Earlier, I promised some discussion of Andrew Steane‘s new paper: Context, spactime loops, and the interpretation of quantum mechanics. Whilst it is impossible to summarize everything in the paper, I can give a short description of what I think are the most important points.

- Firstly, he does believe that the whole universe obeys the laws of quantum mechanics, which are not required to be generalized.
- Secondly, he does not think that Everett/Many-Worlds is a good way to go because it doesn’t give a well-defined rule for when we see one particular outcome of a measurement in one particular basis.
- He believes that collapse is a real phenomenon and so the problem is to come up with a rule for assigning a basis in which the wavefunction collapses, as well as, roughly speaking, a spacetime location at which it occurs.
- For now, he describes collapse as an unanalysed fundamenally stochastic process that achieves this, but he recognizes that it might be useful to come up with a more detailed mechanism by which this occurs.

Steane’s problem therefore reduces to picking a basis and a spacetime location. For the former, he uses the standard ideas from decoherence theory, i.e. the basis in which collapse occurs is the basis in which the reduced state of the system is diagonal. However, the location of collapse is what is really interesting about the proposal, and makes it more interesting and more bizzare than most of the proposals I have seen so far.

Firstly, note that the process of collapse destroys the phase information between the system and the environment. Therefore, if the environmental degrees of freedom could ever be gathered together and re-interacted with the system, then QM would predict interference effects that would not be present if a genuine collapse had occurred. Since Steane believes in the universal validity of QM, he has to come up with a way of having a genuine collapse without getting into a contradiction with this possibility.

His first innovation is to assert that the collapse need not be associated to an exactly precise location in spacetime. Instead, it can be a function of what is going on in a larger region of spacetime. Presumably, for events that we would normally regard as “classical” this region is supposed to be rather small, but for coherent evolutions it could be quite large.

The rule is easiest to state for special cases, so for now we will assume that we are talking about particles with a discrete quantum degree of freedom, e.g. spin, but that the position and momentum can be treated classically. Now, suppose we have 3 qubits and that they are in the state |000> + e^i phi |111>. The state of the first two qubits is a density operator, diagonal in the basis {|00>, |11>}, with a probability 1/2 for each of the two states. The phase e^i phi will only ever be detectable if the third qubit re-interacts with the first two. Whether or not this can happen is determined by the relative locations of the qubits, since the interaction Hamiltonias in nature are local. Since we are treating position and momentum classically at the moment, there is a matter of fact about whether this will occur and Steane’s rule is simple: if the qubits re-interact in the future then there is no collapse, but if they don’t then the then the first two qubits have collapsed into the state |00> or the state |11> with probability 1/2 for each one.

Things are going to get more complicated if we quantize the position and momentum, or indeed if we move to quantum field theory, since then we don’t have definite particle trajectories to work with. It is not entirely clear to me whether Steane’s proposal can be made to work in the general case, and he does admit that further technical work is needed. However, he still asserts that whether or not a system has collapsed at a given point is spacetime is in principle a function of its entire future, i.e. whether or not it will eventually re-interact with the environment it has decohered with respect to.

At this point, I want to highlight a bizzare physical prediction that can be made if you believe Steane’s point of view. Really, it is metaphysics, since the experiment is not at all practical. For starters, the fact that I experience myself being in a definite state rather than a superposition means that there are environmental degrees of freedom that I have interacted with in the past that have decohered me into a particular basis. We can in principle imagine an omnipotent “Maxwell’s demon” type character, who can collect up every degree of freedom I have ever interacted with, bring it all together and reverse the evolution, eliminating me in the process. Whilst this is impractical, there is nothing in principle to stop it happening if we believe that QM applies to the entire universe. However, according to Steane, the very fact that I have a definite experience means that we can predict with certainty that no such interaction happens in the future. If it did, there would be no basis for my definite experience at the moment.

Contrast this with a many-worlds account a la David Wallace. There, the entire global wavefunction still exists, and the fact that I experience the world in a particular basis is due to the fact that only certain special bases, the ones in which decoherence occurs, are capable of supporting systems complex enough to achieve conciousness. There is nothing in this view to rule out the Maxwell’s demon conclusively, although we may note that he is very unlikely to be generated by a natural process due to the second law of thermodynamics.

Therefore, there is something comforting about Steane’s proposal. If true, my very existence can be used to infer that I will never be wiped out by a Maxwell’s demon. All we need to do to test the theory is to try and wipe out a conscious being by constructing such a demon, which is obviously impractical and also unethical. Needless to say, there is something troubling about drawing such a strong metaphysical conclusion from quantum theory, which is why I still prefer the many-worlds account over Steane’s proposal at the moment. (That’s not to say that I agree with the former either though.)

Copyright © 2006 Matthew Leifer. All Rights Reserved.

All we need to do to test the theory is to try and wipe out a conscious being by constructing such a demon – and then determine if that being actually “experiences itself being in a definite state rather than a superposition”, as opposed to meerly saying that it does, which it will in any case.

I remember seing such an experiment descrimed in one of the early Quantum Computer papers (I’m pretty sure it was by David Deutsch). All you need is an AI running on a quantum computer.

Since Quantum Computation is reversible, as long as the relevant “environment” never appears in the output, time can be turned back to before the measurement was made (you don’t need to wipe out the observer completely).

Since philosophers disagree on the question of what (if any) “experience” an AI can have, even on an ordinary computer, I don’t expect the experiment would settle anything.

Hi Matt, great summary of an interesting paper. I like Steane’s idea about not assigning states to isolated systems unless they have interacted with an environment, though I’m a little less comfortable with describing collapse as a “real” process and the detection of spacetime “loops” that is necessary for this to work. But your Maxwell demon example brings up a question about quantum states and consciousness that I have been struggling with a little bit: If a conscious observer perceives him-/herself as having definite experiences of something, is that enough to force his/her state as described by *other* observers to collapse, and not be a superposition of states corresponding to different experiences? I guess this reduces to the question of whether or not pure quantum states are truly objective, or whether they are observer-dependent like probability distributions.

To illustrate with a case where observer-dependent states seem natural, take the classic Schrödinger’s cat-in-a-box scenario. What if anything is then wrong with the following description: First, let’s assume that the vial of poison just makes the cat sick rather than dead. An external observer outside the box would say that, after one half-life of the radioactive atom in the box, the cat is in a superposition of being healthy and of being sick, assuming that we can isolate the box completely from any decoherence sources. But what would the cat say? Presumably, the cat should experience being either sick or not, if it is experiencing anything at all, so it should assign itself an eigenstate of the “sickness” operator. This is at odds with the description that the external observer has, but it is not a paradox unless the two can communicate and disagree. If the external observer simply opens the box, or if the cat can “phone out”, then the state of the cat collapses into a sickness eigenstate according to the external observer as well, and there is no way to tell that there ever was a superposition. The only potential for paradox is if the external observer can subject the box to some control field that is able to cause interference effects of some sort, which would demonstrate (possibly after repeating the experiment many times) that the cat was in a superposition while the box was closed, despite the fact that the cat described itself as being in an eigenstate all along. But to perform such an experiment, the control field would have to connect the “sick” and “healthy” eigenstates in a coherent way, and thus manipulate both the cat’s health, the entire apparatus inside the box, and, most importantly, the cat’s memories as well as any physical evidence of what happened inside the box. Thus, when the external observer opens the box and compares notes with the cat, the cat would have forgotten that it ever described itself as being in an eigenstate, or at least its memories would have to have been manipulated so heavily that the cat could no longer count on its own mind to say anything reliable about what happened. None of this implies that the cat did not have definite experiences while it was in the box, it only implies that the experiment that demonstrated the superposition altered the cat’s memories and effectively rewrote history (or, rather, erased it). Of course none of this answers the question “what really happened inside the box”, but it also does not say that the cat could not have had definite experiences before the control field removed any memories and any physical traces of those experiences.

Given that this description never seems to be mentioned when people write about Schrödinger’s cat, I would think that something about it is philosophically problematic or even inconsistent, but I can’t quite tell what. Any takers? To me it seems more appealing than taking the wave function to be a “real” object and the collapse process to be a “real” phenomenon, but this is obviously a matter of taste. My question is just, is there something blatantly wrong with what I have outlined here?

I wouldn’t say that there is anything wrong with that idea per se. The only trouble is that it does not gel well with the idea that physics is supposed to describe an objectively existing, observer-independent reality. At least this is the goal of most realist interpretations, whether or not you agree that it is a good goal to have.

Now, if you deny that there is an objectively existing pure state of the universe (something I would encourage you to do anyway) then the challenge is to replace it with some other well defined ontology. Presumably, this should account for the subjective experiences of both the cat and the experimenter in a consistent way. The other option is to deny the need for ontology altogether, but then you are on shakier philosophical ground.