To give a complete and modern view of gravity, we have to update to Einstein's theory. The theory of general relativity, is our most profound and precise theory of gravity even though Newtonian gravity works perfectly well in most astronomical situations. These two great scientists, Einstein and Newton, who vie with each other for the reputation of the most brilliant scientist ever, had very different ways of thinking about gravity and also of space and time themselves. Let's compare and contrast their views. To Newton, mass and energy were very different things. Also to Newton, space and time were different things, not really related, and that's our everyday experience. Space is something that we occupy and objects occupy, and time is something that flows in one direction, they seem quite different. To Newton, time and space were both infinite and linear. What about Einstein? Einstein recognized that mass and energy, although they seem quite different, were actually interrelated by his equation E equals mc squared. By removing the distinction between mass and energy, he implied that they're interchangeable. That in some situations mass could be convertible into energy and in others energy be converted into mass. The core of the general relativity theory, is the idea that space and time are not distinct and linear the way Newton imagined. But they are also interchangeable, and are in fact joined at the hip in a hyphenated entity that we call space-time. In Einstein's view, we occupy not three-dimensional space where time just happens to be flowing past us, but we occupy a four-dimensional entity called space-time. Let's look at the difference between Newton's and Einstein's idea of how gravity works as a force. In the Newtonian view, mass tells gravity how much force to exert and force tells mass how to move. That's our familiar sense of gravity as well. Einstein's concept is quite different, quite radical. It's based on curved space-time. In Einstein's view, mass energy tells space-time how much to curve while curved space-time, tells mass-energy how to move. The coupling of space and time in Einstein's theory and its relationship to mass and energy, is exposed in a series of equations. There are tensor equations, second order partial differential equations which is part of why general relativity is fairly intimidating, only taught in graduate school. The equations are complex but they're actually quite simple and beautiful to a mathematician. The implications of curved space time, are that large concentrations or amounts of mass and energy distort space and time, and the larger the concentration the more the distortion. Now general relativity was not required and its absence wasn't felt, because most situations in the universe have relatively weak gravity. So these distortions of space-time are extremely subtle and were in fact undetectable until about a 100 years ago. But they are real and they've now been observed, and there is no doubt that general relativity is the superior theory of gravity explaining more situations than Newton's theory did. However, in the situations of weak gravity, the calculation in general relativity reproduces Newton's results. If there were nothing in our universe, the fabric of space time would be flat. But add a mass, and dimples form within it. Smaller objects that approach that large mass will follow the curve in space-time around it. Our nearest star, the Sun, has forms such as shape and space-time, and our tiny planet Earth goes along for the ride, staying in orbit around the Sun. Let's look at what's implied by the way Einstein talks about gravity. If mass-energy tells space-time how to curve and space-time curved tells mass-energy how to move, then we should see this effect on particles or radiation traveling through the universe. That's in fact how the first prediction of general relativity in his confirmation happened in 1916. Using Einstein's theory which had only been published less than a year ago, Eddington and others decided that the sunlight from a distant star grazing the sun's surface should be bent around the Sun to come to the earth, and show a slightly different deflection than predicted in Newton's theory. This is the gravitational lensing effect. In an eclipse expedition of that year, Eddington and his team observed this deflection as Einstein predicted. An extraordinary situation or a frontier new theory, was affirmed within 12 months of being published, and this is part of what cemented Einstein's reputation as a brilliant scientists. Since then, gravitational lensing has been observed in hundreds, even thousands of situations. Space-time is curved and light follows the curvature of space-time and so is deflected, when there's sufficient gravity. These effects are very small, tiny fractions of a percent in a situation like the Sun. But for a compact object like a neutron star or black hole, these effects can be extreme. In more recent decades, gravitational lensing has been seen in other situations far beyond our galaxy. There are super massive black holes or compact objects, billions of light years from the Earth, where the light passes along different paths around the galaxy and is lensed by that galaxy, producing huge gravitational optic experiments in the universe where multiple images are formed. A mirage essentially caused by gravity. Gravitational lensing is the most routine way we see the general relativity applies in the universe. There are however other effects of general relativity, they've also been observed. General relativity predicts that time slows down in an intense gravitational field. At the event horizon of a black hole time actually stands still. But general relativity was confirmed in a more mundane terrestrial situation. If time slows down in a gravitational field, then an atomic clock carried high above the Earth's surface, should actually run slightly faster than an atomic clock at the Earth's surface. This experiment was actually first done in the 1950's using high-flying spy planes, and early versions of atomic clocks confirming general relativity. The sensitivity of a such experiments is such that in the last year, it's been confirmed even in a laboratory where a super precise atomic clock has been shown to operate or keep time very slightly faster above the lab than in the lab itself. Time slows down in an intense gravity, just as space and time are curved in intense gravity. Let's look in a bit more detail at the curvature of space-time implied by relativity. In Newton's view of the universe, space is infinite and flat. Objects and light do not deviate traveling through space which is euclidean. In Einstein's view of space, space is curved by local gravity or even by global gravity of the universe itself. So we can think of the universe as a slightly crazy fun house mirror where there are subtle distortions of light radiation or particles traveling through the universe, being warped and deflected slightly by the gravity they encounter along the way. In relativity, there are simple ways to characterize curved space-time. Now in relativity, the curvature is in three-dimensional space-time, the space we live in. But it's easier to visualize this in a lower number of dimensions by projecting it onto a surface. Familiar to us, is the euclidean space of a flat sheet of paper, where parallel lines stay parallel and where the angles in a triangle add up to a 180 degrees as Euclid said 2,000 years ago. In relativity, if space is curved, it can have two signs. Can have different amounts of curvature, but the two fundamental differences are whether the space is positively or negatively curved. In positively curved space, in the analogy in two-dimensions, it's like the surface of a sphere or some other contain space-like that. As we know, if you draw parallel lines on the surface of a sphere such as two lines projected north from the equator of the Earth, which would meet at the pole, those lines converge. So parallel light does not remain parallel, there's a focusing or convergence caused by the curvature. We also know that a triangle drawn on the surface of a sphere has angles that add up to more than a 180 degrees, so Euclid geometry does not apply. By contrast, we can imagine in two-dimensions and it can exist in three-dimensions. Negatively curved space. In negatively curved space, the analogous shape is like a saddle. Parallel lines drawn on a saddle shape will actually diverge and if you draw a triangle on a saddles shape, the angles in the triangle add up to less than a 180 degrees. So we can violate Euclidean geometry in these curved space-times. Now what this means in three-dimensional space, is that if space were truly flat in Euclidean, parallel light beam sent out into the universe would never get closer or further apart, they would stay parallel. If we lived in a universe that had positively curved space-time, those light beams would actually eventually meet or converge, and if we lived in a universe with negatively curved space-time, those parallel light beams would diverge. This in principles in experiment we can hope to do to learn about the curvature of our universe. The analogy in two-dimensions is limited, remember we exist in three-dimensional space and that space can be positively or negatively curved too, and we can do experiments while trapped in that three-dimensional space to tell us what kind of universe we live in. Going back to the positively curved analogy in two-dimensions, we can see another feature of general relativity. The surface of a sphere is a bounded surface but it has no edge. If we believe this operates in three-dimensions too, we could have a positively curved universe where light could be infinitely trapped and travel around and around in that universe and never encounter an edge. Yet where the universe would have a finite volume just as the surface of this sphere has a volume or a surface area that you can calculate. In general relativity, our best theory of gravity, space and time are related and they occur by the existence of mass and energy. This is a quite different concept from Newton's theory of Gravity, where space and time are distinct and mass and energy are distinct. In Newtonian Gravity, space is infinite and linear and time also. In Einstein's theory they are coupled and they can be distorted by the presence of matter or objects. The predictions of general relativity started with a slight deflection of starlight caused by the curvature of space time near the Sun. That was confirming his theory within a year of it being published. Since then, this phenomenon of gravitational lensing has been observed thousands of times. Another prediction of relativity, is that time is slowed down by stronger gravity fields and this has also been observed many times. The strongest exposition of general relativity occurs when gravity is intense such as around collapsed objects like neutron stars and black holes. We'll see later in the course that these extreme distortions of space-time are exciting and dramatic. But even the subtle distortions of space and time can be observed in the perimeter of the Earth and in observations, for example the GPS satellite network incorporates general relativity to give accurate distance measurements on the Earth. General relativity is a profound theory of gravity based on beautiful and subtle mathematics, and it's been multiply confirmed by many types of observation over the last century.
