# Physical limits on heat?

Is there a Physical limit to how hot something could be if we didn’t care what happened to it? Thinking of before the big bang.

Well, first off, “before the big bang” probably doesn’t have any physical meaning. But that’s not too big a deal; we can just substitute “really early very soon after the big bang”, which I think gets at the same thing you were going for.

And then, to the question itself, the answer is that we don’t know. It’s reasonable to suppose that the Planck temperature, about 10^32 K, might be the absolute hottest temperature possible, but really, that’s just an informed guess. If anyone ever tells you anything absolutely definite about (almost) any of the Planck scales, they don’t know as much as they think they do.

Oh, and obligatory Straight Dope article:
https://www.straightdope.com/21341968/what-is-the-opposite-of-absolute-zero
Cecil was rather too confident in that answer, because we really don’t know much at all about the Planck scales.

A quick primer: Three of the most fundamental constants of nature are G, the gravitational constant, c, the speed of light, and hbar, Planck’s constant. If you combine those three constants in the right way, you can get something with units of length. Combine them slightly differently, and you can get a time, or a mass, or a momentum, or an energy. Toss in k_e, Coulomb’s constant, and you can get a charge, and toss in k_b, Boltzmann’s constant, and you can get a temperature. In short, for any sort of physical quantity, you can construct a Planck unit for it.

Well, these units are convenient for doing some sorts of calculations (as are units based on only two of those three constants, depending on context), but what do they actually mean? Some of them are very, very large, much larger than any real values we ever encounter, and some of them are very, very small, much smaller than any real values we ever encounter. The Planck speed is, of course, just c, and we know (about as well as we know anything, at least) that that’s the fastest speed possible, so there’s a temptation to say that the other big ones are all the highest <whatever> possible, and the small ones are the smallest <whatever> possible.

But that’s just a guess, and anyway, not all of them are unachieveably extreme. A bacterium might have a mass equal to the Planck mass. A running housecat has a momentum about equal to the Planck momentum. The Planck charge is only about a dozen times the charge of the electron.

And in any case, we don’t actually have any reason to expect that there is even a highest possible temperature, or a smallest possible length. We know that at scales beyond that, what we know of physics definitely doesn’t apply, but the Universe isn’t beholden to our ignorance: There may well be other physics that we don’t know of, in which those extreme situations present no problems at all. There might be a maximum possible temperature, or a shortest possible length, or whatever, and if there is, then the Planck scales are as good a guess as any for them. But we don’t know.

At ridiculously high temps of say a hundred billion degrees to strange things happen to matter or is that just another one of those no way to know things?

Maybe a better question would be is there a temperature at which matter starts breaking down?

Pulling this out to continue to talk about the usefulness of Planck quantities. While the Planck speed c is exactly the universal speed limit, other Planck quantities might just have the correct units, but no specific physical meaning.

This quoted line triggered an old memory: the fine-structure constant “\alpha is a “tuning” constant that determines how strong the electric charge is.

The constant is unitless, which means we can multiply a Planck quantity by it and still have the correct units. And in fact, multiplying the Planck charge by \sqrt \alpha results in the electron charge. I’m sure there’s a deep reason why it’s the square root and not some other power, but I don’t know what it is.

These kind of unitless constants can be used to change all of the Planck quantities. Another obvious one is the 2 \pi baked into \hbar. Whether or not we should throw in factors of \alpha or \pi requires careful consideration. Basically, don’t take the exact value of a Planck quantity too seriously by itself.

Isn’t temperature just the speed of the molecules? In that case the speed of light would pose an absolute upper limit on temperatures.

Not really – temperature is related to the kinetic energy of the molecules. As their speed approaches the speed of light, additional kinetic energy goes more and more into additional relativistic mass rather than additional speed. The amount of kinetic energy approaches infinity as speed approaches lightspeed.

This suggests a “maximum possible temperature” corresponding to putting all the energy in the universe into one particle. However, this runs into another problem – ultra-high energy in just one particle, or a handful of particles, is more accurately described as “hard radiation” rather than “high temperature”.

It’s more convenient to think in terms of very high energies rather than very high equilibrium temperatures, although the two can be interrelated. One important feature of modern physics is that the Big Bang was NOT limitlessly hot the further back you go: How Small Was The Universe At The Start Of The Big Bang?

In particular it apparently never got hot enough to produce topological defects in space like magnetic monopoles, cosmic strings or domain walls. But afaik, there are no theoretical barriers to energies higher than this, so that raises the interesting question of what would happen if we could create a level of energy that our universe has never experienced before?

Because you multiply a charge by another charge in Coulomb’s law. Or to put it another way, if you put two Planck charges a Planck distance apart, the force between them is the Planck force. Or at least, if electromagnetism still works the same way at those scales, which it almost certainly doesn’t.

We don’t know that. We haven’t detected any, but that might just mean that they’re very rare. Some models, for instance, predict that a volume of space equivalent to the visible Universe would be expected to have one monopole in it.

Wouldn’t the observable universe having a net magnetic charge do strange things to cosmology and/or physics?

Sure. For one thing, it would cause electric charge to be quantized.

Er, wait a moment…

Temperature is fundamentally tied to how entropy and energy relate to one another in a system.
For instance, see this post for some kooky stuff that can happen. In most “normal” systems, though, temperature is relatable to the internal energy (both potential and kinetic), and in many of those systems, the kinetic energy is relatable to the speeds of the constituents (but not linearly). But none of this is universally true or definitional.

This one is more straightforward, up to a point. Climbing the temperature ladder, you’ll pass a few sign posts marking the next stage of breakdown, listed here in round numbers for energy units (electron-volts) and temperature units (kelvin), with Boltzmann’s constant relating the two.

• 1 eV or 104 K: breakdown of atoms → formation of plasma
• 1 MeV or 1010 K: breakdown of nuclei into neutrons and protons
• 150 MeV or 1012 K: breakdown of nucleons → formation of quark-gluon plasma
• 150 GeV or 1015 K: electroweak phase transition → the Higgs field changes dramatically, and (thus) so too does almost everything familiar about particles and their interactions.
• [10 TeV or 1017 K: highest energies probed experimentally at any level of detail]
• ??? TeV or ??? K: new physics?

For the last item, there are many reasons why we expect something new to happen at some energy scale, and many are looking for evidence of this next interesting point. This isn’t only done by cranking the experimental energies up directly but also through indirect information gained through high-precision measurements of lower-energy phenomena whose behaviors are influenced by the very existence of higher-energy processes.

(Aside: it is thought that the early universe included a so-called “inflation” period with temperatures in the 1025 K ballpark. There are experiments looking for echoes of inflation in the cosmic microwave background. If found, this would be an indirect probe of obviously much-higher-energy physics than the above list reaches.)

Depending on what you mean by “any level of detail”, you can go maybe a couple of orders of magnitude past that, from cosmic rays. The Oh-my-God Particle had a center-of-mass energy of around 10^15 eV. But yeah, still well short of the Planck energy… In fact, even a head-on collision between two Oh-my-God Particles would be seven-ish orders of magnitude less than Planck.

And one more:
102 - 103 K: molecules start breaking down

This is highly variable, of course. Water starts to disassociate into bare H and O atoms at ~2000 K. Proteins (obviously rather important for life) start to denature at barely above 300 K.

Yeah, I was considering that below “any level of detail”, but it’s notable for sure.

I think I would put the first rung of “matter starts breaking down” at the melting point of whatever substance you’re looking at. And of course, you can look at any of these thresholds as just being a phase change of some sort.

Molecules breaking down seems more… irreversible to me. Of course you can disassociate water into atoms, then lower the temperature and you’ll mostly get water back. But for hydrocarbons or something that isn’t going to happen, whereas you can melt-solidify them repeatedly.

Ask an ice sculptor whether melting is reversible.

On the other hand, if you start with just hydrogen, even quark-gluon-plasmification is probably reversible.

FWIW, this pulsar has a temperature of just over three million kelvins: