söndag 28 augusti 2011

Pushing a Swing: Essence of Blackbody Radiation

Satyr pushing a Nymph on a swing as part of the Dionysian cult.

The essence of blackbody radiation can be understood from a model of a swing containing the elements of
1. swing or oscillator
2. resistance (radiative or viscous dissipation)
3. forcing (exterior force)
from the following balance of forces:
• swing force + resistive force = forcing.
The essence connects to the interaction of the forcing with the swing, more precisely if the forcing is (i) in-phase with with the swing velocity or (ii) out-of-phase with the swing velocity.

In case (i) the swing is pushed by the exterior force when moving in the direction of the force. The force thus changes direction at the extreme positions of the swing.

In case (ii) the phase is shifted by a quarter of a period so that the force changes direction when the swing is in its bottom position.

The interaction between the swing and the forcing according to (i) or (ii) is determined by the size of the resistive force:
• large resistive force gives (i) with little interaction between swing and forcing; exterior force balanced mainly by resistive force,
• small resistive force gives (ii) with possible interaction between swing and forcing; exterior force balanced mainly by swing force.
The catch is now that in blackbody radiation the resistive force is small which means that
there is an interaction between the swing and the forcing as in (ii): Under increasing forcing the amplitude of the swing increases until the energy of the radiation balances the energy of the forcing, with the swing acting as reservoir of (heat) energy.

In other words, under increasing forcing a blackbody heats up until the radiance balances the energy of the forcing.

The interaction between the swing and the forcing can be turned around so that the resistance acts as input forcing and the exterior forcing is considered as the outgoing forcing with the swing acting as an amplifying resonance board allowing considerable output under small resistive forcing (from the strings of a piano or guitar).

In this perspective, there is a cut-off of high frequencies in outgoing forcing, which can be understood as an inability of the resonance board to amplify sufficiently high frequencies.

The mathematics of the above scenario of blackbody radiation is presented in my Sky Dragon article Computational Blackbody Radiation. Also recall Piano as Blackbody.

The basic idea is to understand blackbody radiation in an educated way as a wave mechanics phenomena and not in a primitive way as a particle mechanics phenomenon of massless photons streaming in an out.

A blackbody in equilibrium with some forcing radiates what is absorbed. What is then the distinction from reflection which also sends out whatever comes in?

Yes, you are right: In reflection there is no swing acting as a recervoir of heat energy, which can change under changing forcing:
• A blackbody absorbs the incoming waves into its interior (into the swing) before radiating out what is not stored in its interior recervoir.
• A reflecting body simply sends back what comes in without changing its interior state.
• A blackbody thus represents real interaction between matter and light/radiation (electromagnetic waves), while in reflection there is no such interaction.
The beauty of many blackbodies interacting by radiation, as opposed to many bodies interacting by reflection, is that the internal states of the blackbodies become harmonized to the same common temperature, while the reflecting bodies keep their initial temperatures.

You may compare with the following student reactions to teaching:
1. The student understands, absorbs and re-emits what the teacher says.
2. The student does not understand anything, absorbs nothing and only repeats like a parrot what the teacher says.
It is clear that 1. is more interesting than 2., that blackbody absorption/emission is more interesting than reflection.

3 kommentarer:

1. That's a rather beautiful explanation (even if I maybe don't quite fully understand it).

Might one think of incoming radiation to the blackbody as consisting of little pushes to the swing that occur at some frequency? If this frequency is the same frequency as the swing, the swing will store energy (i.e. swing higher). If not, it won't. And this is why some things (e.g. CO2 in the atmosphere) absorb energy at one frequency but not others?

2. Yes, absorbs and then emits, and heats up from high freq forcing.

3. Claes, thanks for your model of the swing as I eventually made me understood a mechanical significance for the reactive power.
Your forcing F is a tangent force and its useful effect is the tangent velocity v of the swing so that the active power is Fv.
At the same time there acts also a centrifugal force that doesn’t give an active work on the swing as it is always orthogonal to the velocity but it changes the length of the swing and so the potential elastic energy of its ties.
Also this energy is due to the work of the forcing and at the end the useful power absorbed by the swing is lesser than Fv (apparent power) because part of that is exchanged with the ties as reactive power.
In this way there are no longer ghosts and the reactive power assume a real meaning.
Michele