X-Message-Number: 21050
Date: Mon, 3 Feb 2003 22:19:07 EST
Subject: high five

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It is interesting, and challenging, that people who are reasonably (although 
not identically) intelligent, and reasonably (although not identically) well 
informed, and all well intentioned, can have such persistent 
misunderstandings. So I'll try yet again. But first a small reminder that 
some heavyweights have resisted the dominant view in quantum theory, those 
names including Schroedinger, de Broglie, Einstein, Planck, and Dirac.

As another preliminary, note that various writers use varying emphases. The 
text Quantics (Levy-Leblond & Balibar) says that an electron in Paris and an 
electron in Quebec are identical--even though, on the same page, they say 
that only classical particles allow individuation by trajectories, and that 
particles which have trajectories are not identical! (Again, two gamma 
photons in two different cloud chanbers will show two different trajectories. 
And please don't say that the trajectories existed only after observation.) 
At an absolute minimum, then, I think it will have to be agreed that there 
are differences of opinion among experts.

Now, Michael Price writes a reprise:

>the posited hidden attributes of electrons 
>will not cause a future refinement of electrons into subspecies.  
>We know this because the occupancy number of electron orbitals 
>is an absolute measure of the electron species number, not a 
>reflection of our knowledge of electron attributes.

>As with electrons, so with elephants.

>(Note: I'm not saying the electrons may not have some composite

So, electrons do not and cannot have subspecies, and the same is true of 
elephants. I take this to mean that if two elephants are in the same quantum 
state, they are "identical." I see at least five things wrong with this. 

First, once more, it is just an arbitrary and unusual choice of language, no 
doubt protected in the U.S. by the First Amendment but not useful or 
appropriate. I repeat an earlier question: Is a gamma photon "identical" to a 
radio photon? Is such a locution useful?

Second, saying that two elephants are identical is really the claim that 
specifying the quantum state of a system tells you EVERYTHING there is to 
know about the system, and allows you to make any and every prediction about 
the system that is possible in principle. In the same vein, it is often said 
that the wave equation of a particle contains ALL the information about the 
particle that exists. Now, it is not denied that we may find substructure in 
electrons, and we know there is substructure in elephants, or for that matter 
in atoms; but to say that the quantum state or the wave equation holds ALL 
the information is equivalent to saying that the kinds of observations we CAN 
MAKE NOW yield ALL the information than ANY FUTURE TYPE of observation could 
make. Does history or common sense support that? 

Third, quantum physics in some ways reminds us of geocentric astronomical 
models with cycles and epicycles, all circles. You can patch together almost 
anything that way. Well, in quantum theory there has been a lot of patchwork, 
still ongoing. For example, the original uranium wave function wouldn't work 
for radioactive decay, so it was patched up. Probably the original proton 
wave function didn't suggest anything about decay either, but now it is 
thought that protons eventually decay--oops, patch it up. Can't fault them 
for trying, and Ptolemy's epicycles worked too--worked very well, in 
fact--but both are just clumsy ad hoc concepts. Ptolemy was on good ground 
observationally or computationally, but very shaky ground aesthetically and 
philosophically, and so is quantum theory.

Fourth--and I think this is most crucial for getting heads together--look 
again at this:

>occupancy number of electron orbitals 
>is an absolute measure of the electron species number

But the exclusion principle applies only to fermions, not to bosons. Bosons, 
including photons, can have many in the same state at the same time (lasers). 
(Electrons too, for that matter, if they are far apart--farther than Paris 
from Quebec, let's say--and if you define "state" without regard to spatial 
location other than locally.) 

HOW CAN ANYONE KNOW that there could not be different species of electrons, 
the differences being of a sort not affecting symmetry or anti-symmetry? 

Fifth, although this cuts no ice with some people, there is the 
"philosophical" problem with any fundamental indeterminacy. How can there be 
such a thing as ordered randomness? (Quantum waves require randomness WITHIN 
an overall frequency distribution of definite shape.) True, one can just 
shrug and say, that's the way it is, maybe comparable to a question about the 
origin of the universe--we can never know so forget it. That's no different 
than saying "the will of the gods." But virtually all of our progress has 
stemmed from a refusal to accept causeless events, always to keep looking for 
strict rules. Fortunately, some are still looking.

Robert Ettinger


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