Planck units
December 25, 2024 5:04 PM Subscribe
Planck length. (Short!) Planck time. (Brief!) Planck temperature. (Hot!) Planck figurine. (Adorable!)
What will happen if you Planck every day for a minute
posted by They sucked his brains out! at 6:13 PM on December 25, 2024 [1 favorite]
posted by They sucked his brains out! at 6:13 PM on December 25, 2024 [1 favorite]
I came across Learning Curve a while back and was unpleasantly surprised that someone can put that much time and effort into neat educational videos and get such a small audience for it. So I'm glad to see the channel getting a little more exposure.
posted by Pemdas at 6:40 PM on December 25, 2024 [1 favorite]
posted by Pemdas at 6:40 PM on December 25, 2024 [1 favorite]
I watched the first one about Planck length and it honestly wasn't very good. It did say that the Planck length was related to the three constants, but it didn't explain how and why that was so. Why is that the minimum that can be measured and what does that have to do with the structure of the universe? The video did not explain that.
posted by outgrown_hobnail at 8:54 PM on December 25, 2024 [2 favorites]
posted by outgrown_hobnail at 8:54 PM on December 25, 2024 [2 favorites]
https://images3.memedroid.com/images/UPLOADED149/6761a8d6ee2b6.webp
posted by rswst8 at 10:02 PM on December 25, 2024 [1 favorite]
posted by rswst8 at 10:02 PM on December 25, 2024 [1 favorite]
I have no idea where he's getting "sizes" for the quarks and neutrinos. I've written on Metafilter before that atoms aren't mostly empty:
Most people know that there is a connection, which has something to do with Einstein, between energy and mass; that sentence is generally enough to make them jump up and say "E = mc2." This is why physicists will talk about the masses of subatomic particles in energy units. Nobody uses the electron mass of ten-to-the-minus-twenty-mumble kilograms to do practical computations, any more than we measure atomic radii in furlongs. The electron mass is about 0.5 MeV/c2, where the mega-electron-volt is an energy unit, and where we frequently don't bother saying or writing the "c2" part.
When you start talking about angular momentum in quantum mechanics, you introduce Planck's constant ℏ, and that lets you make a similar connection between energy and length:
For example: protons and neutrons are attracted to each other by pion exchange; the pion mass 140 MeV is related to the maximum nuclear diameter of a few femtometers. But protons and neutrons repel each other by exchanging rho and omega mesons, which have masses closer to 800 MeV; this is related to the observation that nucleons act like they have a smaller hard core. The "weak length scale" is about a five hundred times shorter than the "strong length scale" because the weak interaction fields, associated with the particles W± and Z, have masses which are about five hundred times more than the pion mass.
But in practice, we don't actually talk in more than a handwaving way about things happening "inside of a proton." The inside of a proton is very complicated, but it's what we call a "stationary state": there's only one way to be a proton, and that's what protons are doing, all of them, all of the time. We talk instead about the energies of interactions where these other fields play an important role. If you want to see weak interactions, you can (a) wait a long time, (b) measure very carefully, or (c) hit stuff together with energies of 100 GeV or more, so that the W and Z fields have plenty of energy to make their particle-like excitations.
Notice that there is an awful lot of "about" and "or so" and "goes like" in these descriptions. You've maybe had the experience of doing a page of algebra, and at the end everything cancels out and you're left with an answer like "three" or "two-fifths." That happens a lot; we call those results "fractions of order one." You can actually accomplish quite a bit of physics without doing any of that page of algebra, in a technique called "dimensional analysis": you figure out what the relevant constants are in your problem, multiply and divide them so they have the units you want, and work with that unit combination. You know that any number you come up with will probably turn out to be wrong by a factor of two or one-third or something. But that's not really any different from knowing that you're going to the grocery store tomorrow or the next day, and that you'll spend fifty or a hundred dollars, even though you haven't yet made your list.
That's what the Planck scale is: the result of dimensional analysis. When we end up talking about quantum mechanics and gravity at the same time, we're going to have c, ℏ, and G available as constants. There's one way to combine them to make a length, so any intrinsic quantum-gravity phenomena are going to have that length scale. Or, if you don't believe in lengths after this little essay, you use ℏc to convert that length to an energy. If things collide with that energy, quantum-gravity effects are going to be important.
posted by fantabulous timewaster at 10:19 PM on December 25, 2024 [26 favorites]
If I were to make one mark on the world as a science communicator, it would be to put the misconception that “atoms are mostly empty space” into the same useful-but-wrong dustbin as the Bohr model. [...] An atom is full of electrons, which get bigger when they are cold.The number in the video for "the length scale of a quark," about one-thousandth the radius of a proton, is about the same as the "weak scale" that I refer to in that old post. But the neutrino also interacts at the weak scale. Maybe he's taking the square roots of cross sections? I really don't know. In any case, below the weak scale, everything is so intensely quantum-mechanical that it doesn't really make sense to talk about length at all anymore. Instead, we talk about energy.
Most people know that there is a connection, which has something to do with Einstein, between energy and mass; that sentence is generally enough to make them jump up and say "E = mc2." This is why physicists will talk about the masses of subatomic particles in energy units. Nobody uses the electron mass of ten-to-the-minus-twenty-mumble kilograms to do practical computations, any more than we measure atomic radii in furlongs. The electron mass is about 0.5 MeV/c2, where the mega-electron-volt is an energy unit, and where we frequently don't bother saying or writing the "c2" part.
When you start talking about angular momentum in quantum mechanics, you introduce Planck's constant ℏ, and that lets you make a similar connection between energy and length:
ℏc ≈ 200 MeV•fmThis relationship between energy and length turns out to be super-useful when you're thinking of forces that are mediated by massive fields. (Other folks might say "mediated by massive particles," but the murky boundary between a continuous field and its particle-like excitations is the whole reason this video about particle sizes is a little wobbly.) It turns out that if the mediating field has a mass m, then the associated interaction has a length scale like (ℏc)/(mc2).
For example: protons and neutrons are attracted to each other by pion exchange; the pion mass 140 MeV is related to the maximum nuclear diameter of a few femtometers. But protons and neutrons repel each other by exchanging rho and omega mesons, which have masses closer to 800 MeV; this is related to the observation that nucleons act like they have a smaller hard core. The "weak length scale" is about a five hundred times shorter than the "strong length scale" because the weak interaction fields, associated with the particles W± and Z, have masses which are about five hundred times more than the pion mass.
But in practice, we don't actually talk in more than a handwaving way about things happening "inside of a proton." The inside of a proton is very complicated, but it's what we call a "stationary state": there's only one way to be a proton, and that's what protons are doing, all of them, all of the time. We talk instead about the energies of interactions where these other fields play an important role. If you want to see weak interactions, you can (a) wait a long time, (b) measure very carefully, or (c) hit stuff together with energies of 100 GeV or more, so that the W and Z fields have plenty of energy to make their particle-like excitations.
Notice that there is an awful lot of "about" and "or so" and "goes like" in these descriptions. You've maybe had the experience of doing a page of algebra, and at the end everything cancels out and you're left with an answer like "three" or "two-fifths." That happens a lot; we call those results "fractions of order one." You can actually accomplish quite a bit of physics without doing any of that page of algebra, in a technique called "dimensional analysis": you figure out what the relevant constants are in your problem, multiply and divide them so they have the units you want, and work with that unit combination. You know that any number you come up with will probably turn out to be wrong by a factor of two or one-third or something. But that's not really any different from knowing that you're going to the grocery store tomorrow or the next day, and that you'll spend fifty or a hundred dollars, even though you haven't yet made your list.
That's what the Planck scale is: the result of dimensional analysis. When we end up talking about quantum mechanics and gravity at the same time, we're going to have c, ℏ, and G available as constants. There's one way to combine them to make a length, so any intrinsic quantum-gravity phenomena are going to have that length scale. Or, if you don't believe in lengths after this little essay, you use ℏc to convert that length to an energy. If things collide with that energy, quantum-gravity effects are going to be important.
posted by fantabulous timewaster at 10:19 PM on December 25, 2024 [26 favorites]
Excellent comment! I watch a lot of videos like these and some of them are better than others at making it clear they're talking about models that approximate what is actually happening. The guy on the PBS Spacetime yt channel sometimes emphasizes that we know this model is wrong even if we think it's pretty close. Something else I've learned as a theme is that the closer we look at the universe, the weirder it gets.
I have no idea where he's getting "sizes" for the quarks and neutrinos.
Look, I'm not a physics, I'm just some guy, my mind can only get blown so much at once!
About E=mc^2, something I learned only recently is that this a reduction of a more complex formula that takes momentum into account and doing some algebra to rearrange that expanded formula can tell you stuff about how weird space is. Don't ask me to do the math though, that's for real physicists. :)
E2 = (mc2 )2 + (pc)2 is one version but I guess even that's not the full thing? I need to go over that stuff again to understand it better.
This is why physicists will talk about the masses of subatomic particles in energy units.
My understanding here is that this is because it's these of sub-atomic particles interacting that creates the properties that we call mass. Inside the proton is something like a "soup" of all the bits that makeup a proton. They're all lightspeed particles meaning they only travel at lightspeed and have no mass at rest but they're bound by the nuclear forces so they don't just explode in every direction as they would do otherwise. So it's like having a ball and inside are all these particles trying to escape and when they hit the border they bounce off. If all the particles only bounced off one part of the ball, the ball would move that direction. But because this is all so small and so fast, every time a particle hits the border on side, another is hitting the exact opposite spot on the other side which resists the movement generated on the other side and vice versa.
So this ball effectively resists moving every direction at once and it takes some outside force to overcome that inertia. The more energy contained within that system, the hard everything hits and the farther they get before bouncing back increasing the resistance to moving in any direction. Which we experience as mass.
Why is that the minimum that can be measured and what does that have to do with the structure of the universe? The video did not explain that.
I believe this more or less comes down to the heisenbug uncertainty principle. By measuring a thing, you're necessarily interacting with it. As you increase the precision with which you're measuring a thing's position by, say, sending a particle that bounces back at you, you increase how strongly you interact with it. You increase the precision by decreasing the wavelength of your particle (you're basically counting how many complete waves fit between you and the thing you're measuring, shorter wave length is like putting smaller tick marks on a ruler), that requires every higher energies which means your particle hits the thing and imparts ever increasing amounts of momentum. At lower energies you're not getting as precise a fix on the thing's position but you still can still get a pretty good measure of it's momentum. At very high energies you're going to physically move the thing by measuring it increasing it's momentum and decreasing how precise you can measure that momentum.
I'm sure I've gotten some of this wrong but I think that's the general idea.
posted by VTX at 8:53 AM on December 26, 2024 [1 favorite]
I have no idea where he's getting "sizes" for the quarks and neutrinos.
Look, I'm not a physics, I'm just some guy, my mind can only get blown so much at once!
About E=mc^2, something I learned only recently is that this a reduction of a more complex formula that takes momentum into account and doing some algebra to rearrange that expanded formula can tell you stuff about how weird space is. Don't ask me to do the math though, that's for real physicists. :)
E2 = (mc2 )2 + (pc)2 is one version but I guess even that's not the full thing? I need to go over that stuff again to understand it better.
This is why physicists will talk about the masses of subatomic particles in energy units.
My understanding here is that this is because it's these of sub-atomic particles interacting that creates the properties that we call mass. Inside the proton is something like a "soup" of all the bits that makeup a proton. They're all lightspeed particles meaning they only travel at lightspeed and have no mass at rest but they're bound by the nuclear forces so they don't just explode in every direction as they would do otherwise. So it's like having a ball and inside are all these particles trying to escape and when they hit the border they bounce off. If all the particles only bounced off one part of the ball, the ball would move that direction. But because this is all so small and so fast, every time a particle hits the border on side, another is hitting the exact opposite spot on the other side which resists the movement generated on the other side and vice versa.
So this ball effectively resists moving every direction at once and it takes some outside force to overcome that inertia. The more energy contained within that system, the hard everything hits and the farther they get before bouncing back increasing the resistance to moving in any direction. Which we experience as mass.
Why is that the minimum that can be measured and what does that have to do with the structure of the universe? The video did not explain that.
I believe this more or less comes down to the heisenbug uncertainty principle. By measuring a thing, you're necessarily interacting with it. As you increase the precision with which you're measuring a thing's position by, say, sending a particle that bounces back at you, you increase how strongly you interact with it. You increase the precision by decreasing the wavelength of your particle (you're basically counting how many complete waves fit between you and the thing you're measuring, shorter wave length is like putting smaller tick marks on a ruler), that requires every higher energies which means your particle hits the thing and imparts ever increasing amounts of momentum. At lower energies you're not getting as precise a fix on the thing's position but you still can still get a pretty good measure of it's momentum. At very high energies you're going to physically move the thing by measuring it increasing it's momentum and decreasing how precise you can measure that momentum.
I'm sure I've gotten some of this wrong but I think that's the general idea.
posted by VTX at 8:53 AM on December 26, 2024 [1 favorite]
Oh yeah, and as I understand it, the nucleus of an atom with more than just a proton isn't really multiple, discreate protons and neutrons so much as it is all of the necessary sub-atomic ingredients all in there interacting and producing the effects we observe as X protons and Y neutrons. So the "size" of a proton means even less once you add even a neutron into the mix.
What I find most baffling about physics is that more physicists don't very loudly go insane trying to study this stuff enough to expand on our knowledge (earning a Ph.D, for example). Once you start getting into all the weird diagrams that help describe the non-Euclidian nature of our universe my mind starts melting.
This stuff is like, really hard.
posted by VTX at 9:02 AM on December 26, 2024 [1 favorite]
What I find most baffling about physics is that more physicists don't very loudly go insane trying to study this stuff enough to expand on our knowledge (earning a Ph.D, for example). Once you start getting into all the weird diagrams that help describe the non-Euclidian nature of our universe my mind starts melting.
This stuff is like, really hard.
posted by VTX at 9:02 AM on December 26, 2024 [1 favorite]
I have to confess disappointment with the first video. Which covered a lot of ground that I as a non-physicist was already good on. While completely ignoring the QM stuff that supposedly makes the Planck length the shortest possible length. I think the term "quantum foam" was mentioned once, maybe in a graphic. I'm always on the lookout for attempts to talk about that in English and came away here empty-handed.
It did occur to me, as I was watching the bit about Lorentz contraction, that the Planck length imposes a finite maximum velocity under special relativity: when the Lorentz-contracted length of a thing becomes equal to the Planck length and the thing is still accelerating, what happens? I'm sure this is not a new insight, except to me.
posted by Aardvark Cheeselog at 9:25 AM on December 26, 2024 [1 favorite]
It did occur to me, as I was watching the bit about Lorentz contraction, that the Planck length imposes a finite maximum velocity under special relativity: when the Lorentz-contracted length of a thing becomes equal to the Planck length and the thing is still accelerating, what happens? I'm sure this is not a new insight, except to me.
posted by Aardvark Cheeselog at 9:25 AM on December 26, 2024 [1 favorite]
@VTX:
> What I find most baffling about physics is that more physicists don't very loudly go insane trying to study this stuff enough to expand on our knowledge
I fudged a little when describing myself as a non-physicist, at least from the perspective of non-scientists. I was once a very enthusiastic student of physical chemistry, part of which involves quantum-mechanical models of the nature and behavior of atoms and molecules. So I went a little distance on that journey.
A lot of what happens is that you are working with models that explain some kind of phenomenon: one big reason chemistry is interested in QM is spectroscopy, and spectroscopy provides a huge body of phenomenological evidence that gets explained via QM. There are patterns in the evidence that allow you to get some intuitive feel for how the QM explanations apply. Any way that you can make QM-influenced phenomenology part of your everyday world will tend to enable you to develop some intuitions. So there are a lot of scientific and engineering disciplines where this can happen. People who spend all their working time thinking about cosmology or the fundamental nature of matter are the ones out beyond the edge of that.
There is another aspect of having a good enough mastery of the math to be able to push the symbols around until you make things come out with the right units, as previously mentioned.
posted by Aardvark Cheeselog at 9:37 AM on December 26, 2024 [1 favorite]
> What I find most baffling about physics is that more physicists don't very loudly go insane trying to study this stuff enough to expand on our knowledge
I fudged a little when describing myself as a non-physicist, at least from the perspective of non-scientists. I was once a very enthusiastic student of physical chemistry, part of which involves quantum-mechanical models of the nature and behavior of atoms and molecules. So I went a little distance on that journey.
A lot of what happens is that you are working with models that explain some kind of phenomenon: one big reason chemistry is interested in QM is spectroscopy, and spectroscopy provides a huge body of phenomenological evidence that gets explained via QM. There are patterns in the evidence that allow you to get some intuitive feel for how the QM explanations apply. Any way that you can make QM-influenced phenomenology part of your everyday world will tend to enable you to develop some intuitions. So there are a lot of scientific and engineering disciplines where this can happen. People who spend all their working time thinking about cosmology or the fundamental nature of matter are the ones out beyond the edge of that.
There is another aspect of having a good enough mastery of the math to be able to push the symbols around until you make things come out with the right units, as previously mentioned.
posted by Aardvark Cheeselog at 9:37 AM on December 26, 2024 [1 favorite]
Mod note: One deleted, requested by poster
posted by travelingthyme (staff) at 11:47 AM on December 26, 2024
posted by travelingthyme (staff) at 11:47 AM on December 26, 2024
> but I guess even that's not the full thing?
No, you've got it. If you have a particle with mass m and momentum p, its total energy E obeys E^2 = (mc^2)^2 + (pc)^2 = (γmc^2)^2, where γ is the "Lorentz factor." In the early days of relativity the quantity γmrest = mrelativistic was called the "relativistic mass," and "E = mrelc^2" also include the dynamics. But that was confusing for a number of reasons, and the modern literature uses "m" for the rest mass.
posted by fantabulous timewaster at 12:17 PM on December 26, 2024
No, you've got it. If you have a particle with mass m and momentum p, its total energy E obeys E^2 = (mc^2)^2 + (pc)^2 = (γmc^2)^2, where γ is the "Lorentz factor." In the early days of relativity the quantity γmrest = mrelativistic was called the "relativistic mass," and "E = mrelc^2" also include the dynamics. But that was confusing for a number of reasons, and the modern literature uses "m" for the rest mass.
posted by fantabulous timewaster at 12:17 PM on December 26, 2024
Mod note: [Hello! We've made Max space for this thread and fantabulous timewaster's comment on the sidebar and Best Of blog!]
posted by taz (staff) at 1:53 AM on December 29, 2024 [1 favorite]
posted by taz (staff) at 1:53 AM on December 29, 2024 [1 favorite]
« Older One generation begetting brokenness of another... | Warning! This game is not compatible with this... Newer »
This thread has been archived and is closed to new comments
I do not watch many videos but I am off to go look at these. The topic is worthy of departure from discursive text.
posted by Aardvark Cheeselog at 5:26 PM on December 25, 2024 [1 favorite]