Ask Ethan #92: Is there a limit to temperature? (Synopsis)

“Nothing is lost… Everything is transformed.” -Michael Ende

If you take all the kinetic motion out of a system, and have all the particles that make it up perfectly at rest, somehow even overcoming intrinsic quantum effects, you'd reach absolute zero, the theoretically lowest temperature of all. But what about the other direction? Is there a limit to how hot something can theoretically get?

Image credit: A.Greg; Wikimedia Commons user Greg L. Image credit: A.Greg; Wikimedia Commons user Greg L.

You might think not, that while things like molecules, atoms, protons and even matter will break down at high enough temperatures, you can always push your system hotter and hotter. But it turns out that the Universe limits what's actually possible, as your physical system will self-destruct beyond a certain point.

Image credit: Cosmic Inflation by Don Dixon. Image credit: Cosmic Inflation by Don Dixon.

What is that point, and how will it get there? Find out on this week's Ask Ethan!

More like this

If at "some high temperature, you will restore the potential that caused our Universe to inflate, cosmically", can't that be used as proof that there are no physical singularities? Otherwise Black Holes would be adding new spacetime faster than any gravitationally bound objects could traverse to remain gravitationally bound. Supermassive black holes would inflate their galaxies into oblivion.


Then again, that mass hasn't necessarily reached that singularity. It's inside the event horizon and that's all we outside can know.

The problem that comes about even if taken as so is that we need to understand what that "not singularity" looks like and what it will do.

We no longer have a mathematical construct that cannot be solved, and have one that CAN be solved.

We have to work out how the hell we can tell we have it right, though.

Maybe we never will, but we will work out several plausible options, same as abiogenesis. We can't tell which one is "the one that actually happened/happens" but we have shown it's possible to be explained without throwing our hands in the air and giving up (which is what "Goddidit" is: giving up. Until the dude/dudette comes down and admits liability and proves his claim of ability, it remains the same as "I give up").

Of course, you can get HIGHER than infinite temperature in this universe. It also happens to be a negative temperature.

Put something that aligns magnetically in a magnetic field, reverse the field and for a short time you have a state that is a higher energy state than one at infinite temperature. And it will be negative.

Of course, the extra energy will be lost and the alignment accord to the one that this sub-infinite energy state would conform to very quickly.

How is this possible?

Because temperature isn't an actual thing. It's a description of a bulk property, and that description doesn't really have to make much sense when you try to find an exploit.

Beyond normal temperature, the big question is what's the temperature of the Higgs Field and can it distribute temperature like other superfluids?

By Paul Dekous (not verified) on 12 Jun 2015 #permalink

Nathan, you have taught us many wonderful things with your clear, concise and complete descriptions of physics. But in a very small way you are setting a poor example for the 8th graders: The international standard name for temperature is "kelvin" or "kelvins", symbolized by "K", not "Kelvin". The latter is a man's name. See pages 112-113 of "The International System of Units (SI)", 8th Edition, 2006:

" Unit of thermodynamic temperature (kelvin)

"The definition of the unit of thermodynamic temperature was given in substance by
the 10th CGPM (1954, Resolution 3; CR, 79) which selected the triple point of water
as the fundamental fixed point and assigned to it the temperature 273.16 K, so
defining the unit. The 13th CGPM (1967/68, Resolution 3; CR, 104 and Metrologia,
1968, 4, 43) adopted the name kelvin, symbol K, instead of “degree Kelvin”, symbol
o K, and defined the unit of thermodynamic temperature as follows (1967/68,
Resolution 4; CR, 104 and Metrologia, 1968, 4, 43):

"The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of
the thermodynamic temperature of the triple point of water.

"It follows that the thermodynamic temperature of the triple point of water is exactly 273.16 kelvins, T tpw = 273.16 K."

Nathan, thank you so much for your beautiful and lucid explanations of modern physics.

By Ron Charlton (not verified) on 12 Jun 2015 #permalink

@ Ethan

think you made a typo.. "Because the temperature of the molecules is directly related to the kinetic motions — and speeds — of the particles involved."

should be: Temperature of the water is directly related to kinetic motions of particles involved..

A molecule on it's own doesn't have any temperature.

By Sinisa Lazarek (not verified) on 13 Jun 2015 #permalink

Sinisa, As long as the molecules are non monoatomic, there are other degrees of freedom involved (rotational and vibrational). As long as the difference between the lowest energy state, and the next lowest state is within a few kT, a DOF will participate in for example the heat capacity, and the relative populations of the differing states of each DOF should approximate the Boltzmann relationships.

By Omega Centauri (not verified) on 13 Jun 2015 #permalink

The "Oh My God" ultra-high energy cosmic ray was estimated at 3 x 10^11GeV. Ethan says that the Planck limit is 10^19 GeV, which corresponds to about 10^32 K, and the possible limit of triggering an inflation event lower than that at ~10^28 K. Would two OMG particles colliding head-on exceed that?

By Michael Hutson (not verified) on 14 Jun 2015 #permalink

@ Omega

I appreciate your reply and info, but I would still have to disagree, and this is why. We can talk about kinetic energy of a molecule.. or potential, or speeds at which molecules move, which would be different for every single molecule... and the average speed (or kinetic energy) of the entire system of molecules is what defines the temperature of a substance.

I suppose that in principal you could define a temperature for a molecule by using dE/dS (energy over entropy).. and since entropy is dependant on degrees of freedom... it could work.. on paper.. but no one uses that, and noone talk about temperature of a molecule... they talk about kinetic energy.

Since all of this was targeted at 8th graders, who have no knowledge of statistical mechanics..or what energy over entropy is... I still posit that temperature of a molecule is not something which is used.. ever. We only talk about a temperature of a system, which is in direct relation to average kinetic energies of it's constituents (molecules).

By Sinisa Lazarek (not verified) on 14 Jun 2015 #permalink

SL, that IS how temperature is defined.

Each degree of freedom takes the same energy, then the three left over are seen as velocity in three dimensions.

It's called "Equipartition of energy".

Also note that it can be defined other ways too, such as the occupancy of different energy levels in a molecular system. Lasers have inversion and therefore, by the definition of temperature, have a temperature higher than infinity.

Because the occupancy varies with temperature. And all energy levels are equally occupied at infinite temperature. So if the higher energy levels are more occupied than the lower ones, the temperature must be higher than infinity.

The mean velocity (which gives the heat capacity per unit weight, which varies highly, or the molar heat capacity, which varies by integral values, give or take a bit) is merely one way of measuring temperature.

Because temperature isn't a real thing in itself, it's just describing how energy could move about.

Hence the second law.

If one gas has a higher mean internal velocity than another, when mixed, collisions will tend to reduce the faster molecules and speed up the slower molecules.

Since velocity is one definition of temperature, this means heat moves on average from "hot" to "cold".

No need for entropy to enter the discussion.

"There’s only a finite amount of energy present in the entire observable Universe."

It's not the observable universe that matters, it whether or not the universe is infinite. There is no evidence for a finite universe.

@ Michael Hutson

Ultra-high energy cosmic rays are most likely iron nuclei. Iron has Atomic Number 26 so it is a large group of protons colliding with (probably) an other element that produces the ultra-high energy output. Individually the protons within the nucleus (as the whole nucleus itself) travel only 'slightly' faster that the protons in a particle accelerators. So no they would't exceed 'that'.

By Paul Dekous (not verified) on 14 Jun 2015 #permalink

@ Wow & Omega

thanx. I still don't like the verbal construct of "temperature of a molecule/s".. since what it is are their velocities. And hot/cold are just the way our neurons and brains are wired to perceive it.

But if you guys, who are physicists, say that's it's OK to talk about molecules in terms of their temperature, I'll accept it. :)

By Sinisa Lazarek (not verified) on 15 Jun 2015 #permalink

sorry.. just an addition/correction.. velocities or oscilations (if solids)

By Sinisa Lazarek (not verified) on 15 Jun 2015 #permalink

@ Paul Dekous

The references I've read all presume the OMG cosmic ray was a proton, or "probably" a proton. I don't know how they would determine this; the observed particle shower would be different if there was more than one positive charge??

By Michael Hutson (not verified) on 15 Jun 2015 #permalink

@ Wow

after reading in detail about equipartition of energy (from wiki and some other sources), it seems that in general the term "temperature of a molecule" is not used. What is used is "kinetic temperature" for transitional degrees of freedom, or "thermal energy" for particles.

In all textbooks I came across, "temperature" is used to describe the property of a body or a system, not for individual constituents.

In the end, we are not debating physics... which is all good. Just the language and semantics.

By Sinisa Lazarek (not verified) on 15 Jun 2015 #permalink

"And hot/cold are just the way our neurons and brains are wired to perceive it. "

It's how your body can sense "hot": energy passing into your body.

"it seems that in general the term “temperature of a molecule” is not used. "

Temperature of a single (or too few) molecules is undefined.

However, they have a temperature (taking the mean figures such as E=3/2 kT). But temperature is a bulk figure, so actual temperature is the bulk.

It IS, however, expressed by every molecule IN that bulk.

Like tossing a heads on a coin is not the value of the fairness of the coin. But each coin toss result is the result of the fairness of the coin.

@Michael Hutson

Showers of nuclei are shorter vs. those of protons. You could check this article in Nature:

"Cosmic-ray theory unravels"

"... they are seeing small air showers that are indicative of iron nuclei, rather than the larger showers that point to protons."

"The group revealed new data that weaken the link between the high-energy particles and the AGN (active galactic nuclei) ... the team has found evidence that these highest-energy cosmic rays might be iron nuclei, rather than the protons that make up most cosmic rays."

By Paul Dekous (not verified) on 15 Jun 2015 #permalink

Not a physicist but I enjoy your articles tremendously. A bit confused by the following, however:

"Back before the Big Bang, the Universe was undergoing a state of exponential expansion ... and when inflation came to an end, the Big Bang began."

From reading here and elsewhere, I had taken that "the Big Bang" = the universe at its very beginning. I thought that the expression "before the Big Bang" was meaningless, because of space-time starting with the Big Bang. And I've seen mentions of inflation as something that happened to the universe after the Big Bang.

You seem to be using the term "Big Bang" in another way here...any help you could give me and other amateurs to understand would be appreciated!

When heating an initially cold object, there is a practical temperature limit which occurs when you get copious particle/anti-particle production. When that happens, adding energy to the system just makes more particles rather than heating the existing particles by raising their energies. But of course when the density gets high enough the Pauli exclusion principle forces new particle into higher energy states so in that sense the temperature (average energy) increases. That is why really hot places in the universe (cores of giant pre0supernova stars), are also very dense.

By Ted Lawry (not verified) on 16 Jun 2015 #permalink

No, gravitation is what makes the interior of stars so dense.


No FK Wad, there is no "gravitation" at atomic scales so we don'r really know what causes a stars density.

By Ragtag Media (not verified) on 16 Jun 2015 #permalink

Yes, bumbandit, there IS gravitation at the centre of stars.

Dumbass fwit credulous moron.

YOU don't know, cmwad, but just because you're so dumb you cannot work out how your doodle works without some grandpappy telling you still doesn't mean that nobody else does.


The existence of a potentially infinite amount of energy outside of the observable universe is not relevant to the question of how much energy one can concentrate at a location in the observable universe. This unobservable portion of the universe is unobservable precisely because we cannot access any of the energy that might be present in that portion of the universe. Therefore, even an infinite amount of energy in that portion of the universe is irrelevant; we simply cannot, even in principle, access that energy and accumulate it at a region of the observable universe.

Hi Ethan,

Really enjoy these articles. This caught my eye:

"Back before the Big Bang, the Universe was undergoing a state of exponential expansion, where space itself was inflating like a cosmic balloon, but at an exponential rate. All the particles, antiparticles and radiation within it was rapidly separated from every other quantum bit of matter and energy, and when inflation came to an end, the Big Bang began."

I was under the impression that the Big Bang was the start of the universe. Here you have inflation before the big bang. But what is there to inflate before the singularity? And how can we say "Before the Big Bang" if space-time starts with the Big Bang? Help!

By John Kane (not verified) on 17 Jun 2015 #permalink

John, it's been asked before, but on a different thread.

"Big Bang" can be defined as several different things. The original idea was that it was the start of everything. However, inflation meant you could mean when inflation started (which would be before our known physics would have applied, so a conjecture about what they did then) , or when inflation ended. Which really is the "bang" bit of the "Big Bang".

Changing the specifics of the definition in an attempt to make it more accurate in its application.

You will find both meanings used. The older one, with the Big Bang being the actual start of it all, is usually used now colloquially, hence will be used more when not wanting to be accurate, but to be understood by those who don't have a job of looking into it.

What you’ve written is certainly true for systems where the number of available states increases with the energy. However, there are systems where the state space is finite, and in such systems, one can easily reach an infinite and even a negative temperature! Population inversion in a laser is a common example.

Consider, for instance, five ring magnets set on top of a table in a weak magnetic field oriented vertically. The ring magnets would like to align with the field, but there’s not enough energy in the field to flip them over. There’s only one way to align all of them with the field.

If we flip one over, that adds potential energy to the system; there are five ways to flip one, so the temperature is ∆E/∆S = 1/(log(5)–log(1)) = 1/log(5).

Adding another unit of energy, we can flip two; there are ten ways to flip two, so the temperature is 1/(log(10)-log(5)) = 1/log(10/5) = 1/log(2).

Adding another unit of energy, we can flip three; but there are the same number of ways to flip two magnets as there are to flip three! The temperature is 1/(log(10)-log(10)) = ∞.

Adding yet another unit of energy, we can flip four; now the number of states goes down as the energy increases. The temperature is 1/(log(5)-log(10)) = -1/log(2), a negative absolute temperature.

Finally, with five units of energy, there’s only one way to anti-align all the magnets. The temperature is 1/(log(1)-log(5)) = -1/log(5).

The fact that absolute zero is the inaccessible value for temperature and infinity is a perfectly valid value tells us we ought to be using the coolness β = 1/T instead.

By Mike Stay (not verified) on 16 Sep 2015 #permalink

Inversions are not equilibrium positions. Given thermal temperature is a bulk description and based on assumptions like equilibrium, it is not correct to claim such inversions as being proof temperature is invalid.

And zero is only inaccessible because of the quantum limitations, and without which, where the theories of temperature hold, it absolutely IS available.

Within the model of thermodynamics, absolute zero is achievable, hence your closing claim is likewise ad hoc rationalisation rather than logically necessary.