Posted on 01/31/2006 12:52:13 PM PST by PatrickHenry
You mean you're NOT addicted to Free Republic? ;-)
Cheers!
One other note, might want to have the addendum that the old theory should be (at least somewhat) empirically validated: e.g. the law of gravitation vs. Aristotle's de Caelo; phlogiston vs. oxygen. The existence of phlogiston was a widely held [belief? theory? -- people weren't using empiricism as much back then, which was part of the problem :-) ]. Call it a theory. Nonetheless, it was discarded in favor of valence chemistry. Or another example would be Geocentric cosmology (epicycles, etc.). To a certain extent they could correctly predict planetary movements, but at the cost of a lot of trouble. But the theory was completely supplanted by Copernicus etc.
Cheers!
G_W jumping in with an unavailing pun:
I guess that makes me strictly "soft-core." Thanks. I think :-)
Cheers!
LOLOL! Thanks for the chuckle!
I've been up Freeping too late and got an ear infection.
Prayers for the ear, for my self-discipline (in regards to sleep) are welcome.
Flames and taunts regarding the inefficacy of prayer are forwarded to either
a) /dev/null
or
b) your future address by way of the fireplace(*)
(*)Free electronic prize to the first freeper to identify the literary source from which I shamelessly stole choice b).
Cheers!
I pray for a complete healing of your ear, a wonderful night's sleep and a perfect day tomorrow!
It's implied that the theory is applicable. There are not 2 theories though. The old one is an approximation as some limit is approached. " Quantum mechanics reduces to classical mechanics in the limit of large number of particles;"
No, the classical limit applies when the energies of the particles are continuous and much greater than h. That way quantization can be ignored. Consider a metal, a semi-conductor, a plasma, a black body, or the specific heat of a real gas. Quantum mechanics applies, even though these are systems of a large number of particles. In general, field theory involves large numbers of particles. A bowling ball, or a train have E, much greater than h, so quantizing such mechanics doesn't make sense. If h/x*p <<1, where x is the scale of length for the process, and p is the momentum, the wave aspect won't be seen. So it's the scale that allows the approximation. The approximation is the old theory arising out of the new one.
"special relativity reduces to Newtonian physics as v << c. But the new theory usually addresses (at first) specifically those cases in which the old theory fails."
Yes, as v/c->0, special relativity -> Euclidian. In this case, that's the limit. In GR, it's when the local energy density is low and the space is flat.
It was an unproven hypothesis. The correspondance principle only applies to theories based on a solid fundation of real evidence. W/o empirical evidence, there is no theory.
Hmm, the energies of the particles are always quantized. In the macroscopic limit, the large number of particles means that the energy "seems" continuous, due to the additive effect of many small quanta. E.g. the individual energy states are so close together for a macroscopic system (say an automobile) that in practical terms you can't tell them apart. There is a difficulty in measuring small differences in large numbers... As far as the energy being greater than h, pass. The Road Runner notwithstanding, tunneling is not known to occur for macroscopic objects :-)
Grey area due to semantics, there were cases in which it "appeared" to work; and the principles of empiricism were not firmly enough established that people back realized it was an unproven hypothesis. The distinction between hypothesis and theory wasn't as firm back then. One of the drawbacks of scholasticism. (See also Galen...; or some analogy to Owen Barfield's "ancient unities"...)
Cheers!
Only, because h/x*p << 1. "There is a difficulty in measuring small differences in large numbers.."
No. Have some coffe and ponder an electron gas in a metal, or the carriers in a semi-conductor. Then try x-ray scattering. All of these have a huge number of particles in the system. H/x*p is not << 1 here.
Appearances don't count. It doesn't predict anything, because it doesn't explain reality. In most of those old cases that amount to hypothesis, the logic wasn't even that good. In hypothesis like "caloric", testing which could have been done, but was not, until someone finally realized that(Joule, I think.). They failed to note that the heat generated was a function of friction, not cutting. What matters is having a precise definition, independent of state of knowledge, instrumentation and "philosophy".
Also, consider the very first quantum theory. It had to do with heat and light. It was Plank's quantum theory that straightened out the divergence in the Stephan-Boltzman law.
"The Road Runner notwithstanding, tunneling is not known to occur for macroscopic objects"
The probability can be calculated though. Tunneling also depends on the barrier height, the size of the bounding region and the wavelength. Even quantum systems can have an essentially zero probability that tunneling will occur. A bowling ball has already tunneled out of any region it could possibly be held in.
Thanks! :-)
I wouldn't tie faith to material evidence. I don't think that usage would make sense to the other side of the argument.
spunkets:No. Have some coffe and ponder an electron gas in a metal, or the carriers in a semi-conductor. Then try x-ray scattering. All of these have a huge number of particles in the system. H/x*p is not << 1 here.
I think we are talking past one another here, I was not merely referring to uncertainty principle (theoretical limitation on discerning energy precisely), but also to the difficulty of distinguishing continuous from very small discrete steps...(only a practical difficulty, but still exists).
Cheers!
Sounds like a "catastrophe" to me :-)
The probability can be calculated though. Tunneling also depends on the barrier height, the size of the bounding region and the wavelength. Even quantum systems can have an essentially zero probability that tunneling will occur. A bowling ball has already tunneled out of any region it could possibly be held in.
Yes, but for bowling balls the probability is so small as to be much less than experimental error, so it can be ignored for day-to-day work. It's one of the reasons I can't pick up 7-10 splits even AFTER several beers. :-)
Cheers!
Sorry, I was just trying to be complete. What do you do with things like the Mons Angels, Shroud of Turin, etc. where you have either credible eyewitnesses without other axes to grind, or disputed physical evidence (carbon dating of a non-representative sample to muddy the waters, suggestions of Maillard reactions which are consistent with the chemical structure but not "topography" of the image...)
Cheers!
Interesting take. If you say that phlogiston (to choose one example) is not a theory, OK, then the statement about one theory not REPLACING another holds for that case, since phlogiston was not a theory. What do you do about "paradigm shifts" when the original paradigm was not a theory to begin with (see also pre-Copernican cosmology)?
Stirring the pot, part II:
Or for that matter, psychology, which Feynman called "cargo-cult science". It is empircally based, or at least "semi-empirical" ... :-)
How do you classify behaviourism vs. Freudianism, or the dispute between them?
Good point.
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