How Fast Is It - 05 - General Relativity II - Effects (1080p)

hello and welcome to general relativity part 2 in part 1 we covered the equivalence principle non Euclidean geometry and the Einstein field equations Einstein had come up with a totally different way of looking at gravity but was it a difference that made a difference or did his equations predict different physical phenomena the Newton's did you may recall if you've seen how small as a video book that the theory for quantum mechanics and the standard model was developed to explain experimental evidence but with general relativity there was no experimental evidence the theory came first so Einstein came up with three tests to demonstrate that his theory did indeed predict more accurately phenomenon like the orbit of mercury the bending of light and gravitational redshift will cover all three of these and frame dragging a more recent test around how rotating masses can twist and move space around it we'll end by building a black hole where all of these concepts come together we'll use gargantuan the black hole in the movie interstellar but first mercury in 1916 the same year that Einstein published his general relativity paper Karl Schwarzschild published his exact solution for space around a large non rotating mass his metric is now called swartz child metric and it works quite well for slowly rotating masses like the earth and the Sun and the planets in our solar system we'll use this metric for the first three tests let's take a look at what our space-time curvature looks like with this metric if we draw the circumference of the Earth's orbit we get a length that is 2 pi times our distance from the Sun if we existed in flat Euclidean space we would calculate the circumference of an orbit one kilometer closer to the Sun and see that the distance between the orbits is one kilometer but because of our positive curvature if we were to measure the circumference with a radius that is one kilometer shorter than the first we find that it is less than two pi times the shorter radius which means that the distance between the circumference --is would be greater than the one kilometer difference in the radii but only a little we can repeat this process all the way to the surface of the Sun with each successive radius the difference between the orbits would increasingly diverge from Euclidean numbers if we were to telescope this picture you'd see the standard diagrams that are used to help explain general relativity but diagrams like this are misleading in two ways first they represent an external curvature into another dimension when in fact we are talking about intrinsic curvature there is no evidence for the existence of a fourth spatial dimension second it looks like you need a downward force on the object to get it to drop into the hole that would be gravity but that's what the lines were supposed to represent so we'll avoid using this technique for over a half of a century before Einstein's time it was known that there was something odd about the orbit of mercury the elliptical path it carves around the Sun shifts with each orbit leaving its perihelion or closest point to the Sun 56 arc seconds forward on each pass Newtonian equations accounted for all but around 1/2 an arc second per year and of course they couldn't take into consideration the effects of curved space because the idea that space wasn't flat hadn't been considered yet with Schwarzschild metric Einstein came up with the exact number to cover the mysterious half an arc second he had passed the first test of his new theory when light comes close to the Sun the Sun's gravity bends it inward this makes the star look like it's further away from the Sun in the sky than it really is both Einsteins and Newton's gravitational theories predicted this but the theories predicted different values for the amount light would Bend Einstein suggested that a solar eclipse could be used to find the exact number in 1919 a solar eclipse was slated to occur with the Sun silhouetted against the Hades star cluster the nearest open cluster to our solar system here's the Hades star configuration with some of the brightest stars identified the British astrophysicist Arthur Eddington took up positions off the coast of Africa and Brazil and simultaneously measured the clusters light as it brushed past the Sun the images were then superimposed on top of an image taken at night earlier in the year when the Eclipse and night images were compared a gap was found and when the gap was measured it confirmed that Einsteins prediction was correct this same light-bending leads to the warping of light from distant galaxies as the light encounters supermassive galaxies on their paths to us this is called gravitational lensing here's a clip that shows how this lensing works on a grand scale a distant galaxy would be seen here on earth directly if there were no intervening massive cluster to bend the light but with such a cluster the light from the distant galaxies gets bent into rings and arcs to continue on to the earth this is Abell 1689 2.2 billion light years away it's one of the most massive galaxy clusters known the gravity of its trillion stars plus dark matter acts like a 2 million light-years wide lens in space and here's another cluster 5.7 billion light-years away it's the latest from Hubble on gravitational lensing released in late 2015 these foreground galaxy clusters are magnifying the light from the faint galaxies that life are behind the clusters themselves these faint lens 2 galaxies are around 12 billion light years away it's the gravitational lensing that allows us to see that far back in time without the magnification these galaxies would be invisible for us one of the key implications for bending of light is its impact on what's physically possible in heavily curved space-time here's a two-dimensional slice of the future light cone that we developed in the previous segment on special relativity this Purple Line represents a path by anything with mass it's called the world line and can be anywhere inside the light cone in this representation world lines have to remain between the two arms of the light cone because nothing can travel faster than the speed of light the speed of light lines the divider between events that are in your future if it's your light cone and events that are not by in your future I mean that you can be connected to them physically in some way now suppose there is a great mass energy density to the left of the cone the light would be bent in its direction we see that points that were impossible to reach before now fall inside the light cone and are reachable and we see that points that were reachable inside the cone now fall outside the cone and are no longer reachable this is light cone tipping the closer we get to the source of the gravity the greater the space-time curvature and the larger the matter curving the space the greater the curvature we'll take another look at this when we get to black holes one of the most dramatic consequences of general relativity is how space-time curvature affects the flow of time we'll use the elevator thought experiment to illustrate how clocks can run at different rates in the box according to their distance from the source of the gravity we'll see that a clock closer to the source of the gravitational field runs slower than a clock further away to help see how this works we'll take another look at the lightning strike with a person on the train and the person on the ground that we used in our segment on special relativity only this time we'll map the events to our space-time graph the world line for the person standing on the ground is shown in purple we label the lightning strikes a and B and place the two events on the space-time graph with a to the left of the person on the ground and B to the right the plane containing a and B contains all the points that are simultaneous for the person on the ground at the time of the two strikes we call this the simultaneity plane the light from both events travels at the speed of light so their world line always moves at a 45-degree angle they reach the person on the ground at the same time this of course is what makes them simultaneous from the point of view of the person on the ground now let's repeat the lightning strike so that from the point of view of the person on the moving train they strike at the same time in order for the light to reach the person on the train at the same time the strike behind him will need to hit first from the person on the grounds point of view because it will have to travel further to get to the moving person than the light from the strike that hits in front of him so we see that the simultaneity plane with a moving person is necessarily tilted up on the right now we can map the movements of a and B in the accelerating elevator to the space-time graph the center is the source of the acceleration or gravity a is to the right of it and be a bit further to the right reflecting their distances from the source of the gravity as the elevator accelerates the world lines on a spacetime graph are not straight lines they curve outwards because their velocity increases with every second here we have clocks that measure the proper time elapsed along each person's world line they mark the time in their own reference frame at the start they are both at rest so their simultaneity plane is horizontal and they each read each other's clocks reading zero in this example we see that after two seconds we have a slightly tilted simultaneity plane.b sees that at the same time his clock ticks to a's clock ticks 1a also sees his own clock reading 1 when bees clock reads to continuing to a higher velocity with the steeper slope for the simultaneity plane B sees A's clock reading 2 when his own clock reads for a also sees his own clock reading 2 when B's clock reads for a and B both agree that A's clock is ticking slower than B's clock the equivalence principle tells us the same thing will happen near a massive body gravity slows down time Newton's gravitational ocation we see this with our global positioning systems in our segment on special relativity we saw the time dilation due to velocity differences have GPS satellites losing time every day time that must be corrected for to get the right position on the surface of the earth they must also take into account gravitational time dilation due to their being further away from the earth then clocks on the ground based on the Swartz child metric calculations show that the satellites clocks will gain over 45,000 nanoseconds a day due to this general relativity affect the accuracy of our GPS system is strong evidence for the correctness of general relativity in 1959 physicists Robert Pound and Glenn Rebka performed an experiment in the Jefferson physical lab at Harvard to demonstrate gravitational redshift it was based on physicist Rudolf Moss Bauer's effect discovered two years earlier that involves the emission and absorption of gamma rays from the excited states of iron nucleuses here we have an iron atoms nucleus in an excited state when it falls to a lower energy level a gamma ray photon carrying the energy is emitted once this photon enters a like atom it will be absorbed raising the energy level of the encountered atom's nucleus the problem is that when the gamma ray is ejected the nucleus recoils because of energy momentum conservation the recoiling energy reduces the energy of the gamma ray the gamma ray is no longer a match for the other nuclei and it moves right through there is no absorption what mossbauer discovered was that if he embeds the iron atoms in a crystal the recoil is reduced dramatically and absorption can be reestablished pound replica used this mossbauer effect they placed an emitter at the bottom of a tower in the laboratory and installed a detector twenty-two point six meters above it no absorption was detected because gravitational time dilation change the frequency of the emitted gamma rays so no energy match existed in the detector the calculated shift was extremely small but the mossbauer effect is sensitive enough to measure it they adjusted the detectors velocity down until absorption occurred we get the amount the frequency changed using the well understood relativistic Doppler redshift equation just like the Doppler shift in starlight these results came in within one point six percent of the value predicted by Einstein's field equations using Schwarzschild metric although this experiment did not produce new results it showed the gravitational time dilation one of general relativity's most significant findings was consistent with all physical conservation laws this gave the general theory of relativity three successes out of three tests gravitational time dilation is also the answer to the twin paradox that we covered in the previous segment on special relativity the key interval is at the halfway point as the spaceship approaches Vega it decelerates to a stop and then re accelerates back to the earth the traveling twin finds that she is in a gravitational field let's say our acceleration is 10 GS or 98 meters per second squared at this rate it would take her 35 days to decelerate to zero and another 35 days to re-accelerate back to 99% of the speed of light gravitational time dilation shows that as her clock ticks 70 days her twins clock on earth will have ticked 18,000 134 days that's 48 years the twin unearthed agrees so instead of both twins thinking the other should be younger they both agree that the twin on the rocket to Vega and back is younger no contradiction is involved and the paradox is resolved our last test is the most recent it was designed to measure the twisting of space around a rotating mass this twisting is called frame dragging where space is literally dragged along with the rotating mass the effect was derived in 1918 by physicist Joseph flims and Hans theorem it is known as the lens tearing effect they predicted that the rotation of a massive object would distort the space-time metric making the orbit of a nearby test particle precess like a gyroscope this does not happen with Newtonian gravity where the gravitational field of a body depends only on its mass not on its rotation up until now we've been using the Schwarzschild metric which does not show this effect it wasn't until 1963 that a mathematician named Roy Kerr discovered the significantly more complicated metric for rotating bodies that made it possible to calculate the precession one can expect from a given mass and rotation of an object like the earth to test this effect NASA developed a satellite called gravity probe B and put it into orbit 264 kilometres above the earth in 2004 where it operated for a year it used a set of super-sensitive gyroscopes to measure precession due to frame dragging it also included a non gravitational drag identification gyro and compensation micro thrusters to maintain a non gravitational drag free environment it compensated for solar radiation drag and atmospheric disturbances drag by 2011 data analysis had confirmed that frame dragging did occur and measured it to within 15% of the amount predicted by the Qura metric for Einstein's field equations one of the most interesting consequences of general relativity is the structure and impact of a black hole in the Milky Way segment of the how far away is it video book we discussed how they are formed from collapsing massive stars too big for Neutron pressure to halt their collapse to a point called a singularity the Swartz child metric showed that if a mass of a body should contract to a small enough radius it could capture light itself this radius is known as the Swartz child radius and forms a sphere known as the event horizon one of the best illustrations of a black hole was created for the 2015 movie interstellar with the help of theoretical physicist Kip Thorne his black hole called gargantuan was given a mass of 100 million Suns and a super high rotation rate of ninety-nine point eight percent of the speed of light with this kind of rotation we see that gargantuan is indeed a curved black hole at 100 million solar masses the swartz child radius is around the distance from the Sun to the earth that's far enough away to make the tidal forces at the horizon quite unnoticeable will use gargantuan to illustrate the properties of general relativity that we have discussed in this segment so let's build this black hole from the ground up we are viewing it from the equatorial plane and the object is rotating in on the left and out on the right its center is dark out to the Swart child radius the cur metric shows that light can also be captured in stable orbits outside the event horizon for a rapidly rotating black hole the orbital volume around the black hole would be significant this would produce a photon sphere shell encasing the black hole with light from all the stars in the universe accumulated over the entire age of the universe it would be a sight to see but given that the light is trapped in orbit we can only see what leaks out this thin ring around the black hole represents the cross-section of this shell we'd see because of light that leaks out in our direction it is flattened on the Left because light rotating with the black hole's rotation can get closer to the horizon then light rotating against the black hole's rotation next we see a dense sprinkling of stars with a pattern of concentric shells this is the pattern produced by the gravitational lensing further out we see the dislocation of star positions due to the bending of light by the gravity of the black hole this black hole has the remnants of an accretion disk that is no longer feeding the black hole if the disc were not gravitationally lensed the black hole should have looked like this but because of gravitational lensing the massive amount of light rays emitted from the disks top face travel up and over the black hole and light rays emitted from the disks bottom face travel down and under the black hole this combination gives us the full image of how the black hole would actually look in the movie one hour on Miller's planet equals seven years on earth some of this came from time dilation due to the planets speed it's traveling at 55 percent of the speed of light in order to maintain its orbit but the bulk of the time comes from gravitational time dilation and the fact that Gargantuas rotational energy is so large this intensifies time dilation considerably if you watch the movie again you might note that it is the Kerr metric on the professor's blackboard we can use tipping light cones to show how all objects unfortunate enough to cross the event horizon are captured forever here's a light cone far from the black hole the horizontal axis represents distance from the singularity as we saw earlier when space-time is curved by the presence of mass energy the light cone structure gets distorted when the mass is a black hole the tilting reaches 45 degrees at the event horizon this means that all events beyond the horizon are no longer in the future light cone for any object that has gone past it no possible world line gets you out all remaining world lines lead to the singularity distance from the singularity decreases inside the black hole's horizon as surely as time increases outside the horizon in interstellar Cooper flies his ship into the black hole while brand watches from a higher orbit we can use our space-time diagram along with light cone bending again to illustrate what each of them would have seen first we'll take a look at it from Cooper's point of view as he heads directly into gargantuan he sees periodic signals from brand she is far enough away from the horizon for her light signals to all travel in a parallel manner at 45 degrees along her a light cone boundary Cooper crosses the event horizon without even noticing it as signals continue to arrive at regular intervals eventually he will feel the tidal forces of the singularity now things are quite different from Brian's point of view as Cooper approaches the event horizon his light cone tips towards the singularity this means that his light signals back to brand are taking longer with each kilometer traveled the effect is hyperbolic and the light signal he sends from the horizon itself will never get to Brant she sees his clock slowing down to the point that it stops she never sees him enter the black hole what's more because of gravitational redshift the image of Cooper and his ship shift to the red at the horizon it has shifted into the infrared and can no longer be seen by Brian for her Cooper grinds to a halt and goes invisible quite different from what Cooper seeds the general theory of relativity is now 100 years old in spite of the fact there have been a number of tests questions remain one of the theories most interesting predictions is gravitational waves but as yet no gravitational waves have been found if they are ever found would there be an Associated elementary boson particle the graviton like photons for the electromagnetic force a great deal of active research is underway to find out the fate of general relativity remains in the hands of experimental physicists

Channel: David Butler

Views: 132,249

Rating: 4.8637681 out of 5

Keywords: general relativity, Newton’s gravity, Mercury, Schwarzschild, curvature, Eddington, gravitational lensing, light cone, world-lines, Pound-Rebka, Mossbauer, redshift, Kerr Metric, frame-dragging, Gravity Probe B, black hole, red shift, Theory Of Relativity (Literature Subject)

Id: z_orWVhzF6Q

Length: 29min 33sec (1773 seconds)

Published: Sun Dec 13 2015