Superposed ’twixt tick and tock

by Geoffrey Hart

Previously published as: Hart, G. 2020. Superposed ’twixt Tick and Tock. Trouble Among the Stars 5:36-38.

Tick... tock.

Between any two beats of a clock, we find ourselves in the universe of Zeno’s paradox, only for time rather than distance.

Tick... tock.

Slice each moment in half, then in half again, and so ad infinitum so that we find ourselves traveling half the remaining space between our current tick and our subsequent tock, without ever quite getting there.

Tick... tock.

And yet, eppur se muove, we get there. A quantum physicist would, no doubt, opine that Zeno’s paradox only applies to those who don’t understand the concept of the Planck distance, the smallest conceivable distance one can travel and thus, the ultimate non-theological determinant of how many angels can dance upon the head of a pin. Based on that logic, and if light really has a maximum velocity, then time can be sliced no more finely than the time required to travel the Planck distance. Ergo, at that scale, we are eternally superposed between tick and tock, never able to fully travel the distance between those states, yet still, inevitably, we or someone else will eventually observe that we traveled that distance in that time, and we become instantly tock.

Quantum phenomena break down at macro scales; they just seem to stop working when the system includes more than a very small handful of atoms. To the best of my knowledge, no observer determines my destiny. Rather, I’ve always assumed this destiny arises from statistical mechanics: average out the quantum weirdness of all those atoms and you get my behavior and that of other macroscopic phenomena. The lack of macroscopic quanta is one reason why Schrödinger chose the wrong example in his infamous thought experiment about cats in boxes. The more serious problem is that he chose his lab organism so poorly; cats do love their boxes, God knows, but they don't do superposition. Any side of the box they're on quickly becomes the wrong side.

But inside/outside is a binary statement, and nature dislikes binary: there are few blacks and whites in a world where most things, upon closer inspection, reveal more than 50 shades of grey, all of them somehow superposed, unwilling to settle on black or white when there are so many more interesting possibilities. More importantly, and despite the solipsism, I am not binary; I contain all possibilities until someone observes me, or until I observe myself, having chosen to determine my new state, thereby providing only one answer to the question of my position or momentum. (If we choose a sufficiently coarse temporal resolution, we can always know both with “good enough” precision. Humans aren’t quantum particles).

And yet, without denying any of this, I only know what I will be, what choice I made, when I observe the outcome. After I’ve already made my choice. They (the infamous, anonymous, vexatious they) suggest it’s unwise to burn any bridges in life, because you can never return across a burned bridge and it may be prohibitively difficult to build a new one to cross back above the ruins of the old. But every choice, every decision, every action... What is that if not another in an endless series of burned bridges? Good intentions, bad intentions... even a passive lack of intentions or some ill-formed greyly quantum semi-intention. It makes no difference. There’s no going back to the previous state. There always comes some pivotal moment, when having observed the possibility of a choice, one must decide or have the decision made for one. And in so doing, one burns yet another in an infinite series of bridges, the superposition collapses, and we return to tick once more, from whence we face our next tockian decision. If we took this seriously, we’d be paralyzed, caught in Zeno’s paradox, never arriving at the next instant in time. Somehow, we ignore the paradox and move on through time and space, and that comforts me as much as it discomfits philosophers.

Libraries and archives, on the other hand, both fascinate and disturb me, for they are stopped clocks, as if history were frozen in liquid nitrogen or preserved eternally in formalin. Once preserved, those facts cease their evolution through time. But even when the facts remain unchanged, ourselves and how we think of them evolve. The facts remain frozen in time; we don’t. Our time inevitably proceeds, blithely ignoring Zeno’s paradox. Which brings us back, full circle, whence we began:

Tick... tock.

Tick...?

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