The Planck Mass: Not extremely big and not extremely small

I've looked at most of the Planck units. Planck length which is really tiny, Planck time which is really short and Planck temperature which is really hot. But there is one I've been sort of putting off and that's Planck mass which is kind of strange. Let's find out more. So let's get straight into it and describe the Planck mass. This is 2.176 x 10 to the minus 8 kilograms. So that's this much. Unlike my other Planck unit videos we don't need to try to use our imaginations to visualise how big or small this is because we can easily imagine how heavy this is. 10 to the minus 8 kilograms is about 10 times heavier than a human egg cell or about the same mass as an eyelash. So how does this compare to the mass of other things and specifically how does this compare to the mass of particles and the like? So in order to think about this we need a new way of measuring mass and this is going to allow us to compare really small masses quite easily. One way that physicists use to measure very small masses is something called the electron volt, well sort of. I'm no physicist so apologies if my explanation is a bit sketchy but according to Einstein's equation E equals m c squared the E is energy, m is mass and c is the speed of light in a vacuum squared. This then means that energy and mass are kind of equivalent to each other. In fact this is kind of how the sun works it's constantly turning its mass into energy. If I now rearrange this equation I find that mass is equal to energy divided by c squared. The electron volt is actually a measure of energy so I can put this into the equation here. We can now see that mass is equivalent to electron volts divided by c squared or in other words electron volts per c squared. When I'm talking about very small masses, in other words the masses of particles, we often use electron volts per c squared as a unit of mass equivalence. So I hope that makes sense and I hope I haven't mangled the physics too much. So now let's have a look at the mass of some very small particles and see how it compares to the Planck mass. Let's start by looking at one of the least massive particles, the neutrino. This particle usually travels at nearly the speed of light. It appears that all particles want to at the speed of light but their mass slows them down. That's a massive oversimplification but I'll need a separate video to explain this properly. As a neutrino travels so quickly they have a very small mass. Neutrinos are actually really elusive particles. Trillions of them are passing through mine and your body every second and they don't interact with the particles in our bodies at all. This has meant that studying neutrinos is very difficult. It was thought for some time that neutrinos traveled at the speed of light and so therefore had to be massless as only particles with no mass are able to travel at such speeds. It was later discovered that they traveled at slightly less than the speed of light which meant they must have mass but they don't have much mass though. The mass of neutrinos has been very difficult to pin down but in a report published in February 2022 by Humboldt University in Berlin it seems like the mass of a neutrino is somewhere less than 0.8 electron volts per c squared and as we're soon going to learn that's very small indeed. There are actually three types of neutrino and it appears that the combined mass of all three is less than two electron volts but I'm not going to delve into that any further. Let's now think about visible matter. All the matter that we can see and a lot of it that we can't is made up of atoms and all atoms are made up of protons and neutrons in the nucleus with electrons around the outside. The electrons don't really orbit the nucleus like the planets orbit the sun but it's a convenient way of thinking about it. So the neutrino is the lightest particle of those that have mass and next up in terms of mass is the electron from the atoms we just talked about. This particle is negatively charged with a negative charge of minus one and along with protons and neutrons is a major component of all atoms that make up the whole of the universe. The mass of an electron is 511,000 electron volts per c squared or 0.511 mega electron volts per c squared. This is way over half a million times heavier than the neutrino. Let's move a bit heavier and there we find a couple of quarks. These are the fundamental particles that make up all protons and neutrons which are those particles in the nucleus of all atoms. In other words me, you, my house, dinosaurs and the sun. With a mass of 1.9 mega electron volts per c squared we find the up quark. Up quarks have an electrical charge of plus two thirds and at just over twice the mass of the up quark we find the down quark with a mass of 4.4 mega electron volts per c squared. This particle has an electrical charge of minus a third and this is going to become important in a minute. Coming up a little in mass we have another fundamental particle called the strange quark. This particle has a mass of about 95 mega electron volts per c squared and these particles are also found in other particles such as the sigma baryon and the strange d meson. They may also be found in weird celestial bodies called strange stars. The next particles on our little journey are ones we've already mentioned before and these are the protons and the neutrons. Each proton is made from two up quarks and one down quark as well as particles called gluons holding the quarks together. If we look at the charges of these quarks we can work out that the charge on a proton is plus one. The neutron is made from two down quarks and one up quark again held together by gluons. The charges on the quarks that make up a neutron give it a neutral charge. You might think that since we know the mass of the constituent quarks that make up each proton and neutron that we'd be able to calculate relatively easily the mass of a proton and neutron but sadly this isn't the case. Protons have a mass of 938.27 mega electron volts per c squared. Neutrons are slightly heavier with a mass of 939.57 mega electron volts per c squared. The mass of a proton and neutron is therefore much higher than the mass of the quarks that make them up. Well then surely the rest of the mass must come from the gluons that hold them together. Unfortunately that isn't the case either. Gluons have no mass so the answer to the missing mass must lie somewhere else and it's quite a problem as the missing mass isn't just a small fraction of the overall mass of the proton and the neutron. The mass of the quarks only makes up about one percent of the mass of the proton and neutron. That means we have to account for the other 99%. Well the missing mass comes from something called quantum chromodynamic binding energy. This is the energy that the gluons possess to hold the quarks together. Even though the gluons are massless they do possess energy and due to our mass energy equivalence that I mentioned earlier this energy is actually responsible for the missing mass. This means that 99% of the mass of me and you is actually quantum chromodynamic binding energy. Strange. I know in my model of the protons and neutrons I've drawn three gluons for each but we don't really know how many gluons there are or even if asking that question is even meaningful. We just don't know. Well mine's much greater than mine might do but I certainly don't. Anyway let's continue. Next on our list we have the charm quark. This weighs in at 1320 mega electron volts per c squared. This is over 2000 times heavier than an electron. These particles are found in baryons which are heavier particles. Most of these particles however only exist for tiny fractions of a second. Just over three times heavier than the charm quark we find the bottom quark weighing in at 4240 mega electron volts per c squared. You could also say that this is 4.24 giga electron volts per c squared. These also form larger particles by joining with other fundamental particles. Finally we have the largest of all the fundamental particles called a top quark. This weighs in at a whopping 172 giga electron volts per c squared. This is more than 172 times more massive than a proton. It's been calculated that these particles exist for only 5 times 10 to the minus 25 of a second. That's this much of a second. When you consider that an eye blink takes this much time we can see how seriously brief these particles lifetimes are. So short is their existence that there isn't even enough time for the strong force to form. Meaning these particles are unable to join with other particles to form larger particles known as hadrons. Protons and neutrons are examples of hadrons due to them being formed from three quarks each. So in terms of electron volts per c squared how do these particles compare to the mass of the Planck mass? Well in terms of particles and in electron volts per c squared the Planck mass is huge. It's 1.22 times 10 to the 19 giga electron volts per c squared. That's more than a million billion times bigger than the mass of even the largest particle. So where did the idea for the Planck mass come from and what's its significance? Just like the other Planck units the Planck mass is derived from some of the fundamental constants of the universe. In this case the reduced Planck constant, the speed of light in a vacuum and the gravitational constant. It's only when we compare it to other particles that we see how truly huge the Planck mass is. So what does it mean then? Well it is the unit of mass in the system of Planck units. With the other Planck units they form a boundary beyond which our current model of the physics makes no sense but the Planck mass is slightly different. It is however the mass of a Planck particle. This is a hypothetical particle. A particle with this mass would be a tiny black hole with a Schwarzschild radius equal to the Planck length. It's also thought that the Planck mass has some significance in quantum gravity. Quantum gravity may help us explain what happens at the centre of a black hole. Okay I think that's enough for the Planck mass. If there's anything else you'd like me to have a look at then just leave a comment below. But for now and until next time thank you for watching.