by querious » Mon Jun 23, 2008 9:17 pm
As StevenO correctly points out, charge has the dimension of space (length). I've recently come up with an explanation as to WHY that is. The well-known formula for energy of an EM wave, E=hf, indicates that in any photon, there is only 1 variable, the frequency. But all waves need 3 magnitudes to describe them: Speed of propagation, frequency (from which wavelength is trivially derived if the propagation speed is known), and AMPLITUDE. What Plank's constant is telling us is that amplitude (it's E-field component) is fixed AND quantized, no matter the frequency.
In the following analysis, s=space, t=time
Now, "h" has the dimensions of angular momentum, mass t^3/s^3 X velocity s/t X radius s/1 = t^2/s. But it also has the dimensions of Energy (t/s) X time (t), again, t^2/s.
Looking at the formula for the Hartree Energy (the "atomic unit" of energy), we have ke^2 / Bohr radius. These are the right dimensions for energy because Coulomb's constant k (1/4*pi*epsilon) times e^2 has the dimension of time. (permittivity is farads s^3/t per meter, s^3/t / s = s^2/t)
So we have an energy (ke^2(t) / bohr radius(s)) multiplied by a time (actually, it's the Dewey Larson unit of time, 1.51983 X 10<sup>-16</sup>sec), which is exactly Plank's constant, h.
Back to the "charge is space": The fine structure constant is the dimensionless RATIO of wavelength to AMPLITUDE of the Rydberg fundamental frequency.
Of course, if you take a half-wavelength of it, curl it into a circle, and multiply by the fine structure constant (alpha), you get the Bohr circumference. Multiplied by alpha squared, you get the compton wavelength X 2pi, and multiplied by alpha^3, you get the classical electron radius.
So charge is the spacial AMPLITUDE COMPONENT of all photons. Of course, this is why QED deals in probabilities: the Amplitude is a function of phase.