Is energy transport in electric DC setup quantized?

[gerald V]

I have to say first that I found quite a similar question under https://www.physicsforums.com/threads/poynting-vector-dilemma.331375/ However those thread ended without real answer.There shall be the following simple setup: A battery, and quite at a distance a light bulb. They are connected by two parallel wires. The entire configuration shall be located in, say, vacuum, and shall be operated stationarily.

This is what I assume to know:

Apart from minor distortions due to losses in the wires the Poynting vector field looks quite simple: The energy flows in the vacuum, parallel to the wires. In the spacetime picture the energy flux lines are timelike (a typical value for the velocity is about 2/3 of the velocity of light).

Such electromagnetic field is not a radiation field. The vector potential has one temporal component and one spatial component parallel to the wires. Both are independent of time. So there are no waves and no transversal degrees of freedom.

Questions:

• What I said above, is it correct?
• Is it true that energy transfer nevertheless occurs in quanta?
• If so, what field is to be quantized, what is the energy and the current of these quanta?
  

 

[anorlunda]

You are looking at it the wrong way. Field theory, including Maxwell's Equations and Poynting's Theorem can be derived from QED plus some simplifications. QED (quantum electrodynamics) itself is part of quantum field theory which depends on quantum mechanics (QM). QM deals with tiny discrete objects and discrete events and their properties. Those objects, events and properties are the quanta.

It is wrong to think that time, space, or electromagnetic fields are themselves quantized into "chunks"

 

[gerald V]

Thank you for that answer. But my confusion is still there. May I try to ask more precisely:

First, what is the physical situation? Without doubt, the light bulb radiates off energy in quanta (with thermal spectrum). My question is: The energy transfer from the battery to the light bulb, does it occur in quanta as well? I conjecture that the answer is yes and that the energy of the quanta is given by the voltage of the battery.

Second, if the energy transfer from the battery to the light bulb occurs in quanta, what is the adequate mathematical description?

 

[BvU]

My question is

charge carriers 'pop off' the battery and their energy is quantized only in principle: there is so much movement in charges contributing to the fields that the (already extremely close) energy levels are smeared out to a continuum ('band').
The adequate description is Ohm's law .

 

[mfb]

The energy transfer from the battery to the light bulb, does it occur in quanta as well?

I don't think you can define "energy transport" precise enough for such a question.

The light bulb emits energy in discrete steps, but purely based on its temperature, not based on the input electricity. There is no "1 eV in, 1 eV out" going on. This is much more direct with LEDs where the electrons moving from one region to another lead to the emission of photons.