The End of Time: The Next Revolution in Physics

DOWKER. I think that neither your version (which I’ll call JMWI) nor BMWI allows us to make predictions about what we observe (so I disagree with Everett’s statement ‘the theory itself predicts that our experience will be what it in fact is’). Let me take your version. There we have many configurations at time t. The most serious problem is that in a scheme like yours, in which all the possibilities are realized, there is no role for the probabilities. The usual probabilistic Copenhagen predictions for the results of our observations cannot be recovered. An excellent reference which analyses the MWI literature and the various attempts to derive the Born interpretation from MWI is Adrian Kent [1990, International Journal of Modern Physics, A5, 1745]. Adrian concludes that they fail. I’ll just state again the main reason that they fail: when all the elements in a sample space of possibilities are realized, then probability is not involved. Your idea is that it is the sample space itself, i.e. how many copies of each configuration are included in the sample space, which is determined by the (squares of the) coefficients of the terms in the wave function. That is all well and good (if bizarre). But there’s no reason then to call those numbers probabilities, and no way to recover the probabilistic predictions of Copenhagen quantum mechanics. In fact the MWI proponents themselves agree that the failure to reproduce the Copenhagen predictions is a problem and do try to address it, but without success.

BARBOUR. I accept that this is a strong critique. I nevertheless feel that my scheme does in principle have predictive strength. If you could see Platonia and Born’s probability density concentrated incredibly strongly on a tiny proportion of its points that all turn out to be time capsules as I define them and Bell describes them, would you not find that impressive, and something like a rational explanation for our experiences?

DOWKER. As well as the MWI, you base your conjecture of timelessness on the technical result that when a canonical quantization scheme is applied to general relativity, the wave function cannot contain the time. My understanding of the state of affairs in canonical quantum gravity is that, because of this, no one knows how to make the kind of predictions we’d like to make: explanations such as ‘What happens in the final stages of black hole collapse?’, ‘Why is the cosmological constant so very small?’, etc.

BARBOUR. I agree with your first example (and do not think it is too serious—there may be questions that it is just not sensible to ask), but in principle my scheme could predict that virtually all time capsules will appear to have been created in nearly classical universes with a very small cosmological constant. After all, that is what our present records indicate. If all probable configurations seem to contain records that indicate a small cosmological constant, I am okay.

DOWKER. My reaction to the situation is that formulating general relativity in a canonical way has been shown to be the wrong thing to do—we did what we weren’t supposed to—divided up space-time into space and time again. Even if it wasn’t clear from the beginning that it would be incredibly difficult to maintain general covariance of the theory whilst trying to treat space and time differently, I find the lack of any insight into how to recover predictions within the canonical quantum gravity program convinces me that we should look elsewhere for a quantum theory of gravity.

BARBOUR. As he was creating general relativity, Einstein was convinced general covariance had deep physical significance. Two years later, correctly in my opinion, he completely abandoned that position. In my opinion, general covariance is an empty shell (I say something about this at the end of Chapter 10 and in the notes to it). I believe it is not possible to give any meaning to the objective content of general relativity without saying how the three-dimensional slices in space-time are related to each other. That is the very content of the theory. That is why I think the arguments for canonical quantum gravity are very strong indeed. The constraints of the canonical theory are its complete content.

DOWKER. Having made my basic points, let me now just say that I find it incredibly hard to understand how, as a solipsist of the moment, you must view science and the scientific enterprise.

BARBOUR. Answered above I think. Science should explain what we observe. We habitually observe and experience time capsules. Even granting the real difficulties with calling the square of a static amplitude a probability, should it turn out that the Wheeler-DeWitt equation does strongly concentrate the square of the amplitude on time capsules, I think that would be an incredibly strong and suggestive result.