Does Gravity Require Extra Dimensions?

it's been a hundred 20 years since Henry Cavendish measured the gravitational constant with a pair of lead balls suspended by a wire the fundamental nature of gravity still eludes our best minds but those secrets may be revealed by turning back to the Cavendish experiment that steampunk contraption may even reveal the existence of extra dimensions of space gravity is by far the most familiar of the four fundamental forces after all we wrestle with it every day it's no surprise that it was the first force to get a decent mathematical description with Isaac Newton's law of universal gravitation back in the 17th century but what is surprising that nearly 500 years later gravity remains the most mysterious of the four forces it just doesn't seem to gel with the other three forces one big difference is that the strength of gravity is vastly weaker than the other forces I'm talking ten to the power of 24 times weaker than even the weak nuclear force this mismatch is known as the hierarchy problem and understanding the PUE ninis of gravity may help us figure out what gravity really is and to unify it with the rest of the forces but like I said despite the mysteries about why gravity works the way it does our current theories still describe how gravity behaves remarkably well Einstein's general theory of relativity has a perfect track record predicting the behavior of gravity in terms of the warping of the fabric of space and time but even Newton's old theory works great in almost all situations and deviations from Newton's description may point the way to an understanding deeper than Einsteins the key is in understanding the inverse square law Newton's law of gravitation is an example of such a law basically the strength of the gravitational force drops off with the square of the distance between two massive objects if we have a massive object we can depict the gravitational force from this object as little arrows pointing towards the object the density of the arrows at a given distance determines the strength of the gravitational field so as you get further away those arrows are more and more spread out their density and so the strength of gravity drops the arrows get spread out over the surface of a sphere with the gravitating body in the center so the density and the strength of the gravitational field drop proportional to the surface area of that sphere that's 4 PI R squared and that's where the R squared comes from at the bottom of Newton's law of gravitation so gravity sort of gets diluted in strength because it's increasingly spread out over a 2d spherical surface within our 3d space if our universe were two-dimensional say a flat plane then gravity would be spread out over the circumference of concentric circles circumference is 2 PI R so gravity would just be inversely proportional to radius it would drop off more slowly and if our universe had more dimensions say 4 then gravity would spread out over the surface of a 40 hyper sphere that surface would be 3d so gravity would follow an inverse cube law that's a faster drop-off in general gravity drops off as 1 over R to some power and that power is the number of spatial dimensions minus 1 cool so we have a way to test how many dimensions there are Newton's inverse square law for gravity tells us there are two plus one equals three spatial dimensions I guess we already knew that except for the fact that some of the most promising approaches to unifying gravity with the other forces actually proposed that there are more than three dimensions of space and that these additional dimensions may explain the hierarchy problem the relative weakness of the gravitational force so let's talk about dimensions a bit more we perceive a 3d universe but most of our movements from day to day are in only two of them walking across your 2d for driving around the 2d service of your town or city we explore a 2d landscape embedded in a 3d world now we perceive the third dimension but perhaps our three spatial dimensions are similarly embedded in a high dimensional space that we can't perceive well actually that's probably not the case in fact we saw in a previous episode how a particular gravitational wave detection from LIGO seems to rule out the possibility of extra special dimensions but there's a caveat that experiment only ruled out extra-large dimensions and by large I mean that they stretch out over astronomical scales like the familiar three spatial dimensions but there's another possibility the extra dimensions could be compactified in other words wound up very small in that case gravity would only deviate from the inverse square law on tiny scales of these compactified dimensions take another look at the surface Iran right now it seems like a do dimensional surface but we all know that the apparently 2d ground is made up of 3d particles and if we zoomed in on a seemingly flat floor to small enough scale we would see a wildly varying three-dimensional landscape we don't notice this because of the vast difference in scales between us and that landscape another example would be a long thin tube it looks one-dimensional from a distance but up close you see that it's really a 2d surface extended in one dimension but loot in the other and that's the sense in which there may be more than three spatial dimensions in this universe 3 extended dimensions but others that are looped or compactified as we say in physics the most famous example of compactified extra dimensions is in string theory and in modern super string theory there are six additional spatial dimensions coiled up tight at every point in the extended 3d universe but the idea of compact extra dimensions is much older than string theory first proposed by oskar klein in the 1920s as part of what became Colusa klein theory one of the first attempts to unify electromagnetism with gravity although we've never detected these extra dimensions they seem a promising potential solution to unifying gravity with the other forces and in the process explaining gravity's weakness there are different ways of thinking about how compactified extra dimensions can affect the strength of gravity one is that you can imagine gravity trying to propagate through multiple dimensions which would dilute it more quickly we can also think about gravity producing excitations within those extra dimensions that SAP its energy on large scales gravity would still follow the inverse square law but would be diluted due to the hidden extra dimensions and that could explain its relative weakness compared to other forces and on small scales these extra dimensions would actually change the way gravity falls off with distance but to see that you'd need to test the strength of gravity on length scales that are within spitting distance of those compactified dimensions so to search for these hidden dimensions we need a way to test gravity on very very small length scales lots of different approaches have been tried but today I want to tell you about one of the most promising because it's also the oldest it's actually the OG the experiment first used to measure the strength of the force of gravity or the G in Newton's law of gravitation it's the Cavendish experiment performed by Britt Henry Cavendish in the late 18th century the apparatus for the experiment was actually designed and built by another British scientist John Mitchell the same guy who first hypothesized the existence of black holes but Mitchell died before he could conduct the experiment and so Cavendish inherited and improved the device and actually made the measurements the Cavendish experiment looked like this a six foot rod suspended from its centre by a long thin metal wire a LED ball was attached to each end of the rod the whole contraption was then free to rotate on the wire this is an example of a torsion pendulum where the restoring force of the twisted wire can cause the whole apparatus to oscillate the amazing thing about the torsion pendulum is that it's incredibly sensitive if the wire is very thin then very tiny forces will induce a large twist before being halted by the restoring force the amount of twist tells you precisely how much force was a to rotate it so Cavendish placed large masses near each of the LED balls at the ends of the rods the gravitational attraction between these masses and the balls would then rotate the torsion pendulum ever so slightly and by reading the amount of rotation Cavendish made the first measurement of the gravitational constant the device was so sensitive that it had to be protected from the slightest breeze or even the gravitational influence of other bodies including Cavendish's he measured the displacement through a telescope mounted into a hole in the devices shed this allowed him to measure a force of gravity between the masses which was something like 10 million times smaller than the force the LED balls fell due to the earth below the meticulous care paid off Cavendish measured a gravitational constant that agrees with our modern value with 1% uncertainty his measurement remained the most precise for over a hundred years not only did this contribute to our understanding of gravity but also arguably marked the beginning of a grand tradition in physics of making high-precision measurements to learn about the fundamental nature of the universe modern Cavendish experiments look quite a bit different than Mitchell and Cavendish's first apparatus the experiment is now typically done in a vacuum with precise temperature control and electrostatic and magnetic shielding the geometry of modern devices allow more precise positioning between the test masses and the displacement of the masses is measured with far more sophistication than a telescope through a hole in the wall in some cases rotating masses produce oscillations in the torsion pendulum these incredible advances have led to a modern measurement with six digits of precision these advances have also allowed us to place the pendulum masses and the test masses extremely close together as close as 50 microns less than the width of a human hair now that's still quite a bit larger than any likely compactified extra dimensions but we'd still expect a tiny and perhaps detectable deviation from the inverse-square law several orders of magnitude larger than the size scale of those dimensions depending on other factors most importantly depending on the strength with which gravity interacts with these extra dimensions so how many dimensions are there well still just three the inverse square law seems to hold down to the current limits of our measurements and while that may seem anticlimactic it's actually extremely useful ruling out some theories and constraining the space of possibility from others we are still nowhere near being able to probe the size scale of the extra dimensions from string theory though and so string theorists can keep on theorizing so what's next well to build better Cavendish style experiments things get complicated below about 1 micrometer in separation that's where the Casimir force comes into play this is the negative pressure due to the exclusion of quantum vacuum modes or virtual particles between two very closely separated plates but there are other ingenious approaches that we can come back to another time for now we'll have to content ourselves with our merely four-dimensional universe for what were they again space space space time so this is pretty amazingly unbelievable this little show about hard core physics and astrophysics just hit two million subscribers honestly it warms all our hearts to know there are so many kindred nerdy spirits out there we should like all hang out sometime you know after all this is over of course if we did hang out we'd be a whole city in fact we looked it up we'd be the 238 largest city in the world and growing that's right we're coming for you Malta and Pakistan you've been chillin in rank 237 far too long for now I just want to thank you all from the bottom of my heart for your incredible support and speaking of support are wanna give an extra big thank you to our patreon supporters and most especially tourists Agron who's supporting us at the quasar level Christina with your great generosity and excellent taste in YouTube shows I hereby appoint you mayor of space/time City because no one said space-time city was a democracy and I think you'd do an amazing job in last week's episode we talked about the strange regions that lie beneath the event horizon of a rotating black hole regions like the carter time machine and the infinite string of parallel universes unsurprisingly thoughts were head and comments were made Zoltan asks for clarification really asks for confirmation of his hunch which is that the multiverse you get from traveling through black holes has nothing to do with the multiverse predicted by quantum physics results and you have it right the quantum multiverse is what you get when you accept you Everett's many-worlds interpretation which implies that the universe splits at every quantum event that multiverse may or may not be real now the multiverse through the black hole arises from tracing the paths of space-time through the black hole mathematically I'd say the second multiverse is less likely to be real than the quantum multiverse it's almost certainly a mathematical figment arising from idealized types of black hole that don't really exist on a related note poly don't wanna land asks how much of this weirdness inside a black hole is actual weirdness and how much is broken math well the universe on the other side of the black hole is probably a figment in the math which I suppose you can call broken math if you like but really the math is just fine the problem is assigning physical reality after pushing the math too far after all the universe may be incredibly well described and modeled by the math but that doesn't mean that the universe is the math the quality of the predictions of any model depend on the assumptions that go into it and in the case of black holes several unreasonable assumptions allow us to trace geodesics into alternate for example the parallel universe through the non-rotating swats shield black hole requires the assumption that the black hole has been there forever and the string of universes through the rotating Kerr black hole requires the assumption that the impossibly unstable inner structure of the curse space-time doesn't collapse immediately but you're totally right Poli don't wanna land in reality impossible seaming things like an infinite string of universes or a time machine indicate that the math may have led our physical understanding astray and that's even more true when we see that the universe seems to conspire to prevent these things from existing and to wrap up my favorite joke in the comments that I wish I had said in the episode was this instead of you're in for a weird time I should have said you're in for a weird space because space and time switch places inside the black hole at least I could live vicariously through the superior wit of the brilliant doctor poop stick you

Channel: PBS Space Time

Views: 694,786

Rating: 4.9410548 out of 5

Keywords: Space, Outer Space, Physics, Astrophysics, Quantum Mechanics, Space Physics, PBS, Space Time, Time, PBS Space Time, Matt O’Dowd, Astrobiology, Einstein, Einsteinian Physics, General Relativity, Special Relativity, Dark Energy, Dark Matter, Black Holes, The Universe, Math, Science Fiction, Calculus, Maths, Holographic Universe, Holographic Principle, Rare Earth, Anthropic Principle, Weak Anthropic Principle, Strong Anthropic Principle

Id: z91oGI5aP0A

Length: 16min 41sec (1001 seconds)

Published: Wed May 27 2020

Reddit Comments

[u/akanes123]

Yay... Was waiting for this week's video!