Chalnoth and Driftwood1: as Chalnoth has pointed out, this is getting off the original topic, but is nonetheless interesting, so I hope the moderators will allow it to continue.
This is a question which goes back to the debate between the Philosophical Materialists (objective reality) and the Philosophical Idealists (subjective reality). I believe that Physics today has chosen a middle ground, which I will attempt to explain.
First, there are nuances to each side which quantum mechanics have (has?) brought up. Quantum mechanics can be taken to argue against certain versions of either side (which is not the same as arguing for the other side, given the possibility of more than two positions). Take as a concrete example the EPR thought experiment as made precise by Bell’s Inequality. (I won’t get into the debate about whether Aspect’s experiments were really an experimental verification.)
[1] The EPR paper’s original claim was that, given a specific experiment, in which the outcome of a measurement could be known before the measurement takes place, there must exist something in the real world, an "element of reality", which determines the measurement outcome. This argument was then struck down by Bell. So much for this version of Materialism.
[2] On the other hand, the solipsistic versions (single or, incorporating relativity, inter-subjective) of Idealism are struck down as well, since the death of Laplace’s version of determinism by quantum physics rules out humans being able to produce the future in the way that he postulated. [The determinism of the wave equation with the idea that reality really is fuzzy, so that questions of simultaneous determinism of specific quantity pairs is simply meaningless, would seem to throw us back into the possibility of humans correctly being able to predict the future; however, the inability to ever know the universal wave equation, as well as the inability to know if our model of physics is the correct one (a la Lobachevsky) or even whether our model of physics is consistent (a la Gödel), eliminates this possibility of saving the solipsistic position.]
Even given the assumption that our model works, we have the question whether it reflects, even asymptotically, a reality outside of our perception, or whether it is just a good way to order our perceptions. The latter position runs into two problems: one, the predictive power of a theory indicates some meta-principle to this order, and secondly, it becomes equivalent to Hilbert’s Formalism that was struck down by Gödel. However, the former position runs into the problem of Platonism that Idealism tried to solve: to wit, that we are still talking only about perceptions, known in Physics as measurements, and to Kant as phenomena. We are stuck with phenomena, and have no handle on noumena (Kant’s term: the “thing in itself”). Hence, objective reality runs into a problem.
The middle ground is a variation of Feynman’s “shut up and calculate” school. As shown by the enthusiasm for M-Theory, a lot of physicists don’t stick to this classic formula, but they implicitly (ie. in practice) , if not always explicitly (in their philosophizing) adopt its variation, Hawking’s “if a model works, then go with it”. That is, this position acknowledge that these problems belong not to Physics but to meta-Physics, and as such are likely to be insoluble, and hence for Physics, meaningless. A middle position is taken: one deals with measurements (Idealistic element), and use rules of thumb to work out things as if there is an objective reality (Materialistic element), just as one uses infinities as a handy assumption without actually believing that there are infinities in nature. (This “rule of thumb” aspect also plagues the debate as to the “reality” of the wave function, as well as the Many Worlds debate. But that is another story.)
So, what word do I substitute for the word “reality”? In the spirit of mathematics, I first ask the person using the word to precisely define the word; then, if a definition agreeable to both of us is found, I continue a discussion using, provisionally, that definition, always with the proviso that the conclusions apply only to that definition. However, since most people give definitions that are either very vague, or are circular, or are self-contradictory, or otherwise meaningless, I usually bow out of such discussions, and go fix dinner.
Finally, to Driftwood1: do I take your diatribes against mathematicians seriously? Of course not: mathematics is a game which some people play for fun (pure mathematics), and which others use as a tool (applied mathematics). So if you like to play, fine.
First, you would have to come up with a quantification of "truth", and second, you cannot divide by zero.
), I would also like to know why "flat" has to be (?) Euclidean. Or is this an empirical result?
