|MadSci Network: Physics|
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
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