Does nature have a minimal length?

molecules are made of atoms atomic nuclei are made of neutrons and protons and the neutrons and protons are made of quarks and gluons many physicists think that this is not the end of the story but that quarks and gluons are made of even smaller things for example the tiny vibrating strings that string theory is all about but then what are strings made of smaller things again or is there a smallest scale beyond which nature just does not have any further structure does nature have a minimal length this is what we will talk about today when physicists talk about a minimal length they usually mean the Planck length which is about 10 to the minus 35 meters the Planck length is named after Max Planck who introduced it in 1899 10 to the minus 35 meters sounds tiny and indeed it is damn tiny to give you an idea think of the tunnel of the Large Hadron Collider it's the ring with a diameter of about 10 kilometers the Planck length compares to the diameter of a proton as the radius of a proton to the diameter of the Large Hadron Collider currently the smallest structures that we can study are about 10 to the minus 19 meters that's what we can do with the energies produced at the Large Hadron Collider and there is still 16 orders of magnitude larger than the Planck length what's so special about the Planck length the Planck length seems to be setting a limit to our small structure can be so that we can still measure it that's because to measure small structures we need to compress more energy into small volumes of space that's basically what we do with particle accelerators higher energy allows us to find out what happens on shorter distances but if you stuff too much energy into a small volume you will make a black hole more concretely if you have an energy e that will in the best case allow you to resolve a distance of about H bar C / E I will call that distance Delta X here C is the speed of light and H bar is a constant of nature accord Planck's constant yes that's the same Planck this relation comes from the uncertainty principle of quantum mechanics so higher energies let you resolve smaller structures now you can ask if I turn up the energy and the size I can resolve gets smaller when do I get a black hole well that happens if the Schwarzschild radius associated with the energy is similar to the distance you're trying to measure that's not difficult to calculate so let's do it the Schwarzschild radius is approximately M times G over C square with rias Newton's constant and M is the mass we are asking when is the radius similar to the distance Delta X as you almost certainly know the mass associated with the energy is e equals MC square and as we previously saw that energy is just H bar C over Delta X you can unsolved this equation for Delta X and this is what we call the plug length it is associated with an energy called the Planck energy if you go to higher energies than that you will just make larger black holes so the Planck length is the shortest distance you can measure now this is the need estimate and it's not entirely wrong but it's not a rigorous derivation if you start thinking about it it's a little hand wavy so let me assure you that they are more rigorous ways to do this calculation and the conclusion remains basically the same if you combine quantum mechanics with gravity then the plug length seems to set a limit to the resolution of structures that's why physicists think nature may have a fundamentally minimal length max black by the way did not come up with the Planck length because he thought it was the minimal length he came up with that simply because it's the only unit of dimension length you can create from the fundamental constants see the speed of light G Newton's constant and h-bar he thought that was interesting because as he wrote in his 1899 paper this would be natural units that also aliens would use check the information below the video for references the idea that the Planck length is a minimal length only came up after the development of Relativity when physicists started thinking about how to quantize gravity today this idea is supported by attempts to develop a theory of quantum gravity which I told you about in an earlier video in string theory for example if you squeeze too much energy into a string it will start spreading out in loop quantum gravity the loops themselves have a finite size given by the Planck length in asymptotically safe gravity the gravitational force becomes weaker at high energies so beyond a certain point you can no longer improve your resolution when I speak about a minimal length a lot of people seem to have a particular image in mind which is that the minimal length works like a kind of discretization a pixelation of a photo or something like that but that is most definitely the wrong image the minimal length that we are talking about here is more like an unavoidable blur on an image some kind of fundamental fuzziness that nature has it may but does not necessarily come with a discretization what does this all mean well it means that we might be close to finding a finer theory one that describes nature at its most fundamental level and there's nothing more beyond that there is possible but remember that the arguments for the existence of a minimal length rests on extrapolating 16 orders of magnitude below the distances that we have tested so far that's a lot that extrapolation might just be wrong even though we do not currently have any reason to think that there should be something new on distances even shorter than the Planck length that situation might change in the future still I find it intriguing that for we currently know it is not necessary to think about distances shorter than the Planck length thanks for watching see you next week

Channel: Sabine Hossenfelder

Views: 318,068

Keywords: science, physics, gravity, Einstein, quantum mechanics, universe, nature, does nature have a minimal length, is there a minimal length, is there a smallest length, what is the smallest length, Planck length, what is the Planck length, Max Planck, final theory, hossenfelder, quantum gravity

Id: nyPdIBnWOCM

Length: 6min 24sec (384 seconds)

Published: Sun Feb 02 2020