Planck's constant is a thing we all hear about in high school physics classes, but no one really talks about why it's cool.

Textbooks will talk dryly about "blah blah theories of quantum gravity" and teachers will repeat that "something something a photon's energy to its frequency. And sure, these things are true. But when people say stuff like that, they're really burying the lede.

Planck's constant is about the limits of what's physically possible in the Universe!


A Planck length is a unit of length which can be derived from Planck's constant. It is the smallest length which is possible in our Universe.

And it's unimaginably tiny. A hundredth of a billionth of a billionth of the size of a proton. But this is significant. Anything smaller than a Planck length cannot exist. It would not make physical sense.

Planck lengths are basically Universe pixels.

A Planck time is the time taken for light to travel one Planck length. As Einstein proved, it's impossible for anything to travel faster than light. That's the upper speed limit for anything travelling through the spacetime fabric of our Universe.

So the Planck time is arguably the smallest unit of time which can possibly exist and still have any meaning.

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At the other end of the scale you have the upper limits which are also absurd.

A Planck temperature is 140 thousand billion billion billion degrees. That's the highest possible temperature in our Universe. Nothing hotter can exist.

A Planck density is roughly 100 billion billion times the mass of the Sun squeezed into the size of an atomic nucleus. It is the highest density which can possibly exist. But that one's theoretical. A black hole would form long before anything could get that dense.

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Weirdly, a Planck mass is neither absurdly big nor small. It's about 21 micrograms which is roughly the same mass as an eyelash.

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I just like to ramble about these things sometimes because I think they're cool. I'm glad y'all agree 💚

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@InvaderXan O_O
But.. I thought we were only allowed ignore Zeno's paradoxes by assuming time wasn't divided into quanta?
Also.. seems to me like there ought to be something profound between Inflation and Planck Lengths, and I'm gonna have to defer reading it up because I'm trying to work and it's not as interesting as this

@cathal Why would we want to ignore Zeno's paradoxes, and how is that related to quantisation of time at infinitesimal scales?

@InvaderXan Wait, I’m not sure to understand how that last one is supposed to work. We have objects with a mass way smaller that 21 micrograms.

@Sylvhem Which is why it's weird. It's not an upper limit or a lower limit ¯\_(ツ)_/¯

@InvaderXan Maybe it’s because mass isn’t an inherent propriety of an object?

@Sylvhem That seems very likely!

After all, mass changes with an object's energy and that's an external property. Hmmm... I've never much thought about this before.

@InvaderXan Are you a physicist by the way? Or do you just like physics.

@Sylvhem Yeah, I'm a physicist. An astrophysicist though, so this area isn't exactly my speciality. I know a few cosmologists who understand all of this a lot better than I do.

@InvaderXan Wait, you are an actual astrophysicist? You mean I was mutual with an astrophysicist all this time and I didn’t know :blob_aww:?

This is just a guess... because Planck density and Planck length is already defined as a maximum and a minimum respectively, Planck mass is somewhere in between.

@InvaderXan It happens to me frequently in physics as well as biology: When you just hold on for a few minutes and start thinking and digging into a topic like this and it always blows my mind how insanely cool it is

@aymm Oh totally. Everything is fascinaing, and it becomes more and more fascinating the closer you look!

@InvaderXan Is the impossibility of anything beyond Planck the reason that a lot of people wish for the impossible by blowing an eyelash away from the fist?

@InvaderXan Nothing hotter can exist in our universe under the same rules as everything else that is, it is possible that above the plank temperature, there are other, hotter temperatures, but at those temperatures the laws of physics literally change, we don't understand exactly how they change or what to, all we know is that they would.

@starwall Honestly, I'm skeptical of any hypothesis which requires us to literally move the goalposts, particularly where there's no evidence that those goalposts are even movable. It's questionable how many of those hypotheses would survive Occam's razor.

@InvaderXan Well, at a certain temperature in the past of the universe, the laws of physics were different. various independent forces were conjoined and worked differently, for the first brief moments of reality this is what the universe was like. the plank temperature is basically a definition of that limit which we can't look past, where the math breaks down. it's a line in the sand marking where our theories cannot tread past with any certainty. Absolute Hot is a hypothesis, whereas at least with Absolute Zero we've basically proven it to be impossible to get to in the lab

@InvaderXan this is one of those extremely cool regions of physics where the answer is still, basically "dunno"

@starwall @InvaderXan No-one ever talks about the more humble areas of physics where the answer is 'dunno'

@diffractie @InvaderXan there's a lot of theories on what Absolute Hot may be, or if it may be at all. the string theorists have their camp, the Plank temperature is one candidate, and there are yet more hypothesizes. "The temperature scale from cold to hot runs +0 K, …, +300 K, …, +∞ K, -∞ K, …, -300 K, …, -0 K."

absolute zero and absolute hot can mean the same thing depending on interpretation. Asking if there's an absolute hot at all is dependent entirely on who you ask!

@diffractie @InvaderXan then again we're talking about an area where the math breaks down for ALL of us, the math breaks down for me just about as soon as I need to take my astronomy test haha.. this is all very much above my paygrade.

@InvaderXan when I hear "absolute limits" I think "we aren't being creative enough, let's experiment"

Aaand this is why I shouldn't study theoretical physics

@elfi I used to think the same. From what I've seen though, you can be as creative as you like, but that doesn't necessarily mean the Universe will play along.

@InvaderXan I mean it's all fun and games until I restart the universe trying to experiment with the density one

@elfi I was about to type that I'm not sure if that's possible, but I'm not sure this is a challenge I want to accidentally give you 😂

@InvaderXan if you think about it, the big crunch is just the universe unwinding its stack

@elfi Fun fact about the big crunch, if it happens there will be a point near the end of the Universe where everything everywhere will be the temperature of liquid water, so everything will be habitable. I'm going to build a beach house on Pluto.

@pfx That's a nice description for it! I'm going to have to remember that one.

@pfx Don't worry. Much like the end of the Universe, typos are inevitable.

@professor_stoke Yes, there would be a highest possible frequency which would make any physical sense in the Universe. I don't think I've heard it called a Planck frequency before, but that's totally what it is.


I think it also plays an important role in strings theory as it determines the size of the strings.

@InvaderXan Absolutely - merely noting Planck length is at the base of the theory!


I love thinking about the “resolution of the Universe”.

@zzz I'm glad we live in a high resolution universe. It would be pretty weird if the Planck length was like, a centimetre.


I love this sort of stuff. On a similar note I spend a lot of time thinking about how real numbers are represented on computers. How the resolution of numbers makes us do weird things


The start of the 🐰 hole comes from a question like: If you can only have a finite collection of numbers, which do you take? And then see which ones did the hardware designers decide to give us.

The following link spells out some more of that mystery, but it's worth doing the thought experiment before clicking:

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