Quantum Gravity: How quantum mechanics ruins Einstein's general relativity

in 1687 isaac newton changed the way we humans view the cosmos by connecting a force we experience on earth with the force that controls the movement of heavenly bodies that force of course is gravity and he expressed this analytically in a remarkable equation that is still used today the law of universal gravitation this equation explained the movement of planets and it remains very accurate even today under most circumstances but it had a few problems one of which was the idea of action at a distance that even newton had trouble accepting this was the idea that a massive object could exert a force instantaneously to another massive object at a distance without ever touching it later in 1859 newton's laws could not explain the rate of precession of mercury the way its elliptical orbit rotates around the sun and is not fixed newton explained gravity as an innate property of objects a constant instantaneous force that could act over long distances 250 years later in 1916 einstein changed this paradigm with the publication of the general theory of relativity it solved the riddle of mercury's precession and explained that gravity was not a mysterious force acting at a distance in the background of space and time but was a result of a bending of the background itself the curvature of space-time it was a new paradigm that could explain more things today a hundred years after einstein's publication we find some holes in einstein's theory as well such as its inability to explain the singularity inside black holes and the big bang one of the biggest pursuits in physics is the attempt to find a better theory a quantum theory of gravity in order to understand quantum gravity though you have to first understand general relativity however the mathematics of general relativity is so difficult that even a genius like einstein could not easily derive it and there are still papers being written today on specific solutions to these equations i'm going to try to explain those equations to you intuitively and visually to give you an idea of what the math is trying to say and i hope that this will help you better understand quantum gravity that explanation is coming up right now [Music] before i get into general relativity and quantum gravity let me tell you part of my inspiration for doing this video i watched a fascinating two episode documentary on magellan tv today's sponsor called the amazing world of gravity it's not only in 4k but also hosted by one of my favorite educators jim alcaley magellan is a new type of streaming documentary service founded by filmmakers and producers who bring premium in-depth documentary content featured subjects include history nature and my favorites science and space you can watch it on any of your devices as well as your tv anytime without any ads and they have a huge library of 4k content magellan tv has a special offer right now for arvanash viewers if you use the link in the description you will get a free one month trial i highly recommend magellantv be sure to use the link in the description if we look at newton's equation for gravitation and einstein's equation for general relativity we see a remarkable correlation for one thing newton's gravitational constant is present in both equations in newton's equation we have a force on the left side created by a mass on the right side in einstein's equation we have the analog of force the curvature of space time on the left side it has two components that describe the curvature and how distances in the curvature are determined this is the analog of force described by newton i want to be careful here because in general relativity gravity is not a force within the background of space-time like it is in newton's equation but it is a curvature of the space-time background itself in other words gravity does not cause the curvature of space-time it is the curvature of space-time the right side of the general relativity equation tells us about the mass energy content this is represented by something called the mass energy momentum tensor it's a source of the curvature in the context of these equations think of a tensor as a multi-dimensional array of mathematical components this can be an array of vectors scalars or other tensors and it's represented by an n-by-n matrix a vector is a type of tensor represented by an n by one matrix in general relativity the dimensions are four so the vectors are four by one and the tensors are four by four matrices so this equation describes what john wheeler said so succinctly about general relativity space-time tells matter how to move matter tells space-time how to curve the right side is the matter and energy which tells space-time on the left side how to curve in return the left side the curvature resulting in gravity tells matter on the right side how to move essentially what this equation shows is that matter and energy results in a curvature of space-time which we perceive as gravity although this looks like one somewhat simple equation it is actually ten equations and is very complicated mathematically if we wrote down all the ten equations fully it would take up more than a page of text a simplified version is shown here it is so complicated in fact that einstein was skeptical about being able to solve them there are papers written to this day on various solutions to these equations let's take a closer look at what these equations are trying to say the equations describe the curvature of space time by treating it as being flat at infinitesimally small distances so you can consider that general relativity behaves like special relativity at these small distances with no bending or curvature but overall curvature is taken into account r mu nu is the richie curvature tensor it tells us how space time is deviating from flat it tells you how space time curves at a given point the second term on the left side is composed of r the scalar curvature it tells you how much the space is changed at any given point such that you know how to correctly measure distances little g mu nu is the metric tensor it tells you the geometry and structure of space time together this term defines how distances are calculated given a curvature at any point note that sometimes the third term is added lambda times g mu nu lambda is the cosmological constant this term describes the intrinsic energy density of the vacuum or empty space it's the mathematical expression for what we observe as dark energy the accelerating expansion of the universe it would comprise energy and opposition to gravity lambda is a very small number about 1.1 times 10 to the negative 52 inverse meter squared at small distances this effect is largely negligible on the right side t is the stress energy momentum tensor which tells us the density of energy and momentum at each point in space-time it is the source of the curvature there's also a constant which is equal to 8 pi g divided by the speed of light to the 4th power g is newton's gravitational constant but this whole term is sometimes referred to as einstein's gravitational constant it's really just a conversion factor to make sure we get the proper units the way these equations are formulated is by treating space time in four dimensions three spatial dimensions and one dimension of time this is incorporated in the mu and new subscripts the value of mu and nu can be 0 1 2 or 3. the zero subscript conventionally represents time and the 1 2 and 3 represent the three spatial dimensions this is why we have 10 equations so for example if we draw a matrix of all the values that mu and nu could have we would see that there are 16 possible combinations but this matrix is symmetrical so 0 and 1 for example is equivalent to 1 and 0. so if we take all the non-symmetrical combinations we come up with 10 combinations hence 10 equations let's look at what some of these combinations mean so for example one equation is where mu and nu are zero and zero zero represents the dimension of time what this would describe on the left side is the speeding up or slowing down of time at a point in space and the right side would describe the energy at that point similarly in another equation the value of mu and nu can be zero and one this would represent time in one direction and one spatial direction in another so the left side in this case represents the combination of the stretching of time with one spatial dimension the right side in this case would be the momentum or momentum density in another equation the value of mu and nu can be 1 and 1. this would represent spatial dimension for both mu and nu in this case the left side is describing the stretching of space in one of the dimensions the right side in this case would describe the pressure at that point in space the same can be said if mu and nu are 2 and 2 or 3 and 3. here's a matrix of what the various combinations of mu and nu mean for the stress energy tensor note that the combination of the curvature in two different spatial dimensions is called shear stress is general relativity true yes in general for example it predicts the bending of light around massive objects this has been observed for our sun as well as gravitational lensing around large clusters of galaxies it predicts the time will run more slowly on the surface of earth than on a mountain top this has been confirmed with atomic clocks so why do we think that it's incorrect or at least incomplete the problem is that it does not fit with what is probably an even more accurate theory and that is quantum mechanics there is no theory that describes how gravity works at quantum scales or even very small scales nobel laureate stephen weinberg of electroweak theory fame said that no one should take general relativity seriously for distances shorter than about 10 to the negative 35 meters so for example let's take a simple hydrogen atom which is composed of one electron and one proton quantum theory says that the electron is in a superposed state meaning it is in multiple positions at various distances from the nucleus at the same time we only know the probability of finding it at a particular radius if we were to measure it since the electron has mass according to general relativity it must curve space-time but it is in multiple locations at the same time then the question is where is the curvature is it also at multiple locations at the same time we don't know there's nothing in general relativity akin to superposition like there is in quantum mechanics a second problem occurs in the case of black holes general relativity predicts matter and energy being compressed to an infinitely small point in space with supposedly infinite curvature but the theory breaks down here if you go back to our original equation of general relativity it's easy to see why it breaks down since the equations treat space-time mathematically as being flat at infinitesimally small distances and then calculate the overall curvature based on this presumption a problem occurs when space is seemingly not flat at infinitesimally small distances this occurs at the singularity since it's supposedly an infinitesimally small point so how do you calculate space-time curvature using flat space-time with an infinitely curved point it's a hole in space-time the mathematics of general relativity seem to describe singularities in this way but mathematical infinities like this are usually wrong so there's probably something else going on here that we just haven't figured out there are some other issues as well when you try to integrate general relativity with quantum mechanics such as the problem of information loss due to hawking radiation the bottom line is we don't really know how gravity behaves at quantum scales general relativity has been tested to scales of about 1 10th of a millimeter at atomic scales and below there's probably some better theory that will describe it the problem is that quantum mechanics works fine with space-time curvature as the background the problem with gravity is that it is not something that works with space-time curvature is the background it is the space-time curvature space-time curvature is gravity do we have anything that comes close to describing gravity at really small scales there are two theories that seem to be promising loop quantum gravity and string theory and these will be the subject of my next video so stay tuned you won't want to miss it i'd like to thank my generous supporters on patreon and youtube if you like my videos consider joining them and if you have a question leave it in the comments below and i will try to answer it i will see you in the next video my friend [Music] [Music] you

Channel: Arvin Ash

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Keywords: quantum gravity, general relativity, general relativity explained, einstein field equations, einstein field equations explained, stress energy tensor, stress energy momentum tensor, stress energy tensor explained, ricci curvature explained, cosmological constant, quantum mechanics, why is general relativity incompatible with quantum mechanics, quantum gravity explained, quantum gravity arvin ash, quantum gravity theory, general relativity visualized, gr intuitive

Id: S3Wtat5QNUA

Length: 14min 1sec (841 seconds)

Published: Sat Oct 17 2020