Wiki wrote:
In mathematical physics and quantum mechanics, quantum logic is a set of rules for reasoning about propositions which takes the principles of quantum theory into account. This research area and its name originated in the 1936 paper by Garrett Birkhoff and John von Neumann, who were attempting to reconcile the apparent inconsistency of classical boolean logic with the facts concerning the measurement of complementary variables in quantum mechanics, such as position and momentum.

Wiki wrote:
In his paper "Is logic empirical?" [2] Hilary Putnam, whose PhD studies were supervised by Reichenbach, pursued Quine's idea systematically. In the first place, he made an analogy between laws of logic and laws of geometry: once Euclid's postulates were believed to be truths about the physical space in which we live, but modern physical theories are based around non-Euclidean geometries, with a different and fundamentally incompatible notion of straight line.

In particular, he claimed that what physicists have learned about quantum mechanics provides a compelling case for abandoning certain familiar principles of classical logic for this reason: realism about the physical world, which Putnam generally maintains, demands that we square up to the anomalies associated with quantum phenomena. Putnam understands realism about physical objects as involving that the properties of momentum and position exist for quanta. Since the uncertainty principle says that either of them can be determined, but both cannot be determined at the same time, he faces a paradox. He sees the only possible resolution of the paradox as lying in the embrace of quantum logic, in which he believes this is not inconsistent.

DJPavel wrote:
I would answer that there is no decision to be made. The existing state is a weighted average of all the possible states of the system. That’s what the superposition means. The next state is determined by the evolution of the wave function for that system. The wave function is itself deterministic, but it doesn’t determine a specific macro state of the system, it determines the probabilities of all possible states, and thus the overall classical macro state as, yet again, weighted average of all possibilities.

DeathMonkey wrote:
If you think about it, the cental issue here is the assumption of what Putnam is calling "realism". Specifically, he is basically axiomatically asserting that properties such as position and momentum must be real, well-defined properties of quanta.

DeathMonkey wrote:
The problem, of course, is that quantum mechanics seems to pretty clearly indicate that they are not.

DeathMonkey wrote:


This issue is a bit tricky to understand.

First, if one looks at the formal math of quantum mechanics, without trying to make any physical interpretations, there really is no mysterious "measurement problem".

As you said, the wave-function evolves deterministically. A measurement is really nothing more than an interaction between the system in question, and a "measurement system", which is itself just another very complex quantum mechanical system. When this interaction occurs, decoherence is the result. The wave-function (and remember I'm just talking about the math here) does not collapse to a single value. It collapses to a superposition of many discrete values.

The thing is, due to the linear nature of the superposition, we can easily show that this resulting wave-function can be expressed as a linear combination of all the wave-functions you would have gotten, had the wave-function randomly collapsed to a single value.

This is what leads to the many worlds interpretation of QM. We can imagine each of these discrete values as being a single universe, in which that particular outcome occured. The math says that these universes will not interact, so to any individual observer, it will appear as though the wave function collapsed to a single value, but really that is just because his part of the wave-function doesn't interact with the others.

Of course, that is just one possible interpretation. There are many others. But what it demonstrates is that the so-called "measurement problem" is a product of choosing an interpretation in which a single outcome is somehow "chosen", rather than some other interpretation. We have no way of justifying the claim that this actually does happen, and therefore no justification is asserting that the measurement problem is a real problem at all. In effect, it is a manufactored problem, rather like trying to figure out who would win at arm wrestling, Superman or the Hulk?

DeathMonkey wrote:
The bottom line is that the math works. We don't know exactly why the math works, but that is a fundamental fact of life in Physics.

DeathMonkey wrote:
I fully expect whatever more fundamental theory ends up replacing QM, to be even more counter-intuitive than QM is.

Death Monkey wrote:


There are some very important differences.

First of all, the assumption of realism is an assumption about the nature of the world. The axioms of logic are the framework of a formal system. What you could say is that by attempting to use logic to describe the world, I am assuming that this form of logic can be used in that way. But even then, this is a provisional assumption. If it did not work, then we should abandon it and use something else. In fact, that is what this discussion is really about. What I am disputing is the argument that ordinary logic doesn't work, and should be replaced by some sort of quantum logic. But the fact of the matter is that ordinary logic works just fine. What doesn't work is the assumption of classical realism, which is itself formulated in terms of ordinary logic.

This brings me to the second point. As I mentioned before, I can't assume the kind of realism that is being disputed here without first axiomatically assuming ordinary logic, because it is formulated in terms of it. Again, I think it is important to note that what is being suggested by proponents of quantum logic is not that the assumption of classical realism can be somehow saved by using quantum logic instead of ordinary logic, but rather that classical realism can be replaced by some new form of realism that is formulated in terms of quantum logic, and that this new form of realism will somehow satisfy our intuitive notions of realism in a way that cannot be achieved with ordinary logic.

DJP wrote:

I borrowed it from Dennett, who I thought made a brilliant comment when he was asked about a possibility of a zombie acting exactly like a human, but lacking consciousness. His reply was that it's like asking to imagine a human whose organs are funtioning properly, but who is not healthy. It's a dressed up contradiction!