Timeline for How many colors exist?
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10 events
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| Jan 19, 2012 at 7:17 | comment | added | Luboš Motl | Dear @Ron, I agree you may be right: the Hubble-scale issues were sketched in the part of my answer about the lower limit on frequencies. For a universe with boundaries, one could indeed get a quantization of frequencies, like in a box, but with an insanely low spacing. | |
| Jan 19, 2012 at 7:16 | comment | added | Luboš Motl | Dear @Zassounotsukushi, apologies if the explanation was not written clearly in my answer. I think that I wrote that the frequency is a genuinely continuous quantity but I may have failed to justify the statement. David Zaslavsky is totally right and Lorentz invariance is able to prove the continuity of the frequencies, too: nothing can change about it by quantum effects (except if one works in a box which only allows standing waves). BTW, David, a quantized Lorentz group could surely not be a usual subgroup of $SO(3,1)$ - no "dense enough" subgroup like this exists. | |
| Jan 19, 2012 at 5:33 | vote | accept | Martin Thoma | ||
| Jan 19, 2012 at 2:48 | comment | added | Ron Maimon | @David: right. Also, the quantization rule in this case is not based on the wavelength, but based on the size of the receptor. Since the receptor is a molecule, each receptor individually is incapable of distinguishing two photons in a huge range of frequencies, about a factor of 2 (the reception peaks are that broad). You can't tell the difference between photons in this range using one receptor, you have to look at how they excite different receptors and make an average. | |
| Jan 19, 2012 at 2:44 | comment | added | David Z | That's not actual quantization, though. (Well I guess it depends on the geometry of the universe) | |
| Jan 19, 2012 at 2:21 | comment | added | Ron Maimon | @David: The same argument that gives a lower bound on frequency gives a lower bound on two distinguishable frequencies. Two frequencies whose wavelength is different by an amount which makes less than a cycle over the observable universe are indistinguishable. Needless to say, this has nothing to do with vision. | |
| Jan 19, 2012 at 2:20 | comment | added | David Z | @Zassounotsukushi: QFT restricts the energy that can be stored in a mode of oscillation at any given frequency to discrete values. But it doesn't restrict the possible frequencies. That's another conclusion you can get from the Lorentz invariance argument Lubos mentioned: a photon can be red-/blueshifted to any frequency by making an appropriate change of reference frame. (Unless Lorentz transformations themselves are quantized, but that's a rather crazy idea.) | |
| Jan 18, 2012 at 21:29 | comment | added | Alan Rominger | I'm reading as closely as I can, but it seem that you addressed the prospect of a lower limit and an upper limit but didn't really address the finiteness of the spectrum. Does quantum not place any sort of limits on the # of allowable frequencies within a given band? It seems like, at some point, virtually everything in the universe can be hypothesized to have discrete states, I have trouble believing that photons would be different. | |
| Jan 18, 2012 at 20:38 | history | edited | Luboš Motl | CC BY-SA 3.0 |
added 994 characters in body
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| Jan 18, 2012 at 20:32 | history | answered | Luboš Motl | CC BY-SA 3.0 |