Schrödinger’s Chef: Quantum superposition and the result-less-ness of unperformed experiments

Curiously, Schrödinger’s cat came to mind one night when I was getting dinner together from a kit my kid gets in the mail every week.  I had asked whether I should add the basil-and-caper sauce on the pork chop.  Simple question with a yes/no answer.  Instead, the reply was, “If you like.”  Four times I asked, and four times I got, “If you like.”

This led me to think of Asher Peres’s influential paper on quantum mechanics, which stated, “Unperformed experiments have no results¹.”  Though I was getting nowhere with the pork chop, it did occur to me that this situation was a cooking superposition.  The pork chop could only have two states: 1 = sauce or 0 = no sauce.  After preparing the pork chop, I made a conscious decision (the experimental addition of sauce), but before the preparation, I was in a superposition.  There is no decision to be made; only the observation—an unprepared pork chop has no results.  But was it like a quantum superposition?

The situation may be like being in Paris on the Rive Gauche at a restaurant with a famous but indecisive chef.  The waiter comes to your table, and you ask, “How does the House pork chop come, with sauce or without?”  The waiter gives you a one-shoulder shrug but no words.  So, you ask again.  His reply is, “The chef does what the chef does.  About half the time, it comes out with the sauce; the other half of the time, it does not.  I swear, the chef does not even know what he will do until he does it.”   You ask, “Is it worth it?”  The waiter says, “You will have to order it to find out.”

What is quantum superposition like?  Asher Peres’s paper is the key.  In it, he confirmed Bell’s Theorem,² which crushed the idea posited by Einstein, Podolsky, and Rosen (EPR).  EPR claimed that quantum mechanics was incomplete and that there had to be some hidden variables.  Essentially, EPR said that quantum mechanics makes no common sense; the state (cat or pork chop) had to be already determined (dead or alive, sauced or without sauce) before you viewed it, so there must be something else going on.

In any macroscopic, classical state, there is an underlying definiteness—the Quantum Chef does something, and the cat is really alive or dead, and certain of these states are irreversible (alive or dead).  Not so with, for example, the spin states of electrons in an orbital or any other state governed by the Uncertainty Principle⁴.  There is no definiteness in the quantum state before it is measured; again, unperformed experiments have no results.  The way quantum mechanics physicists say it is that the traditional interpretation of quantum mechanics rejects counterfactual definiteness⁵.   For example, you can measure the spin state of one of an electron pair and obtain the answer, but only then can you infer the spin state of the other.  There is no experiment on the second electron until you measure the first. 

This idea of result-less-ness of an “unperformed experiment” is not so unfamiliar to chemists.  I remember a student with a long-ago forgotten chromatography experiment asking what to do.  I gave him instructions, and he asked, “So, what is going to happen?”  I told him, “I don’t know.  If I knew, we—read 'you'—wouldn’t need to do the experiment.”  Or perhaps the experiment determining the results is more like football, where they say, “Play the game.”  The macroscopic uncertainty is probed by experiment or competition to discover the hidden.  In one, chromatography has values that are hidden from the chemists, and in the other, football has a host of variables to make prediction lucrative but impossible. 

The freaky part of quantum mechanics is that there are NO HIDDEN VARIABLES underlying it.  The experiment determines the results.  Obviously, the rules of quantum mechanics are adhered to, but the result of the measurement (the macroscopic probe of the quantum space) is unknowable until it is performed.  Bringing in different versions of result-less-ness—cat, cook, chemist, competition—gives the instructor a path to discussion with the students about the difference between the uncertainty in various macroscopic phenomena and quantum mechanical uncertainty. 

There is delight and frustration in quantum mechanics.  Delight in how much and how well it explains the physical world, but frustration that it does not seem to follow Common Sense, a Common Sense rooted in the macroscopic world.  This frustration is part of the heritage of every student and instructor of General Chemistry, and hopefully, this blog post will bring a little delight to quantum mechanics. 

Let me make this clear, despite the failure of EPR, Einstein is still my hero, but he was always frustrated by his insistence on following his incredible Sense of Nature.  This sense led him, for example, through the invariant speed of light to Special Relativity and General Relativity.  It failed him, though, as he could never acknowledge there was a different Common Sense to the quantum world.  We need not judge him too harshly, as the resolution of the two types of Common Sense between Gravity and Quantum Mechanics remains the unsolved challenge of our age.