The central problem of physics at the turn to the 20th century concerned the emission and absorption of radiation as interaction between matter and light, formulated as the problem of blackbody radiation.

This is analogous to the interaction between a loudspeaker as matter and sound waves in the surrounding air.

There are two approaches to this problem, depending on the nature of light as streams of light particles or as light waves, one trivial and one non-trivial. One may compare with sound as “streams of sound particles” or as sound waves.

In the trivial theory light is viewed as particles with a trivial interaction between different particles, between matter as material particles and light as immaterial particles named photons. The mathematical model is a trivial particle model with material particles absorbing and emitting photons.

In the non-trivial theory a distinction is kept between matter as a system of material resonators and light as electromagnetic waves. The mathematical model is non-trivial as a wave equation with small damping subject to forcing describing a non-trivial interaction between material resonators and radiation as a balance of forces.

The non-trivial model is analyzed in Mathematical Physics of Blackbody Radiation and Computational Blackbody Radiation and discussed in a sequence of posts preceding the present one.

An unfortunate result of the trivial model, which has become very popular because of its triviality, is that the term “radiation” is used with two different meanings, as

electromagnetic waves
transfer of heat energy between material bodies.

The confusion has led to the popular idea of two-way transfer of heat energy between two material bodies with transfer of heat energy both from warm to cold and from a cold to a warm as “backradiation”. This idea is a result of the confusion: Since electromagnetic waves can propagate spontaneously in all directions, also heat can spontaneously transfer in all directions, both from warm to cold and from cold to warm.

In particular, the trivial model has obscured the essential difference between spectrum and heat transfer.

Maintaining the confusion the debate on “backradiation” can continue for ever, while understanding the distinction between 1. and 2. will end the debate.

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iceskaterfinland
March 12, 2012

Backradiation does not take place in a situation of two way heat transfer.

Backradition is part of a cooling process. Heat is flowing only from a hot body to a colder body.

Radiation is however travelling in two directions.

Radiation is not heat.

Heat is not radiation

*nobody* who understands the principles is talking about a two way transfer of heat when they speak of backradiation

Reply
- iceskaterfinland
  March 12, 2012
  
  Please take the time to watch this video I have made. The left hand block was heated to 80C in my oven and then left there for around 40 minutes or more before the video was made
  
  The temperature rises at the surface because the interior of the brick is heating the surface. The presence of the other brick which is slightly warmer than the cold room slows down the rate of cooling of the hotter brick and enable the internal heating to create a temperature rise where even so heat is continually flowing out of the surface of the brick at all times.
  
  Reply
  - Tor
    March 12, 2012
    
    Really nice experiment.
    
    Good job!
Tor
March 12, 2012

In the trivial theory light is viewed as particles with a trivial interaction between particles

Could you please be more specific what this trivial theory is.

What is a trivial interaction?

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Tor
March 12, 2012

Cleas, you do have a theory about interaction.

The problem I see is that it doesn’t resonate (pun intended 🙂 ) with a real physical description of light matter interaction based on classical electrodynamics.

Do you have some references to show that infrared emission must be a collective phenomenon? Since this seems to be you rational for your theory it seems to fail if infrared waves could be generated from small oscillators, like molecules or atoms.

So it may seem as your theory isn’t only against a particle description. It may also be against a classical electromagnetic description.

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Tor
March 12, 2012

Let me clarify by quoting from Hecht’s Optics.

Dispersion corresponds to the phenomenon whereby the index of refraction of a medium is frequency dependent. All material media are dispersive; only vacuum is nondispersive.

Maxwell’s Theory treats substantial matter as continuous, representing its electric and magnetic responses to applied E- and B-fields in terms of constants, epsilon and mu. Consequently, K_E and K_M are also constant, and n is therefore unrealistically independent of frequency. To deal theoretical with dispersion, it’s necessary to incorporate the atomic nature of matter and to exploit some frequency-dependent aspect of nature. Following H.A. Lorentz, the contribution of large numbers of atoms can be averaged to represent the behavior of an isotropic dielectric medium.

From here it is natural to study Jackson (in this context there is only one Jackson 😉 ) chapter 7.5 Frequency Dispersion Characteristics of Dielectrics, Conductors and Plasmas

Especially the part on water and its strong resonance band in the IR-range is more than readable 🙂

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claesjohnson
March 12, 2012

A trivial interaction is an interaction without a clear mathematical model, an interaction only described in words like “IR photons are emitted in all directions”.

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Tor
March 12, 2012

So you want a clear mathematical model for it.

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- Tor
  March 12, 2012
  
  Oh, I forgot.
  
  The photons are in there, if you know where to look…
  
  Reply
Claes Johnson
March 12, 2012

What is matter and what is light in the model?

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- Tor
  March 12, 2012
  
  Matter is the psi and light is in the F-field and in the covariant derivative D_mu.
  
  Reply
- Tor
  March 12, 2012
  
  Do notice that it is a Lagrangian density.
  
  Reply
claesjohnson
March 12, 2012

OK, what is then the conclusion concerning blackbody radiation from studying solutions to the equations?

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- Tor
  March 12, 2012
  
  You really don’t know what the model is?
  
  You were asking about a clear mathematical model concerning interactions between light and matter. It does not get expressed clearer than that.
  
  Reply
claesjohnson
March 12, 2012

Yes, I know, but I am a practical man and would prefer to see something coming out from the model so that it is not just an ornament.

Reply
- iceskaterfinland
  March 12, 2012
  
  Claes, If you are a practical man why do you keep ignoring the experimental evidence that is totally opposite what you claim is evidence supporting your position??
  
  Obviously a hot object can absorb radiation from a colder object.
  
  1. You have maxwells experiment which can easily be demonstrated to you by a chemistry department in Sweden
  
  2. being warm blooded at 310K will not protect you from the deadly gamma rays coming from a radiation source inside liquid helium at 4K
  
  Reply
- Tor
  March 12, 2012
  
  The model is very well tested for high energy situations.
  
  For practical situations with lower energy you should variate the Lagrangian with respect to the field A^mu (it’s contained in the D_mu) and arrive at
  
  which simply are Maxwell’s equations.
  
  Which brings me to your model. I honestly can not see what that system has to do with real radiating and absorbing atoms and molecules.
  
  It seems as if your model cuts off frequencies to conform it to a cut off, but in the process you decouple the theory from frequencies that are classically accessible. The finite precision argument are not valid since there obviously are a lot of phenomenons that develops in a way that are can not be calculated by a classical algorithm. Conclusion, a finite precision classical algorithm can not be the fundamental workings of nature.
  
  Reply
  - Tor
    March 12, 2012
    
    (ok, technically you vary the action formed from the Lagrangian density. Sorry for the sloppy use of terms)
iceskaterfinland
March 13, 2012

Claes, Do you have a reference for your definition of heat or can you specify what you mean by heat please?

For example does an atom bomb or a kilo of TNT at absolute zero contain heat?

My point being why are you saying that light contains heat?

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- iceskaterfinland
  March 13, 2012
  
  And I think it worth pointing out that when Tor was discussing this earlier with you, Tor was using definitions of heat that are not used by Europeans and the resulting conversation became very confused.
  
  However I think Tor had a point that got lost in that discussion because of the different definitions and resulting frustrations that developed out of that.
  
  Reply
iceskaterfinland
March 13, 2012

From the earlier spectrum to heat conversation

From Spectrum to Heat Transfer

———begin quotes——————

Claes

heat in thermodynamics is internal energy and internal energy = total energy – kinetic/potential/chemical energy, and this is the definition I use.

Claes

The set-up is thermodynamics with internal energy = vibrational energy of resonators = sum of kinetic and potential energies of resonators. In addition there is radiation energy and forcing energy, and there is a balance between all these energies.

Tor

Am I getting you right that you mean that heat is sensible energy in matter?

Claes

Yes, I use heat as sensible energy.

Iceskater

do you have a definition for “sensible energy?”

Tor

sensible energy corresponds to the excitation of the inner mechanical degrees of freedom in a quantum mechanical sense, so it includes electron excitation and spin.

———–End quotes

So it seems we agree already that heat energy is not the same energy as radiation energy?

So we agree already that light contains no heat?

So why is there an argument over backradiation where equal amounts of radiation are exchanged between a hot body and a cold body for the backradiation flow from cold to hot where no heat is being exchanged? 😦

Reply
- iceskaterfinland
  March 13, 2012
  
  From
  
  Two Proofs of Planck’s Law vs Backradiation
  
  Claes said:
  
  “I object to the idea that there is spontaneous transfer of heat energy from a cold body to a warmer body, because that violates the 2nd law, and I prove the 2nd law from basic wave mechanics”
  
  Firstly if you have a hot body and a colder body, that are not physically contacting by a conductor you cannot legitimately say that heat flows from the hot body to the colder body unless you use a definition of heat favoured by Tor. All you can say is energy flows from the hot body to the colder body due to the difference in vibrational energy of their molecules.
  
  Heat is not a substance that can flow via radiation.
  
  Using electronics for example you can have a large amount of power passing from battery A at 12 volts via a resistor to battery B at 6 Volts and have an electronic battery charger operating from B that is charging A with a smaller amount of power. The voltage of A will inevitably decline towards the voltage of B and the charging power thru the resistor until the charging power from B via the electronic charger to A will be in balance.
  
  Such an arrangement obeys the laws of conservation of energy and the second law of thermodynamics dispite the two way flow of energy.
  
  Heat is not a substance that can flow by electricity
  
  Reply
  - iceskaterfinland
    March 13, 2012
    
    A better electrical example would be the use of a very simple two metal electrical connection between two objects where the thermocouple so produced creates a voltage proportional to the temperature difference by cooling one junction and heating the other due to the Peltier effect discovered in 1834.
    
    Ie this simple two wire connection, one object is electrically cooled and and the other electrically heated while there is a temperature difference.
    
    Using the same method of generating electricity by the temperature difference between the hot object and the cold object, which cools the hot object and warms the cool object , additional circuitry could be used to electrically heat the hotter object by extracting heat from the cold object using the same Peltier effect. 🙂
    
    Heat would not be flowing other than by non-electrical conduction via the wires.
claesjohnson
March 13, 2012

Heat can be transferred by light (radiation) from one body to another, with heat the internal energy of the body as the sum of the kinetic/potential energy of the system of resonators forming the body.

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- Tor
  March 13, 2012
  
  This is, in your own words, an example of a trivial statement. One without a clear mathematical model.
  
  If you want to stay in a classical treatment, you should use Maxwell with dielectric properties.
  
  Reply
- iceskaterfinland
  March 13, 2012
  
  Claes, heat is not a substance that can be transferred between bodies via radiation.
  
  Please see my example of the Peltier effect to emphasise this
  
  Heat is not a substance that can be transferred by electricity.
  
  The peltier effect absorbs heat, creates electricity and electrically heats another object
  
  Reply
Tor
March 13, 2012

There is another very important issue you need to address.

You need to motivate your use of the Abraham-Lorentz force. Can you give your estimate where you show that the force contributes at all to the present situation?

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- iceskaterfinland
  March 13, 2012
  
  Tor, are you able to conform to the traditional description of the word heat so that we can agree that heat cannot be transferred? It seems the key to the issue dividing Claes from ourselves.
  
  Your definition was that heat is what is transferred when two bodies are different temperatures
  
  Claes said that heat is internal energy related to vibrations
  
  And yet Claes is mixing your ‘American’ definition with my ‘European’ one to say that heat is transferred by radiation.
  
  I have to say that i think your definition is wrong. And it is demonstrated as being wrong by adiabatic processes that do not have meaningful heat flow across the system boundary.
  
  Can you work with me on this please? We can if necessary go back to the other thread to see if we can resolve our differences on the heat definition back there. 🙂
  
  Reply
  - Tor
    March 13, 2012
    
    “Your definition was that heat is what is transferred when two bodies are different temperatures”
    
    You have misinterpreted the definition.
    
    The important thing is that heat is not something that gets transferred (heat is not a noun). Heat only exists at the interface between two systems. Energy is not heat when it enters the interface, and energy is not heat when it leaves the interface. Increase in internal energy has no fancy hairdos, there’s no identity in energy after transfer.
    
    As a side note, I don’t think this is an issue about, American vs European definitions. I’m educated at a European University here in Sweden.
  - iceskaterfinland
    March 13, 2012
    
    Tor, Earlier you were clearing making a distinction between thermal energy and a thing you called heat.
    
    (http://en.wikipedia.org/wiki/Thermal_energy)
    Thermal energy is distinct from heat. In the strict use in physics, heat is a characteristic only of a process, i.e., it is absorbed or produced as an energy exchange, but it is not a static property of matter. Matter does not contain heat, but thermal energy. Heat is thermal energy in the process of transfer or conversion across a boundary of one region of matter to another.
    
    What is your heat??
  - Tor
    March 13, 2012
    
    “Thermal energy is distinct from heat. In the strict use in physics, heat is a characteristic only of a process, i.e., it is absorbed or produced as an energy exchange, but it is not a static property of matter. Matter does not contain heat, but thermal energy. Heat is thermal energy in the process of transfer or conversion across a boundary of one region of matter to another.
    
    What is your heat??”
    
    What you write here is more or less identical with the definition of heat I use. Heat is defined as an inexact differential, it is not a statefunction, hence bodies can never contain heat.
  - iceskaterfinland
    March 13, 2012
    
    Tor, I quoted your definition of heat. 🙂
    
    I think you are confused due to your education.
    
    Total system energy is a state function. Potential energy is a state function.
    
    If a system has zero heat and has potential energy then if potential energy reduces then heat as a state function must be produced.
    
    Ie when that damn piece of lead falls heat gets created!
iceskaterfinland
March 13, 2012

Anyway. You agree that heat is not transfered by radiation or electricity?

Or do you?

When you say the following i cannot work out what you are saying

>>You have misinterpreted the definition.

The important thing is that heat is not something that gets transferred (heat is not a noun). Heat only exists at the interface between two systems. Energy is not heat when it enters the interface, and energy is not heat when it leaves the interface. Increase in internal energy has no fancy hairdos, there’s no identity in energy after transfer.”

So in a body that emits radiation, no heat exists in the body, but heat exists when emission occurs……but does not exist while in transit, then upon absorption it exists, then it does not exist???????

Reply
- iceskaterfinland
  March 13, 2012
  
  OK you are saying heat is what exists during the transfer?? But it is not something that gets transferred?
  
  Tor what the hell are you talking about please. 😦
  
  Reply
  - Tor
    March 13, 2012
    
    I think we are talking about the same process we only use different semantics. I mean that you misinterpret my description from the definition.
  - iceskaterfinland
    March 13, 2012
    
    Tor can you show me where heat exists and where it does not exist for the simple process of a body A cooling via emission and then another body B heating via absorption.
    
    1. Thermal energy exists in A
    
    2. Energy is emitted by a particle in A and thermal energy reduces and the body is cooler
    
    3. Radiation travels thru space
    
    4. Energy is absorbed by B and thermal energy increases and the body is hotter.
    
    Please make it clear to me where heat exists and where it does not exist for that simple process. Does heat exist? Or is it different to something that exists?
Tor
March 13, 2012

Claes, can you show the estimate of the Abraham-Lorentz force?

First I didn’t really think about it, but now I think that it is completely dwarfed by the other energies present in the model. Effectively it should be zero for an electron and anything heavier for all type of thermal radiation.

Reply
Tor
March 13, 2012

Here is my own estimate.

From the Larmor formula we see that the energy radiated is approximately

E ~ q^2*a^2*t / (6*pi*epsilon_0*c^3)

If f is the mechanical frequency of the oscillation and l the length scale we have

E_osc ~ mf^2*l^2

If the mechanical energy is much larger then the radiated energy the force is negligible

E << E_osc

The acceleration a for an oscillator fullfils

a ~ l*f^2

This gives

q^2*(l*f^2)^2*t / (6*pi*epsilon_0*c^3) <

(q^2/6*pi*epsilon_0*c^3*m)*f << 1

t = (q^2/6*pi*epsilon_0*c^3*m)

is a the timescale so we have the criteria

t << 1/f

as the a criteria for when the Abraham-Lorentz force is negligible.

For an electron this gives a timescale

t_electron ~ 10^-24s.

This corresponds to frequencies of 10^24 Hz.

Hence the force is only important for radiation wavelengths shorter then

lambda ~ 10^-16m.

This is well outside the range of thermal radiation.

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Tor
March 14, 2012

Ah, I was a little bit tired when I wrote down this earlier.

This gives

q^2*(l*f^2)^2*t / (6*pi*epsilon_0*c^3) <

(q^2/6*pi*epsilon_0*c^3*m)*f << 1

t = (q^2/6*pi*epsilon_0*c^3*m)

is a the timescale so we have the criteria

t << 1/f

After the first step the line isn’t complete, it should say

q^2*(l*f^2)^2*t / (6*pi*epsilon_0*c^3) << mf^2*l^2

Then notice that for one oscillation t ~ 1/f. This is not the same t as the later

t = (q^2/6*pi*epsilon_0*c^3*m)

Reply
Tor
March 14, 2012

For clarity I re-post the estimation.

*************************************************************************
From the Larmor formula (the formula gives the power radiated so we need to multiply with time duration) we see that the energy radiated is approximately

E ~ q^2*a^2*T / (6*pi*epsilon_0*c^3)

q is the electric charge, a is acceleration, T is the time duration.

If f is the mechanical frequency of the oscillation and l the length scale (amplitude) we have

E_osc ~ mf^2*l^2

If the mechanical energy is much larger then the radiated energy the Abraham-Lorentz force is negligible so we take

E << E_osc

as a criteria.

The acceleration a for an oscillator fullfils

a ~ l*f^2

This gives

q^2*(l*f^2)^2*T / (6*pi*epsilon_0*c^3) << mf^2*l^2

Using that T ~ 1/f gives

(q^2/6*pi*epsilon_0*c^3*m)*f << 1

Introducing

t = (q^2/6*pi*epsilon_0*c^3*m)

as a timescale we get the criteria

******************
*t << 1/f *
******************

as the criteria for when the Abraham-Lorentz force is negligible.

For an electron this gives a timescale

t_electron ~ 10^-24s.

This corresponds to frequencies of 10^24 Hz.

Hence the force is only important for radiation wavelengths shorter then

lambda ~c/f ~ 10^-16m
*************************************************************************

Reply
- Tor
  March 14, 2012
  
  This shows that the use of the Abraham-Lorentz force isn’t applicable in the present model. It’s obvious since we need emission of highly energetic gamma rays for any noticeable effect from the force.
  
  Reply
  - iceskaterfinland
    March 14, 2012
    
    Tor, I have put a bit of effort into trying to understand what you are saying about heat and what exactly heat is by your definition. I think you know that i have asked you to help me? My post is immediately before the last series of posts by you about 5 posts back.
claesjohnson
March 14, 2012

In my model the radiative damping is small, yet it has effect, and so I don’t see the logic of criticizing the model for have a small radiative damping. The model I consider is essentially the wave model considered by Planck in 1900, with a different analysis than Planck’s statistical.

Reply
- Tor
  March 14, 2012
  
  Small?
  
  It’s more than 10^9 magnitudes off from the limiting value where the effect becomes negligible.
  
  That is if you want to model existing matter, like electrons. And it gets worse for heavier particles since it scale as 1/m.
  
  Reply
  - Tor
    March 15, 2012
    
    10^9 magnitudes should of course say 9 orders of magnitude.
Michele
March 15, 2012

I think that in resonance the forcing on the oscillator can be thought of as given by a spring leaning on it at one its end while the other end is moved harmonically. The spring can only push and this happens if the speed of the forcing spring (Uf) is greater than that of the oscillator (Uo), the force exerted is F = a (Uf – Uo), the power generated is Pf = F*Uo = (Uf*Uo – Uo^2) that, in resonance, is equal to the sum of the dissipated power Pd = d*Uo^2 and that radiated Pr = r*Uo^4.
That is, the oscillator emits as the parabola Pr = a*Uf*Uo – (a + d)*Uo^2 which vanishes with Uo = Uf/(1 + d/a).
Of course, the formalism of the formulas should be revised and corrected.

Reply
Michele
March 15, 2012

Of course, the cut off is due to velocities, not to frequencies.

Reply
iceskater
March 16, 2012

Another observation about light and temperature that supports Prevost exchange theory that has been known about for hundreds of years is the following.

red glass absorbs green light and freely transmitts red light.

Surprisingly if you heat red glass it glows green in the dark. Which is pretty amazing and yet still absorbs green light and transmits red. The same thing is true for a variety of different materials. Pottery for example reverses the pattern when heated

So if the hot coals behind red glass are cooler than the hotter dimly glowing but now green glass you see a mixture of the red coming from the cooler hot coal mixed with the green from the hotter red glass.

Strange but true and known since long before Maxwells time.

And of course, as already commented upon, we would expect to see the cold green fungus as being near invisible when viewed thru hot red glass.

Reply
- iceskater
  March 16, 2012
  
  Similarly copper when in the presence of chlorine produces a green flame. If copper was in the hot coals glowing green then you would not expect to see the green light thru hotter red glass so you could easily compare the brightness of the green emitted by the glass only, to see if that were true. Nobody has disproved Prevost theory by experimental observation so a Nobel prize awaits the person to do the experiment if the results are not as expected.
  
  Reply
  - iceskater
    March 16, 2012
    
    And as i said before not realising that Maxwell had done a version of my experimental suggestion, somebody must surely have already looked at the cold copper flame thru hot red glass