A Usenet post on the interpretation of quantum mechanics, with extensive commentary

One day, paul@mtnmath.com (Paul Budnik) wrote:

McIrvin (who is a supporter of Everett's interpretation) was objecting to any objective events and wave function evolution that is limited by such events.

The "Everett interpretation" is the one commonly called the "many-worlds interpretation," though some have argued that there is a difference. The idea, basically, is that reality is described by a single, global wave function that does not collapse when there is a measurement event. When a system is in a superposition of states with different values of some observable quantity and you measure that, you become superposed too, whether you know it or not. The world could be in a superposition of states in which vastly different histories occurred. Whether or not these are properly called "parallel worlds" is a matter of debate...

(Budnik was arguing here in favor of a particular interpretation in which the wave function does collapse.)

Then egreen@nyc.pipeline.com(Edward Green) wrote:

I'd like to hear his slant.

So I wrote:

I suppose it's been a while since I wrote this all down. Maybe there should be something about my opinions on my Web page.

The way I once put it was, "I'm a supporter of the Everett interpretation, and I don't even believe it." I don't think that strict Everettism is the only or even the best way to view QM, but I think that it isn't stupid and that contemplating it, especially by reading Everett's paper instead of others' sensational glosses on it, is a salutary thing to do.

My actual position is that I don't know what constitutes absolute reality and what doesn't, but I do know that if you use quantum mechanics to calculate conditional probabilities, and do not assume that any kind of other collapse process occurs between the events for which you're calculating the conditional probability, you will always get the right answer. At least, this is supported by every experiment I know of on the subject, including this most recent one.

This was an experiment in which an atom was put in a superposition of states in which it was at two different positions in space. The experiment is described in C. Monroe et al., Science, 24 May 1996.

If the intermediate process involves another macroscopic measuring apparatus, then the effect of that apparatus, when properly included in the wave function, is sufficient to make the conditional probabilities consistent with an interpretation in which "collapse" occurred in the meantime. The apparatus, and the people reading it, may be described as "superposed" in the wave function, but the effects of that superposition are in practice impossible to detect.

I should give an example, and I didn't in the post. Suppose that you have a box containing a silver atom whose spin points to the left. Then it is in a superposition of spin-up and spin-down states. The box also contains an apparatus, a piece of laboratory equipment of everyday size, that is capable of detecting and recording the difference without doing anything violent to the atom (nothing in QM forbids this).

At time t₁ you close the box, at time t₂ the apparatus measures the spin, and at time t₃ you open the box and look inside. A "collapse interpretation" of quantum mechanics, such as taught in many classes on QM, would argue that the wave function of the system instantaneously collapses at time t₂ into a state in which the atom is spin-up or spin-down.

But if you want to calculate the probability of a certain spin-up/spin-down state at time t₃, you do not have to assume this! Furthermore, even if the detector is in a superposition of "atom is spin-up" and "atom is spin-down" states, the superposition has no observable effects. You can't devise a second detector that will tell you, by examining the atom and measuring apparatus at time t₃, that they are in an "atom was spin-left at time t₁" state. The phase information that would reveal the identity of the previously-spin-left state was hopelessly scrambled by the interaction with the apparatus back at time t₂, since a beyond-astronomical number of atoms in the measuring apparatus are now in a superposition of very different states that are correlated with the spin-up/spin-down state of the atom. Detecting the superposition would involve somehow doing separate interference experiments on every one of the measuring apparatus's atoms, taking care not to observe it normally in the meantime, lest your state become badly correlated with that of the apparatus! It's possible in highly abstract principle, but impossible in practice. Of course, you know that the atom was originally in a spin-left state because you set it up that way and measured it at time t₁, but, again, that's the case whether or not any collapse really occurred at time t₂.

I wrote:

Similarly, as long as you believe that our non-delusional sensations ought to correspond to some kind of physical detection process (an important, and, I suppose, somewhat speculative proviso) there's no way a superposition in our wave function could cause us to somehow "feel superposed."

That is a common objection, which I support, to Wigner's argument that consciousness must somehow cause collapse, known as "Wigner's friend." Wigner, avoiding the issue of cruelty to Schrödinger's infamous cat, imagined putting a human observer in the box with the quantum system and the (nonlethal) measuring apparatus. In terms of my example above, at time t₃, Wigner opens the box and asks his friend what he experienced, and the friend doubtless reports nothing out of the ordinary: the atom turned out to be spin up or it turned out to be spin down, and at no time after time t₂ did Wigner's friend feel uncertain about the outcome. Wigner argues that if his friend's reports are at all correlated with what his friend really feels, then he cannot possibly be in a superposition of radically different states after time t₂.

But this outcome is precisely what QM predicts even if there is no collapse; the state might be superposed, but in the time immediately after time t₂, any traces of the superposition rapidly become unmeasurable due to the scrambling of relative-phase information. So it's hard to see any way that the friend could report a funny feeling from quantum superposition, unless some sort of force beyond physics affects his phenomenal behavior. For all I know that might be the case (though admittedly I doubt it), but assuming it is hardly a convincing way to shoot down a QM interpretation.

Reasoning much as Wigner did: If the friend's reports correspond to his subjective feelings, then he could be in a superposition of states in which he feels quite definitely that the spin was up, and in which he feels quite definitely that the spin was down! He feels no uncertainty about the issue whatsoever. But, as I said, I don't think the wave function is necessarily the true reality here; all QM really tells you is how to calculate the probability of one phenomenal outcome or the other.

I wrote:

And in all cases that are simple enough that we can detect effects of the superposition, lo and behold, it's there in the data-- no fundamental collapse process destroys it.

Suppose, for instance, that our measuring apparatus is not a big piece of laboratory equipment, but a system of only a few particles that is somehow affected by the spin state of the silver atom. Then we might actually be able to disentangle the phase information and detect the superposition--what's called a "quantum eraser" experiment, since the "measurement" is effectively erased in the process. The equivalent of this experiment has been done--not with the setup I've described, but something analogous--and, sure enough, there are measurable effects of superposition. QM time evolution, unmodified by any extraneous collapses, gives the right answer.

Note that I've explicitly included the probabilistic nature of QM in my "interpretation," and made no particular postulates about the wave function of the whole universe being the true reality, or anything like that. So it's not pure Everett in that sense. But Everett importantly recognized that you are never forced to include a collapse in the middle of a wave-function evolution at a place where you do not want to calculate any probabilities. (John Baez used to proselytize for a "shut up and calculate interpretation" much like this one before he got bored with it; the idea really goes back to some of von Neumann's ideas, and in a way it is apparently more like the original Copenhagen school of thought than like Everett.)

Baez's version also incorporated some interesting borrowings from Bayesian statistics. He keeps threatening to write a book about it someday when the spirit moves him; I'll let him explain it then.

Newspapers tend to report the results of these fundamentals-of-QM experiments as if they were shocking and inexplicable threats to known physics. It's gotten to the point where whenever I read the introduction to one of these articles, I close my eyes and predict what the reported results will be, and I'm always right. The results are always consistent with simply taking quantum mechanics at face value.

These experiments are valuable because they push further and further back the realm in which interpretations with a fundamental "collapse" process have to place their collapse. Eventually it may get to the point where the only allowed collapse is something that simply has no practically measurable effects, in which case the distinction between the interpretations will be pushed entirely into the realm of metaphysics. I have nothing against metaphysics, it's healthy and fun, but it's not the same thing as physics. We're not quite there yet, though.

Meaning: we're not yet at the point where the difference between interpretations is entirely metaphysical! I should mention, though, that most proponents of collapse seem to have anticipated this kind of experimental result, and believe in a form of collapse that is sufficiently hard to trigger that the difference from a collapse-less interpretation probably is entirely metaphysical. To them, collapse only occurs in situations where a macroscopic, thermodynamically irreversible measurement occurs, or a conscious being makes an observation, or something similarly macroscopic happens.

To sum up my own position, I'm a pragmatist about this. I believe that QM is a very accurate description of observable phenomena. It gives you procedures for calculating conditional probabilities that correspond to experimental data with fantastic precision. Furthermore, if you are calculating the probability of state B at time t_B given state A at earlier time t_A, at no time are you forced to assume that the quantum-mechanical wave function undergoes anything other than smooth, linear time evolution, with no jumps or collapses whatsoever, between t_A and t_B. This is true even though, in the meantime, it may seem to describe a superposition of vastly different macroscopic states or histories.

Does that really mean that there are parallel universes with alternate histories, or that the world goes into a superposition of macroscopically different states when you make a quantum measurement? I don't know, and I don't think it's necessary to assume anything one way or the other in order to use quantum mechanics.

It may seem to you that I am caught in a contradiction here, because I have no objection to talking about the probability of state B as if, ultimately, it definitely obtains or does not obtain--yet if somebody at some later time were to calculate the probability of some other state C, he or she would have to include both possibilities in the intermediate evolution of the wave function! It's only a contradiction, though, if you believe that the wave function is the one true description of reality. All I know is that it is the only thing that enters into the calculation of conditional probabilities. The rules of quantum mechanics seem to allow treating events one way when they're the initial or final states in a conditional-probability calculation, and another way when they're intermediate steps. What this means, I don't know.

However, I agree with the Everettists that it is extremely premature to claim, as some do, that the phenomenon of wave function collapse requires a modification of the calculational rules of QM itself. I haven't seen any evidence that there is a phenomenon of collapse at all.