- #71
sophiecentaur
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sru2 said:I have a problem with Mr Shannon's work, or perhaps it is an interpretation of it. Read this:
How can R exceed C?
Let me provide an example. Lets assume I open a channel on 20Khz. I define 1 bit to be exactly 1/20000 per second, in other words, a single period. The maximum I can send information (i.e. R) is 1/20000 per second, but the capacity (i.e. C) is 20000 bits per second.
Now this may seem strange until I mention this part. What size is a photon?
A hertz is defined as cycles per second. So a 1Hz photon is the same size as a 20Khz photon, that is, they are both 1 light second long. The wavelength of 14,990m must be packed into that 1 light second. This means, at 20Khz, each period is:
299 792.458m / 14990m = 19.99m
The question then becomes, is a photon 1 light second long, or is it 19.99m long and 20000 represent a 20Khz signal?
Now if this seems odd, consider the following. If the photon was 1 light second long, then every signal, regardless of its frequency, would take the same amount of time to detect (i.e. at least 1 second). Thus, a photon must be a single period.
This means that Mr Shannon is wrong, or his work has been interpreted incorrectly.
Did he understand quantum theory?
Do you? I think this is a bit of a blind ally in your view of the system and that photons are not relevant to any of this classical / mathematical topic. You say that a photon is "a single period". Where is your justification for that? Single period of what? If you have a channel, operating at 10GHz and 1Hz wide, your photons are a million times the energy / frequency of photons in a similar channel that is operating at 1kHz. Your channel, in principle, need not involve EM in the link at all (apart from the EM forces involved between atoms); you could use modulated sound. Discussing the 'extent' of a photon is a very slippery slope. As far as I am aware, photons are regarded as point particles (of no extent), these days and that seems to fit the evidence.
What do you mean by that statement? Do you mean a bitstream in which the bits have a period of 1/20,000s? Do you mean that you are modulating the 20kHz carrier with a binary bitstream with a rate of 20kb/s? Shannon is not concerned with just a binary channel, in any case and the possible bits per channel Hz is not as simple as you imply. You can have a multilevel signal, operating in a given bandwidth and the limit arises, basically from the uncertainty in which discrete level to choose in your receiver in the presence of noise. (Hence the SNR factor). The limit is what you can achieve with infinite computing power / decoding time but the practical limits seem to be never better than than half the attainable limit (Not the Shannon limit).