>>Me:
>>Mass, energy, momentum, electric charge, spin, charm, and color,
>>are all digital quantities.
>Dejan Vucinic <dejan@mit.edu> On Sat, 22 Mar 1997
>Digital they aren't, discrete is what you probably meant. And
>discrete they are not either. Spin and charge of particles are
>observed as discrete values, the discreteness of color charge is
>deduced indirectly, but mass, energy and momentum are observed
>as continuous.
Max Planck started the entire revolution by proposing that energy is NOT
continuous, everything followed from there. Take a beam of light for example,
it has momentum nhf, h is the Planck constant, f is the frequency of the
light, and n is an INTEGER, the number of photons. Digital.
If you want to find the momentum of an individual photon, hf, you can find it
by using the formula hN/X , h is the Planck constant again, and N is the
number of wave crests the photon makes over a distance X. Digital.
If you want to find the energy of a photon multiply the digital momentum by a
constant, the speed of light. Digital.
Of course, there is a basic randomness built into the fabric of the universe,
so if we were to actually perform this experiment when we got near the end of
distance X it would not be entirely clear if we should include the last wave
crest or not. We could minimize this problem and get a more accurate
measurement of momentum by making X bigger, but then you'd know less about
the position of the photon, X. Momentum and position have an inverse
relationship, the more you know about one the less you know about the other,
however randomness is NOT a continuous quantity, in fact it is as far from
that concept as it is possible to get.
As for matter, it comes in particles, it is not smeared around, only the
probability of finding it. If you look for an electron at a particular spot
you may find one or you may not, you can't be certain, the best you can do is
come up with probabilities. However one thing you CAN be absolutely certain
of is that you will find an electron OR you will not. Digital. There is no
middle ground, there is no chance you will find half an electron or "sort of"
an electron. If an electron is detected when it hits a phosphorous screen it
will produce a photon of light. If it is not detected it will not produce a
photon of light. There are no other possibilities, it will never produce
half a photon of light. If an electron is detected it ALWAYS acts like a
particle. The probability of finding the particle acts like a wave and is
not deterministic hence the random element.
John K Clark johnkc@well.com
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