"The amazing thing is that this is a scientifically productive rule - finding a new representation that gets rid of epiphenomenal distinctions, often means a substantially different theory of physics with experimental consequences!"
Yeah, I never understood this. The fact that switching two electrons should have no experimental consequences has dramatic experimental consequences. The fact that the phase of a wavefunction doesn't matter matters a great deal.
Physics shouldn't have logical contradictions.
"No math = no physics"
I would say that as a practical matter, this is true, because often, many theories make the same qualitative prediction, but different quantitative ones. The effect of gravity on light for instance. In Newtonian gravity, light affected the same as matter, but in General Relativity, the effect is larger. Another example would be flat-Earth theory gravity versus Newtonian. Flat-Earthers would say that the Earth is constantly accelerating upwards at 9.8 m/s^2. To a high level of precision, this matches the idea that objects are attracted by G M/ R^2. Difference becomes large at high altitudes (large R), where it is quantitatively different, but qualitatively the same.
One could probably get by setting up experiments where the only possible results are (same, different), but that's really the same as defining numbers of terms of what they lie between; i.e., calculating sqrt(2) by calculating the largest number < sqrt(2) and the smallest number > sqrt(2).
The rate of scientific progress jumped enormously after Newton, as people began thinking more and more quantitatively, and developed tools accordingly. This is not an accident.
I'd be a bit careful where you put bold text. When I skimmed this entry the first time, I got a very different impression of your thoughts than actually were there. It's always good to hear somebody give the correct, non-consciousness-centric view of QM when talking for the public. As opposed to say, Scott Adams, who interprets the double-slit experiment as the future affecting the past.
Linearity of QM can be proven? I didn't know that. I don't suppose you'd be able to sketch out the proof, or provide a link to one?
Silas: The uncertainty principle comes from the fact that position and momentum are related by Fourier transform. Or, in laymans terms, the fact that particles act like waves. This is one of the fundamental principles of QM, so yeah, it sort of does depend on the validity thereof. Not the Schrodinger equation itself perhaps, but other concepts.
As for whether QM proves that all probabilities are inherent in a system, it doesn't. It just prevents mutual information in certain situations. In coin flips or dice rolls, theoretically you could predict the outcome with enough information. Most probabilistic situations are that way; they're probabilistic because you don't have that info. QM is a bit different, and scientists still argue about it, but the fine detail of behavior of atoms doesn't have any effect on a poker game.
"Is the water colder, because we know more about it? ...Yes! Yes it is!"
You're kidding, right? Knowing something about a system doesn't change the system (neglecting quantum, of course). The statistical way to define entropy (as you mentioned) is the log of the number of microstates. The fact that you know all the trajectories/positions couldn't matter less to the glass of water, the only thing that matters is (using your jargon) the phase space volume it occupies.
Reshape the space for a second. Call it 6-D, with each particle a point, instead of 6N-D. Now the entropy would correspond to the volume actually occupied in 6-D space, rather than the possible volume among which your single point can choose. W
With the single point, you get sucked into the fallacy that because you know where the point is at one time, that's the only possible location it can have, and you're tricked into believing the entropy is much smaller than it is.
Statistical physics assumes exact particle trajectories are random and unknowable, although this was never believed to be fundamental. It was just a convenient way to ignore things nobody cared about, and take averages. Restricting yourself to that one point in phase space, you violate that assumption.
It's a dressed up version of "This sentence is a lie". It's only self referential, so it's truth value can't be determined in any meaningful, empirical sense.
Jester should've remembered the primary rule of logic:
Don't make somebody look like an idiot if they can kill you.