[That is an ascending series.
Some things that are
true,
may yet be inaccessible to us -- temporarily, or forever;
a
veracious
person is someone who asserts only what he sincerely believes to be true (and
-- for this quality to have any practical value -- has reasonable warrant for
so believing, reasonable relative to the contemporaneous state of the art.)
Verifiable means
that the assertion is ‘in the running’ for being experimentally (or
proof-theoretically) verified, even though these happy results have not yet
eventuated.
Vindicated means
that the result has been confirmed, whether by (theory-supported) experiment,
formal proof, or revelation.]
[Original post from 7 VI 2015]
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.
Exactly the same concerns were voiced, a good decade
earlier, by the mathematician-physicist Roger Penrose, in the section “Can a
wrong theory be experimentally refuted?” (p. 1020 ff.), in The Road to
Reality (2004), concerning “un-Popperian” practices in physics.
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
.
~
Einstein was speaking of his theory of gravitation. But similarly for particle physics.
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
And:
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
And more generally:
Polanyi delighted in drawing
attention to cases where the scientific community ignored or waved aside or
explained away seeming
counter-evidence to accepted theories.
He seems to have felt that a scientists would abrogate his personal
responsibility for his beliefs if
he allowed them to be at the beck and call of experimental results.
-- John
Watkins, Science and Skepticism (1984), p. 29
Nor must we wait until our own extravagant age of
post-modernism and M-theory, to find ourselves confronted with an “All is
Permitted” ethos in the realm of physics.
Karl Pearson, as a pioneer of statistical thinking in a wide
range of fields, is in that respect
a representative of a hard-headed, just-the-facts-ma’am,
shut-up-and-calculate approach to messy realities. But when doing (what he thought of as) physics, his
Romanticism, which early on was a major strain of his make-up, got the better
of him. In the years around
1890, he theorized about atoms in terms of the then-regnant ether theory:
He spoke not of causation
but of analogy, indeed “analogies … of the vaguest description”, and in
the context of this paper, his doubts
about the human capacity to get at real objects or real causes functioned as a license to invent …
Since his ether model so far had strange, almost inconceivable
properties, he discarded physical
plausibility as a criterion of a good theory.
-- Theodore Porter, Karl Pearson
(2004), p. 187
~
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?
[Update July 2015] Bzzt! No sooner had I posted that, than experiments claim to have spotted one of the elusive critters:
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 retrospect, 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
Theophysical note:
Here we see a reference to “faith”; its truth-functional content may be roughly equivalent to “working
assumption”, but since we are indeed dealing with such deep and ultimate
matters of Platonism, the theological overtone is not actually out of
place.
Similarly, my casual reference to “revelation” above, as
denoting one of various routes to knowledge, was not flip. Compare, from our hard-headed
flinty-eyed philosopher of science:
If we had a hot line to the Author of
Nature, and if we had a clearly formulated IP [for which see below], an
excellent question to put to him would be: Is our IP true?
If he answered ‘Yes’, we could happily set a computer to work to print
out all those h[ypothese]s that are
singled out by our evidence in
conjunction with this authoritatively endorsed IP.
-- John Watkins, Science
and Skepticism (1984), p. 93
And if that strikes anyone as credulous, note that most of
us largely treat computers as oracles as well (e.g. in the proof of the
Four-Color Theorem, or any of innumerable unsurveyable and possibly
preposterous simulations).
Back to the sadder-but-wiser Penrose:
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 convergent. … 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.)
~
Donning our old lexicographer’s hat, let us look a bit more
into the matter of vocabulary, the Wortfeld
of terms for justification.
Our negative result so far,
entirely in line with Hume’s, is that, without an inductive principle, there
can be no legitimate ascent from level-0
[i.e., things like “yellow patch, for me, here, now”] to level-1, or
from level-1 to level-2, and that any inductive principle strong enough to “legitimise” the ascent could not itself be legitimised. If that is so, then it is obvious
that there can be no legitimate ascent to still higher levels.
--
John Watkins, Science and Skepticism (1984), p. 105
In the following, we see a fine distinction drawn between justification and “vindication”.
The philosopher John Watkins imagines a principle, call it
the Inductive Principle, which would answer Hume’s objections, to the
satisfaction of inductivists. What
would then be the status of the IP?
He distinguishes several possible theses : that it is “synthetic and true a-priori”, “synthetic and
provable by a transcendental argument” (which latter turns out to be little
more than “Well, it seems to work”), and:
* IP is synthetic and empirically justified.
* IP is synthetic, and, although it cannot be justified either a priori or a
posteriori, it can be vindicated.
--
John Watkins, Science and Skepticism (1984), p. 93
The verb vindicate
is slightly odd here; usually it
has moral overtones, of someone having been right against opposition or against
the odds. You verify someone’s age on his driver’s-license; you validate
a parking-stub; you vindicate a
statesman’s course of conduct.
The term justification
also has a richly complex ethico-theological usage in Christianity, quite
opaque to an outsider.
~
More fine distinctions, this one semi-defined on the fly:
One’s
degree of rational assent to a hypothesis should be controlled by its degree of
confirmation (‘confirmation’ being
understood in some quasi-verificationist
or probabilist sense).
--
John Watkins, Science and Skepticism (1984), p. 118
Watkins then spins off into the world of
proofs-and-refutations, abduction, and the like:
The
sought-for relation between e[vidence]
and h[ypothesis] is now
inverted: instead of an upward, quasi-verifying inference from e to h,
we have a downward, explanatory derivation of e from h.
--
John Watkins, Science and Skepticism (1984), p. 119
Note those squirrely “quasi”s, by the way. For all the wealth of the verificatory Wortfeld, no term seems quite to fit.
