Another Comment on “Physical Reversibility is a Contradiction”

Scott Aaronson, whose argument on reversibility of quantum systems I mentioned in this post, responded to it (and vehemently disagreed with it).  Here is his reply:

Your argument is set out with sufficient clarity that I can unequivocally say that I disagree.

Reversibility is just a formal property of unitary evolution.  As such, it has the same status as countless other symmetries of the equations of physics that seem to be broken by phenomena (charge, parity, even just Galilean invariance).  I.e., once you know that the equations have some symmetry, you then reframe your whole problem as how it comes about that observed phenomena break the symmetry anyway.

And in the case of reversibility, I find the usual answer -- that it all comes down to the Second Law, or equivalently, the "specialness" of the universe's past state -- to be really compelling.  I don't see anything wrong with that answer.  I don't think there's something obvious here that the physics community has overlooked.

And yes, you can confirm by experiments that dynamics are reversible. To do so, you (for example) apply a unitary transformation U to an initial state |Ψ>.  You then CHOOSE whether to
(1) apply U^-1, the inverse transformation, and check that the state returned to |Ψ>, or
(2) measure immediately (in various bases that you can choose on the fly), in order to check if the system is in the state U|Ψ>.

Provided we agree that Nature had no way to know in advance whether you were going to apply (1) or (2), the only way to explain all the results -- assuming they're the usual ones predicted by QM -- is that |Ψ> really did get mapped to U|Ψ>, and that that map was indeed reversible.  In your post, you briefly entertain this obvious answer (when you talk about lots of identically prepared systems), but reject it on the grounds that making identical systems is physically impossible.

And yet, things equivalent to what I said above -- by my lights, a "direct demonstration of reversibility" -- are now ROUTINELY done, with quantum states of thousands of atoms or even billions of electrons (as with superconducting qubits).  Of course, maybe something changes between the scale of a superconducting qubit and the scale of a cat (besides the massive increase in technological difficulty), but I'd say the burden is firmly on the person proposing that to explain where the change happens, how, and why.

I sincerely appreciated his response... and of course disagree with it!  I’m going to break this down to several points:

You then CHOOSE whether to
(1) apply U^-1, the inverse transformation, and check that the state returned to |Ψ>,

First, I think he is treating U^-1 as a sort of deus ex machina.  If you don’t know whether a system is reversible, or how it can be reversed, just reduce it all down to a mathematical symbol corresponding to an operator (such as H, for Hamiltonian) and its inverse, despite the fact that this single operator might correspond to complicated and correlated interactions between trillions of trillions of degrees of freedom.  Relying on oversimplified symbol manipulation makes it harder to pinpoint potentially erroneous assumptions about the physical world.

Second, and more importantly, if you apply U^-1, you cannot check that the state returned to |Ψ>.  Maybe (MAYBE!) you can check to see that the state is |Ψ>, but you cannot check to see that it “returned” to that state.  And while you may think I’m splitting hairs here, this point is fundamental to my argument, and his choice of this language indicates that he really doesn’t understand the argument, despite his compliment that I had set it out “with sufficient clarity.”

The reason you cannot check to see if the state “returned” to |Ψ> is because that requires knowing that the state was in U|Ψ> at some point.  But you can’t know that, nor can any evidence exist anywhere in the universe that such an evolution occurred, because then the state would no longer be reversible.  (You also can’t say that the state was in U|Ψ> by asserting that, “If I had measured it, prior to applying U^-1, then I would have found it in state U|Ψ>,” because measurements that are not performed have no results.  This is the “counterfactuals” problem in QM that confuses a lot of physicists as I pointed out in this paper on the Afshar experiment.)  So if you actually apply U and then U^-1 to an isolated system, this is scientifically indistinguishable from having done nothing at all to the system. 

or
(2) measure immediately (in various bases that you can choose on the fly), in order to check if the system is in the state U|Ψ>.  …In your post, you briefly entertain this obvious answer (when you talk about lots of identically prepared systems), but reject it on the grounds that making identical systems is physically impossible.  And yet, things equivalent to what I said above -- by my lights, a "direct demonstration of reversibility" -- are now ROUTINELY done, with quantum states of thousands of atoms or even billions of electrons (as with superconducting qubits). 

In this blog post, I pointed out that identity is about distinguishability.  I didn’t say that it’s impossible to make physically identical systems.  It’s easy to make two electrons indistinguishable.  By cooling them to near absolute zero, you can even make lots of electrons indistinguishable.  But the only way to create Schrodinger’s Cat is to create two cats that even the universe can’t distinguish – i.e., not a single bit of information in the entire universe can distinguish them.  In other words, for Aaronson's argument (about superpositions of billions of electrons in superconducting qubits) to have any relevance to the question of SC, we would have to be able to create a cat out of fermions that even the universe can’t distinguish. 

Tell me how!  Don't just tell me that this is a technological problem that the engineers need to figure out.  And do it without resorting to mathematical symbol manipulation.  I'll make it "easy."  Let's just start with a single hair on the cat's tail.  Simply explain to me how the wave function of that single hair could spread sufficiently (say, 1mm) to distinguish a dead cat from a live cat.  Or, equivalently, explain to me how the wave functions of two otherwise identical hairs, separated by 1mm, could overlap.  Tell me how to do this in the actual universe in which even the most remote part of space is still constantly bombarded with CMB, neutrinos, etc.  So far, no one has ever explained how to do anything like this.

Of course, maybe something changes between the scale of a superconducting qubit and the scale of a cat (besides the massive increase in technological difficulty), but I'd say the burden is firmly on the person proposing that to explain where the change happens, how, and why.

I strongly disagree!  As I point out in “The Invalid Inference of Universality in Quantum Mechanics,” the assumption that QM always evolves in a unitary/reversible manner is an unjustified and irrational belief.  Anyway, my fundamental argument about reversibility, which apparently wasn’t clear, is perhaps better summarized as follows:

1)     You cannot confirm the reversibility of a QM system by actually reversing it, as it will yield no scientifically relevant information.

2)     The only way to learn whether a system has evolved to U|Ψ> is to infer that conclusion by doing a statistically significant number of measurements on physically identical systems.  That’s fine for doing interference experiments on photons and Buckyballs, but not cats.