# Uncertainty-principle and the Maxwell formalism of electromagnetic waves

An electromagnetic wave (like a propagating photon) is known to carry it's electric and magnetic field-vectors perpendicular and each depending on the differential change of the other thus "creating" each other and therefore appearing in-phase and reaching their minima/maxima together. I'm interested to know whether there was any uncertainty as a principle discussed in the underlying principles of the Maxwell equations, like $\Delta E \Delta B \geq \hbar$. I appreciate links, hints and answers.

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Classical, i.e. Maxwellian, Electrodynamics is a non-quantized theory, so it's not bound to have this kind a heisenberg-like uncertainty relation. QED have this kind of relation for Electromagnetic field amplitudes. Remember that you can have a electrostatic field configuration(think on a uniformely charged) sphere that have (classically) $\vec B=0$ in the whole space, and also you have a well defined $\vec E$ so both $\Delta E$ and $\Delta B$ are zero. Also remember that the electromagnetic field is a single object, in both classical and quantum electromagnetic theory. – Hydro Guy May 7 '13 at 15:03
@user23873 All right, I have to admit that classical mechanics always bothered me because of it's idiosyncratic assumptions. I think I'll have to have a deep look in a Feynman lecture of QED. – JuSchu May 7 '13 at 15:53

One can see the consistency with the Heisenberg Uncertainty Principle by the definition of wavelength and frequency of the electromagnetic wave:

lamda*nu/c=1 where c is the velocity of light

Multiplying both sides by h and considering lamda as delta(x) and p=h*nu/c for a photon,

lamda*h*nu/c~h

delta(x)*delta(p)~h

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Yes, @anna v, but still, within this uncertainty of the electromagnetic wave in itself (as a hole), I can not see whether it could be theoretically possible to detect the magnitude of the electric and the magnetic vector simultaneously. – JuSchu May 8 '13 at 10:19
the photon is an elementary particle, it has no E or B in the sense of classical EM wave. If you want to see how the classical wave is built up by an ensemble of photons see this blog entry motls.blogspot.com/2011/11/… – anna v May 8 '13 at 11:54
Thx @anna v. I was just trying to glue this with the statement "The electric and magnetic fields of a single photon in a box are in fact very important and interesting", being part of a broadly accepted answer <a href = "physics.stackexchange.com/questions/47105/… this question</a> concerning the work of Serge Haroche. I am willing and ready to read and to learn and the road to reality needs good shoes. – JuSchu May 8 '13 at 15:30
@mods. A wrong mini-Markdown formatting occured. My fault. Did I miss a preview function on comments before adding my wrongly formatted link to the comment? How can I fix it? – JuSchu May 9 '13 at 15:17
@dmckee there is a comment for mods here – anna v May 9 '13 at 19:16