On 4/8/2014 2:27 PM, Henry Baker wrote:
Let's do an actual example with green light ~550nm wavelength = 5.5x10^-7 meters.
hc ~ 2x10^-25 Joule meters, so the energy of a green quantum:
E = hc/lambda = 2x10^-25/5.5x10^-7 Joules ~ 3.64x10^-19 Joules.
Planck length ~ 1.62x10^-35 meters. So the wavelength of green light is
5.5x10^-7/1.62x10^-35 ~ 3.4x10^28 Planck lengths.
So the total energy (using these units) is 3.4x10^28 * 3.64x10^-19 ~ 1.24x10^10 Joules.
1 kilowatt-hour ~ 3.6x10^6 Joules, so the total energy in kWh is
1.24x10^10/3.6x10^6 ~ 3.44x10^3 kWh ~ 3.44 MWh (that's a pretty healthy green laser!)
That's one interpretation. The other would be that dividing by Planck lengths doesn't mean anything physical.
The whole point of this exercise is to show that while Shannon wants to put more "information bits" into shorter wavelengths, Planck tells us that there are fewer quanta per bit at shorter wavelengths.
Yes, Shannon made an analysis in terms of 'bandwidth', i.e. switching frequency, which didn't consider quanta. But his analysis was to determine the maximum information transfer rate. Longer wavelength photons take more time to detect dt ~lambda/c. The number of quanta per bit doesn't change (it's 1photon=1 0photon=0) with wavelength, but the number you can transmit per unit time does.
There's also another type of problem: as the universe expands, the "same" light gets redder (= longer wavelength = more quanta). Thus, the number of quanta isn't a property of the light itself, but of something else -- perhaps the granularity of the space where it is detected.
The number of quanta is a conserved property of the light. What's not conserved is the energy per quanta, each photon gets red-shifted by the expansion of the universe. Brent