Poynting's vector - Observable - Force?

• member 11137
In summary, the conversation discusses the significance and limitations of the Poynting's vector in theories and works involving radiation. The vector must be zero in any inertial frame and there is a distinction between true and not really true physical parameters. It is also discussed whether the Poynting's vector is gauge independent in the electromagnetic theory and whether it can be associated with an observable. There is a suggestion that the Poynting's vector may not always be zero in an inertial frame and this raises questions about the existence of forces that only vanish if the observable associated with the vector commutes with the Hamiltonian. The discussion also touches on the tricky nature of the Poynting's vector and its invariance in different
member 11137
Certainly an horrible way of thinking and that's why I should like to get a fundamental critic about this:

As I can read in some threads, the Poynting’s vector is of a great importance (e.g.: to know if a radiation is present or not) in a lot of works and theories; in mine too. One of the biggest limitation in all discussions around this vector is the fact that it must be zero in any inertial frame and that we mainly stay in one frame of this kind.

I also have seen that one have to make a distinction between true and not really true physical parameter; i.e., true parameter are gauge independent. Is the Poynting’s vector gauge independent in the EM theory? [My answer to this question is yes if one can find a gauge for which the Schwarz’s condition of integrability holds along the time].

If yes, then it must be possible to associate an “observable” Ŝ to this Poynting's vector S and this observable should obey the usual law concerning an evolution along the time:
d< Ŝ >/dt = (i/hbar). <[H, Ŝ]> + <partial deriv. of Ŝ/along time>
Result: even in an inertial frame where obviously < Ŝ > = 0, one gets:
0 = (i/hbar). <[H, Ŝ]> + <partial deriv. of Ŝ/along time>
As one can demonstrate that (1/c²). partial deriv. of S/along time as the same physical units than a force per unit volume, if (1/c²). partial deriv. of Ŝ/along time can be understood as the equivalent of (1/c²). partial deriv. of S/along time in the language of the observables, then, even in inertial frames, one should have a relation like:
<partial deriv. of F/per unit of volume> equivalent to - (i/hbar.c²). <[H, Ŝ]>

What do you think of that? Is it the signature for the obligatory existence of forces that only vanish if the observable associated with the Poynting’s vector commutes with the Hamiltonian H of the system under consideration?

What are these forces? Logically, it should concern any system (set, collection) of EM waves. Also, it must concern a solely wave “travelling” in one of our laboratories and this would mean that this photon should “feel” or react to this force.

If all the demonstration made here is true (I have some doubts) then a solely photon could show a deviation each time that circumstances lead to <[H, Ŝ]> not equal to 0 in the laboratory. Has someone here a concrete example what are these circumstances looking like?
Thanks

Why must it be zero in an inertial frame?

masudr said:
Why must it be zero in an inertial frame?
Well; I think I was referring to considerations concerning the so-called famous ZPF. Could be that it is not always true. In fact the Poynting's vector is parallel to the speed vector of the wave and the wave has a constant speed (c) in an inertial frame.

It can't be zero.It's a part of $\Theta_{\mu\nu}$ for the classical em field...Unless the field is static (electro/magneto)...

Daniel.

dextercioby said:
It can't be zero.It's a part of $\Theta_{\mu\nu}$ for the classical em field...Unless the field is static (electro/magneto)...

Daniel.
Sorry for this question but what does $\Theta_{\mu\nu}$ mean for you? The EM strength tensor in the classical approach? If one consider the eigen(self) fluctuations of the static EM field, is the Poynting vector not zero? Despite of this, is the rest of my demonstration valid?

dextercioby said:
It can't be zero.It's a part of $\Theta_{\mu\nu}$ for the classical em field...Unless the field is static (electro/magneto)...

Daniel.
If the energy-momentum tensor is does not vanish then this does not imply that the Poynting vector is non-zero. The Poynting vector can be zero in one frame and non-zero in another frame. Recall that this vector determines the momentum of radiation as well as the flow of energy.

The Poynting vector is a tricky little bugger. Ya gots to be carefull with it.

Pete

pmb_phy said:
If the energy-momentum tensor is does not vanish then this does not imply that the Poynting vector is non-zero. The Poynting vector can be zero in one frame and non-zero in another frame. Recall that this vector determines the momentum of radiation as well as the flow of energy.

The Poynting vector is a tricky little bugger. Ya gots to be carefull with it.

Pete
Coming back to the discussion.
1°) "The Poynting vector can be zero in one frame and non-zero in another frame"; what you say means: the PV is not invariant (I interprete this relatively to the problematic of a frame transformation); it doesn't really answer to my question about the independance relatively to the EM gauge (I refer for this problematic to formula in Tanoudji)
2°) If one consider each event in "vacuum" as an EM oscillator: is it not correct to write <S> = 0 for an observer at rest at the middle point of these oscillations?
Thanks for more precise explanations

1. What is Poynting's vector?

Poynting's vector is a mathematical concept used in electromagnetism to describe the flow of energy in a given electric and magnetic field. It is denoted by the symbol S and has units of watts per square meter (W/m²).

2. How is Poynting's vector related to observable phenomena?

Poynting's vector is related to observable phenomena in that it describes the flow of energy in electromagnetic waves, which are observable in the form of light, radio waves, and other forms of electromagnetic radiation. It helps to explain how energy is transferred and propagated through space.

3. What is the significance of Poynting's vector in physics?

Poynting's vector is significant in physics because it helps to describe the fundamental relationship between electricity and magnetism, known as electromagnetism. It also plays a crucial role in understanding energy conservation and the behavior of electromagnetic waves.

4. How is Poynting's vector used to calculate force?

Poynting's vector can be used to calculate the force exerted by an electromagnetic field on a charged particle. This is done using the Lorentz force equation, which takes into account the electric and magnetic fields, as well as the velocity of the particle.

5. Can Poynting's vector be applied to other fields besides electromagnetism?

Yes, Poynting's vector can be applied to other fields, such as acoustics and fluid dynamics, to describe the flow of energy. However, its primary application and significance lie in the study of electromagnetism.

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