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.)
*****
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.
