Tuesday, December 16, 2014

Infinite Regress

Achilles Penthesileia BM B209  
Some of the arguments for the existence of God as a First Cause depend on the assertion that there can be no infinite regress of causes.  It is safe to say that although such an assertion is plausible, it is not self-evident. I thought it would be just as well to attempt to construct an example.  My attempt fails, but it is an interesting failure (at least to me).

The idea is this:  Achilles throws his spear, which we will take to be made of continuous, infinitely divisible matter.  (Sorry Democritus!)  In making his through, he obviously does not hold the spearhead directly; he holds the spear by somewhere near the middle of the shaft, but the push of his hand is ultimately responsible for the motion of the spearhead.  Ultimately responsible, but not directly responsible!  We can divide the shaft between his and and the spearhead (of length L) into halves:  Achilles pushes the first half, the first half pushes the second half, and the second half pushes the spearhead.  We can divide this again, so that now we have quarters:   Achilles pushes the first quarter, which pushes the second quarter, which pushes the third quarter, which pushes the fourth quarter, which pushes the spearhead.  We can continue, a la Zeno, to divide the shaft indefinitely, but each time we do, there remains a well-defined chain of causes, with the last piece (ending at distance L) being pushed by the penultimate piece (ending at distance (1 - 2-N)L).  Isn't this an example of an infinite regress?

Well, no.  It is a finite regress of arbitrary length, and no one has ever had a problem with finite (though long) regress.  We are safe as long as the number of divisions of the shaft is an arbitrarily large but finite number, but what happens if we do what the Greeks would never feel comfortable in doing and "complete" the infinity of divisions? Then the last piece, at distance L, will be pushed by the penultimate piece at distance (the largest rational number less than 1)L.  But there is no such thing as "the largest rational number less than 1".

Of course, another way to avoid a first cause is to have a closed causal loop.  Those may be possible in General Relativity, but it is highly doubtful that they can describe the universe as a whole.  Worse, although the cause of each element in the loop may be well defined, the loop as a whole seems very ... artificial, a thing even more unsatisfying and in need of an explanation than a chain of events going back into the infinite past (with apologies to the Big Bang).

Thursday, December 4, 2014

Elgin Marbles on the Moon

Ac marbles
Author unknown [GFDL or CC-BY-SA-3.0], via Wikimedia Commons

Last night I dreamed that there were huge carvings on the surface of the moon.  They were similar in style to the Elgin Marbles, but each figure was at least 1 mile high, and were easily visible from Earth through sufficiently powerful telescopes.  Although there were heroes, centaurs, etc., the carvings did not correspond to any known characters or stories from any mythology; I had the vague feeling these might correspond to a mythology from the age of the Titans, before Zeus overthrew his father.  There was an accompanying inscription in very old Greek; a few people could read it, but I never found out what it said.  The whole display was clearly meant to be seen from Earth.  Naturally enough, there was a mission planned to visit the carvings in the hope of learning something about how they had been made, whether this meant that people had once lived on the moon and it once had (surprisingly) an atmosphere, etc. 

My dreams are still better than SyFy made-for-TV movies.

Wednesday, December 3, 2014

Is String Theory Too Timid?

Lately I've been watching the series of YouTube videos put out by Stanford University in which Leonard Susskind lectures about string theory and M-theory.  He really is an excellent lecturer, so even though I have had little cause to use advanced quantum mechanics over the past two decades, let alone particle physics or string theory, it's easy to follow his lectures.  (They are not lectures for the general public, though, because they do require having had at some time a pretty good background in physics, but they are OK for an advanced undergrad or someone who is very rusty.)

I have tended to be a skeptic regarding superstrings, mostly because it is too often presented to the general public in exactly the same way ancient Greek philosophers presented their physics theories:  long on an appeal to what a beautiful idea it is, but almost completely lacking any evidence from experiment or observation.  That is very bad form for a scientist!  It hasn't helped that some of the theory's proponents have even suggested that perhaps it is the ONLY possibility, so that "God had no choice" but to build a universe out of superstrings -- a statement that is at least borderline blasphemous and which displays a mind-boggling absence of imagination.  Happily, though, the actual science behind string theory is not quite so muddle-headed as the popularizations. 

One thing that is still surprising, though, is how reliant string theory seems to be on physics that is backed up mostly by our experience with molecules, atoms, and nuclei.  In particular, Susskind starts off with a string of masses connected by springs, considers that string in a reference frame in which it is moving close to the speed of light, then applies the standard techniques to quantize it.  This is all pretty basic stuff, very similar to what is used in the Debye model of a generic crystal.  The only thing is, he wants this to apply all the way down to the Planck scale.

To me that seems to be unjustified optimism.  Quantum mechanics has of course been phenomenally successful in explaining or predicting all kinds of phenomena, but there are, after all, a number of foundational problems about it, and it requires a huge jump to go from they physics of hadrons and mesons to the Planck scale.  Somehow, it seems likely to me that along the way, we will have to replace Quantum Mechanics itself with something new that will be even weirder.  Quantum Mechanics would remain as a "low energy" approximation for whatever comes next, just as Newtonian Mechanics remains as an approximation for Quantum Mechanics.