:
Physics advances by dint of Physicists’ Encyclicals.
These are almost never arrived at purely deductively;  neither do they come out of nowhere.

Schrödinger’s equation -- Feynman’s path-integrals -- the laws of thermodynamics:  inspired guesses, which awaited the mathematicians to tidy things up.

-- Not trying to debunk, here;  simply being historical.
(Feyerabend, too, was long  historical  in this sense, before he went over to the dark side.)

[July 2015]  Essay updated here:

No comments:

Post a Comment