Highest Possible Temperature

  1. FeDeX_LaTeX

    FeDeX_LaTeX 444
    Gold Member


    Does this exist? We have absolute zero, so is this possible?

  2. jcsd
  3. I would expect that lightspeed would impose an asymptotic limit on the speed of particles in a plasma, but I don't know if this places a strict limit on temperature.
  4. sylas

    sylas 1,734
    Science Advisor

    There's no upper limit on temperature, as far as I know. What counts is the energy of particles, not their velocity, and that is unbounded, in principle.
  5. Planck temperature is about the highest theoretical temperature associated with current knowledge:


    It may be that space, time, and everything we know might not be possible at higher temperatures....just as Planck size might be the smallest quantum of space.
  6. i assume that plank temperature existed before inflation. is that correct?
  7. sylas

    sylas 1,734
    Science Advisor

    I'd never heard of Planck temperature before this thread. Neat.

    Planck temperature is about 1.4×1032 K. Wow.

    According to Brief History of the Universe at Ned Wright's cosmology pages, this is the temperature at the Planck time, which is indeed pre-inflation.

    So, yes, it looks like this temperature would have to be pre-inflation. The other thing, however, is that we don't have a good quantum theory of gravity which would be required to give meaningful physical consideration of these conditions. Notions of time and temperature and so on break down as well.

    Cheers -- sylas
  8. Plank Temperature and Absolute Hot are the same temperature, just being expressed with different nomenclature. They are the same.

    Thank you Sylas for your answer. I guess when the four forces separated from each other after the disruption of the singularity, you read how it got really really hot. I still do not understand how that disruption would cause an "inflation" in temperature from "nothingness" to 10e32 so quickly (10e-44 seconds). I mean between T=0 and T=10e-44, the temperature went from 0 to 10e32. Is this type of "temperature inflation" just as impressive as "space inflation" that happened after the rise in temperature?
    Last edited: Mar 8, 2010
  9. sylas

    sylas 1,734
    Science Advisor

    Um; we don't have a clear model for T=0 to T=10-44. We don't have a good account of physics able to handle those conditions. There are ideas, but testing them is hard and none stands as a complete consistent theory yet.

    Hence there's no basis for thinking that temperatures increased in that way. Before T=10-44 you probably don't even have temperatures in the usual sense of the word, but we're guessing.

    Cheers -- sylas
  10. Disregarding cosmology, we can still idealize a highest possible temperature for many systems.

    If the system has a lot of degrees of freedom, each with different possible energy levels, then at absolute zero each degree of freedom should be at the ground state. As we introduce some heat, the degrees of freedom become excited, but still prefer the ground state. There are the more of them in the lower energies than at the higher energies.

    Generally, the proportion of degrees of freedom at a the [itex]i[/itex]th energy level, which has energy [itex] E_i [/itex], is proportional to

    [itex] P(i) \propto e^{-E_i/T}[/itex]

    As the temperature rises to infinity, this becomes a flat distribution, so infinite temperature would occur when all the available energy levels are populated equally. For example, a bunch of two state systems (spins, for instance) would be infinitely hot when half were in the lower energy configuration and half were in the higher energy configuration.

    If you got more than half in the high-energy configuration, the temperature would actually be negative. The highest possible temperature would be if every degree of freedom was in the highest possible energy state. Such a system couldn't absorb energy any more - energy would flow out to anything it came into contact with, so it's the hottest possible temperature. Apparently, the hottest temperature is approaching zero from below.
  11. sylas

    sylas 1,734
    Science Advisor

    Thank you. You have just exploded my brain. :eek:

    Actually, I like having my brain exploded. Keeps me humble; keeps me learning. I'll have to think about that one some more.
  12. rhody

    rhody 710
    Gold Member

    I laughed :rofl: when I read Sylas's response, "You just exploded my brain". that got my attention.

    Just curious, when you say approaching "zero from below" in the last sentence, are you talking about a matrix difference calculation involving an equal number of energy states ? or possibly a zeroth degree of freedom in the calculation ? I am betting that if you used a slightly different choice of words the confusion would have been avoided.


    Obviously in software you can define a circular data structure that could contain a temperature profile that when you reached the end (highest temperature) would wrap to the first or 0 th temperature entry.

  13. Hi Rhody,

    I'll just stick to the ensemble of 2-state systems. In that case, more of them should be at the lower energy level under most conditions. For a given temperature [itex]T[/itex], we'd have

    [itex]P(low) \propto e^{-E_{low}/T}[/itex]

    [itex]P(high) \propto e^{-E_{high}/T}[/itex]

    using the Boltzmann distribution in units where k = 1. If we define the zero of the energy scale by [itex]E_{low} = 0[/itex] and [itex]E_{high} = \Delta E[/itex], this becomes

    [itex]P(low) \propto 1 [/itex]

    [itex]P(high) \propto e^{-\Delta E/T}[/itex]

    The way I've written it, it looks like [itex]P(low)[/itex] doesn't change, but it does because the normalization constant depends on temperature. Requiring

    [itex] P(low) + P(high) = 1[/itex]


    [itex]P(low) = \frac{1}{1+e^{-\Delta E/T}} [/itex]

    [itex]P(high) = \frac{e^{-\Delta E/T}}{1+e^{-\Delta E/T}}[/itex]

    From this, in the limit as [itex]T \to 0_+[/itex] they all go to the low energy state. As [itex] T \to \infty[/itex] they get split 50-50. This is also true as [itex] T \to -\infty[/itex]. But, as [itex] T \to 0_-[/itex] the exponential in the denominator grows very large, and the probability to be in the low-energy state goes to zero. That's what I meant when I said that the hottest possible state has temperature approaching zero from below.
  14. rhody

    rhody 710
    Gold Member


    Thanks, I knew it had to be some factor, which you explain as the probability to be in the low energy state going to zero.
    From what I have been able to learn from the RHIC analysis of the data, temperatures of the jets as the quarks are deconfined approaches 400 * 1012. From a Brief history of the Universe
    That BB temperature still puts us a little over two and quarter times less than the temperature being created and studied for the first time from RHIC collisions.

    From analysis of the data being collected, there must be models that predict the temperature and time delta's from 400 * 1012 to the predicted BB temperature of: 1032K ?

    I realize we are in unknown territory here, I will leave the next steps/theories to the professional physicists.



    If anyone who is a HE Particle Physicist reads this, I for one would like to know once you get into the trillions of degrees range, what method or combination of methods do you use to distinguish say a jet temperature (hypothetically, just for explanation) of say 4 trillion degrees versus 400 trillion degrees ?


    Last edited: Mar 10, 2010
  15. 0 K is Absolute Zero, correct? So the highest possible temperature would be approaching 0 K from below, like -1 K would be close to the hottest temperature?

    Of course I'm assuming that by definition, a relatively hotter object would transmit heat energy to a relatively cooler object.

    So -1 K would transmit energy to 5000 K? Or is there something I'm missing out on?
  16. yeah that's right. 0k is also known as ABSOLUTE ZERO. Kelvin was made based on absolute zero.

    If 0K is absolute zero, and nothing is lower than absolute zero, then does that not suggest that there are
    no negative values measured in Kelvin?
    Last edited: Mar 16, 2010
  17. FeDeX_LaTeX

    FeDeX_LaTeX 444
    Gold Member

    If this is the highest theoretically possible temperature, how could one reach such a temperature?
  18. With a lot of energy.

    Nah actually ... I don't think we've ever artificially heated any substance to such high levels...
  19. The hottest things we heated were the particle collisions from various experiments. Don't know the energy involved, but that is the only indication of temp.
  20. But it did they actually reach Planck?
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