There is no length or space in anything you just mentioned, hence no wave _length_. You talked about only time & energy -- obviously complementary quantities, but no space. I'm interested in electromagnetic waves that propagate, and that involves space. Of course you're not going to find my interpretation in the standard textbooks; I wouldn't bother posting if I didn't think that there was some novel insight here. At 09:09 AM 4/8/2014, Eugene Salamin wrote:

The quantization of the electromagnetic field has nothing to do with any possible graininess to space; that would only be an issue for quantum gravity.

An electromagnetic vibration can be resolved into normal modes.

Each normal mode is a harmonic oscillator, and behaves exactly as a particle in a harmonic potential, or a mass on a spring.

The energy levels are quantized: E[n] = (n + 1/2)hν, where ν is the frequency.

For the electromagnetic oscillator, when it has energy E[n], we say that there are n photons in that mode.

The number of wavelengths that occur in the mode volume doesn't affect the energy.

-- Gene

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________________________________ From: Henry Baker <hbaker1@pipeline.com> To: Eugene Salamin <gene_salamin@yahoo.com>; math-fun <math-fun@mailman.xmission.com> Sent: Tuesday, April 8, 2014 8:50 AM Subject: Re: [math-fun] What if Turing/Shannon/Bekenstein were wrong?

A single cycle of a wave; i.e., from 0 to 2pi.

This is my whole point: one way of looking at the quantum nature of electromagnetic waves is that it hints at the graininess of space itself. The wave is getting "sampled" by this grainy space into individual quanta.

At 08:12 AM 4/8/2014, Eugene Salamin wrote:

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From: Henry Baker <hbaker1@pipeline.com> A single photon of an electromagnetic wave of wavelength lambda has energy E = h*c/lambda.

The energy of a complete wave is computed by multiplying this equation by the wavelength to get:

Total energy = E*lambda = h*c = constant. --------------------------------------------------------------------------- What's a "complete wave"?