There is no agreed-upon value, among physicists, for a maximum possible temperature. Under our current best-guess of a complete theory of physics, the maximum possible temperature is the Planck temperature, or 1.41679 x 1032 Kelvins. However, it is common knowledge that our current theories of physics are incomplete, thus leaving open the possibility of still higher temperatures.

I found a great article that could explain why it is so hard to provide a solid answer.

http://www.pbs.org/wgbh/nova/physics/absolute-hot.html

There is no agreed-upon value, among physicists, for a maximum possible temperature. Under our current best-guess of a complete theory of physics, the maximum possible temperature is the Planck temperature, or 1.41679 x 1032 Kelvins. However, it is common knowledge that our current theories of physics are incomplete, thus leaving open the possibility of still higher temperatures.

I found a great article that could explain why it is so hard to provide a solid answer.

http://www.pbs.org/wgbh/nova/physics/absolute-hot.html

Not yet, because we had chances to know the maximum possible temperature because of the time following theories in physics for this problem are underway to recognize this phenomenon. Yes, leave it to future time ...

The idea of the Hagedorn temperature can also be applied to systems of strings: we have exponential degeneracy of the states at high energy. In this context it is often interpreted as a maximum temperature and is below the Planck temperature.

It seems to be all about the phase diagram of Pressure versus Temperature of the fundamental particles of matter. Consider the confinement of electrons in such a diagram.

In principle, if one thinks in terms of kinetic temperature then the simple equation mv^2 = 3k T, would say that if v=c,

the maximum velocity,the temperature should be maximum. However, normally temperature being a macroscopic entity defined through the thermal equilibrium of a statistical system, it might not be meaningful to talk about a maximum unless the system is totally isolated which indeed is a completely hypothetical situation.

As Plilip mentioned, there is no agreed-upon value for a maximum possible temperature.

The formula used by Aragam Prasanna is non-relativistic. The kinetic energy of the molecules is linked to the temperature and there is no upper limit on the kinetic energy - so no, there is no upper limit on the temperature

Absolute zero or 0 degree K is counted as the minimum possible temperature, thermodynamically: Should it relate to some absolute state of rest or minimum possible velocity?

Pumping energy to the system raises its temeperature but also a mass due to the mass-energy equivalence. But when the mass exceeds a certain value the system may become a black hole and go away from our view. (under condition of non-expansion). So in this sense there exists a limiting temerature an (observable) system can reach.

Although there actually may not be maximum temperature, if temperature happens to become unbounded then spontaneous transformation will be activated for that system.

Thanks Sood. Can those quantum fluctuations be harnassed?

The thermodynamical definition derives temperature from the entropy-energy relation. In order to believe in the Planck temperature as upper limit one has to believe in the classical black hole and the Hawking-Bekenstein entropy formula.

The Hagedorn temperature is specific to systems with a typical equation of state, here the usually monotonic relation between the temperature and the average energy per degree of freedom saturates. This is not an absolute limit, quark matter exceeds it - probably already experimentally. At least spectra are seen which are compatible with temperatures over the Hagedorn value. I would say there are some theories, but no proof of a maximal temperature. Of course the total energy of a finite Universe concentrated onto one degree of freedom is a factual maximum. But then it seems to be an accident, not a natural law.

Thanks Sood!

The subject: ((light velocity in matter)) is very interesting and provide use the data for consideration of the interaction between molecules in matter also interaction between light and molecules of matter. The light velocity increases as the interaction between light and molecules (or interaction between molecules of matter) decrease. In high temperature (or maximum temperature) the distance between molecules will be maximum and the interaction between them minimum. Then we can say the value of light velocity will be maximum in where that temperature is maximum.

In the same way, would you be saying that the light velocity will be minimal when the temperature is minimum? Black Holes.

Howard,

Adam and "T. Biro" have nicely answered the question of maximal temperatures.

I suggest that you read up on the Hagedorn limit (applicable only to certain 'classical' systems - this temperature limit exists because near this limit there is an exponential rise in the number of paths by which a system can cool. No matter how fast you heat a system, near this limit it can lose heat faster.

(I paraphrase grossly and appreciate that it is not the full story)

As for your other question, "no", to first order the speed of light (in vacuo) is not affected by the temperature of its environment. I suspect that Mr Koohyar is referring to the change in refractive index of a material, which generally will show a temperature dependence.

You mention black holes, but it is not clear to me what your question is.

Temperature of vacuum does not make thermodynamic sense.

Light travels in non-vacuum media as well: I wish to ask two questions:

1. Does light slow down and speed up with temperature in non-vacuum media?

2. Absolute zero is a thermodynamic entity: What happens to velocity of light, when the temperature of the medium reaches absolute zero?

Thank-you Garry and Vijayachandran,also to Koohyar whose question I was referring to.

My first reaction to this question was that it was a silly misinterpretation of the definition of temperature -- any system with a maximum in the entropy as a function of energy (such as a finite number of spins in a magnetic field) goes through a zero in the inverse temperature at that entropy maximum, and therefore the temperature diverges. Duh.

But then I saw we were talking about quantum gravity, details of which I acknowledge to be beyond my ken; so I was willing to be credulous (the only honest option available to the ignorant).

But then, as I wondered how quantum gravity folks define temperature in the first place, I remembered that my favourite example from Quantum Stat Mech (N spins in a magnetic field) actually belies the classical definition of 1/T = dS/dU because neither S nor U are continuous variables -- each has discrete values! And so if we wanted to be rigourous about defining temperature, it would have to be some sort of a tensor quantity -- and would definitely have a maximum value.

At which point my head started hurting as I considered the alternative to remaining ignorant and credulous: another career's worth of study. I'll leave this one to you guys.

Thanks Jess!

It seems to me that all mass-energy is controlled by gravity, temperature and the velocity of light.

I propose this thought experiment, where in the deepest of space, between chains of galaxies, exist a volume of space free of particles, or at most 1 particle per cubic yard. An active galaxy black hole has a jet pointing straight into this region. All particles are travelling in excess of 99% of the speed of the light. There is no heat loss mechanism from the surrounding space. What if one of those particles is a proton travelling at 99.999% of the speed of the light?

So, to answer the question, temperature as defined by your choice of mathematical equation, typically states temperature is proportional to kinetic energy (speed times mass). This implies as either or both speed and mass increases, that temperature increases.

Given the thought experiment, the answer to the question of is there a 'maximum temperature' is highly dependent upon the situation, and the equation used to define temperature.

Given the thought experiment is my idea of the only situation where a "maximum temperature" could be created and measured, the answer reduces down to the speed distribution probabilities of the largest active galaxy black hole jet. This distribution is likely to go beyond 99.999% of the speed of light, therefore the upper maximum is quite high, if not infinite.

To conclude my reply with one other thought experiment, that of a particle falling from infinity through the event horizon of the largest black hole, where that particle is the second largest black hole, once this particle is inside the event horizon, it's speed will exceed the speed of the light, until the two singularities merge. This is the maximum possible temperature I can think of.

@Peter

I have some doubts if the collective movement can be interpreted as temperature. And why to look at jets produced by black holes. Protons in the LHC accelerator move in bunches with speed of this order (99.999%) and when dumped they produce a lot of heat, of course. But it can be hardly interepreted as a result of the protons temperature. Internal temperature of such a bunch (containing about 10^11 protons) is maintained very low in order to maximize the bunches lifetime (chromaticity). By the way, for relativistic particles it is better to use a gamma factor (which is actually about 4300) instead of beta.

Classically, would calculate the maximum temperature by its proportionality to average translational kinetic of the molecules, using the speed of light as maximum, defining maximum temperature of the gas as a function of the mass of the molecules:

(m v^2)/2 = (3/2) kb T

maximum temperature = (m c^2)/(3 kb)

For O2: http://www.wolframalpha.com/input/?i=%282+oxygen+atom+mass%29%28speed+of+light+squared%29%2F%283+boltzmann+constant%29

@Eliseu

When going to higher and higher trmperatures one leaves the realm of classical physics. But your final formula is correct under condition that the mass is considered to be a relativistic one. Then it grows to infinity when the speed approaches that of light and the same happens with T. So no maximum temperature can be reached.

Thanks.

Of course: The Bekenstein bound implies it as a f(1/R)

Usng a classical argument, wouldn't it be the mass of the universe x speed of light squared (and dark energy) divided by Boltzmann's constant?

If we assume the Wikipedia value of 3.14×10^54 kg, that (ignoring dark energy contributions) translates to 2 x 10^94 K (as a lower limit).

Temperature is not a fundamental parameter like speed of light or the mass of an electron. It is derived from Maxwell-Boltzmann statistics as a measure of the average distribution of energies for Maxwell-Boltzmann energy distributions. It can be zero if there is no energy distribution, but is there a limit to higher energy distributions?

The maximum of temperature has probably been produced in the first instant after the Big Bang, which created the universe. This temperature should be about 4 trillion degrees Celsius, which is approximately 250,000 times hotter than the temperature at the core of the sun. I think there isn't any temperature higher than it. This is the maximum temperature, which has ever been produced to date. This is true that the Planck temperature is the highest one, and about 1.41×1032 degrees Kelvin, but it is a concept in mind, which postulates the existence of a highest attainable temperature of matter. It is not feasible in our physical world, unless we can completely simulate the Big Bang event.

Actually the highest ever produced temperature was achieved in the LHC experiments with colliding lead ions (2.76 TeV per nucleon), namely about 5.5 trilion degrees Celsius. This is considered to be the temperature of the Universe just few microseconds after the (so called) Big Bang. More can be read in

http://news.discovery.com/space/alice-topples-record-temperatures-set-by-phenix-120821.html

Obviously the maximum temperature occurred when Big Bang happened(accepting that it indeed happened). But the idea of a maximum temperature is related to the events happening right now up there. Could be the centre of the sun, the stars, supernova etc. Indeed the concept of a maximum temperature is of limited relevance unlike that of the speed of light.

I think the best hint towards the answer was given by Woskow. Temperature is a derived parameter, based on Maxwell-Boltzmann distribution. What is the meaning of this statistics when at high energies new particles are formed, whilst the distribution is primarily based on low energy elastic/inelastic collisions. Radiation and matter at high energies are entangled and it is hard to see what is the meaning of some steady state that has some distribution. One should also consider relativity and gravity (general relativity) because one must assume that such an environment happens where the matter has high density. In my opinion defining temperature above, say, tens of millions K has no meaning.

"Radiation and matter at high energies are entangled and it is hard to see what is the meaning of some steady state that has some distribution" Very well said SB! In the light of this statement I would jump to the distribution that gives 3 K as the remnant of the creation of the universe. Generally I feel questions of biggest/highest temperatures are relevant to local regions of spacetime -be they stars or black holes. And in each case temperature enters as a parameter usually in comparison to an energy term- often as a ratio. Familiar example is the Boltzmann distribution. Rare matter such as the upper atmosphere is much cooler than even the faintest star. A direct reflection of density.

The speed of light is the limit for temperature since it determines the upper limit of energy possible for any given mass particle. A further observation is that as the limit (c) is approached any matter becomes quark soup so the incremental energy limit becomes the quark mass*(c) - that is almost all the energy of the universe in one quark mass. Of course if you believe in the String Fairy then you can decompose the quark to string sub mass and get a bit hotter limit yet.

Note that this is just a limit that like light speed can never be reached, anymore then its meaningful to talk of a universe in which all the energy goes into one particle or string. Almost as foolish as the never seen and never will be seen or sensed singularity in a black hole.

Other then in relation to real matter temperature has no meaning. The CMB is cold only in that it is a wavelength radiated by a black body at a thermal temperature relatively close to absolute zero.

As some contributions above state, I do not understand why this question of maximum temperature even arises. A velocity having an upper limit does not restrict energy (kinetic) and thus temperature having an upper limit.

Hello Vijay

It was exactly my point sstated already some time ago.

Yes Adam, thanks. Unfortunately, I am a bit too quick to have a little grasp and start to write. I should have recorded your name in my brief comment.

The temperature is defined as the average kinetic energy of a particle or system, KE. As the KE increase the temperature, T, increase. If we fix the maximum particles velocity to C we are limiting the KE and T values. The zero temp Law is an empirical. That does not mean that the maximum velocity of a particle must be C, but what Einstein's postulate in his Theory. To solve other un-solve Physics issues we may have to consider velocities greater than C.

Dear Pappas, You said it! Frequency. Most fundamental! Indeed!! Frequency relates immediately to energy. And energy is perhaps the most fundamental. Most intiriguing. Probably the only seminal concept ever. Continua and spectra coexist in this universe.

One that is recognized, velocity and temperature can be comprehended satisfactorily.

Thanks for the motivation.

You can talk about the temperature of matter, or black body emission temperature of radiation but without direct or indirect real matter particle or mass reference temperature has no useful physical meaning. Gamma rays, tsunamis, and megawatts can all be converted to temperature - which has no useful physical meaning at all.

By useful physical meaning I am referring to an insight into the workings of the universe not an abstract manipulation of man made symbols.

Cool it guys

It can only get cooler

But not coolest

Hot OK

But not hotter not hottest

Newton's law of cooling

With a little correction

Would perhaps work

It's just a family of

Cooling curves!!!!

This universe

At the moment

It is a non-equilibrium universe by all counts. It has been cooling and cooling. Our planetary system is a result of this cooling. The 3 degree K radiation which has been very nicely measured is a remnant of this extended cooling process. The only estimate of temperature that is relevant is that of the tiniest of blobs of-BIG BANG. One could look at the sun data over the millenia. As evidence of this cooling. Because sun has been around for quite some time. The cosmic background is really a very valuable piece of evidence. You are right.

hf=kt or Wien's law is less useful in this discussion then de Broglies form for wavelength:

1st de Broglie Equation KE = (1/2) mv2

Equation Number Two: λ = h/p

There are three symbols in this equation:

a) λ stands for the wavelength of the particle

b) h stands for Planck's Constant

c) p stands for the momentum of the particle

This does make the answer simple since the planck limit 10^-35 is the highest possible temperature, however there is a point at which the energy in a volume exceeds the requirements for a black hole. Wavelengths of 10^-22 and below meet this "black" criteria and the particle pops into world of the black hole.

Is not exactly c always? Does fluctuate velocity or wavelength? Does it depends that the observer cannot be at vacuum? Sorry if I said anything wrong.

c is a number derived by Maxwell based on the electromagnetic field theory of light. It is related to the magnetic permeability and dielectric constant of the medium through a simple algebraic equation. It is a fundamental constant of physics.It does not 'fluctuate'. What 'fluctuates' usually is the intensity of light travelling through a material medium. The cause for this fluctuations is the density of the medium(say water or some crystal).

Forgot to add: c is measured quite accurately by a number of ancient and modern methods.

CS Sunandana

Measures of c which assume any of the ancient absolutes are inherently flawed. The most common being a perfect vacuum.

The velocity of light datum is published every year-I repeat every year. And the number is accurate for most purposes. The velocity of light measurement by Fizeau is relevant even today

Dear Vic Kley,

The existence of pure vacuum is recognized by epsilon 0 while for a material medium epsilon r is used. For high frequency epsilon infinity is employed. The Michelson-Morley experiment to measure ether drift is perhaps the most celebrated work for the velocity of light.

B= 2 pi r . 2 10at-7 . (sec at2)/ 2 pi . 1/ m at2 . i (Is to take the constants?) Sorry, I don't stand so well. (I must translate all in Spanish).

I have another questions, sorry if I said anything wrong.

What is the molecule whose can achieve the max Temperature? Atomic weight is important?

What is radiation spectrum of the max T?

Max T of matter depends of quantity of mass?

Infrared is important?

If infrared have longer lambda implies that c can be bigger?

Thank you very much, Chris.

(> lambda => < f => less E, I know it)

Less atomic nucleus (H+) => max velocity

< mass => > v

> mass => < v

¿T? max v implies max T? (I think no).

Can we achieve total vacuum in a volume?

I am reading this, thanks.

http://www.sc.ehu.es/sbweb/fisica/cuantica/negro/radiacion/radiacion.htm

I stand radiation,

E= h.f, E=h.c/lambda, f of each radiation, bigger lambda infrared,

But I have only two class of Physics (pure, only physics, in the University, Pharmacy. Sorry, for me is an hobby).

(And my English is not so good).

This is very good to learn more English too.

Thanks Chris for for answering Ana's many questions.

Howard

Chris

I very much appreciate your deep insight on the subject.The step by step logic you follow is highly commended.

Think of the temperature at the core of stars. Think of the temperature at the core of young galaxy. similarly think of the temperature created at the time of birth of the universe, will it not be the maximum temperature?

"Until someone comes up with a widely accepted quantum theory of gravity, the Planck temperature, for conventional physicists like Steven Weinberg, will remain the highest temperature".

But that is not the end of the story. There are different answers from different well known physicists. No one really knows if there's a hottest-of-all temperature. That uncertainty only fuels physicists' speculations.

http://www.pbs.org/wgbh/nova/physics/absolute-hot.html

Thanks for your contributions.

If the Tª (temperature) not be only positive, not only be added, (also be subtracted what is considered "cold").

In the beginning of Big Bang Tª was created too, is it?

I feel the first instants of BB like the creation of a gradient (because the time) where all things placed in their possible position to maintenance the equilibrium between all, under the rules of origin.

Very true. When we speak of a Fermi temperature or Debye temperature in Solid State Physics we mean very specific contexts in which temperature concept is valid.

Happy to know of the Lorentz non-invariance of temperature. Something to think about,

Actually the highest temperature ever reached in the laboratory is that obtained in heavy ion collisions at the LHC - it is measured in trilions of Kelvins: http://public.web.cern.ch/public/en/lhc/Heavy-ion-en.html

and correponds to the temperature our Universe had just few microseconds after the Big Bang.

Thanks Chris. "In the end, however, temperature is more truly considered in ambient terms." Just this one line-call it punchline if you wish-makes me very happy. Ambient temperature contains the fingerprints of the past AND the footprints of the future. And the beautiful concept 'temperature' is perhaps the superclue from minus to plus eternity!

Thanks Chris, ..... I like Hector's assertion that T can be infinite. It requires very high temperatures to create Black Holes, it seems, naturally in our universe. Has anyone made a Black Hole in the laboratory? How? Not Metamaterials?