Does the Universe have Higher Dimensions? Part 1

this video was sponsored by the great courses plus space the way we experience it has three dimensions left right forward backward and up down but why three why not 7 or 26 the answer is no one knows but if no one knows why space has three dimensions could it be that it actually has more just that we haven't noticed for some reason that's what we'll talk about today the idea that space has more than three dimensions may sound entirely nuts but it's a question that physicists have seriously studied for more than a century and since there's quite a bit to say about it this video will have two parts in this part we will talk about the origins of the idea of extra dimensions collusion client theory and all that and in the next part we will talk about more recent work on it string theory and black holes are the large hadron collider and so on let us start with recalling how we describe space and objects in it in two dimensions we can put a grid on a plane and then each point is a pair of numbers that says how far away from zero you have to go in the horizontal and vertical direction to reach that point the arrow pointing to that point is called a vector this construction is not specific to two dimensions you can add a third direction and do exactly the same thing and why stop there you can no longer draw a grid for four dimensions of space but you can certainly write down the vectors they're just a row of four numbers indeed you can construct vector spaces in any number of dimensions even in infinitely many dimensions and once you have vectors in these higher dimensions you can do geometry with them like constructing higher dimensional planes or cubes and calculating volumes or the shapes of curves and so on and while we cannot directly draw these higher dimensional objects we can draw their projections into lower dimensions this for example is the projection of a four-dimensional cube into two dimensions now it might seem entirely obvious today that you can do geometry in any number of dimensions but it's actually a fairly recent development it wasn't until 1843 that the british mathematician arthur cayley wrote about the analytical geometry of n dimensions where n could be any positive integer higher dimensional geometry sounds innocent but it was a big step towards abstract mathematical thinking it marked the beginning of what is now called pure mathematics that is mathematics pursued for its own sake and not necessarily because it has an application however abstract mathematical concepts often turn out to be useful for physics and these higher dimensional geometries came in really handy for physicists because in physics we usually do not only deal with things that sit in particular places but with things that also move in particular directions if you have a particle for example then to describe what it does you need both a position and a momentum where the momentum tells you the direction into which the particle moves so actually each particle is described by a vector in a six-dimensional space with three entries for the position and three entries for the momentum this six dimensional space is called face space by dealing with phase spaces physicists became quite used to dealing with higher dimensional geometries and naturally they began to wonder if not the actual space that we live in could have more dimensions this idea was first pursued by the finnish physicist gona not stream who in 1914 tried to use a fourth dimension of space to describe gravity it didn't work though the person to figure out how gravity works was albert einstein yes that guy again einstein taught us that gravity does not need an additional dimension of space three dimensions of space will do it's just that you have to add one dimension of time and allow all these dimensions to be curved but then if you don't need extra dimensions for gravity maybe you can use them for something else theodore colossa certainly thought so in 1921 calusa wrote a paper in which he tried to use a fourth dimension of space to describe the electromagnetic force in a very similar way to how einstein described gravity but calusa used an infinitely large additional dimension and did not really explain why we don't normally get lost in it this problem was solved a few years later by oscar klein who assumed that the fourth dimension of space has to be rolled up to a small radius so you can't get lost in it you just wouldn't notice if you stepped into it it's just too small this idea that electromagnetism is caused by a curled up fourth dimension of space is now called collusa cline theory i have always found it amazing that this works you take an additional dimension of space roll it up and out comes gravity together with electromagnetism you can explain both forces entirely geometrically it is probably because of this that einstein in his later years became convinced that geometry is the key to unified theory for the foundations of physics but at least so far that idea has not worked out does collusa client theory make predictions yes it does all the electromagnetic fields which go into this fourth dimension have to be periodic so they fit onto the curled up dimension in the simplest case the fields just don't change when you go into the extra dimension and that reproduces the normal electromagnetism but you can also have fields which oscillate once as you go around than twice and so on these are called higher harmonics like you have in music so collusa client theory makes a prediction which is that all these higher harmonics should also exist why haven't we seen them because you need energy to make this extra dimension wiggle and the more it wiggles that is the higher the harmonics the more energy you need just how much energy well that depends on the radius of the extra dimension the smaller the radius the smaller the wavelength and the higher the frequency so a smaller radius means you need higher energy to find out if the extra dimension is there just how small the radius is the theory does not tell you so we don't know what energy is necessary to probe it but the short summary is that we have never seen one of these higher harmonics so the radius must be very small oscar klein himself by the way was really modest about his theory he wrote in nineteen twenty six or pinterest whether these indications of possibilities are built on reality has of course to be decided by the future but we don't actually use collusa client theory instead of electromagnetism and why is that is because collusa client theory has some serious problems the first problem is that while the geometry of the additional dimensions correctly gives you electric and magnetic fields it does not give you charged particles like electrons you still have to put those in the second problem is that the radius of the extra dimension is not stable if you perturb it it can begin to increase and that can have observable consequences which we have not seen the third problem is that the theory is not quantized and no one has figured out how to quantize geometry without running into problems you can however quantize plain old electromagnetism without problems we also know today of course that the electromagnetic force actually combines with a weak nuclear force to what is called the electro weak force that interestingly enough turns out to not be a problem for collusa crime theory indeed it was shown in the 1960s by richard kerner that one can do collusa climb theory not only for electromagnetism but for any similar force including the strong and weak nuclear force you just need to add a few more dimensions how many for the weak nuclear force you need two more and for the strong nuclear force another four so in total we now have one dimension of time three for gravity one for electromagnetism two for the weak nuclear force and four for the strong nuclear force which adds up to a total of 11. in 1981 edward whitten noticed that 11 happened to be the same number of dimensions which is the maximum for supergravity what happened after this is what we'll talk about next week this video was sponsored by the great courses plus i'm always looking for new brain food and while youtube is really useful to get inspiration it's not particularly good for providing structured educational content for structured learning i have found the great courses plus an amazing place the great courses plus is the subscription on-demand video learning platform that allows you to stream lectures on your browser or using an app on your phone it's like netflix but for learning the great courses plus have more than 11 000 video lectures from recognized experts about whatever it is that you are interested in from science and math to linguistics and cooking the great courses plus now offers a free trial for viewers of this channel which is a double benefit because it both serves your curiosity and supports this channel to make use of this offer 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Channel: Sabine Hossenfelder

Views: 231,100

Keywords: dimensions, dimensions of space, extra dimensions, other dimensions explained, higher dimensional space, higher dimensions, science, universe, unified theory, kaluza klein, do extra dimensions exist, are there higher dimensions, space, hossenfelder, science without the gobbledygook, theory of everything, string theory, physics, how many dimensions are there

Id: ZS2hJLIN1DM

Length: 11min 4sec (664 seconds)

Published: Sat Apr 10 2021