Does the Universe have Higher Dimensions? Part 2

in science fiction hyperdrives allow spaceships to travel faster than light by going through higher dimensions and physicists have studied the question whether such extra dimensions exist for real in quite some detail so what have they found are extra dimensions possible what do they have to do with black holes at the large hadron collider and string theory and if extra dimensions are possible can we use them for space travel that's what we will talk about today this video continues the one of last week in which i talked about the history of extra dimensions as i explained in the previous video if one adds seven dimensions of space to our normal three dimensions then one can describe all of the fundamental forces of nature geometrically and that sounds like a really promising idea for a unified theory of physics indeed in the early 1980s the string theorist edward whitten thought it was intriguing that seven additional dimensions of space is also the maximum for supergravity however that numerical coincidence turned out to not lead anywhere this geometric construction of fundamental forces which is called collusa client theory suffers from several problems that no one has managed to solve one problem is that the radii of these extra dimensions are unstable so they could grow or shrink away and that's not compatible with observation another problem is that some of the particles we know come in two different versions a left-handed and a right-handed one and these two versions do not behave the same way this is called chirality that particles behave this way is an observational fact but it does not fit with the carlusa cline idea witten actually worried about this in his 1981 paper enter string theory in string theory the fundamental entities are strings that the strings are fundamental means they are not made of anything else they just are and everything else is made from these strings now you can ask how many dimensions does the string need to wiggle in to correctly describe the physics we observe the first answer that string theorists got was 26 that's 25 dimensions of space and one dimension of time that's a lot turns out though if you add supersymmetry the number goes down to 10 so nine dimensions of space and one dimension of time string theory just does not work properly in fewer dimensions of space this creates the same problem that people had with colusakine theory a century ago if these extra dimensions exist where are they and string theorists answered the question the same way we can't see them because they are curled up to small radii in string theory one curds up those extra dimensions to complicated geometrical shapes called collaborial manifolds but the details aren't all that important the important thing is that because of this curling up the strings have higher harmonics this is the same thing which happens in colossal client theory and it means if a string gets enough energy it can oscillate with certain frequencies that have to match to the radius of these extra dimensions therefore it's not true that string theory does not make predictions though i frequently hear people claim that string theory makes the prediction that these higher harmonics should exist the problem is that you need really high energies to create them that's because we already know that these curled up extra dimensions have to be small and small radii means high frequencies and therefore high energies how high does the energy have to be to see these higher harmonics here's the thing string theory does not tell you we only know that these extra dimensions have to be so small we haven't yet seen them so in principle they could be just out of reach and the next bigger particle collider could create these higher harmonics and this is where the idea comes from that the large hadron collider might create tiny black holes to understand how extra dimensions help with creating black holes you first have to know that newton's one over r squared law is geometrical the gravitational force of a point mass falls with one over r squared because the surface of the sphere grows with r squared where r is the radius of the sphere so if you increase the distance to the mass the force lines thin out as the surface of the sphere grows but here's the important point suppose you have additional dimensions of space say you don't have 3 but 3 plus n where n is a positive integer then the surface of the sphere increases with r to the 2 plus n consequently the gravitational force drops with 1 over r to the 2 plus n as you move away from the mass this means if space has more than 3 dimensions the force drops much faster with distance to the source than normally of course newtonian gravity was superseded by einstein's theory of general relativity but this general geometric consideration about how gravity weakens with distance to the source remains valid so in higher dimensions the gravitational force drops faster with distance to the source keep in mind though that the extra dimensions we are concerned with are curled up because otherwise we'd already have noticed them this means into the direction of these extra dimensions the force lines can only spread out up to a distance that is comparable to the radius of the extra dimension after this the only directions the force lines can continue to spread out into are the three large directions this means that on distances much larger than the radius of the extra dimensions this gives back the usual 1 over r squared law which we observe now about those black holes if gravity works as usual in three dimensions of space we cannot create black holes that's because gravity is just too weak but consider you have these extra dimensions since the gravitational force falls much faster as you go away from the mass it means that if you get closer to a mass the force gets much stronger than it would in only three dimensions that makes it much easier to create black holes indeed if the extra dimensions are large enough you could create black holes at the large hadron collider at least in theory in practice the large hadron collider did not produce black holes which means that if the accelerations exist they're really small how small depends on the number of extra dimensions but roughly speaking below a micrometer if they existed could we travel through them the brief answer is no and even if we could it would be pointless the reason is that why the gravitational force can spread into all of the extra dimensions matter like the stuff that we are made of can't go there it is bound to a three-dimensional slice which straight theorists call a brain that's b-r-a-n-e not b-r-a-i-n and it's a generalization of membrane so basically we are stuck on this three-dimensional brain which is our universe but even if that was not the case what do you want in these extra dimensions anyway there isn't anything in there and you can't travel any faster there than in our universe people often think that extra dimensions provide a type of shortcut because of illustrations like this the idea is that our universe is kind of like this sheet which is bent and then you can go into a direction perpendicular to it to arrive at a seemingly distant point faster the thing is though you don't need extra dimensions for that what we call the dimension in general relativity would be represented in this image by the dimension of the surface which doesn't change indeed these things are called wormholes and you can have them in ordinary general relativity with the ordinary three dimensions of space this embedding space here does not actually exist in general relativity this is also why people get confused about the question what the universe expands into it doesn't expand into anything it just expands what does this mean for space travel well it means that traveling through higher dimensions by using hyperdrives is scientifically extremely implausible therefore my ultimate ranking for the scientific plausibility of science fiction travelers third place hyperdrives because it's a nice idea it just makes no sense scientifically second place wormholes because at least they exist mathematically though no one has any idea how to create them and the winner is warp drives because not only does the mathematics work out it's in principle possible to create them at least as long as you stay below the speed of light limit how to travel faster than light i'm afraid we still don't know but maybe you are the one to figure it out this video was sponsored by audible i love listening to audiobooks and podcasts but i hate having to deal with several different apps that all don't quite work the way you think they should that's why i like audible audible is the best provider of audiobooks and their plus catalog has so many more offers like podcasts and guided fitness programs on audible i'm currently listening to lawrence krauss's new book the physics of climate change which is read by krauss himself as an audible member you get one audio book per month free and you get full access to their plus catalog to check out what they have to offer go to audible.com sabine or text sabine to 500 500. the audible app is free simple to use and can be installed on all smartphones and tablets with an audible membership you can download titles and listen offline anytime anywhere once again that's audible.com sabine or text sabine to 500 500 thanks for watching see you next week

Channel: Sabine Hossenfelder

Views: 168,132

Keywords: physics, dimensions, dimensions of space, extra dimensions, other dimensions explained, higher dimensional space, higher dimensions, science, universe, unified theory, do extra dimensions exist, are there higher dimensions, space, hossenfelder, science without the gobbledygook, space time, theory of everything, string theory, black holes, large hadron collider, lhc, black holes at LHC, hyperdrive, wormholes

Id: UHZam0Zf1FQ

Length: 11min 9sec (669 seconds)

Published: Sat Apr 17 2021

Reddit Comments

[u/robTheRedRob]

I wonder if flatlanders also thought that a third dimension was a tiny balled up space? 🤔

[u/[deleted]]

When Eric talks about the people who start jumping on top of you telling you for this and that reason your new idea obviously can't work, that is this video. This is like Niel De Grass Tyson if he were a manic depressive. There is no good reason to make a video explaining higher dimensions in this way unless you think most people are idiots who need to be nullified.