Re: If energy is quantum then are there quantum velocities?

Hi William

To clarify, energy and "angular" momentum are quantized in systems such as
atoms.  In an atom, the electron is only allowed to be in discrete (or
quantized) energy levels or orbitals.  This explains why we see discrete
spectral lines for atoms and molecules.  Also, the quantization of angular
momentum means that a particle can only have an angular momentum which is a
multiple of h/2Pi where h is Planck's constant (definitions of these
terms can be found at http://roland.lerc.nasa.gov/~dglover/dictionary/
).

Planck length and time are what we derive when we take the natural
constants G (universal gravitational constant), h (Planck's constant), and
c (the speed of light) and rearrange them so that we get the units of
length and time.  The planck length turns out to be about 10^(-35) meters
and planck time is 10^(-43) seconds.  This does not mean that time and
space are not continuous (see http://www.madsci.org/posts/archives/mar97/853895142.Ph.r.html
).  It turns
out that these are just the physical limits to our current theories.  For
this reason, we can't say what happened in the universe before 10^(-43)
seconds after the big bang.  Quantum mechanics breaks down here, and
physicists are still working on a theory that pushes these limits.  It
turns out that the ratio of planck length and time is c, the speed of
light, which is an upper limit to how fast something in the Universe can
travel.

As I mentioned above, electrons can only have discrete (quantized)
energies in atoms.  However, if you have a particle by itself, you can hit
it with a photon and give it any velocity.  This is because a photon's
momentum is Planck's constant/wavelength (momentum and energy do not depend
on mass here since the photon is massless).  You can have a continuous
spectrum of photons (and hence continuous values of momentum are possible),
so you could give a free particle any velocity (less than the velocity of
light, but that's getting into Relativistic Theory).

Erika