I have heard the “lack of counterfactual definiteness” loophole from several people, but I have a hard time understanding what it is supposed to mean. Bell’s theorem does not assume that unperformed measurements have definite outcomes. In Bell’s original proof, counterfactual definiteness is not assumed, but rather derived from the fact that the singlet state has perfect anti-correlations. In later proofs, such as CHSH, even this is not assumed. The measurement results need not come into existence until the measurement is actually made. They just have to have well-defined probabilities that satisfy local causality. Because of this, I have a hard time understanding where the loophole is supposed to be here.

Well, we already know that all times, past and future, are real: http://en.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argument

The Rietdijk-Putnam argument seems to imply superdeterminism (e.g. the fact that the measurement result is real prior to the experimenter’s “choosing” of the conditions of the experiment). The lack of counterfactual definiteness is apparently yet another means to defuse Bell’s theorem. And it is hard to not imagine retrocausal influences when an in-progress experiment is already bound to yield fixed results.

The remark about doing the whole computation before the input does apply classically, but it is pretty useless. What it corresponds to is choosing an input at random and then making a copy of it. The correlated state of the two copies then corresponds to the maximally entangled state. Then, you run the computation on one of the copies. When you want to perform the computation on your chosen input you then just check whether it is the same as the randomly chosen input, this being analogous to the Bell measurement. If it is then you accept the output of the computation in the second copy and if it isn’t then you reject it and start the whole process again. Obviously, this is a pretty useless procedure as the probability of correctly guessing the input goes down exponentially with the number of bits, but this is conceptually no different from what is going on in quantum gate teleportation.

Btw, I wonder if your remark about doing the whole computation before the input is supplied also applies classically.

The question they are addressing is whether there is an appropriate way to use the quantum formalism itself retrodictively, rather than first computing the classical probabilities and then inverting them. Peres’ argument seems designed as an argument against a realist reading of the two-state vector formalism of Aharonov et. al. On this point I agree with him. I think you quickly get into problems if you think that the results obtained in a pre- and post-selected experiment are somehow already “real” in between the pre- and post-selection. However, he is not saying that the probabilities obtained from quantum theory in those experiments are wrong.

Penrose is trying to make an argument about the lack of time symmetry in the measurement process by arguing that if you apply the same reasoning backwards in time that we ususally use in the forwards direction then you get an incorrect result. Again, the conventional formalism only mandates inferences forwards in time, so this is not actually a contradiction between quantum theory and experiment. Nevertheless, I believe that Penrose’s argument is wrong because he has failed to correctly describe the time-reverse of the experiment under consideration. If you run the experiment back in time then there has to be a possibility for the photon to come from two places in superposition: the ceiling or the detector. These two components then interfere at the beamsplitter resulting in a single beam going back to the laser, so you get that the photon came from the laser with probability 1, as you should. It is a question of asymmetry between the events that you choose to condition on in the forward and reverse versions of the experiment. Even in classical physics, the issue of how to correctly time-reverse an experiment is subtle. You need to carefully ensure that you impose the correct time-reversed boundary conditions in addition to the time-reversed dynamics. It is easy to introduce apparent asymmetries by hand without noticing that you are doing it, and even the greatest minds of physics have fallen into this trap on occasion. Huw Price essentially wrote a whole book about this, which I recommend.

Although retrodictive formalisms go beyond the conventional understanding of quantum theory, I believe they are useful and, when done properly, do not contradict quantum theory. For my take on how to do this, see this paper. However, I would put this type of work definitively in categories 2 and 3. It is not an attempt to refute quantum theory, but an attempt to reformulate it in such a way that certain aspects of the theory, including the time-symmetry between prediction and retrodiction, become more clear.

There is also a slightly bizarre suggestion due to Adrian Kent that Bell experiments might fail to violate a Bell inequality if the outcomes of the measurement are coupled to a difference in position of very massive objects and this is done quickly enough that a signal could not travel to the other wing of the experiment before the mass has been moved. This is based on a loophole in Bell’s theorem to do with the idea that collapse might not occur until the results of the measurements are brought together and compared. A related suggestion due to Scarani and Suarez is that Bell violation will fail if the experiment is done with moving detectors such that the measurement of the other particle happens first according to the frames in which both of the measurement devices are moving, i.e. neither Alice nor Bob believe they are making the first measurement according to their own frames. This is based on the rather naive way of talking about collapse that we often use in which we say that Alice’s measurement causes the collapse at Bob’s side, or vice versa. Even if this is the case, I find the idea rather implausible because there is no reason why collapse should occur in the frame of the measuring device as opposed to some other natural fame like the frame of the particle itself.

One can find several similar types of suggestion in the literature. As far as I am concerned they are all highly implausible, although they will lead to testing of quantum predictions in situations in which they have not been tested so far, which is a good thing. Such experiments may turn out to be technologically useful. However, if this is what most physicists think we are doing then I am unsurprised that Lubos Motl calls everyone who works of quantum foundations an “anti-quantum zealot”. As I said in the post, I find goals 2 and 3 more promising.

You say “The goal of QF is to correctly predict the result of an experiment for which the standard approach to QM gives the wrong result.” Can you please give specific examples of experiments where the standard approach to QM gives the wrong results?

Thanks,

Michael

I am sympathetic to the idea that we need to understand what is going on in the measurement process in order to fully understand quantum theory. However, that does not mean that we should have a myopic focus on solving the measurement problem as the only interesting project in quantum foundations. We can also ask and answer other questions about the internal structure of the theory that are interesting in their own right.