Does light have a temperature?

[Juan R.]

Does light have a temperature? Is it measureable? Often in photography they talk about color temperature...

DOES LIGHT ITSELF HAVE A TEMPERATURE?

Everything on Universe has a temperature.

 

[Chronos]

I disagree, Juan. Temperature can only be measured by thermometers. And only fermions make useful thermometers.

 

[Renge Ishyo]

It is my understanding that temperature is a measurement of energy as it is transferred by collisions between *molecules*. Light energy is transferred by interactions with electrons. By definition it seems that measuring an energy transfer via a heat exchange (temperature) is a very different process then energy transfers via electromagnetic interactions. The light energizes the electrons which leads to the movement of the molecules, but the idea of temperature starts with the molecules already moving.

At least that's how I understand it. I am pretty sure when temperature was originally defined, people didn't consider how it related to interactions below the molecular level because the knowledge that there even was something below the molecular level came about at a considerably later time.

 

[FunkHaus]

What about PHONONS?

OK so here's a little question that all this discussion has brought to mind. Do phonons, that is, modes of vibration of a lattice of particles (approximated as a continuous fluid), have a temperature?

Reif (in Fundamentals of Statistical and Thermal Physics) has a great section on quantum stat mech that uses a partition function with Bose statistics to determine the distribution of photon (quantized EM radiation) energies in equilibrium (that is, the distribution of wave frequencies nu).

I haven't taken QFT yet so I don't understand field quantization at any formal level--I only understand it up to using bose statistics on a gas of "particles" that obey the dispersion relation:
$$E = pc$$

But I've been very interested to know just how similar modes of quantized fields are to modes of lattice vibrations. That is, how similar is fluid mechanics to field dynamics?

Could one talk about an equalibrium distribution of phonon modes (fluid vibrational modes)? Would this distribution be a Maxwell-Boltzman distribution or would it be B-E or F-D? Could one construct a temperature using the usual relation (see Reif Ch. 3)

$$\frac{1}{kT} = \frac{\partial \ln \Omega}{\partial E}$$

Where $$\Omega$$ is the number of accessible states?
Could one then construct a phonon partition function

$$Z = \Sigma e^{E/kT}$$

where T is the phonon temperature ?

Some of my thinking may be a bit misguided, but hopefully I'm not too far off. If anyone has any insight or comments, it would be most appreicated. Thanks!

 

[SpaceTiger]

It is my understanding that temperature is a measurement of energy as it is transferred by collisions between *molecules*. Light energy is transferred by interactions with electrons.

Light interacts with free electrons, molecules, atoms, and many other things. It is certainly incorrect to say that temperature applies only to molecules, since atoms and electrons obey exactly the same laws of thermodynamics.

By definition it seems that measuring an energy transfer via a heat exchange (temperature) is a very different process then energy transfers via electromagnetic interactions.

Temperature is not a measure of heat exchange, it is a statistical measure of energy content.

The light energizes the electrons which leads to the movement of the molecules, but the idea of temperature starts with the molecules already moving.

I think you're missing the point. My argument has nothing to do with how light influences matter, it has to do with the statistical distribution of component particles, whether they be atoms, electrons, or photons. It doesn't matter where the energy comes from, only how it's distributed in equilibrium.

 

[Renge Ishyo]

It's a circular argument. Temperature really is just another way to measure an energy transfer. Light is an energy transfer. They are both energy transfers. So yes, if you go beyond the words, you can directly relate one form on energy to the other since from the submolecular level up all energy transfers basically link into one another.

However, "temperature" is a man made term used to describe a specific phenomenon (measuring thermal equilibrium between two or more different sets of molecules in contact with one another). The scales and instruments we use to measure temperature for example cannot be used (as far as I know) to measure the energy in light directly. When we bring out a thermometer out on a "hot" day, we get a reading because the movement in the molecules in our atmosphere interacts with the molecules in our thermometer until they both reach equilibrium with one another. Then the temperature (or average movement of atmospheric molecules in the air and our thermometer) can be reported. On places like the moon on the other hand, the same light might be reaching there not too far off from here, but the temperature measured is vastly different due to the difference between having an atmosphere with jiggling molecules in it to measure and not having one (or at least my understanding is that the moon's lack of an atmosphere is the reason why it can't keep in it's heat and ends up so damn cold; if I am wrong about any of this, please correct me).

I guess the argument is whether or not "temperature" is an all encompassing term or a term used to refer to a specific and small part of energy transfer at a specific level of interaction. If it's all encompassing than sure, as someone said just a few posts ago "everything on [sic] universe has a temperature." However, the very nature of a "word" is to isolate one idea from another. That's why I am inclined to agree with an earlier poster who stated that what we call "temperature" simply is not defined in terms of light.

In general, I think if you invade classical physics with the ideas of quantum physics and start arguing over terminology you are bound to drive yourself and everyone else insane. Maybe it is best to separate them to make the distinction easier to understand

 

[SpaceTiger]

It's a circular argument. Temperature really is just another way to measure an energy transfer. Light is an energy transfer. They are both energy transfers.

Unless you're reinventing English, that's not right. Light is a form of energy and it can be transferred from place to another, but it is not itself an energy transfer.

Even if I give you the benefit of the doubt and assume you're just not entirely familiar with the use of those words, the above is still incorrect. Not all light has a temperature; in fact, not all matter has a temperature. Temperature is only used to refer to an object in equilibrium. It is not just a measure of energy.

So yes, if you go beyond the words, you can directly relate one form on energy to the other since from the submolecular level up all energy transfers basically link into one another.

That sounds like nonsense to me. What do you mean by "link into one another"?

The scales and instruments we use to measure temperature for example cannot be used (as far as I know) to measure the energy in light directly.

If you put a thermometer in a blackbody radiation field and give it sufficient time to settle, it will give the correct temperature reading. The light will transfer energy to the mercury just as molecules do. I can't speak for every method of temperature-measurement, but then we don't define quantities by the tools we construct to measure them.

On places like the moon on the other hand, the same light might be reaching there not too far off from here, but the temperature measured is vastly different due to the difference between having an atmosphere with jiggling molecules in it to measure and not having one (or at least my understanding is that the moon's lack of an atmosphere is the reason why it can't keep in it's heat and ends up so damn cold; if I am wrong about any of this, please correct me).

The above is correct, but it doesn't refute the possibility of light having a temperature. It's true that the same light shines on the moon as the earth, yet they have different temperatures. All this means, however, is that the light is not in equilibrium with either of the atmospheres.

I guess the argument is whether or not "temperature" is an all encompassing term or a term used to refer to a specific and small part of energy transfer at a specific level of interaction. If it's all encompassing than sure, as someone said just a few posts ago "everything on [sic] universe has a temperature."

No, I wish you'd read the rest of the thread before replying because most of this ground has already been covered. Depending on what we're willing to call a "thing", one might say that everything in the universe can have a temperature, but it is certainly not true to say that everything does. The laser beam was one such example.

However, the very nature of a "word" is to isolate one idea from another. That's why I am inclined to agree with an earlier poster who stated that what we call "temperature" simply is not defined in terms of light.

Now this is just absurd. Should we abolish the word "human" because it doesn't isolate you from me?

In general, I think if you invade classical physics with the ideas of quantum physics and start arguing over terminology you are bound to drive yourself and everyone else insane. Maybe it is best to separate them to make the distinction easier to understand

As best we can measure so far, quantum physics is correct. Classical physics is not. Our terminology should take that into account. Are you mad at Einstein for extending the definition of energy to mass? Should he have called it something else, like maybe "shmenergy"? In physics, they tend to define quantities such that they have maximal value in understanding/simplifying the workings of the universe. If we were to go around creating new terms for every new object we saw -- "I've discovered the pion! Let's say it has pinergy and pimperature!" -- then we would be driven insane.

 

[Renge Ishyo]

Now this is just absurd. Should we abolish the word "human" because it doesn't isolate you from me?

No. The word "human" serves it's purpose in that it isolates "us" both from chimpanzees, alligators, or any other kind of animal. The word "animal" does not isolate "us" from chimpanzees, but it does differentiate "us" (a term now including the chimpanzee) from say, rocks. "Matter" does away with this differentiation and so on. But the point of my bothering to chime in here is not to lecture everybody on what I think a word is, but more so to try and draw attention to the idea that what is really being argued about here is what the word "temperature" means (what is inside the scope of the term's meaning and what is outside of it). Once a concrete definition has been established then you can answer the original question at the start of the thread.

From my vantage point, your frustration Space seems to be more so that the definitions that go along with ideas in classical physics are limited in their scope compared to what you study later on in quantum physics. From what I can gather, you don't see much of a point of bringing such limited ideas along. This can't be helped. You are left with either two choices, do away with the study of classical ideas entirely like "Newton's laws" and "temperature" (which both have narrow definitions in classical physics that don't encompass everything) and redefine them to include the sort of ideas that Einstein brought forth, OR continue to bring these ideas along out of tradition and separate the "classical study" from the newer studies of the Physics that go much further than these ideas do.

It's the reason they still teach the Bohr model of the atom for example, not because it's right, but because it is a part of Physics history and it still helps identify a few basic ideas about the Hydrogen atom (it doesn't have to be a complete picture of what an atom "really" is to still be useful, and the same goes for the concept of temperature).

 

[SpaceTiger]

No. The word "human" serves it's purpose in that it isolates "us" both from chimpanzees, alligators, or any other kind of animal.

That's right. So given what I said above, how does my definition of "temperature" distinguish itself from other concepts, like energy and momentum?

But the point of my bothering to chime in here is not to lecture everybody on what I think a word is, but more so to try and draw attention to the idea that what is really being argued about here is what the word "temperature" means (what is inside the scope of the term's meaning and what is outside of it). Once a concrete definition has been established then you can answer the original question at the start of the thread.

This has been stated several times in the thread and, honestly, I think it's self-evident.

From my vantage point, your frustration Space seems to be more so that the definitions that go along with ideas in classical physics are limited in their scope compared to what you study later on in quantum physics. From what I can gather, you don't see much of a point of bringing such limited ideas along. This can't be helped. You are left with either two choices, do away with the study of classical ideas entirely like "Newton's laws" and "temperature" (which both have narrow definitions in classical physics that don't encompass everything) and redefine them to include the sort of ideas that Einstein brought forth, OR continue to bring these ideas along out of tradition and separate the "classical study" from the newer studies of the Physics that go much further than these ideas do.

Let me make sure I'm understanding you. You've reduced everything to two options, so if I'm correct in assuming that you've chosen the second, the following would be true:

Since energy was a classical concept, we should not be polluting it with the ideas of modern physics and, in answer to the question:

Does stationary matter in empty space have energy?

...you would answer "No".

It's the reason they still teach the Bohr model of the atom for example, not because it's right, but because it is a part of Physics history and it still helps identify a few basic ideas about the Hydrogen atom (it doesn't have to be a complete picture of what an atom "really" is to still be useful, and the same goes for the concept of temperature).

I'm not sure how this turned into an argument about whether or not classical concepts are still useful. I don't disagree with the use of the Bohr model as a teaching tool, but if someone asked me, "What is the structure of the atom?", I would not tell them that the Bohr model is the correct physical description. Furthermore, the analogy isn't even appropriate because the classical definition of temperature is included in the one I use -- meaning that kids can learn all of the classical concepts of thermodynamics in school and not be carrying over anything erroneous to their study of quantum physics. In other words, it would still be correct that the temperature represented the average kinetic energy of molecules in a gas, but it would also represent other things, like the energies of photons in a blackbody radiation field.

 

[Chronos]

Would it be redundant to say 'temperature' is what thermometers measure? ... Probably. ST is attempting to give a working definition [i.e., measurable] that makes sense. It is not useful to extend that definition beyond his excellent example of a perfect gas in equilibrium.

 

[SpaceTiger]

Would it be redundant to say 'temperature' is what thermometers measure?

Come on Chronos, I addressed this issue in the post above, as well as several other places in the thread. Thermometers can measure the temperature of blackbody radiation.

... Probably. ST is attempting to give a working definition [i.e., measurable] that makes sense. It is not useful to extend that definition beyond his excellent example of a perfect gas in equilibrium.

It would not be correct either. If the photons or particles were out of equilibrium, then they would not have a temperature. Most of the light we see is out of equilibrium with its environment and therefore does not have a temperature, even if you accept the definition I support. I've also said this several times.

 

[Renge Ishyo]

Just to clarify a few things:

Since energy was a classical concept, we should not be polluting it with the ideas of modern physics and, in answer to the question:

Does stationary matter in empty space have energy?

...you would answer "No".

Einstein did not redefine what energy was. He found a way to express matter as another form of energy. That hadn't been done before. Energy was not redefined in the process, matter was. You are incorrect in assuming that people that study classical physics are automatically going to answer questions about quantum physics incorrectly. Quantum Physics doesn't render classical physics useless, it just takes the ideas further to the subatomic level or shows special cases where the calculations you make in classical physics are only estimates because they don't take things like super high velocities into account. The basic principles behind "what's going on", haven't really changed much. In another 50 years, maybe technology will be able to get to the point where the ideas we have now in Quantum Physics will be limited in scope and there will be something new around to extend (not replace, unless something is proven to be out and out wrong) that level of knowledge? This practically isn't even speculation, if we don't annihilate ourselves before then you can almost count on it.

Second, there is nothing wrong with the way classical physics defines temperature. It has not been proven to be wrong like the concept of caloric. It just doesn't encompass all vibrating particles in nature or go into the subatomic level at all. It shouldn't. If the scientific community broadened the term to include subatomic energy transfers they would run into a problem trying to tell the kid standing on the moon and on the Earth on a hot day why his "readings" are so vastly different when the light hitting him is essentially the same in both places. They would have to invent a "new term" to describe something that only measures molecular movement and neglects energy transfers on the atomic level and that is stupid because we already have a perfectly acceptable term that does that.

 

[Juan R.]

I disagree, Juan. Temperature can only be measured by thermometers. And only fermions make useful thermometers.

That you say is rather incorrect. The concept of temperature is not restricted to fermionic matter. In fact nuclear matter, or even the proper spacetime, has a temperature.

Any thing described by QM has a temperature since has a entropy. And do not forget that T = 0 Kelvin is also a temperature.

 

[SpaceTiger]

Einstein did not redefine what energy was. He found a way to express matter as another form of energy. That hadn't been done before. Energy was not redefined in the process, matter was.

Apparently you're either not reading or not understanding my posts. Temperature was not redefined either, it was only extended to light, just as "energy" was extended to matter.

You are incorrect in assuming that people that study classical physics are automatically going to answer questions about quantum physics incorrectly.

Don't put words into my mouth.

Quantum Physics doesn't render classical physics useless, it just takes the ideas further to the subatomic level or shows special cases where the calculations you make in classical physics are only estimates because they don't take things like super high velocities into account.

Your posts are like a massive red herring. I never suggested that quantum physics rendered classical physics useless, in fact I stated the exact opposite at one point.

Second, there is nothing wrong with the way classical physics defines temperature. It has not been proven to be wrong like the concept of caloric.

You can't prove a definition wrong. You can prove theories and predictions wrong, but not definitions.

It just doesn't encompass all vibrating particles in nature or go into the subatomic level at all. It shouldn't. If the scientific community broadened the term to include subatomic energy transfers they would run into a problem trying to tell the kid standing on the moon and on the Earth on a hot day why his "readings" are so vastly different when the light hitting him is essentially the same in both places.

Not if they knew what they were talking about. As I already said, that light is not in equilibrium with its surroundings. It's a very simple concept and I suspect that you aren't giving children enough credit. Nonetheless, this discussion was about physics, not education. Why don't you go into the quantum physics forum and try to teach people about the Bohr model of the atom? I'm sure you'll get a great response.

They would have to invent a "new term" to describe something that only measures molecular movement and neglects energy transfers on the atomic level and that is stupid because we already have a perfectly acceptable term that does that.

You're free to use any definition you like, but your reasons as stated so far are nonsensical. The analogy with matter and energy still applies and I think you should think seriously about that before continuing your objection. If you wish to refute the analogy, you need to come up with a way in which extending the definition of temperature will cause problems for classical thermodynamics. Saying that it will "confuse kids" is not sufficient.

 

[Renge Ishyo]

You can't prove a definition wrong. You can prove theories and predictions wrong, but not definitions.

I am so happy you agree. Then it's settled. From wikipedia.com:

On Temperature:
"Formally, temperature is that property which governs the transfer of thermal energy, or heat, between one system and another. When two systems are at the same temperature, they are in thermal equilibrium and no heat transfer will occur."

Temperature is related to heat transfer.

On Heat:
"Heat flows between regions that are not in thermal equilibrium; in particular, it flows from areas of high temperature to areas of low temperature. All objects (matter) have a certain amount of internal energy that is related to the random motion of their atoms or molecules."

Heat is related to internal energy.

On Internal Energy:
"The internal energy of a system (abbreviated E or U) is the total kinetic energy due to the motion of molecules (translational, rotational, vibrational) and the total potential energy associated with the vibrational and electric energy of atoms within molecules or crystal."

Internal energy is defined to be the SUM of all the energy within the molecules of a system.

On Blackbody Radiation:
"How much electromagnetic radiation they give off just depends on their temperature."

A distinction is formally made between the temperature of a body and the light it produces. Since we are only talking about definitions here there is nothing to debate. Case closed.

 

[SpaceTiger]

I am so happy you agree. Then it's settled. From wikipedia.com:

Read the thread! It's really frustrating having to cover the same ground over and over. 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.

 

[Andrew Mason]

Come on Chronos, I addressed this issue in the post above, as well as several other places in the thread. Thermometers can measure the temperature of blackbody radiation.

How? Thermometers measure heat. Blackbody radiation will heat a thermometer but it will not heat the termometer to the temperature of the blackbody that emitted it (thankfully for all of us Earth dwellers). To measure the 'temperature' of a blackbody spectrum (by which one necessarily means the temperature of the blackbody that emitted it) I think you need a spectrometer.

AM

 

[SpaceTiger]

How? Thermometers measure heat.

No, thermometers measure temperature.

Blackbody radiation will heat a thermometer but it will not heat the termometer to the temperature of the blackbody that emitted it (thankfully for all of us Earth dwellers).

In a closed system, a thermometer and field of blackbody radiation will eventually reach the same temperature. The sun and the Earth (or thermometer) are not a closed system. In our everyday experience, virtually none of the radiation we see can be said to be in a closed system. It does happen, for instance, in the interior of the sun, where the radiation and matter both have small mean free paths and can thermalize on a reasonably short timescale. The entire sun is not at the same temperature, but in our models, we use an approximation known as Local Thermodynamic Equilibrium (LTE), in which the distributions of particles and photons are given by the local temperature.

On a sidenote, you reminded me of another caveat for giving a radiation field a temperature -- it must be isotropic. The light emitted from the sun doesn't satisfy this condition, while the light in its interior does (approximately).

To measure the 'temperature' of a blackbody spectrum (by which one necessarily means the temperature of the blackbody that emitted it) I think you need a spectrometer.

A spectrometer is a good way to estimate an object's temperature without being in thermal contact with it.

 

[Andrew Mason]

No, thermometers measure temperature.

But they do that only indirectly. They measure changes in matter due to gain or loss of heat. We know that these changes are (approximately) proportional to temperature so we use these changes to indirectly measure temperature: eg. mercury, alcohol, thermocouples, thermistors, bimetalic strips.

In a closed system, a thermometer and field of blackbody radiation will eventually reach the same temperature.

How does a system of radiation alone become closed? If a closed system necessarily includes matter, how can one say that the radiation by itself has temperature?

AM

 

[SpaceTiger]

But they do that only indirectly. They measure changes in matter due to gain or loss of heat.

It's true that there must be heat involved in order for the thermometer's reading to change, but it's a bit of a stretch to say that the thermometer is "measuring" that heat. Now, this could just be discordant definitions again, but my understanding of "heat" is that of just transferred energy. This being the case, the temperature reached by the thermometer after given a certain amount of heat would be dependent upon its specific heat, as well as the initial temperature.

How does a system of radiation alone become closed? If a closed system necessarily includes matter, how can one say that the radiation by itself has temperature?

https://www.physicsforums.com/showpost.php?p=718331&postcount=18

 

[Andrew Mason]

It's true that there must be heat involved in order for the thermometer's reading to change, but it's a bit of a stretch to say that the thermometer is "measuring" that heat. Now, this could just be discordant definitions again, but my understanding of "heat" is that of just transferred energy. This being the case, the temperature reached by the thermometer after given a certain amount of heat would be dependent upon its specific heat, as well as the initial temperature.

Specific heat of the thermometer's measuring substance will affect calibration of the thermometer. Very true. But, fundamentally, it seems to me, the thermometer measures heat not temperature. Temperature is defined as a measure of the peak of the Boltzmann distribution of translational kinetic energies of the molecules in the substance being measured. Thermometers do not do statistical analysis. They measure the magnitude of certain physical changes due to flows of heat into our out of the thermometer.

It may be a bit of a semantic argument, but in the case of a thermometer in contact with the matter whose temperature is being measured, heat flows into or out of the thermometer until it reaches thermodynamic equilibrium. At that point, the magnitude of the physical change from the reference point is measured. The magnitude of that physical change is proportional to the amount of heat added to the thermometer's measuring substance. By calibrating this change, the temperature is determined. So thermometers simply measure the physical effect of changes in heat content. The temperature is inferred from this physical change.

AM

 

[SpaceTiger]

So thermometers simply measure the physical effect of changes in heat content.

Insomuch as the temperature reading would be incorrect if either the thermometer or the system being measured were out of equilibrium, I agree with you. My point was merely that two thermometers that give the same reading of "temperature" will not have received the same amount of heat. However, if we take this much further, we might have to start debating the definition of "measurement", and I think the "temperature" argument is bad enough.

 

[Juan R.]

Einstein did not redefine what energy was. He found a way to express matter as another form of energy. That hadn't been done before.

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.

 

[Renge Ishyo]

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.

 

[SpaceTiger]

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.

Not all of the definitions in Chronos' link mention heat. Besides, I've searched the web and, not surprisingly, found multiple definitions of heat as well. There is no doubt that some of the given definitions apply to matter only, but if you think the point of this discussion is to search wikipedia and carefully analyze their choice of words, then I'm done with you.

 

[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

$$\frac{1}{T} \equiv \frac{\partial S}{\partial U}$$

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

$$\frac{1}{T} = \frac{S}{U}$$

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

$$\frac{1}{T} = \frac{S}{U} = \frac{\rho _{S}}{\rho _{U}}$$

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

$$\frac{1}{T} = \frac{S}{U} = \frac{s}{u}$$

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

$$U = N \ u$$

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.

$$T = \ <T> + \ \delta T$$

Precisely average temperature $$<T>$$ -or average kinetic energy $$<KE>$$, 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

$$\frac{1}{T} = \frac{s}{u}$$

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.