Analog is Bunk

John K Clark (
Sat, 26 Apr 1997 21:15:44 -0700 (PDT)


On Fri, 25 Apr 1997 Dejan Vucinic <> Wrote:

>No, you cannot count crests of a single photon. By "counting" a
>single crest you are destroying the photon.

Sometimes yes but not in general. When an excited mercury atom returns to its
ground state it emits 2 photons, the two are forever linked even if they are
on the other side of the universe, you can make a destructive measurement on
one and it will tell you what the measurement of the correlated, still
existing photon must be. This sort of thing was done by Clauser and Aspect in
their experiments on Bell's inequality that proved it was violated.

>It is certainly true that some observable quantities, like spin, have
>discrete (you prefer "digital") spectra, but energy/momentum/mass
>do not.

It's not just spin that's digital, so is the quantity of electric charge,
and the type of electric charge (2), and baryon number, and electron family
number, and muon family number, and magnetic moment, and parity, and the
number (6) of different types of quarks, and the number (3) of "color"
charges that quarks come in.

Even polarization is digital, sort of. Pick a direction at random, and for
any photon of unknown polarization there are only 2 choices, it must be
polarized in that direction or at right angles to it. If it makes it through
your polarization filter, it could make it through a thousand set in the
same direction, and so could any twin photon correlated with it. If it
doesn't make it through then the photon was polarized at right angles to the
polarization filter, as can be proven by the correlated photon.

>To the best of our knowledge, muon is an elementary particle. It
>decays into an electron and two neutrinos.

If it decays into something lighter and more stable then it can't be
very elementary.

>If what you are saying were true, momentum of the electron in the
>rest frame of the parent muon would be quantized, meaning it could
>only have values from a discrete set, and the spacing between the
>possible values would be some constant. This is not observed.

I see your point and it's a very good one. The energy (and thus the momentum
too) of the electron is indeed random and limited to the range from zero to
52 MeV. It's interesting that the range of energy of something like an alpha
particle given off by a nucleus in not continuous, because it's the only
particle given off in the decay reaction. When the muon decays on the other
hand, 3 particles are created and the electron must share the energy with the
other 2 particles in an arbitrary ratio. I'll just have to find comfort in
the fact that the total momentum in the rest frame is quantized, to zero in
this case. :>)

I could eliminate all my problems with energy and momentum if I could invoke
digital space and time, in a way that would be a cheat but in another way it
wouldn't be. Today's Physics can tell us nothing about what happens when time
gets smaller than The Plank Time of 5.4 * 10^-44 second or distance gets
smaller than The Plank Length of 10^-33 cm, photons of that wavelength are so
small and have so much energy that they become Black Holes, and Black Holes
contain a singularity. We had no choice, we've already made a defacto
quantization of space-time. However, I admit I'm not comfortable using this
dodge, because at these very small distances Quantum Mechanics and General
Relativity and not compatible, so obviously the last word has not been spoken.
We need a quantum theory of gravity before we can know for sure.

>The point is that c and h are more fundamental than meter or second.

Yes, but not more fundamental than space or time.

>don't forget that all these weirdnesses are problems of
>interpretation, not of quantum mechanics itself.

I disagree, an interpretation is part of any theory, quantum mechanics has
several, all weird.

>QM works.

I agree, in fact I would say that no theory in the history of Science has
been more successful than Quantum Mechanics. It works, it's true, it's crazy.

John K Clark

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