X-Message-Number: 20996
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Date: Tue, 28 Jan 2003 20:54:05 EST
Subject: wrap

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Another physicist has written me privately to support Michael Price's 
view--which is also that of the general physics establishment--regarding 
"identical" particles. He writes in part (in response to my example that 
particles can interfere with each other without being identical):

>To take your most recent example of interfering red and orange photons:
>the quantum mechanical wavefunction of two photons (numbered 1 and 2)
>cannot be
>psi_1(red) psi_2(orange)     particle 1 red, particle 2 orange
>but instead must be
>psi_1(red) psi_2(orange) + psi_1(orange) psi_2(red).
>In other words, since photons are identical particles, we can't say which
>one is red and which is orange.  The only wavefunction allowed by quantum
>mechanics is a symmetric combination of the two possibilities.  

If this means what it appears to say--that every photon is identical to every 
other photon--then not only is a red photon identical to an orange photon 
(whether they occur in the same experimental setup or not), but also e.g. a 
gamma photon is identical to a radio photon. If you ask a cloud chamber 
whether a gamma photon is identical to a radio photon, it will answer no. 

It should also be noted that some authoritative writers do NOT insist that 
one can never identify individual particles such as electrons--only that it 
is sometimes difficult or impossible. If two electrons are close enough, 
their  wave packets may overlap, so to speak, and identifying them separately 
may be difficult or impossible. But in many cases the particle is 
sufficiently isolated, or two particles sufficiently separated, so that 
keeping track of them isn't difficult. Certainly, once more, we can often 
follow a trajectory in a cloud chamber, the track of a particular particle. 
In other words, not all writers insist that a particle can be in more than 
one place at the same time, except in special circumstances. 

Just a couple of more reminders, and then I'm really, really going to try to 
quit. 

1. Most, if not all, Hamiltonians and wave functions are only approximations. 
For complete accuracy you need, but can't get, the wave function of the 
universe. For example, there is no such thing as a free particle, since every 
particle interacts with its environment, through gravitation if nothing else. 
Beyond that, most or all "particles" are believed to be "entangled" with 
others from previous history, providing possible inferences.

2. As mentioned in a previous note, the very concept of "particle" is 
uncertain and is best regarded merely as a metaphor for visualizing certain 
types of experiment. We started out with the "planetary electron" and then 
got the smeared periodic wave, moving on to strings and extra dimensions etc.

3. Necessity is not sufficiency. Two particles can both be bosons, or both 
fermions, and yet be different in other respects. The definition of "quantum 
state" can change.

4. Sloppy language, and unjustified assumptions, are often unimportant, but 
can sometimes be seriously misleading. It baffles me that anyone can be 
confident about his ontological interpretation of a field full of  mystery, 
disagreement, and rapid change.

Robert Ettinger

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