Balls, Strikes and Eigenfunctions

I’ll explain this well; or I won’t.  There’s a decent probability of either outcome.  You might understand this; you might not.  The outcome might matter.  But it might not.  Regardless; Enjoy!  (Or not.)

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I’m no physicist, and I certainly have mathematical limitations.  But I love reading gift books, and I was recently fortunate to receive “In Pursuit of the Unknown: 17 Equations That Changed the World” by Ian Stewart (2012).  It’s exactly my kind of book; imagine a proper and challenging read for a liberal arts course in a given subject for a non-major.  Demanding enough to require and retain my attention, and yet not so far over my head that I drown; not so much about the subject as about the connections of the subject to others.  Reading such a book will remind me of much I know; confirm much that I don’t know; open my eyes to some wonder; and generally humble me.  Mostly, I’ll be left in amazement of what is (thought to be) known; and the simple fact that we figured (an approximation of) it out.

I’d pretty much enjoyed my journey through a dozen or so equations when I came to Chapter 14: Quantum Weirdness.  At this point in the book, I was definitely out of my comfort zone (mathematically), but because it’s not really a math book, I was able to stay with it.  I’m familiar enough with the particle/wave dual nature of light (and matter?) and rudimentary quantum mechanical concepts to still have been reasonably receptive to what the author was saying…when he really started talking to me.  A parameter of interest (something worth knowing or observing) has some relationship in space and time.  Accounting for either space or time; you can interpret the effect of the other on that parameter.  (You might say that I am uncertain about this and that I only understand this marginally; but I’m probably explaining it even less effectively.)  Each of these space-time relationships for a parameter is called an eigenfunction; and reality (or at least a quantum approximation of reality) is the superpositioning (supposition?) of multiple eigenfunctions (as many as you need, recognize, or can handle.) 

Which brings me to baseball.  It’s my favorite team sport, in my estimation the most beautiful of team sports, and has been a constant thread through my life.  One thing I like about baseball, is that it is not uncommon for a game to offer something you’ve never seen before, or a situation you’ve not yet encountered, which is pretty outrageous given the amount of baseball that’s been played, or that I’ve watched. 

But at the core of the game, consider a single pitch or play.  Ball or strike? Out or safe?  I’ve long been perplexed by the numenon of the issue.  Is the truth of the distinction between ball and strike (out and safe) based on physics and location; or by the umpire’s perception and call?  I don’t know.  I know umping is more difficult than playing; and that I was a better player than umpire.  But what is the truth for a given pitch, or a given play?  Slow-mo HD can (sometimes) provide an interpretable approximation of what happened; but The Call has (until recently, at least, with the advent of certain allowed reviews at the MLB level) always defined the outcome; and so I guess The Call is The Truth.  After all, that’s what gets recorded in the scorebook.

And yet, I know that during a certain game in the summer of 1982, with my team on a serious run for the playoffs, we opened the top of the first with a single, a stolen base, and another single.***  So I stood at first, having driven in the game’s first run, and received the steal sign.  I took off with the pitch and slid head-first into second base.  Just after my hand touched the base (and take this from me, I was closest to the play), the second baseman swiped my calf; and I was surprisingly pronounced “Out!”  Per physics (and what I would consider to be reality), I was clearly “safe”; but with the umpire’s pronouncement, I trotted off the field after a brief, polite discussion.  I was, definitively, “Out.”

The exact scenario (amazingly enough) repeated itself a couple of innings later: single; stolen base attempt; beat the throw; trot off the field, having been called “Out!”  So with the score tied in my last at-bat of the game, I simply broke it open with a bases-clearing double.  At least I’d avoided the possibility of getting thrown out at second again; I know Coach K would have sent me.

Similarly, as an umpire, I’ll simply apologize for ending a team’s season with a called strike; on a full count; with the bases loaded and the tying run on third; after a pitch in nearly exactly the same spot as the previous pitch, which I had declared to be “Ball 3!”  Certainly the last pitch was too close to take, but it could have been a smidge low or outside.  Regardless, I was seemingly powerless as my right arm raised itself and I declared “Strike 3!”  It was a strike because I proclaimed it so; but other than that proclamation, was it any different than the pitch identified as “Ball 3?”  In my defense, I had no interest in these outcomes; I wasn’t knowingly biased; and each of these calls almost surprised me, as if they’d made themselves.  Like I said, umpiring was way more difficult than playing.  But again, what represented the core truth of these plays?  The physical events, the perception, or the utterance?

Back to Chapter 14; each eigenfunction explains only a portion of a system; and in examining any single component, you disturb your ability to analyze other components contemporaneously.  Here we have a logical mathematical construct of some utility, and yet if it describes something scientifically demonstrated to be non-observable (or measurable), does it really have any valid scientific meaning?  Does it really matter what actually happened in a baseball play if it is perceived as (or declared to be) “Ball!  Strike!  Fair!  Foul!  Safe! or Out?” 

Well, apparently “The Copenhagen Interpretation” of quantum measurement is something along the lines of this; while there’s a probability of a parameter having one value or the other, instantaneous observation of the parameter defines (“collapses”) the state of that parameter.  So while we can all accept that a cloud of probable states surrounds (defines?) “some being”, that pattern of statistical probability is not a real thing, but rather a likely explanation of that being.   The Copenhagen Interpretation of an observed parameter defines the being’s state.  The Observation simply Is.  It was “Strike 3” because that’s how I saw it, and that’s how I called it. So it was, simply, Strike 3.

This Interpretation could be accepted as either Convenient or True.  You might not be able to tell me which.  Because one of the folks most disturbed by its collapsing consequences was a Giant in the Field.  To convey his concerns, Physicist Schrodinger developed the Thought Experiment that became known as The Cat in the Box.  Accepting that radioactive decay is a quantum event; and that an atom is either “decayed” or “not decayed”; that an individual atom’s decay is a probabilistic event, but recognizing that the individual decay could, in fact, happen immediately or belatedly; and further accepting that a cat is either “alive” or dead”; imagine a mortal cat in an isolated box, co-existing with a radioactive source and a flask of poison.

Simple enough; upon decay, the flask will release the poison; the cat will die.  We’ll disregard resistant flasks, poorly-concocted potions, hearty cats, other causes of feline death, or inaccurate observations.

Knowing the physics of our radio-active source, we know the probability at any given time (following the final packaging of the system) of decay; and so we know the probability of the cat being instantaneously alive (or dead) when the box is opened and the cat’s state observed.  The cat will have a defined state; it will be either wholly alive or dead; it won’t be partially dead or probably alive.  And the observation of the cat defines the cat’s state at the time of the observation.  Repeat the experiment, and sometimes the cat is alive; but sometimes the same cat is dead.

Apparently this all works out mathematically (and so is super-attractive to the quantum folks), except for (possibly) the collapse.  Schrodinger used his cat to propose the mathematical fallacy of the collapse; and yet everything works out so conveniently that the concept of the simultaneously alive-and-dead cat became an acceptable model at macroscopic scales.  The absolute truth of the cat’s state depends on the observation.  The result of a dead cat observation is equally as valid as observing a live cat.  Neither observation is more correct.  The cat’s state simply is, as observed.  Ironically, Schrodinger’s thought experiment has been held up in support of quantum eigenfunctional representations of our world.

From the web!

Bottom line; since an observation has a probability (p) of landing in a given state, then there is another probability (1-p) of landing in the alternative state.  That state’s existence is equally valid, and so a legitimate consequence of all this is that in an alternative universe, that alternative state was observed.

It really was Strike 3!  But more interestingly, I was safe at second; just not in this universe.  But things have still worked out pretty well here, so I’ll let this play go.  Similarly, I can see that, once again, results don’t matter so much as our participation in the process.  So even if I don’t have the math or the physics quite right; I probably do elsewhere!  Here and now (which is really all I have access to), I can recognize the value of simply receiving the gift, reading the book, pondering stuff and writing this. 

*** Sorry about the borish details, but this probably was my greatest game, at my highest level of competition, ever.  And on both sides of the field; I threw two runners out at home, too!  Now, to be completely honest, my heroics were all the more meaningful because I had committed an error at second base that allowed the tying run to score late in the game, in the half-inning before my last at-bat.