Sunday, September 27
Shadow

Letting Schroedinger's Cat Out of the Bag

skepticAt least one perennial philosophical puzzle has been put to rest by quantum theory: the question of whether events are contingent or determined. By "contingent" I mean the possibility that the future is "open" in the sense that  future events have not already been determined by antecedent conditions.  By "determined" I mean the opposite:  that future events have already been determined by past and present conditions. I have never seen any paper or book or journal article, much less a popular discussion of the subject, that actually went so far as to draw the logical inference. But the answer to the question of contingency vs. determinism implicit in quantum mechanics is: the question itself is a phony question, a non-question. Newtonian mechanics was shown to be incomplete by Einstein’s demonstration that, contrary to the Newtonian model, there are no such things as absolute space, absolute time, and absolute simultaneity. Analogously, quantum theory demonstrates that there is likewise no such thing as absolute contingency or absolute determinism. In both cases, relativity and quantum theory, the question is shown to be meaningless apart from first specifying one’s frame of reference. Let’s get at the contingency / determinism question by way of the by-now-classical thought experiment of Schroedingers Cat.

Just about everyone who has ever done any reading in popular treatments of quantum theory is familiar with Schroedinger’s Cat. (From now on, let’s call Schroedinger’s Cat the “S-Cat”.) Suppose you place a live cat in a box, and close the lid on the box. Inside the box is a vial of deadly gas, stoppered and sealed. The vial of gas is connected to a mechanism that monitors the decay of a tiny piece of some radioactive isotope. That mechanism is also connected to, say, a small hammer resting on the side of the vial. You pick at random a particular atom of that isotope, and you specify that, if and when that particular atom of the isotope decays, the detecting mechanism sends a signal to the hammer that causes the hammer to smash the vial – releasing the deadly gas and killing the cat. Suppose you also know that, after a certain period of time depending on the decay rate of the isotope, there is a 50-50 chance that that particular atom will have decayed. Let’s say the critical time is 10 minutes: 10 minutes after sealing the cat inside the box and activating the detect-and-smash mechanism, there will be a 50-50 chance that the cat will be dead … or still alive. So you seal the box and turn on the mechanism. You wait 10 minutes. Question: without actually looking inside the box, after 10 minutes, will the S-cat be dead or alive? The astonishing answer of quantum theory is that the cat is neither dead nor alive, prior to actually peeking inside the box. Or, to phrase things differently, prior to an actual observation, the cat will be in a “superposition” of quantum states: in a certain sense, 50 percent dead and 50 percent alive. Absent an actual observation, there is no state of absolutely dead or absolutely alive. The state of the cat – prior to an observation – is a kind of mixture (“superposition”) of the two. Furthermore, there is no question of refining one’s observation or of “experimental error” or any of that. The statistical formalism of quantum theory tells us all there is to know: there is no such thing as the state of the S-Cat prior to an actual observation. Beyond the equations, there is nothing more to be known. Asking if the S-Cat is really dead or alive is like asking if Oliver Twist parted his hair on the left or on the right.  Prior to an actual observation, the status of the S-Cat is contingent.

(Disclaimer:  in the description of this thought experiment, no cats, physical or "virtual", were harmed.  In fact, your Faithful Skeptic-In-Residence likes cats.) s_cat

But now let’s complicate the S-Cat experiment slightly. Instead of having only one observer, let’s have two … or, anyway, more than one. But two will suffice for illustration. We are both present when we put the S-Cat in the box with the poison gas. Then we set the timer for 10 minutes, but I leave the room. It is critical that I leave the room. After 10 minutes, the alarm sounds, but because I am absent, only you hear it. You open the box and find out if the S-Cat is dead or alive. Since I am absent when you open the box, I have no idea if the S-Cat is alive or dead. You, on the other hand, having already opened the box, know the state of the S-Cat. Suppose, finally, that – drunk with the intoxication of privileged knowledge – you decline to communicate the state of the S-Cat to me. Now – after the act of observation – let’s ask the previous question again: Is the S-Cat really alive or dead?  

It turns out that it matters critically whom you ask. You know the state of the S-Cat, because you were the one who opened the box and performed the observation. If you see the S-Cat dead, then the probability that the S-Cat is dead is identically 1.000. If you see the S-Cat alive, then the probability that the S-Cat is alive is likewise identically 1.000. On the other hand, not having participated in the act of observation, I am still stuck with the array of probabilities we started with after the 10 minutes had expired but before the observation. I still think – actually, I know because this is what the quantum formalism tells me … but this is all it tells me – I know the dead / alive probabilities are 50 / 50. For you, one of those probabilities (the one not realized) has gone to zero, while the other (the one that was realized) has become 1.000.  From your point of view, the status of the S-Cat is determined; from mine, it is still contingent.  The quantum formalism entails -- and affirms -- both answers at once. Note also that, because quantum theory tells us all that can be known about the status of the S-Cat, it does not permit one to argue that the S-Cat is "really" alive prior to an act of observation in the two-observer case any more than it permits such a conclusion in the one-observer case.  Knowledge about the status of the S-Cat does not "magically" appear out of thin air when we add a second observer to the experiment.

So … is the S-Cat really dead or alive? schrodengers-cat-500

Absent a specification of the context, of the frame of reference – whether the question is being asked from my point of view or yours – the question is meaningless. Asking Is the S-Cat really dead or alive? Is like asking How long is a piece of rope?: given the way both questions are phrased, the only correct answer in either case is It all depends. Suppose we put the S-Cat in the box, turn on the timer-and-hammer mechanism – whereupon a strategic thermonuclear war or a global zombie-virus plague, with an incubation time measured in seconds, occurs immediately thereafter, exterminating all life on earth. (In the latter case, I suppose we could all shamble off and go to work for Michele Bachmann.) Game over! Hit the showers and no towel-snapping!  In that hyper-apocalyptic case, with no observers left – I am assuming cockroaches don’t count – to open the box and ascertain the state of the S-Cat, the question Is the S-Cat dead or alive? would be unanswerable, even in principle, from any point of view – because there would be no “points of view” left. Eventually, of course, the S-Cat would die, but whether because radioactive decay caused the vial to break or for other reasons, no one would ever -- could ever -- know.

Our little thought experiment entails a couple of important consequences … (actually, a boatload more than just a couple, but given the limited space … ) … such as …

o We should be extremely cautious about drawing any conclusions regarding whether human beings’ actions are “really” free or determined – regardless of the meaning we assign to the word “really”. In the case of human behavior, we are both the S-Cat inside the box and the experimenter outside. Trying to assess whether our own actions are free or determined involves some logical paradoxes that always follow from situations involving self-reference, i.e., when the person being experimented upon and the experimenter are one and the same. This is why scientists are so reluctant to be subjects in their own experiments: it’s a matter of emotional bias, of course, but also of logical conundra. If you’re interested in this, go Google up the phrases “Liar’s Paradox”, “Paradox of Epimenides”, “Russell’s Paradox” – or, if you are really ambitious, “Goedel’s Incompleteness Theorem”. Or declare a really serious “Self-Flagellation-A-Thon” and spend a leisurely summer burrowing at tectonic-plate speed through Douglas Hofstadter’s Goedel, Escher, Bach: The Eternal Golden Braid. Or read anthologies of short stories by the Argentinian author and former head of Argentina’s national library, Jorge Luis Borges – though that latter requires some background in combinatorial math and transfinite set theory in order for you to really get it.  I would suggest starting with Borges' unforgettable and typically enigmatic short story "The Library of Babel".

o We should also be very careful about cavalierly tossing around terminology like “determinism” – even when we use such terms about the natural world in contexts where we ourselves are not the subject. To mention just one example, our own solar system has long been cited as an instance of a fully determined physical system whose future states / configurations are exhaustively predicted by Newton’s laws of motion. But it turns out that, in terms of non-linear dynamics (so-called “chaos theory”), even the sun and planets constitute a chaotic system – actually, a “multi-body problem” – whose behavior is, in the extremely long run, meaning trillions of years, strictly unpredictable. It appears absolutely stable only because, certainly on time-scales that utterly dwarf the human lifetime, it very closely approximates absolute stability. Also, on extremely fine scales comparable to the Planck length, something as apparently smooth and uneventful and static as space-time itself is most likely a seething mass of chaos with black holes and white holes and wormholes and exotic particles and “specks” of time itself constantly and spontaneously emerging from the Void of the “vacuum potential” and being dissolved back thereto. While there is no slam-dunk proof, there are strong hints that many … most? ... all? … of our most cherished physical laws are large-scale illusions resulting from the “averaging-out” of chaotic / random effects on the subatomic scale, like a coherent picture emerging from a multitude of discrete grey-scale dots. tim

o Finally, all the above should motivate us to temper all our oh-so-self-assured statements about God and Divinity with Gibraltar-sized grains of salt. Most of what we believe we know about the Universe is only a pretty good approximation valid over time-scales of age-of-the-Galaxy orders of magnitude. And that is true of the natural order. When we venture into the supernatural order, we would be well advised to do so with soft voices, downcast eyes, an embarrassed smile, and toe-scuffing modesty. Epistemological reticence is a virtue no less sublime than chastity. The thought experiment about the S-Cat, or some form thereof, should be taught at denominational seminaries and theological schools.

That could be the start of a new theological discipline: S-Cat-ology.

Yeah … OK … sorry … . Bye.  

James R. Cowles

9 Comments

  • Mind blowing and magnificent! Talk about putting our lives in perspective! I’d say you can take this … potential / 50-50 / maybe / take it or leave it / it is or it isn’t / it all depends … debunking of all developed theorem of life, the universe and everything and … well … debunk it or accept it with a shrug of the shoulders and say to yourself: “does it really matter what is happening in our own solar system, our own galaxy or in one at the other end of the universe or what will happen to it all in another billion or a trillion years time?” Should it bring us back to a state of mindfulness of the present, of who we are now and how we should stop running around in mad circles trying to build our little empires, stand still and stare at the wonder of it all…?

  • **** YES! YES! YES! **** a ba-jillion times yes! (Hope I didn’t lose you in the technical language … 😎 … ) “The universe is not only stranger than we imagine, it is stranger than we CAN imagine” — J. B. S. Haldane

  • […] In the wee small hours of one morning, three years ago, I had one of those elusive moments of clarity; in fact, one of those moments so aptly described by Kona Macphee on the introduction of her excellent blog site in December 2010. Apart from the lack of sleep, this was a consequence of watching a documentary about the universe – always guaranteed to stir my brain into action – combined with thinking, as I am wont to do with my recently discovered propensity for getting in touch with my literate side, about the human condition, our general outlook on life and how we deal with it; pessimism and a lack of eagerness on the one hand; optimism and enthusiasm on the other. It is a perspective, in other words, but one that fills me, not only with hope, but also with wonder, especially when you view that perspective in the dramatic light of the universe. This essay seems also to tie my thoughts in rather well with those, recently published on Terri Stewart’s excellent and stimulating ‘Begin Again‘ blog, of J R Cowles in his mind-blowing essay on Schroedinger’s Cat. […]

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