Many years ago, I wrote a sotie which began:
<< We know, on scientific grounds, that penguins cannot exist.>>
https://worldofdrjustice.blogspot.com/2010/12/on-existence-of-penguins.html
That was in essence simply a transcription of C.S.Lewis’s Miracles into the key of penguin. It has been used, on occasion, in the classroom, at the intersection between Christianity and folklore.
More substantively, for a substantial period of modern physics (the Maxwell’s Equations golden-age), one could with even greater cogency have proclaimed:
<< We know, on the firm ground of physics, that atoms cannot exist.>>
BLUF: It was a firm prediction of the theory of the time, that electrons circling the nucleus should radiate-away their energy, and the whole rickety assemblage disappear in a puff of fairy-dust, before you could say “Jack Robinson”.
It was a very serious challenge to theory, one which most practicing physicists basically put aside in their minds, in the interest of simply getting on with whatever it was they did in the lab, hoping that someday it would all be put right. By someone.
In time, it was put right; but this required an entirely new, astonishing, still-undigested and perhaps indigestible new intellectual development: Quantum Mechanics.
Then for a while, all was well, practically and philosophically. Notable new developments were achieved within the new framework. Meanwhile, sheep grazed; farmers tilled the fields; lass and lad fell in love and wed, bringing forth those astonishing miracles that we call children.
And now, this:
In his very readable classic, The Emperor’s New Mind, mathematician/physicist Roger Penrose examines “the question of stability: whether, as t increases [i.e., as time passes], the region R remains localized, or whether it begins to spread out over the phase space.” (p. 180).
Think of R as simply The Way Things Are in Mr Rodgers’ Neighborhood, one fine autumn day. We expect things to change a bit, as the afternoon wears on: a few leaves fall, Mr Rodgers takes out the recyclables; but we don’t expect the leaves to shoot towards the sky, or for Mr Rogers to be himself recycled and emerge a dragon: which is basically what can happen if matters spread indefinitely over phase-space. In other words, no matter how stable that patch of God’s earth may seem at a given moment, over time things should go all higgledy-bobbledy.
Concretely:
“We think of R as being dragged along the Hamiltonian vector-field as time proceeds. … What can be said about Hamiltonian systems generally? Do regions in phase space tend to spread with time or do they not? It might seem, that for a problem of such generality, very little could be said.” (p. 181)
(Pause, and tuck that apophthegm away in your cerebral chambers, for it applies profoundly to a host of problems, well beyond physics. “It might seem, that for a problem of such generality, very little could be said.”**)
However, it turns out that there is a very beautiful theorem, due to Liouville (1809 - 1882), that the volume of any region of the phase space must remain constant under any Hamiltonian evolution.
Saved! Hooray! Thank’e kindly, Mr Liouville. -- The farmer returns to his plow with a will, whistling.
But hark -- Lo, on the horizon, skies darken, and a rumbling may be heard from afar. For:
Despite the fact that Liouville’s theorem tells us that phase-space volume does not change with time-evolution, this volume will normally effectively spread… (p. 182)
That is, it splits into many strands, and those into strandlets -- all the while summing to the original constant in volume, but losing all sense of neighborhood.
And here’s the punch-line, the punch in the stomach:
This spreading effect in phase-space has another remarkable implication. It tells us, in effect, that << classical mechanics cannot actually be true of our world! >> (p. 183)
(Schrecklichkeit-italics in original.)
Now, there is a twist to this new alarm. The conundrum of the stability of atoms applied to all atomic matter whatsoever. But this new one most acutely concerns only solids -- fluids (liquids and gases) really do slosh around and spread out. QMech once again to the rescue? “Quantum theory is needed in order that the actual structure of solids can be properly understood.” (p. 184) That sentence might, to anyone who seeks to relax back into intellectual slumber, seem reassuring; but note its successor: “Somehow, quantum effects can prevent this phase-space spreading.” (Sturm-und-Drang-boldface editorially added.) Somehow. It’s not in the bag. Something must prevent prevent the spreading, but that something might turn out to be a whole new theory which we do not yet glimpse.
*
I have previously posted about the existence, and relative stability, of solids: specifically, of coffee-cups (without the benefit of whose nestling, fresh-brewed beverage, this essay could not have been born). I came to the conclusion that this matter was strictly speaking insoluble, but for certain assumptions, both scientific/metaphysical and (in one case) theological.
So, brew yourself a strong one -- no decaf! -- and check it out:
https://worldofdrjustice.blogspot.com/2014/12/a-new-proof-of-existence-of-coffee-cups.html
*
** A couple of concrete examples, from Jerry Fodor What Darwin Got Wrong (2010):
Extreme context-sensitivity of the ways of getting rich make it unlikely that there could be a theory of ‘getting rich’ per se.
Sociologists and political scientists please copy. -- There is ever a temptation, among practitioners of factually non-nomological sciences, to overreach in this way.
That observation was simply an accessible, spoonful-of-sugar preface to his real target: Darwinian explanation and its discontents. As,
Size affects fitness, but it does not follow that there are laws that determine the fitness of a creature as a function of its size.
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