Planck Length - Sixty Symbols

right now i'm standing here like a plank plank length yes what is the plank length well the first thing to say about is very very small and physicists tell us that it's the smallest length scale imaginable really the subject today is the plank length now this is a length of a plank but this is not what a plank length is this is about 1.6 meters it's the height up to about my nose so that's 1.6 meters and i want to talk about something which is a bit smaller well a lot well i can't give you an idea of how much smaller it is suppose i take this length and i chop it into ten equal sections and now that i take this tenth and i divide that up into ten one two three four five six seven eight nine ten and so then i take this small piece here i can't show you any more because it's going to be a tiny little sliver down there that's chopping it three times in order to get down to the plank length i had to chop this 35 times that is do this process of contracting by a factor of 10 35 times so it goes down to 1.6 10 to the minus 35 meters an unimaginably small quantity you can see this length coming down to that that you can visualize but seeing it done 10 to the 35 times is ridiculous this is a length which is smaller than the size of a proton by a factor of 10 to the power 20. let me write it down and do you have to have to do all these 35 with them one two three four five six and eight nine ten and so on and 35 of those zeros now i'm going to write this number down so you can see how ridiculously small it is it's not naught point no no no no that would be five zeroes it's that with another five oh that with another five and if i stop there that would be ten to the minus fifteen meters which is about the size of a proton the smallest thing that people can more or less visualize oh no you can't visualize it we're going to carry on one two three four and that's 10 to the minus 20 not not not nor that's i can't work it out i'm going to have this plus another 10-15 i feel so ridiculous doing all this but there it is down there with these extra four sets of zeros with the one at the end that's the distance and then it's 1 6. so in meters so this is the planck length it's arrived at by taking three fundamental constants planck's constant the gravitational constant big g and the speed of light now planck was the first person to come up with this length because he just invented quantum physics by studying black body radiation the history of it's quite strange because back in the 1880s max planck and others were thinking about the heat energy that was heat and light energy was coming out of hot bodies and in the course of that he started getting a feeling for that there was something quantum mechanical happening from that he came up with an idea of fundamental units for mass length and time and the unit of length is called the planck length so the planck length is telling you that when you try to merge the fields of gravity through newtonian constant big g with the velocity of light which is something comes it comes in electromagnetism with quantum mechanics and merge them all together out of it comes somehow a natural length called the planck length let's just write down the three constants then here's planck's constant h or is it sometimes written h upon 2 pi which we could signify like this this is big g the gravitational constant that tells us why gravity is as strong as it is why the earth has got its its strength of gravity on the surface or it of course big g and the mass of the earth determines the orbiting of the moon around the earth and then the other constant is uh c now the curious thing is if you multiply h bar and g and then divide by c cube the cube c that gives you the square of a length or if you like an area and that's called the planck length so the planck length if we now take square roots i want the length itself we take the square root of that quantity and that then gives me the planck length and if you want to talk about the early stage of the universe the period before that it expanded to the planck length we have no idea of the laws of physics because to do that we'd have to have a quantum theory of gravity and none exist well if they exist they exist in a form that nobody knows whether they're right or not now what does it all mean physically well of course this is this what it's telling us is that perhaps if we take quantum mechanics and gravity into account space itself is not really properly defined on length scale smaller than the planck length maybe space time gets foamy as they say on these sorts of length scales and then all the particle physics guys and these cosmologists start worrying about their ideas of bubble universes springing out out of the plank length but you better go and talk to a cosmologist or if you get a black hole for example if i fell into a black hole i would be spaghettified turned into long strands of thing and disappear but as i go into the black hole all the entropy associated with me my complete disorder how my hair is untidy everything about that will be dissolved in the black hole and in order for the laws of thermodynamics to hold the entropy of the universe must increase and if the black hole is part of the universe the total entry must increase and the black hole must have an entropy and the person who wrote down the formula for the black holes entropy originally was beckenstein and then um stephen hawking and he wrote down the entropy is equal to boltzmann's constant times the area of the black hole divided by four times the planck length squared so there it comes in in this model of the entropy of a black hole and that is believed by most theoreticians despite the lack of any evidence to be the entropy of a black hole so there is a practical use for this plank length well if you're a cosmologist or a particle physicist i have to say in my everyday work on semiconductors i don't use it too much but it's great to think about because it's such a small length

Channel: Sixty Symbols

Views: 734,100

Keywords: max, planck, length

Id: _Y8HgmOoLCM

Length: 6min 47sec (407 seconds)

Published: Mon Jul 12 2010