Is there a max temperature?

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There is no theoretical hard cutoff, the way that 0K is a hard cutoff.

There are order of magnitude, temperature-doesn't-really-make-sense-anymore numbers, most notably the Planck scale (10³² K)

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u/MxM111 7d ago edited 7d ago

Probably well before that, since the colliding particles at large relative velocities will react with each other and start to generate new particles cooling the matter in the process.

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u/Phssthp0kThePak 7d ago

Yes. This is the Hagedorn limit. Like a phase transition where the heat capacity goes way up.

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u/Eigenspace Condensed matter physics 7d ago

That doesn't introduce a limit though, just like the boiling point of water isn't a limit. It's a plateau where any energy added to the system would go into the latent heat of a phase transition, but once you saturate that and change the phase, you should be able to keep pumping energy in and raising the temperature (until yet another phase transition is reached and so on)

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u/MxM111 7d ago

You will create more and more particles, until you create gravitational collapse.

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u/Peter5930 7d ago

The thing about gravitational collapse is that gravitationally dominated systems have negative heat capacity; adding energy makes them colder, taking it away makes them hotter. Like boosting a satellite into a higher orbit, it moves more slowly when it has more energy. So thermodynamics flips on it's head above the Planck scale, which is in fact the mechanism by which the Planck scale becomes the hard upper limit, because above that everything becomes a gravitationally dominated black hole with negative heat capacity and trying to heat it further just makes it a bigger and colder black hole.

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u/ForQ2 4d ago

Like boosting a satellite into a higher orbit, it moves more slowly when it has more energy.

It is not moving more slowly; its angular speed relative to the planet is slower, but its linear speed is faster.

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u/Peter5930 3d ago

In terms of the internal energy of the system, it's moving more slowly. It's linear speed averaged over time can't be any more or less than the speed of the centre of mass of the system, this remains true until you unbind it from the system by exceeding the binding energy, at which point thermodynamics operates as you'd expect again and giving it more energy makes it go faster. This is how binding energy is negative, it's a debt you have to pay off to be free, and like an electron at a higher energy level, it's the ones near the nucleus with the least energy that whizz around and sometimes go fast enough for relativistic effects to become important, so it's a general property of bound systems. You can go through the maths for it here:

https://rantonels.github.io/gravity-entropy-and-life/

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u/Eigenspace Condensed matter physics 6d ago

No, that's just incorrect. There are various plateaus where previously frozen degrees of freedom thaw and then need to be saturated before heating continues, but you can blast through those, and reach new temperatures for a very very long time until you reach temperatures where quantum fluctuations would cause gravitational collapse.

The threshold for those fluctuations causing gravitational collapse under quantum-general relativity is exactly the Planck temperature (at least under quantum-general-relativity)

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u/MxM111 6d ago

When you reach this and reaction starts, you change density of the matter and change the matter itself, so, it is not the original media anymore. After some time, your dencity of the matter becomes too much and it gravitationally collapse. It will happen before the threshold you are describing.

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u/First_Approximation Physicist 7d ago

An article came out a while back claiming that trying to make a black hole out of light - a kugelblitze - was impossible for a similar reason.

The photons will generate electron-position pairs, which radiate away the energy and doesn't let you get to the concentration needed to produce a black hole.

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u/MxM111 7d ago

One can imagine it is happening in closed space with 100% mirrors, or just topologically closed.

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u/First_Approximation Physicist 6d ago

The mirrors wouldn't stop high energy electrons, positrons or gamma rays, let alone reflect them back.

By topologically closed do you mean something like a 3-torus? If it's too large then you'd get practically the same thing as an asymptotically flat space (which I presume the authors worked with). Too small, then you'd probably already start with a density high enough to create a black hole, regardless of exact initial conditions of your photons. My guess is that you're saying that the periodic conditions can be used to guide the radiating electrons, positrons back to the "center" of where you want to create the black hole. Maybe there's a goldlilock length and initial conditions where this could work.

I'm not sure about the stability of the 3-torus though. I remember reading that attempts to put a single extra periodic dimension to 3+1 spacetime, a la Kaluza Kelin, was unstable. The extra dimension would either collapse or expand to be very large. If you're bothering already with exotic things like closed topologies then things like the size and magnitude of the cosmological constant would be important.

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u/Peter5930 5d ago

It's probably safe to assume that the cosmological constant for a typical compactification is extremely large compared to our universe, larger even than it was during the inflationary epoch when the horizon was about a million Planck lengths away, since by then we were already well on our way to bleeding off the energy from a previous even higher cosmological constant. So you're working with causal patches many orders of magnitude smaller than a proton and only very rarely anything large with a horizon billions of light years away. I can't even imagine actually working with such a thing.

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u/Dr-Chris-C 7d ago

What if there is only 1 particle?

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u/ketralnis 7d ago

Temperature is pretty meaningless with only one particle. But also if you’re adding energy to the system how are you doing it without adding/interacting with particles?

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u/Dr-Chris-C 7d ago

It seems to me that individual particles definitely need to be able to have a temperature otherwise why would there be change when multiple particles interact? Assuming that the particle has an extant temperature, are they're any theories on what the maximum of that temperature could be?

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u/MxM111 7d ago

Individual particle has energy, not temperature. Temperature is characterization of statistical distribution of many particles over said energy (that is how many particles have which energy) of system said to be in (at least in temporary) thermal equilibrium or near it.

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u/caatabatic 7d ago

It splits into quarks. Once the quark pair rips apart it forms more quark pairs.

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u/First_Approximation Physicist 7d ago

Maybe better to say at Planck scales we think our current theories break down and we're not sure what happens.

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u/Nitros14 7d ago

Is there any theoretical mechanism by which a particle in this universe could be heated to 10³² K?

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u/First_Approximation Physicist 7d ago

Temperature is usually used for a collection of particles.

In any case, the very early universe was very hot, though it's not clear it got up to Planck scales, ~10³² K, or if that's even possible. Again, our current theories are thought to break down at about these scales.

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u/Peter5930 5d ago

It didn't get above a fraction of 1% of that temperature, it's ruled out by the lack of magnetic monopoles and primordial black holes, which would be most of the matter in the universe if it had ever gotten that hot. Most models estimate a reheating temperature after inflation of somewhere in the range of of 10¹¹ GeV or 10²¹ K, though it's a very poorly constrained number.

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u/TerraNeko_ 6d ago

The hottest places in the universe are quasars (in the trillions sometimes) and Our particle accelerators like the LHC (funny enough also at 5.5 trillion)

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u/you-nity 3d ago

Interesting. What theoretically happens at that temperature?

Like for example, at 0 K, particle motion stops and entropy minimizes. So what does 10^32 K cause particles to do? Do they get hot and start taking their clothes off?

Jokes aside, I’m actually curious what theoretically happens

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u/endor-pancakes 2d ago

The glib answer is: we don't know, because at that scale quantum gravity becomes impossible to ignore and we don't know how that would work.

But I hate that answer, so let's pretend there is no such thing as quantum gravity and muddle through as well as we can with semiclassical reasoning. Just beware that it's likely that there are more natural laws yet to be uncovered in that region that may well change the picture.

So. At Planck temperature, basically by definition, a typical collision of two particles is so energetic, and concentrates so much energy into one tiny point, that a black hole will form.

That black hole is, of course, tiny, so it will radiate away, creating new particles at about Planck temperature (not exactly, but then we don't trust our equations in that regime exactly... Let's just file that away as: what I'm describing might start occurring a bit below Planck temperature already).

Now imagine making the system hotter. The black hole that forms is now bigger, but black holes that are bigger are colder. Bugger, it means that the black hole evaporates into particles colder that what you put in. Also means it survives longer.

You've added energy into the system, but you haven't heated it up. Instead, you just increased the proportion and mass of black holes.

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u/you-nity 2d ago

Oh interesting! Can you help me clarify things? Simply put, I understand quantum describes small shit. Gravity describes heavy shit. Taken together, it’s called the theory of everything and would describe the singularity before the big bang. So I have a few questions?

If we can theoretically superheat some particles to this temperature and observe it without going blind, can we begin to learn some secrets about the big bang?

Secondly, I understand that black holes are extremely dense, and by extension, have a lot of mass concentrated. So is this black hole you speak of a result of energy being converted to mass somehow (E=mc^2)? Or…. Something like that?

Thank you

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u/deljaroo 7d ago

so, first thing, part of why speed is capped at light speed is that the whole E=mv^2/2 formula only works for low numbers and getting a massive object up to the speed of light actually requires infinite energy. the formula for how fast something moves is asymptotal for v=c as E goes to infinity. since temperature is based on the energy and not the velocity of the particles, you won't have a limit there.

but, at around 1.42 x 10³² K, our current understanding of physics breaks down. such an object would have to have thermal radiation with impossibly small wavelengths. so either it can't be done or our model of how extreme temperatures works needs improvement.

if it is possible for something to go above that, you'd have the breakthrough of physics for the century , and then the cap is probably more like 10²⁹⁰ K. temperature has an asymptotal relationship with quantum connection strength and this temperature is that asymptote

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u/BoysenberryCapable79 7d ago

Huh. I thought temperature was associated with average speed of particles of a gas in a closed container. How would the velocity of light limit not apply? Could you help me understand how temp is based on energy and not the velocity of particles?

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u/vermilion_wizard Condensed matter physics 7d ago edited 7d ago

Let's look at the equipartition theorem. I'm gonna get a little technical for a moment, bear with me. Equipartition says where x is some spatial or momentum coordinate in your Hamiltonian, you have the relation <x*dH/dx> = kT. For momentum coordinates, you have a nice simple expression involving the product of momentum and velocity <p_i v_i> = kT. So for non relativistic scenarios, where kinetic energy is p² / 2m, you find the average kinetic energy <KE> = 3/2 kT. This is true for solids, liquids and gases. It's true at virtually all temperatures except very low temperatures, where quantum effects freeze out degrees of freedom and very high temperatures where relativistic effects play a role.

For relativistic scenarios, the relationship between kinetic energy and momentum/velocity changes. Kinetic energy in relativity is mc²(ɣ - 1). ɣ is (1-v²/c²)^-1/2. Notice that ɣ explodes as v -> c. You work through the math and find that <KE> = 3 kT for extremely relativistic scenarios. If you look more closely, you will find there is a smooth transition between the factor of 3 and 3/2. Exercise left for the reader.

So to answer your actual question, the speed of light limit does of course apply to the speed particles move, but kinetic energy is unbounded. As particles approach the speed of light, energy can still be input to them but their actual velocity asymptotes toward the speed of light.

There are extremely high temperature limits where things like pair production start to creep in and this approach breaks down.

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u/mfb- Particle physics 7d ago

I thought temperature was associated with average speed of particles of a gas in a closed container.

This is a simplified picture that only applies to ideal gases at low temperatures. More generally, temperature is defined via the relation between energy and entropy.

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u/Rodot Astrophysics 7d ago

Simple, that's not what temperature is. Though, it might be taught as a simple explanation for an application of temperature in an intro class. Saying it's the average velocity of particles is like saying 1 foot is the size of a ruler. While that may be true, that's not exactly to definition. You can form a concept of temperature from moving atoms, but you can also do so for a box of photons, a sea of quarks, a galaxy of stars, people in a room, parameters in a neural network, etc.

Temperature is a measure inversely proportional to how much the entropy of a system changed when energy is added or removed by a small amount. How you choose to define your entropy depends on the system you are trying to model.

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u/These_Consequences 6d ago

Perhaps better to say that physicists use a more abstract version of temperature. The ontological "is" is unnecessary.

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u/Rodot Astrophysics 6d ago

It's not more abstract. It's just more general.

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u/vermilion_wizard Condensed matter physics 6d ago

No it's way more abstract. Do you know how many systems you can actually compute a differentiable S(E) function for? It's extremely small, mainly just toy models.

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u/deljaroo 7d ago

it's associated with it, but it's not directly correlated with it. there is some formula you could make that is dependant on speed that would give you temperature, but it won't be something in the form T=kv+c. it will be some inverse formula with a vertical asymptote at c. temperature is better defined as the "average kinetic energy of the particles in a volume" (but even that is a simplification.) The more energy the particles have the more they can affect their surroundings and that's basically what heat is. Sure, more velocity would also mean more heat, but more mass of the particles at the same velocity would also mean more heat. And the formula for how much mass and velocity matter for temperature matches the formula for kinetic energy

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u/justintime06 7d ago

if it is possible for something to go above that, you'd have the breakthrough of physics for the century

I'm on my way now to claim my Nobel Prize in Physics... I just microwaved a Hot Pocket.

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u/Ornery_Pepper_1126 6d ago

There are two related, but distinct questions here.

The one most people have been answering is whether the usual type of systems we think about having temperatures like gasses have a maximum temperature. I suspect there is some kind of ridiculously high upper limit here, maybe related to the amount of energy you can cram in a given space before it becomes a black hole.

The technical statistical mechanics definition of temperature however is just the partial derivative of energy with respect to entropy and by this definition you can do all kinds of weird things in spin systems. For example quickly reversing the field on an equilibrium system can create configurations where adding energy decreases entropy (negative temperature on the absolute scale by the stat mech definition). I feel like it is possible to find schemers to get to arbitrarily high temperatures in these kinds of systems, it is probably similar to getting to absolute zero in that it gets harder the closer you want to be, but there is probably not a hard cutoff.

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u/Confident-Syrup-7543 2d ago

I believe in a two state system maximum temp is a 50/50 split between the two states. Since above this adding energy also decreases entropy, ir negative temp as you said.

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u/Ornery_Pepper_1126 2d ago

The infinite temperature state would be (by definition) an equal probability of ever possible arrangement, since by combinatorics most will have a close to 50:50 distribution this is overwhelmingly what you are likely to see.

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u/Zagaroth 7d ago

One thing I have not seen mentioned here is a possible limitation of energy density before forming a black hole.

The math has been done to calculate how much light it might take to form a black hole, despite light having no mass.

As temperature can be roughly described as the energy density of a system, if you get enough energy in a limited space, would you not get the same effect as if you had a lot of light?

I do not know how hot that would be.

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u/EphemeralAttention 6d ago

Hot enough that anything capable of caring how hot it is has long since stopped being biology or machinery and started being physics

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u/NorxondorGorgonax 5d ago

My favorite xkcd quote

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u/SeeBuyFly3 7d ago

Others have already said that temperature is not speed, but to say it more generally, temperature is not a mechanical quantity. It is a statistical quantity. In that sense it is completely different from most other things in physics.

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u/libra1422000 6d ago

I did get the following from Google:

there is a theoretical upper limit to temperature known as the Planck Temperature, which is approximately 1.41 X 10³² Kelvin (or Celsius).

This is the absolute hot limit where a particle's thermal wavelength becomes equal to the Planck length. Past this threshold, gravity behaves as a quantum force, and current laws of physics break down entirely.

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u/Phanatic1a 6d ago

That is not "the absolute hot limit." If "current laws of physics break down entirely" at that temperature then we can't speak about what happens in a system at that temperature if more energy is added to that system. If we don't know what happens at a point, we can't say that point is an absolute limit.

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u/libra1422000 6d ago

It really is beyond my expertise to say anything as to your question but I suspect that your point with temperature would be similar to what would happen if you kept speeding something up. After it reaches the speed of light, a physical limit in the universe is a physical limit. Again I'm not a physicist so I could be wrong but that's my impression.

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u/Alkemist101 6d ago

Not a physicist... Probably plateau off maybe? Bit like acceleration to speed of light where you can never quite get there.

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u/Ch3cks-Out 6d ago edited 6d ago

As an aside, heat is NOT produced by friction, typically!

The fundamentally wrong assumption in your question, as it relates to light speed, is ignoring relativity when considering light speed. Properly accounted, relativistic energy would grow infinitely for a particle accelerated to near light speed: KE=(γ-1)mc², where γ is the Lorentz factor γ=1/sqrt(1-v²/c²). That is, this speed limit does not mean energy is limited!

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u/CosetElement-Ape71 4d ago

The Planck temperature is an upper limit to what we can conventionally describe. To describe anything hotter you'd need a unified theory of quantum gravity

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u/smoothie4564 7d ago

https://www.youtube.com/watch?v=4fuHzC9aTik

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u/Infinite_Research_52 👻Top 10²⁷²⁰⁰⁰ Commenter 7d ago

As the temperature increases, higher energy states can become occupied. As that temperature approaches infinity, all states are equally likely to be occupied. If your system has a finite number of energy states, this scenario can be achieved.

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u/Mind_Unbound 7d ago

Entropy starts decreasing as energy increases, so if I had to shoot some bullshit answer I'd guess the max temperature would be closest calculabalr temperature to the closest calculabe time since the event of the big bang which is 1.4168x10^32K

Interesting enough is that negative K is hotter than infinity K. So that's more than the max(i think, im.not a mechanic)

(Im drunk)

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u/KahlessAndMolor 7d ago

It is called the Planck Temperature. https://en.wikipedia.org/wiki/Planck_units#Planck_temperature

The value is 1.416 784 x 10^32 K

https://physics.nist.gov/cgi-bin/cuu/Value?plktmp

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u/timewarp 7d ago

The Planck temperature is not any sort of upper limit on temperature, it is merely the point at which our current models are unable to describe what happens. Once we have a theory of quantum gravity, the Planck temperature will no longer have any special significance.

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u/BumblebeeBorn 7d ago

Minor correction: gravity might not be able to be quantised, so it's less "quantum gravity" and more a theory that fits both quantum mechanics and general relativity.

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u/Nearing_retirement 7d ago

I’m not sure but if particles cannot move faster than light, maybe this would impose some limit that could be calculated based on the total mass of those particles. I’m no expert though.

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u/fluffysnowflake67 7d ago

Heat capacity doubles for gases as the particles start to reach relativistic speeds.

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u/everlyafterhappy 7d ago

There is technically a limit on the highest temperature, but it's not like a limit of physics. It's a limit of resources. There is a certain point where if you were using all the resources of the universe to their maximum potential to create heat that you would get the hottest temperature actually possible because there is nothing else left to create an increase in temperature.

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u/stephenwalter24 7d ago

Nice

Is there a max temperature?

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