Does light have a temperature?

[natski]

Thanks for all the input and interest so far. Some interesting points made and some other rather unneccessary heated comments somewhat off-topic. I have made a few observations about this argument.

- The definition of temperature is not very clear and is depserately needed to give this debate closure.

- We have to use a quantum view over classical since when it comes down to it classical radiation isn't a great description of reaility e.g. UV catastrophe.

- Is there a quantum definition of temperature for us to use?

Another point of interest to me is considering light as an electromagnetic wave as opposed to the photon model which has been favoured so far. Light is afterall simply a magnetic field propogating orthogonal to an electric field, which are both self-perpetuating. In this view, can you really assign a temperature to a magnetic field for example? Can you take an iron magnet and say the field has a temperature of x K? I appreciate this is somewhat different to an electromagnetic wave but it is a point worth considering.

Secondly, in terms of colour temperature, as is sometimes used, I believe this is referring to a hypothetical blackbody radiator emitting light of wavelength x nm and therefore being at a temperature of y K. This is an example of the temperature assigned to the light *not* being of the light itself.

Finally, talking about thermometers seems rather pointless to me. If you shine a beam of light on a thermometer, yes you are heating up the thermometer but at the end fo the day the thermometer is still only measuring the temperature of its outer casing.

Natski

 

[Andrew Mason]

That is a myth. E = mc^2 was not obtained by Einstein. His 1905 derivation is wrong and the formula was already known before for radiation by other people. The firts that derived E = mc^2 for any kind of energy was Poincaré, one of true fathers of relativity theory.

Are you saying that Einstein was not one of the true fathers of relativity?

AM

 

[SpaceTiger]

- Is there a quantum definition of temperature for us to use?

I think as long as it isn't specific about kinetic energy or motions of molecules, then the classical definition works perfectly well in the quantum world. The thrust of my argument is that the concepts are all the same for radiation, it's only the history and practicality that has limited some of our definitions to matter.

Another point of interest to me is considering light as an electromagnetic wave as opposed to the photon model which has been favoured so far. Light is afterall simply a magnetic field propogating orthogonal to an electric field, which are both self-perpetuating. In this view, can you really assign a temperature to a magnetic field for example?

The classical analogy to an equilibrium distribution of photons would be a distribution of oscillating modes. However, it turns out that this view doesn't even work in reproducing the blackbody spectrum (see Ultraviolet Catastrophe), so classical E&M fields probably can't carry a temperature.

Secondly, in terms of colour temperature, as is sometimes used, I believe this is referring to a hypothetical blackbody radiator emitting light of wavelength x nm and therefore being at a temperature of y K. This is an example of the temperature assigned to the light *not* being of the light itself.

"Color temperature" is not a real temperature, even by my definition, it's just one of those "effective" temperatures I was talking about earlier.

Finally, talking about thermometers seems rather pointless to me. If you shine a beam of light on a thermometer, yes you are heating up the thermometer but at the end fo the day the thermometer is still only measuring the temperature of its outer casing.

Yes, I don't like the idea of using our measuring instruments to define a concept either. If they were designed to measure something, then we must have had some concept of that "something" prior to constructing them.

 

[Renge Ishyo]

I posed the question of "Does light have a temperature?" to one of my friend's good pals, who is busy at the moment polishing off a PHD in Physics. His response? A lot of laughter, followed by "That's almost as good as asking whether or not light has a sound."

I suppose the proof of the wisdom gained in his studies is that he never actually attempted to answer the question...

 

[SpaceTiger]

I posed the question of "Does light have a temperature?" to one of my friend's good pals, who is busy at the moment polishing off a PHD in Physics. His response? A lot of laughter, followed by "That's almost as good as asking whether or not light has a sound."

This is getting really childish. If your friend would like to contribute or you would like to repeat a real argument he has to my posts, by all means. Otherwise, I don't see what you're adding to this thread.

 

[Juan R.]

Chronos already provided a link which gave multiple definitions for the word "temperature" and concluded that there was no established one. The wikipedia is not universally considered to be the final word on physics definitions.

Actually, you have to go a bit deeper than the standard definition of temperature to find out what limits it. The definitions for temperature ARE vauge (even the one on wikipedia). However, temperature's definition no matter where you look depends on heat, and heat is a concept directly related to internal energy. It is the definition of internal energy that limits what the term temperature can encompass, that term is not defined for particles below the molecular level (since it is a generalization that stands for the sum of all energy processes taking place below the molecular/atomic level). Unless you can find a defintion of internal energy that contradicts that?

That is a myth...His 1905 derivation is wrong and the formula was already known before for radiation by other people.

I wouldn't be surprised, but at the same time my understanding is that Einstein did do a binomial expansion that included the rest energy of matter in it sort of as a sidenote (people discovered the signficance of it completely independant of Einstein?). Either way, if we argue about definitions and can't get our story straight you don't even want to touch history.

If your refer to this link http://www.temperatures.com/wit.html

I would say that definition (initial and point 5 on website) is restrictive. Other beliefs about temperature are wrong. The wiki is not a good reference also.

The link initially refers to the concept of energy in ideal gases. That is, gases of molecules without internal structure (pointlike ones) and with a rigid spheres intermolecular potential. In that restricted case (and only then) T is

A measure proportional to the average translational kinetic energy associated with the disordered microscopic motion of atoms and molecules.

the concept of temperature is related but not restricted to heat. I heard in this thread that temperature is "not defined" or "ill-defined". This is not correct, the only definition of temperature (axiomatic one) is

<br /> \frac{1}{T} \equiv \frac{\partial S}{\partial U}<br />

Note that the concept of heat is not directly invoked in the definition.

Above definition when applied to an ideal gas recovers the kinetic temperature which is defined on translational motion only.

Temperature, as already said is valid "elsewhere". Has a single atom temperature? Of course.

Take a macroscopic system at equilibrium. It is at T. A system is at equilibrium if you split it into two parts and each part has temperature T. Doing this spliting again one obtains that the temperature of a single atom in the systems is T. Formally this follows from the extensive property of both internal energy and entropy.

In fact for a system at equilibrium one has

<br /> \frac{1}{T} = \frac{S}{U}<br />

and if one works in the "field representation" of thermodynamics (TIP)

<br /> \frac{1}{T} = \frac{S}{U} = \frac{\rho _{S}}{\rho _{U}}<br />

where the "rhos" are densities (field quantities) which follows from extensive property. Working at molecular level, one can write

<br /> \frac{1}{T} = \frac{S}{U} = \frac{s}{u}<br />

which also follows from extensive property. s and u are molecular (atomic or particle) quantities verifying the extensive property. for example.

<br /> U = N \ u<br />

with N the total number of molecules (atoms or elementary particles).

regarding E = mc^2 simply to say that Einstein derivation is restrictive and wrong and formula was obtained before by other people (e.g. Poincaré) therefore there is an idea of Einstein plagiarized Poincaré works. A thesis sustained by Einstein claim that newer read work of Poincaré and Lorentz when historical evidence says the contrary.

On any case, the formula, in its modern sense, is atributed to Poincaré.

 

[Juan R.]

Are you saying that Einstein was not one of the true fathers of relativity?

AM

Still i am researching that but all point to Albert is not. The most surprising is that there is a sound basis for claiming that Einstein plaguiarized the work of others. For example, a recently discovered and studied correspondence with Hilbert shows that Einstein says not the true to Hilbert, doing wrongly believe to Hilbert that Einstein had been the father of GR. See

http://canonicalscience.blogspot.com/2005/08/what-is-history-of-relativity-theory.html

for some preliminary data. There are some small errors, like the title of reference 1 and translation from French of one of quotes (as correctly pointed by Javier Bezos on sci.physics.research (e.g. see https://www.physicsforums.com/showthread.php?t=85787)) but, basically, the web document is correct and well based.

I am working now in showing how Poincaré relativity is not diferent of Einstein relativity and how Einstein plaguiarized it in the light of new data i obtained.

Note: perhaps this interpretation of history is shocking for you but idea of Einstein is not the father of relativity was already sustained in the famous two volume work by Whittaker (see reference 4 in above link) and is sustained by more and more modern works.

 

[Andrew Mason]

Temperature, as already said is valid "elsewhere". Has a single atom temperature? Of course.

Take a macroscopic system at equilibrium. It is at T. A system is at equilibrium if you split it into two parts and each part has temperature T. Doing this spliting again one obtains that the temperature of a single atom in the systems is T.

I think you are forgetting the fact that the atoms at a given temperature can have a wide range of kinetic energies, including 0. If the last atom has 0 KE, does this mean it is at absolute 0?

Temperature is fundamentally a macroscopic quality. A single atom cannot have a temperature any more than a single water molecule can feel wet.

AM

 

[Juan R.]

I think you are forgetting the fact that the atoms at a given temperature can have a wide range of kinetic energies, including 0. If the last atom has 0 KE, does this mean it is at absolute 0?

I think that you are confusing average temperature with instantaneous temperature. Of course, temperature for a small system is a fluctuating quantity but is still defined.

T = \ &lt;T&gt; + \ \delta T

Precisely average temperature &lt;T&gt; -or average kinetic energy &lt;KE&gt;, if one restrics just to ideal gases where there are not others forms of motion- is computed precisely by the average over all temperatures or kinetic energies availables to each atom (particle, molecule, etc).

Absolute zero is when there is not motion. An atom at rest has 0 K translational but still the rest of components of temperature (electronic, nuclear, etc.) are not zero.

Temperature is fundamentally a macroscopic quality. A single atom cannot have a temperature any more than a single water molecule can feel wet.

AM

This is a common misconception. There is nothing on the concept of temperature related to macroscopic matter. That is, one can define temperature for non macroscopic matter, including single atoms or nucleus.

I already said in post #66

<br /> \frac{1}{T} = \frac{s}{u}<br />

where s is the entropy of a single particle (atom, molecule, etc.) and u its internal energy.

I know this very well because one of our research programs is on nanothermodynamics.

In physchem/0309002 already did a general discussion of commom misconceptions regarding thermodynamics of small systems and presented a general formulation of thermodynamics (beyond classical one) which received rather interest from experts (e.g. i was invited to participate on the conference "Frontiers of Quantum and Mesoscopic Thermodynamics"
26-29 July 2004, Prague, Czech Republic but then i rejected because my other obligations).

Once some copyright issues were solved, the above preprint and other novel material including a webpage will be freely available on www.canonicalscience.com in brief

Whereas, you can consult

Ger J. M. Koper and Howard Reiss. Length Scale for the Constant Pressure Ensemble: Application to Small Systems and Relation to Einstein Fluctuation Theory. J. Phys. Chem. 1996, 100, 422-432.

on literature for an common application of thermodynamics to systems as small as 10 or 100 molecules.

 

[Renge Ishyo]

Juan, I cannot prove you wrong. At the same time I am inclined to agree with Mr. Mason, and support the notion that "temperature is fundamentally a macroscopic quality". If someone were to ask me, "Does light have a sound?", my answer to that would also be that sound is fundamentally a quality associated with molecular movement and simply is not defined in terms of light or any other process below the molecular level. Personally, do I really think that the rules of physics do not extend to processes occurring below the molecular level? NO, but that's not the point here! The point is that we don't create the terminology, we try to figure out what the consensus is in the scientific community and why they agreed to define things in such and such a way (ultimately, the definitions and words we are using belong to "the group" after all).

In this case, an overwhelming number of sources that I have read in my studies (and in a quick glance online) have linked temperature to heat and thus ultimately to internal energy. Internal energy limits our discussion to the "molecular/atomic level". So the question is, why does a large portion of the scientific community define it this way? This distinction, to ME, makes sense, because we can measure and verify processes at the molecular level directly whereas submolecular processes we usually have to measure indirectly, which limits the amount of things we can "carry over" into quantum physics (unless/until our technology makes the transition fully possible). I am sure you know, mathematics aside, it's very hard to find experimental evidence to support many of the theories brought forth once you go below the atom (not saying it hasn't been done, just that it's very hard...which probably explains why it's taken us so long to get to quantum physics. If we can't even know what light really is, how CAN we experimentally measure it's temperature and be convinced that our results aren't misleading us?).

For me, when the kid on the moon asks me "why the great discrepancy in measured temperature?" after doing his experiment, I tell him that on Earth light interacts with the electrons in atoms which ultimately gives rise to their molecular movement (increasing the air's "temperature"). The increase in movement in the molecules in air means that they in turn interact with the molecules in your thermometer until the two reach a relative equilibrium with one another. In contrast, on the moon there are no "molecules" in the atmosphere. So when light passes through it does not interact with any electrons or molecules because they simply are not there. Since there is no molecular movement in the "air" due to the lack of molecules present, light cannot induce an increase in temperature in the air in the same way it can on earth. Your thermometer would read a much lower temperature than that on Earth even though the same light is present. Am I right in saying that? Maybe maybe not, but at least I can test my hypothesis experimentally, so it's still science.

If your friend would like to contribute or you would like to repeat a real argument he has to my posts, by all means. Otherwise, I don't see what you're adding to this thread.

Well, we ARE squaring the circle here. If you think I have any expectation that anything I am going to say is going to sway your opinion and provide some notion of progress to the conversation then well... I don't. I am just expressing my opinion on the matter, which is what these places are for Maybe you guys will find some experimental evidence someday that conclusively proves that light (for example) can gain and lose heat/temperature as it travels through space independent of any kind of interaction with molecules (hence, conclusively proving that it behaves identically to temperature and the transfer of heat as they are defined in thermodynamics). If/when you can do that, I'll owe you both a drink.

 

[Juan R.]

Juan, I cannot prove you wrong. At the same time I am inclined to agree with Mr. Mason, and support the notion that "temperature is fundamentally a macroscopic quality".

I'm sorry to say this but i think that you are rather confounded in those topics.

Let me simply to say

"Frontiers of Quantum and Mesoscopic Thermodynamics"

Quantum and mesoscopic =/= macroscopic.

Of course, you can claim that the only known thermodynamics is that of 19th century that you appears to know very superfitially. Temperature is not defined in terms of heat transport or similar. I already said which was the definition. Of course you can ignore it.

No problem

I wonder like people measure heat capacities for single nucleus!

 

[SpaceTiger]

Juan, I cannot prove you wrong. At the same time I am inclined to agree with Mr. Mason, and support the notion that "temperature is fundamentally a macroscopic quality".

What bothers me most is that you are arguing with me, yet you don't understand my objection. It has nothing to do with macroscopic vs. microscopic (AM's quote was taken out of context), it has to do with one type of particle to another. Photons and electrons (for example) are both elementary particles and they both have equilibrium distributions corresponding to a certain temperature. The primary difference, as I said before, is their relative self-interaction rates. There are many particles that can interact (such as the neutrino), but only do so very seldom. As a result of this, their behavior (in this respect) is very similar to that of light, yet they are matter and they would qualify for most of the definitions of temperature that light doesn't fit.

Maybe you guys will find some experimental evidence someday that conclusively proves that light (for example) can gain and lose heat/temperature as it travels through space independent of any kind of interaction with molecules (hence, conclusively proving that it behaves identically to temperature and the transfer of heat as they are defined in thermodynamics). If/when you can do that, I'll owe you both a drink.

Despite your misunderstandings and misuse of the word "molecules", I would say that this is a good way to conclude the argument. As far as we know right now, light cannot interact with other light without some influence from matter. I don't think this is qualitatively important for the definition of temperature, but you're free to use whatever definition you choose.

 

[Gir]

But the question asked whether LIGHT ITSELF had a temperature. We often say that light has a certain temperature, but what we really mean is that a black body would have to have that temperature in order to emit that wavelength of light. But this does not mean that the LIGHT ITSELF has that temperature.

AM

the light is stimulating atomic movement, so technicly, it is generating heat.

 

[Jonny_trigonometry]

I've always thought that a photon is at absolute zero, since it doesn't perceive time, and therefore has to movement in it's rest frame. Being that temperature is a measure of average kinetic energy or simply movement of the things contatined within the sample, if the sample is a single photon, then it's at absolute zero because all kinetic energy, velocity, momentum is time dependant. hmmm, come to think of it, it's division by zero, so it could very well be at infinate temperature.

 

[leright]

the light is stimulating atomic movement, so technicly, it is generating heat.

You don't understand this thread. There's a difference between light GENERATING heat by stimulating atomic movement (therefore producing a temperature in the surrounding atoms or molecules), and the light itself having a temperature. Think of light in a vacuum...does this light have a temperature in the absence of molecules and atoms? I don't think the idea of a thermometer heating up in this light-containing vacuum necessarily means the light itself has a temperature. I think to answer this you need to know if the photons themselves have mass, because to have kinetic energy (and therefore temperature) you need to have mass. IF photons have mass, then I suppose light has temperature. The question of whether or not photons have mass is beyond me.

 

[timeformation]

one word, superconductivity, study it, you will understand... cosmic foam.

 

[ZapperZ]

one word, superconductivity, study it, you will understand... cosmic foam.

Can you please explain how what you wrote here have any relevance to the thread?

Zz.

 

[tdunc]

If I had to define temperature I would Include somewhere in my definition the magnitude of potential energy, such that whenever it happens to collide or however it happens to transfer its energy it does so according to potential energy. So Gamma rays have a potential energy of x, radio waves a potential energy of y being considerbly less than x. A photons temperature can be said to be its energy level with reference to the EM Spectrum, correction its wavefunction, and is inherently a value determined by what electron emitted it. So in other words we can go further to say that an electron itself has a temperature and it can gain or lose temperature by emitting a photon such that the photons energy is the "temperature lost equivilent". This photon will inevitibly be absorbed later on by another electron, governing the transfer of heat per say or it is at least one definitive aspect of the quantum mechanical process of thermodynamics and statistical temperature.

Temperature can be measured by humans. Temperature in that context is purely an invention by our mind to know when a change in normal thermodynamic modes in our bodies molecules occurs-- this information handled by our nervous system. That is the top of the "what is temperature" pyramid along with anything that can show the difference in Temp for a Nbody system, thermometor of course. Breaking that down one level I think we all know how that works, interaction between molecules/ atoms blah blah, Thermodynamics. Breaking it down one more level to atomic particles themselves... "Do photons have an temperature?" Why Not? Of course you could say that, absolutely. But an GOOD point was made...

"I think to answer this you need to know if the photons themselves have mass, because to have kinetic energy (and therefore temperature) you need to have mass. IF photons have mass, then I suppose light has temperature."

Not to mention it would need some kind of mass to EXSIST and to SCATTER.


Space Tiger, I just want to clarify something. You say

"Boson-boson scattering does occur"

Which I was going to ask you about without a doubt, cause I got to know if its true, but then I keep reading and you said

"As far as we know right now, light cannot interact with other light without some influence from matter."

So now I am confused, seems like a contradiction of statements? Or this some influence with matter part the part that makes it not contradict?, care to elaborate? I hope you don't mean it being absorbed kinda interaction...then again, what else is there? No mass, no charge...

FYI I do not think photons can scatter NOR interfere with other photons DIRECTLY if we assume no mass nor charge exsists. Which goes to say that I agree with your statements regarding various light sources being able to be present without interaction with each other to become in equilibrim of energies such that light could never obey a law defined by thermodynamics with interaction in itself. You could mathmatically find an average temperature ie. average kinetic or otherwise energy level, But light will never find an average temperature with itself, because light does not and cannot interact with other light. The very definition of a boson is such that it can occupy the same space Without Interference -- not enough localized mass. Only in context of a very large almost finite degree of decoherence could the argument be made that a potential exsists for light - light interaction. This is how I attempt to deal with how light is able to scatter with Any particle, because it and whatever little mass it has becomes localized ie. collapsed wavefunction. - Adding to that the Decrease in probability amplitude of P defines the classical particle nature at that time such that a classical elastic collision can and will occur given a mutual collision course with another particle whose wavefunction happens to be or at the moment of wavefunction interference, collapse ie. Free ionized electrons in air, Compton scattering.

Back to topic, You'll find that the temperature as it relates to photons is ALSO related to the density of said photons per unit area, such that for example focusing light by means of a magnifying glass, you increase the energy density of an arbitrary unit of space. This energy is absorb as is and translates into a greater change in kinetic energy for a greater energy density. Meaning if the light was more spread out whatever absorbs it will absorb fewer photons per unit area. Photons that are absorbed transfer their energy perhaps not even in the form of kinetic energy, but it is then translated or converted into kinetic vibrational energy ie. EXCESS vibrational energy that the electron is given and maintains so long as it keeps interacting* with photons, absorbing photons, then after it stops absorbing photons it normalizes and settles into its normal new wave function after having perhaps jumped a level or several. Since atoms are connected together in a material or substance By electrons in some fashion... whatever may not have absorbed any photon energy directly will still feel the residual effects following some sort of inverse square law according to material density and composition ie. #electrons # exchanges, I would assume...Thermodynamics. ;)

*if the photon does not match the electron resounance and does not fullfill the requirement for absorption, thus a new electron level, it will simply pass by perhaps giving a jolt to the electron which is translated into excess vibrational kinetic energy that the electron will "work off" and settle into its NMWR. This can be related to temperature perhaps, such that we always have the option to say well maybe temperature is several things one of them being not necessarily anything to do with the electron radiating energy - a purely semi-classical mechanical explanation.

 

[SpaceTiger]

If I had to define temperature I would Include somewhere in my definition the magnitude of potential energy, such that whenever it happens to collide or however it happens to transfer its energy it does so according to potential energy. So Gamma rays have a potential energy of x, radio waves a potential energy of y being considerbly less than x.

Are you simply saying

x=h\nu?

That would seem to be equating temperature with energy, as mentioned earlier in the thread. I think there's more to it than that...

A photons temperature can be said to be its energy level with reference to the EM Spectrum, correction its wavefunction, and is inherently a value determined by what electron emitted it. So in other words we can go further to say that an electron itself has a temperature and it can gain or lose temperature by emitting a photon such that the photons energy is the "temperature lost equivilent".

People will often quote "effective temperatures" in which they basically equate it to energy, but I don't think this is a very practical way to define temperature in the more general sense. For example, if I'm going to say that an elementary particle has a temperature, from which property will I determine it? A free monatomic particle has three degrees of freedom, each of which will correspond to a different temperature (assuming E=0.5kT). I can assign a temperature based on the total energy, but it still cannot be distributed evenly amongst its degrees of freedom, so an ensemble of systems, each containing a free elementary particle, cannot be used to define an "average" energy per degree of freedom. We can take your definition to the macroscopic level and say that the individual (identical) particles of a gas in equilibrium each have their own temperature, T, and when they're combined, they yield a gas of temperature, T₀. Then

T_0=&lt;T&gt;

meaning that the temperature of the combined system is the average of the individual components. However, since all of these systems (i.e. the individual particles) are in thermal contact, the zeroth law implies that the equilibrium state should be one of equal temperatures. That is

T_0=T

which will only occur in the macroscopic limit.

In other words, if we use the zeroth law to define temperature, it must be a statistical property, not one of individual particles.

Temperature can be measured by humans. Temperature in that context is purely an invention by our mind to know when a change in normal thermodynamic modes in our bodies molecules occurs-- this information handled by our nervous system. That is the top of the "what is temperature" pyramid...

Yes, I suspect that many of the people in this thread were arguing with an intuition founded on the above notion of temperature. This is fine for everyday purposes, but for doing real physics, I would say that it's insufficient.

Space Tiger, I just want to clarify something. You say

"Boson-boson scattering does occur"

Which I was going to ask you about without a doubt, cause I got to know if its true, but then I keep reading and you said

"As far as we know right now, light cannot interact with other light without some influence from matter."

So now I am confused, seems like a contradiction of statements?

Well, no, the top statement was not meant to be general; that is, I was not saying that boson-boson scattering occurs for all bosons, just that it can occur for some bosons. This was not relevant for most of the discussion in the thread -- I was just responding to Chronos. You're right, however, that I was waffling on whether or not the scattering of two photons could occur. The basic reason was that QED does allow photons to exchange energy, but only with matter as the mediator.

FYI I do not think photons can scatter NOR interfere with other photons DIRECTLY if we assume no mass nor charge exsists.

As far as I know, you're right. I've been careful not to contradict this anywhere in the thread.

 

[Juan R.]

The zero law for small systems is not so simple like

T_{A} = T_{B}

which is the second law for large systems.

See my work CPS: physchem/0309002 and references therein (it will be freely available online in www.canonicalscience.com in the section of research, when copyright issues solved I wait in 15-50 days).

for example,

4. ČÁPEK, V. Zeroth and second laws of thermodynamics simultaneously questioned in the quantum microworld. Eur. Phys. J. B 2002, 25(1), 101–113.
5.

However Cápek asumes that macroscopic zeroth law would be applicable to microsystems, which is obviously false. See my physchem for the details. The general zeroth law read

1/T_{A} = 1/T_{B} + f(1/N)

for macroscopic bodies, N is of order of Avogadro and one recovers the usual equality of temperatures.

See also

KOPER, GER J. M; REISS, HOWARD. Length Scale for the Constant Pressure Ensemble: Application to Small Systems and Relation to Einstein Fluctuation Theory. J. Phys. Chem. 1996, 100, 422–432.

for a similar rule for presures.

 

[tdunc]

Well, no, the top statement was not meant to be general; that is, I was not saying that boson-boson scattering occurs for all bosons, just that it can occur for some bosons. This was not relevant for most of the discussion in the thread -- I was just responding to Chronos. You're right, however, that I was waffling on whether or not the scattering of two photons could occur. The basic reason was that QED does allow photons to exchange energy, but only with matter as the mediator.

Example. Or should I know this? ;)

 

[SpaceTiger]

Example. Or should I know this? ;)

There's some nice discussion on it in this thread. I've seen some speculation that it might not require a medium to occur in some situations, but I don't think it has been observed.

 

[tdunc]

SpaceTiger

Would you object to the idea that Gamma rays have a greater magnitude of potential energy per degree of freedom than radio? Degrees of freedom being either an electric or magnetic potential ie. "electric & magnetic field" of the photon; That in turn being related to polarization.

The Displacement or I call Amplitude of the wavefunction is according to mass/energy and its important to note that while radio waves may displace more space per degree of freedom, that the magnitude of potential energy per degree of freedom is less than Gamma rays. So it is the Displacement Potential rather than the actual Displacement of a particle in the context of then relating thermodynamics and temperature.

And your right there is a lot more to it...I wish someone would come in and lay it out for us, if not give me a couple of days ;) I admittedly never concieved or attempted a quantum explanation of temperature, even if in the end its not even appropiate to do such. I suspect there's something to be said though, or not said just considered.

Something else I might add. While the electron energy lost is the energy of the photon, the photons energy is not equal to the remaining energy of the electron. So the statement that regards the temperature of light is equal to the temperature of what emmited it is not necessarily true. In fact, the temperature of the blackbody should Decrease the more energy it loses, so the temperature of the light can theoretically be greater than the temperature of the blackbody, vice versa. Of course that is only in regards to one aspect of how light is radiated, and of course radiation is in turn only one aspect of temperature... you its complicated.

If we can say that wavefunction (includes amplitude and degrees of freedom) of a particle is according to mass/energy, then potential energy is _insert simple equation_ per degree of freedom. Not forgetting that the forward velocity of light, which is one of its degree of freedom, is faster than a free electrons "FV" AND more importantly that forward velocity is not equal to the rate or speed at which a particle oscillates; That is, in simpler terms, it can vibrate up and down FASTER than it can go forward through space at the same time which happens to be C. C being a fundamental speed limit of some aspect inherent to space (dont want to say medium) not the particle, to explain the same speed of light regardless of spectrum.

"For example, if I'm going to say that an elementary particle has a temperature, from which property will I determine it? A free monatomic particle has three degrees of freedom, each of which will correspond to a different temperature (assuming E=0.5kT)."

Not to mention the wavefunction velocity is not constant, meaning that a collision could occur at any point along its wavefunction at any instance of times, so I see little hope to come up with a simple solution.