# Re: A mirror reflecting a plane wave may receive spin

>I wrote many times that E = - dA/dt. So, A is perpendicular to E. Modulus of A is proportional to E. Only if you consider E = E_0 exp(iwt), A = iE/w
>i the imaginary unit and w frequency ! Now A is proportional E or ? Just calculation with complex vectors ! You disprove yourself.
-------For a circularly polarized wave
E = Re{(x+iy) exp[i(z-t)]},
A = -\int E dt = Re{(-ix+y) exp[i(z-t)]},
(E.A) = (x+iy).(-ix+y) = -i+i = 0

>And if E is real A is purly complex and the Real part zero.You can turn it how you want - its not sensful !

> In vacuum sigma the conductivity is zero, so undeprndent how A looks J x A is zero because sigma = 0. So your waves on the vac have zero spin and this of shure is no reasonable spin theory.
> -------In vacuum J x A is zero because J x A is torque rather than spin flux. But torque, J x A, acts on the conductive mirror.

Nevertheless your torque is zero e.g. in a conductor (spin absorption).

-------I considered an ideal conductor (without absorption) in the
paper under consideration.

What about the surface torque for example at a glass - air surface when
light is total reflected in the glas. What's the torque in glas -
calculation please ! Whats the surface torque - if any in your opinion.

--------In the paper "Discrepancy between theory and experiment"
absorption of a circularly polarized light beam without an azimuth
phase structure in a dielectric is calculated in the frame of the
classical electrodynamics. We consider transferring of angular momentum
and energy to the dielectric. Our theoretic result differs from the
experimental result of Bishop et al. [6] (Phys. Rev. Let. V. 92, 198104
(2004)). We found that the torque acting on the dielectric consists of
a surface part and a bulk part that equal one another. The theoretic
value of the total angular momentum of the beam is twice as much as the
experimental result.
This paper is published at http://www.sciprint.org/

> Spin can only be defined if one assumes a complex field for radiation..
> Special relativity does not handle this So the only contribztions of relativity with respect to radiation is that photons are frequency shifted
> if you measure their frequency in a moved coordinate system. And i think thats fully enough.
> --------You are right, electromagnetic field is not a complex vector field, and electromagnetic field is a real vector field. But physicists use a mathematical tool, they write E = Re{E_0 exp(iwt)}. And let us stand a moved coordinate system aside.
You think only the real part is important ? This interpretation works
for the energy flux density (Pointing vector) thats right. Why do you
think that the index of refraction is complex ?
----------In the case of a complex refraction index you take the real
part in the end of a calculation as well.

You use complex fields or ? Why dont you strictly formulate your theory
in the real ? Probable because it is simply not possible. Again you are
wrong.
-----------Just the paper under consideration, i.e. "A mirror
reflecting a circularly polarized plane wave receives spin", is written