The Planck Length; The resolution of the Universe¿

What's the smallest thing that you can imagine? Well depending on how good your imagination is you might be able to imagine pretty small but can you imagine plank length small? Well let's find out. I make a new and quite frankly geeky video each week so if you enjoy this geekery then hit that subscribe button for more geeky goodness. The plank length is 1.6 times 10 to the minus 35 of a meter or in other words it's this small. But we can't just start off by trying to imagine something that small, we need to practice a little bit first otherwise we risk some serious imagination injuries. So let's start off by using our imaginations to think of some very small things and then kind of work our way up or actually down for that matter to the plank length. In the early 1800s John Dalton revived the idea of the atom originally theorized by the ancient Greeks. In his initial model the atom was the smallest unit of matter and it couldn't be divided. Also atoms couldn't be created and they couldn't be destroyed. So here we have a hydrogen atom and this is very small, much much smaller than we can actually see even with the most powerful microscopes but we can go smaller than that. When this here we have a hydrogen atom the size of this atom is 31 picometers or 3.1 times 10 to the minus 11 meters. Let's just put that into perspective at the second. Let's put that into a bit of perspective. If I took a grain of sand and scale that grain up so that along each side was 30 kilometers, that's my 18 miles, the size of an atom would be the size of a grain of sand. That's how small atoms are. In 1911 Ernest Rutherford conducted an experiment in which he shot positively charged alpha particles at a very thin sheet of gold foil. He found that most of these particles passed straight through the gold without any deviation whatsoever. This meant that atoms were largely empty space. So let's now imagine the nucleus inside the atom. Here to make things a little easier I'm going to imagine a hydrogen atom and the nucleus of this is just a single proton. I said the atoms were largely empty space but what I really meant was almost completely empty space. If this is the size of an atom then the nucleus would be this small. Or to put it another way, if the atom was the size of Wembley Stadium and if you're not familiar with Wembley then just imagine any other large sports stadium, then the nucleus would be the size of a marble on the center circle. This proton then is 1 times 10 to the minus 15 of a meter. So can we go smaller than a proton? Most definitely. Protons are made of quarks. Three quarks make one proton and for a proton it's two up quarks and one down quark. The up and down business is the flavor of the quark and things are now starting to get a little bit strange here and sizes from here on down are not actually confirmed but we've got to go on. Holding the quarks together is another elementary particle called the gluon. A quark is one thousandth of the size of the proton. In other words if the proton was the size of a beach ball then the quark would be the size of a grain of sand. A quark is 1 times 10 to the minus 18 of a meter. So are we Not even close. Well is there anything smaller than a quark? The smallest I could find and this is a million times smaller than a quark and here we have the neutrino. This means that a neutrino is 1 times 10 to the minus 24 of a meter. Let's put that into perspective. If a quark was a kilometer in diameter then a neutrino would again be the size of a grain of sand. Surely now we must be nearly at Planck length. Still nowhere near. Planck length is a hundred billion times smaller than even a neutrino. But before we finally try to visualize this let's learn a little bit about the Planck length. Well how did we get to this unbelievably small size? I'm not going to delve into the maths too deeply but there are three constants in the universe. Well there are three that we're interested in and because they're constants they're always the same. There is the speed of light in a vacuum. This is always constant no matter how fast you're traveling. Also there's the gravitational constant but we've come across that before haven't we. There's also the Planck constant and this relates a photon's energy to its frequency. All of these constants have units associated with them and it's possible to combine these constants together so that most of their units cancel out and all we're left with is a length. That length is the Planck length. So why is it important? Well by our current understanding of physics it's impossible to measure anything smaller than this length. In reality we can't measure even anything closely approaching this size at the moment but imagine it was possible to build a measuring device that could measure absolutely any length in the universe. It would still be impossible to measure smaller than this. The Planck length is also the scale at which it's thought that quantum gravitational effects become relevant. There's another effect of the Planck length and that's to do with special relativity. According to special relativity as you travel faster and faster and approach the speed of light then your length in the direction of travel will appear to an observer to get shorter and shorter. This phenomenon is called length contraction. You don't actually get shorter it just appears to an observer that you do. This means that if two people are moving at different speeds then they will disagree on the length of an object. However it's believed that will always agree on the size of the Planck length no matter how fast they're traveling. So finally back to our final imagining of Planck length. Just as a final way of imagining just how mind-meltingly small the Planck length is. Here we have a 30 centimetre or 12 inch ruler. Here we can see one millimetre. The human egg cell is 0.1 millimetres in diameter. Coincidentally this is about the smallest thing that can be seen with the naked eye. The human egg cell is halfway. What I mean by that is it's halfway in size between the Planck length at one extreme and at the other extreme we have the size of the observable universe. Let me put this another way. If this tiny egg cell here was scaled up so that it was the size of the observable universe that's all two trillion galaxies then the Planck length will be the size of this egg cell. That's really truly tiny. Well it's time to come back to our normal scale and things that we can actually see and until next time thank you for watching.