### What is absolute hotness?

Is there such a thing as absolute hot – the hottest you can possibly get? And no, I’m not talking about some it-person de jour being voted ‘hottest’ on the planet by some scatalogically-minded magazine trying to up its sales figures. I’m talking about the laws of physics. Temperature. And temperature beyond… er …. temperature. Let me explain.

First, let’s think of the opposite. Is there absolute cold, from a physics standpoint? You betcha. It’s well known, so much so that the Kelvin temperature scale starts with it – in short, absolute zero is just that in Kelvin. It’s also −273.15° Celsius (Centigrade) and −459.67° on the scale I was brought up on, Fahrenheit. Absolute zero is the coldest it’s possible to get – it’s where all molecular movement stops and is, of course, impossible to reach. Experiments have got close – and have produced what’s known as a Bose-Einstein Concentrate. This is a peculiar form of matter that our friend Dr Albert Einstein predicted had to exist at close on absolute zero, after reading a paper by Satyendra Bose. Einstein was, of course, absolutely right.

It stands to reason that absolute zero must exist, because things move more slowly as they get cold. And yes, if things get cold enough – even particles stop. But is there an upper limit to temperature? And if there is, how can we calculate it?

It turns out that there is indeed such a limit, and it doesn’t have much to do with velocity. You might think that this was a limit – particles move faster as they become more energetic, and obviously a particle can’t exceed light-speed. But it turns out that this doesn’t actually define absolute hot. Instead, the limit is all to do with the way the particle re-radiates energy put into it. It works like this. If you put energy into a particle, you get energy out, typically electromagnetic – heat, for instance. Add more energy, and that turns into heat and light. Light is simply electromagnetic energy with a shorter wavelength than heat – technically, exactly the same thing apart from the wavelength.

This is the issue; the more energy you put into a particle, the shorter the wavelength at which it re-radiates it. If you add yet more energy to the particle after it’s radiating visible light, it’ll radiate in ultraviolet, then in soft X-rays, and so on. Every time, the wavelength of the emitted energy is shorter.

There is, of course, an end point. That happens when the particle reaches a temperature of about 1.416833(85) x 1032 degrees Kelvin – calculations vary a bit, so other figures around 1032 Kelvin are also cited. At that point, the wavelength of the emitted energy hits 1.6 x 10-35 metres. It’s infintesimally small. This is what’s known as the Planck Length, and it’s the doorway to quantum mechanics.

And that’s it. According to this theory (which is one of several competing ones) nothing can get hotter. Well, it can – but at that temperature, the laws of physics as we know it cease to apply. We don’t know what happens.

In case you’re wondering, there is actually a temperature scale known as the Planck scale. It has two numbers in it. The first is 0. This defines absolute zero – and the other is 1. That’s the Planck temperature. Everything between is expressed as a fraction of it.

How cool is that? Er – I did just say ‘cool’ didn’t I…

## 10 thoughts on “What is absolute hotness?”

1. I’d never heard of the Planck temperature, or scale, Matthew – and that maximum temperature is phenomenally high – more than the hottest star (and flares) we currently know about I suspect.

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1. Yes, for sure – way hotter even than the core of a star. It’s hard to even imagine temperatures that high.

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1. According to my OED (the full 20 volume second edition, Oxford 1971) the adverb ‘infinitesimally’ means extremely small, which seems a reasonable description of the Planck length.

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1. Of course, but just for fun, let me observe that the OED definition shifts the burden to the word, “extremely,” where much the same issue arises.

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1. I don’t wholly understand what you are getting at here, as you haven’t stated specifically what your issue is. I presume, from context, that you’re conflating the adverb ‘infintesimally’ with the adjective ‘infintesimal’, which is a different word – no need to answer that, of course, I’m simply stating how it presents to me. The OED lists ‘infintesimal’ separately and, at least in my edition, is clear that ‘infintesimal’ (among other things) means the ‘inverse of infinite’, ie: infinitely small. Obviously the Planck length is a discrete non-zero figure, thus this word wouldn’t do to describe it.

But that’s not the word I used, which has its own separate listing and definition as stated.

It’s an interesting distinction, though – and English is constantly evolving. My edition OED, while complete (and exceptionally informative relative to etymology) is also fairly old. So I’ve just looked both words up on the OED’s online sources. It’s curious. Their current online meaning of ‘infintesimally’, ‘to an extremely small degree’, is essentially the same as in my source, ie: explicitly non-zero. It’s here:

https://www.oxfordlearnersdictionaries.com/definition/english/infinitesimally

What I find curious is that the OED’s current online definition of ‘infintesimal’ – which they still treat as a separate and different word – also defines the adjective as ‘extremely small’ (ie: explicitly non-zero), which does differ from the OED I have. It’s here:

https://www.lexico.com/en/definition/infinitesimal

I find it interesting on many levels, as it underscores the way English evolves as a language. When the Third Edition OED comes out in 2037 it’ll be interesting to see how they handle it then. Thanks for the discussion.

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1. My comments were tongue-in-cheek (in intention, although perhaps foot-in-mouth in execution). If I were to write something serious about the infinitely small, as opposed to the infinitely large, and I wanted to use “infinitesimal” or “infinitesimally,” I would be sure to distinguish their original meanings from the current conventional meanings. In something of a similar spirit, I would distinguish between “strictly extreme” or “extremely, in the strictest sense,” and “sort of extreme” or “extremely, in a loose sense.”

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2. I’d heard of the Planck Length but didn’t really know what the hell it was, or what it was good for. Now I know. 🙂

But tell me, do all the rules change once you hit the quantum universe? And no, I don’t understand that either. I’ve just read that it’s very…different.:/

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1. This is the essential conundrum of current physics! No, the rules don’t change… but – er – there seem to be two different rule sets and the cut-over point is the Planck length. The problem is that both rule sets work perfectly in their own realms – quantum mechanics below Planck lengths, Einsteinian determinist physics above. However, we also know that quantum mechanics have real effects in the world we ordinarily perceive – they are, indeed, being harnessed to create quantum computing, for instance. The issue is reconciling them. Einstein – who, in addition to defining the way the whole determinist universe worked, was also closely involved in the discovery of quantum mechanics from the 1920s – thought that the irreconcilability was because physicists had missed something. I suspect he was probably right. Part of the issue is that the current understanding of quantum mechanics comes from Niels Bohr and a conference held in Copenhagen in 1940. This ‘Copenhagen interpretation’ became doctrine. But there were other theories as to its mechanisms. Now, we know quantum mechanics exists, we know what it does – we can, as I say, even harness it. But it’s possible that we might have got the wrong end of the stick in terms of how all that is happening. This is being looked into by physicists right now – the problem being, as in every field, the issue of challenging the orthodoxy in circumstance where academic repute, ability to get funding, ability to publish, and the nature of peer-review comment when publishing, all favour orthodoxy. Actually this is true of every field… Hmmn… Anyhow, stuff is gonna get interesting, that’s for sure…

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1. Orthodoxy. Yes. I remember when stomach ulcers couldn’t possibly be caused by bacteria because no bacteria could survive in the acid of the stomach.
Sadly the history of science is littered with orthodox knowledge that was eventually proved to be wrong. Of course, it’s also studded with brilliant, glorious theories that proved to be right.
I hope I’m still around when physicists discover the right end of the quantum stick. 🙂

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