Continuous EM fields vs. fixed freq photons

[csmcmillion]

I understand the classical view of EM fields as being (theoretically) continuous. What I don't quite get is how this can be reconciled with the QM view of photons coming only in fixed frequencies (The electromagnetic field may be thought of in a more 'coarse' way.). Is the number of possible photon energies/freqs just so great that we can treat EM fields as continuous for practical purposes? Perhaps related to Planck's constant?

Suppose I build a transmitter tuned at 100.00000000 MHz. By the classical view I can easily tune the transmitter to 100.00000001 MHz. But under the QM view I may not be able to, if the next freq of photons is, say, 100.00000005 MHz.

- Confused

 

[xts]

In an open space photons may take any energy (=frequency) you like. The frequency is quantizied only in closed areas, but the same you have in classical EM - where only \frac{\lambda}{2}=\frac{L}{n} waves are allowed. Actually, the quantisation is exactly the same as for classical EM.

Other issue is Heisenberg principle - in order to precisely measure energy, you must spend long time. But here again, you have exactly the same limit as for classical EM. In order to distinguish between 100.00000000 MHz and 100.00000001 MHz signals, you also need at least \frac{1}{2\pi}100{\rm s} (if I counted 0's properly...)

 

[Hellabyte]

Not sure if this is correct but...

When you pick a photon of a certain frequency it will have an electric field associated with it. Yes you can only have photons of discrete frequencies (with boundary conditions) but the electric field associated with whatever frequency you pick will be continuous in space.

 

[csmcmillion]

I didn't word my original question very well. What I meant to ask was as the number of possible photon energies/freqs just so great that we can treat the EM _spectrum_ as continuous for practical purposes?

 

[xts]

You just have to use common sense - if you consider small containers, which dimensions are comparable to \lambda then its better to be cautious. But in most cases continuous approach works fine.

 

[Bill_K]

If you're talking about a closed container, then the allowed frequencies for both electromagnetic waves and photons are discrete, since they're required to satisfy boundary conditions at the walls. If you're talking about an open domain, then both electromagnetic waves and photons can have any frequency whatsoever.

Furthermore, a photon does not have to have a unique frequency. Like any other quantum particle it can be a wave packet containing a spread of frequencies.