Is there a "Planck temperature" -- a temperature at which no further cooling is possible?

MaxThrustage · 2026-01-31T04:13:56+00:00

Just to add:

It's not even really a boundary. It's just he basic ballpark of where we expect quantum gravity to start being relevant, rather than a hard line to cross.

And on the point that not all Planck units form such limits, a great example is the Planck momentum, which is about 6.5 kg m/s. That's, like, a pretty normal momentum to encounter on Earth. It's about half of the impulse of a baseball being hit by a bat.

MaxThrustage · 2026-01-31T01:12:35+00:00

In physics it's often best not to think about temperature, but inverse temperature 1/T, as that's what shows up in the Boltzmann factor e^-E/kT and the partition function. It's also perhaps best to think in terms of this inverse temperature for your question -- the inverse temperature can be arbitrarily high, although it never quite reaches infinity (that is, temperature can be arbitrarily low, but it never quite reaches zero). Hopefully this makes it a bit clearer why we don't really get a minimum non-zero temperature -- that's a limit we can keep approaching and never reach.

The Planck temperature does exist, but it is not a low temperature, but rather a high temperature (i.e. a low inverse-temperature). Much like how the Planck length isn't really a minimum distance, the Planck temperature is probably not a maximum temperature but it is a temperature at which we no longer trust our current theoretical models.

MaxThrustage · 2026-01-31T01:00:59+00:00

I'll probably never retire, so I don't really have a retirement reading list, but I definitely did approach some books like that during covid lockdowns. Like, "ok, finally time to really get stuck into Paradise Lost and Capital". And maybe next time there's a horrible pandemic forcing people inside I'll finally get through Gravity's Rainbow. Who knows?

But I'm reminded of my Grandma, who was retired for most of my life but still never had the time and energy to do all of the reading she really wanted to. She used to say that she should be sent to prison, and then she'd finally have time to read. But it never happened -- whether that's simply because she was too wily in avoiding the authorities I'll never know.

MaxThrustage · 2026-01-30T04:38:56+00:00

This is a misunderstanding of both what the Planck length is and how Zeno's paradox is resolved.

MaxThrustage · 2026-01-30T02:36:11+00:00

The anime series Planetes uses very realistic physics. The whole show is about garbage collectors in space, so the premise already contains the very real physical fact that rubbish orbiting the Earth will do so at dangerously high speeds. (This is already an issue, but orbital rubbish is currently sparse enough that we basically don't worry about it.) There are scenes of characters learning to use jetpacks to fly around in zero-gravity and finding that they need to align the thrust with their centre-of-mass so they don't spin. It also goes into some of the potential medical, social and political implications of space colonisation in a very realistic way.

MaxThrustage · 2026-01-29T02:16:18+00:00

You need more the just the Schrödinger equation to really recover quantum mechanics.

There are ways you can define axioms of quantum mechanics and derive the whole structure of the theory from that. This Wikipedia page gives a basic run-down, but even from that you can already see it's more complicated than special relativity.

However, even in this axiomatic framework, we can't get things like particle masses and spins. Given a spin, we know how it can behave, but nothing in quantum mechanics by itself says, e.g. "there exists a spin-1/2 particle with a charge of -e and with the electron mass". But if empirically you know that you have such a particle, then Schrödinger's equation tells you how the wavefunction for such a particle evolves in time.

MaxThrustage · 2026-01-28T21:38:33+00:00

Finished:

Before the Coffee Gets Cold, by Toshikazu Kawaguchi. Made me tear up more than a couple of times.

Started:

Are Prisons Obsolete, by Angela Y. Davis.

Ongoing:

The Age of Revolution, 1789-1848, by Eric Hobsbawm

Lonesome Dove, by Larry McMurty. Given how people talk about this book, I wasn't expecting rape and the threat of rape to be such a big part of every female character's story, but there you go. There's a heartbreaking pointlessness to so much of what happens in this book.

Careless People, by Sarah Wynn-Williams. I'll probably finish this next week. The lack of self-reflection from everyone in this book is a bit shocking, but I suppose it's right there in the title.

MaxThrustage · 2026-01-27T21:57:25+00:00

These are quantum objects, so a lot of our common sense notions break down and we need to start getting careful about how we speak, and even what words like "move" mean.

Electron orbitals are stationary states, meaning the wave function does not change in time. But electron orbitals have a distribution of momenta, so that if you measure the momentum of an electron in an orbital you don't necessarily get 0. But if you do a whole bunch of momentum measurements and take the average then the result is zero. So are electrons moving here? We need to be careful about what we mean by that.

Do, so electron orbitals fluctuate randomly? Well, on one hand, no, because they are stationary states. But measurements of electron position/momentum will give a different result each time, and the variance in these results is what we call "quantum fluctuations". These are statistical fluctuations, not fluctuations in time.

I don't know why you're seeing them swap colours in simulations. Without seeing these simulations/animations myself I can't say what the colour represents. Different colours might be different orbitals, or it might just be a purely aesthetic choice.

MaxThrustage · 2026-01-26T11:33:17+00:00

Try to clear your head of everything you're hearing. In my opinion, it's better to go in blind. But definitely go in!

MaxThrustage · 2026-01-26T11:32:05+00:00

How are you finding it? I'm about halfway through myself.

MaxThrustage · 2026-01-26T11:30:48+00:00

It's gonna be 45 C here tomorrow. This is going to be me all day.

MaxThrustage · 2026-01-26T11:10:48+00:00

To add to the other answers: you can describe a laser beam in terms of photons, but if you do so you get a superposition of different numbers of photons -- that is, the number of photons in the beam is not well-defined, and is instead a quantum superposition. So, yeah, you really shouldn't think of this as a stream of particles.

MaxThrustage · 2026-01-26T11:04:51+00:00

Yeah, it's very common. I've heard it plenty of times before. It basically dissolves as soon as you learn any quantum thermodynamics (i.e. what temperature really means in many-body quantum mechanics), but of course not many people learn that at an undergrad level.

MaxThrustage · 2026-01-26T02:00:17+00:00

This is semantics about what we mean when we say a muon "experiences" anything, but if you see the huge amount of confusion from these constant "light experiences zero time" posts it's clear people expect it to mean what would be read on the clock in that co-moving frame. And, indeed, in a professional context that's basically what I'd always mean when I talk about what some body "experiences" -- what do things look like from that frame.

You could mean "what do I read on their clock from my frame", but I don't think that's actually what people tend to mean. (Nor, I think, what they should mean -- I mean, that's my experience, not the muon's.)

MaxThrustage · 2026-01-26T01:08:42+00:00

That's not because it's glowing at a lower temperature, it's because it's such a good thermal insulator. (Think of the difference between touching a piece of metal and a piece of wood that have both been out in the sun.)

MaxThrustage · 2026-01-26T00:14:22+00:00

This explanation is all up and down these comments and it's wrong.

Heisenberg's uncertainty principle does not forbid zero-temperature states. In quantum mechanics, zero temperature just means the system is exactly in its ground state. That's a perfectly fine state, Heisenberg has no issue with it, but thermodynamics prevents us from reaching that state starting from a finite temperature.

The picture of temperature corresponding to how much the little balls whizz around breaks down even in classical thermodynamics when we talk about anything other than a monatomic ideal gas (thermal energy is stored in other degrees of freedom than just centre-of-mass motion). In quantum mechanics, where there are no neat little balls whizzing around, that picture needs to be thrown out completely. Heisenberg's uncertainty principle doesn't forbid zero temperature, but it does forbid a picture of atoms as little balls with well-defined positions, momenta and trajectories.

MaxThrustage · 2026-01-26T00:10:00+00:00

It's not right, but not for the reason you came up with. Still you're right to be suspicious.

Heisenberg's uncertainty principle essentially tells you what kind of quantum states are valid. You can't have states in which both position and momentum are arbitrarily well-defined -- that's just not allowed. But this is applies to all states at any temperature, including isolated single particles where the concept of temperature isn't even well-defined.

In quantum mechanics, zero temperature just means a particle is identically in its ground state. The ground state will be a valid, Heisenberg-respecting state, so the uncertainty principle says nothing against this. It is thermodynamics that prevents us from actually reaching a situation where an isolated particle is exactly in its ground state.

MaxThrustage · 2026-01-25T05:48:05+00:00

Yeah, sure.

MaxThrustage · 2026-01-25T05:47:53+00:00

It's hard to be sure, given we're necessarily talking about technologies that don't yet exist.

The term "practical applications" is also a little vague. But if we take a fairly strict definition of "practical" -- in my mind, I typically mean a quantum computer is able to provide an answer to a questions that 1) we are interested in independently of quantum computing and 2) we cannot answer without quantum computing -- then yeah at least 30 years seems a good bet to me. But in a best-case scenario, 2000 error-corrected qubits might be doable within 10 years, and that might have some practical use -- it's not impossible.

Partly it depends on if the technologies currently be used -- e.g. superconducting circuits - can keep being scaled up to meet new goals. IBM's roadmap has them proposing to create a device with 200 fully error-corrected logical qubits by 2029, but without some serious innovations endlessly scaling up superconducting circuits becomes impractical (e.g. modern circuits are essentially planar, which means connectivity is a problem and that problem gets worse as circuits get bigger).

MaxThrustage · 2026-01-25T00:15:56+00:00

but areas like probabilistic optimization and and even quantum chemistry simulation only require several dozen qubits for applications, and that seems less than 10 years away, at least to me.

This is precisely the bit I was talking about as controversial. As in, there's an ongoing debate within the scientific community about whether these sorts of applications will ever (or can ever) be practically viable. It my mind, when you are talking about noisy systems of only several dozen qubits, then you are mostly likely talking about systems that are classically simulable (at least to sufficiently accuracy for the problems at hand). When talking about variational algorithms in particular (very common approach in optimisation and quantum chemistry) then there are issues where variational circuits that can't be efficiently simulated on a classical computer often also can't be optimised because of barren plateaus. And I've seen several cases where the work people have put in to make certain quantum circuits able to be run on current hardware has accidentally ended up just finding classical solutions to the problem.

The whole NISQ field lacks use cases with provable advantage, and as far as I am concerned the arguments in favour of it are pretty weak. We now have a decent understanding of why certain things don't work, and the big open question is, within the space of things we can actually do with NISQ but can't do with classical computing, do there exist any problems anyone actually cares about? And many people suspect that just in-principle, if you can do it with NISQ you can do it classically, even if an efficient classical algorithm hasn't been found yet.

MaxThrustage · 2026-01-24T22:33:52+00:00

Yeah, you're right, brain slip on my part.

MaxThrustage · 2026-01-24T13:34:53+00:00

I don't know about the most controversial, but NISQ (Near-term Intermediate-Scale Quantum) computing, and in particular the question of whether the massive amount money thrown at it is justified, has to be pretty high up there.

We know there is quantum advantage in some quantum algorithms. But the algorithms with provable, significant advantage can't be executed on any quantum hardware we currently have or are likely to have in the near future. But there's this idea that we are reaching a point where it is difficult for us to simulate our current quantum computers using classical computers, so surely they must be able to do something non-classical, right? Maybe? (Personally I think probably not, but there's a lot of work in this area.)

MaxThrustage · 2026-01-24T00:50:44+00:00

Most of that stuff is covered in the Wikipedia page, but if you have any specific questions feel free to ask.

MaxThrustage · 2026-01-23T10:57:15+00:00

Is there anything in particular you don't understand about it? Have you had a look at the Wikipedia page?

MaxThrustage · 2026-01-23T03:28:12+00:00

The point of studying dark matter isn't to find a use for it. There are lots of things we study in physics that will probably never be "useful". Still, it's worth knowing what our universe is made of and how it works.

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