Signal to noise ratio scales as one over square root of number of photons. The energy of a single photon is proportional to its frequency, and, at a given power, number of photons in a lower frequency electromagnetic wave will be larger. Does it mean that lower frequency signal can transfer, in principle, more information than a higher-frequency one if both have the same power? The question is about principle limitations, regardless current technical possibilities of relevant devises. On the other hand, if the answer to this question is ""yes", do practical applications exist, or expected in future, where this limitation is important?
NO, it's not the number of photons which decides how much info you can send, it's the frequency.
JES
Hi Y.L. Shoshin ,
I guess "more information" means "more information per time unit". But a high baud rate is inherently represented by a high frequency signal. If you take a low frequency carrier and modulate it using a high frequency signal, the result is located at signal frequency +/- carrier frequency => instead of the low frequency photons of the carrier you'll get high frequency ones, located near the signal frequency.
However, there should be another effect: If two sources, located in empty space (no ionosphere or similar obstacles) generate EM fields of equal power and directivity, the frequency and baud rate of one low and of the other high then the critical distance at which the signal dips below the noise level is larger for the low frequency one.
I.e. slowness is rewarded with range.
Since information hasn’t been defined, the question simply doesn’t make sense. Since E(ω)=N(h/(2π))ω, it’s obvious that, for fixed E, N is inversly proportional to ω... There’s nothing particularly deep in this statement. The total energy, if the radiation is made up of photons of different frequencies, is a sum over the frequency range. Nothing very surprising about all this.
What is surprising and has non-trivial consequences (that aren't obvious from the relation between energy and frequency, however) is that the photons are not distinguishable particles
The non-trivial statement is that there exist physical processes that are sensitive not, just, to the product N(h/(2π))ω=E, the intensity of the radiation, but to ω, the frequency. The typical example is the photoelectric effect, where, whatever the number of photons, of frequency below a threshold frequency, nothing happens (the electric current remains zero) whereas, whatever the number of photons of frequency above the threshold frequency (not energy!) something happens (there's a non-zero current, whose value then does depend on the number of photons) even though the corresponding products may be very different.
This doesn't have anything to do with information, however.
The information carried by electromagnetic radiation is related to the entropy of the configuration of photons (when these can be resolved); it's minus this entropy. The relation between the energy flux, carried by electromagnetic radiation, and the corresponding entropy flux, has been worked out in the following Article Entropy of Radiation
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