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Transcript

General Theory of Relativity STOR vs GTOR • Special Theory looked at only inertial frames. General theory looks at accelerated frames of reference • Einstein added this 10yrs after special theory to deal with gravity, mass, and acceleration and how it applies to spacetime. Gravity vs Acceleration: Imagine yourself in a spaceship on a launch pad on EARTH holding 2 bricks above the floor. If the bricks are dropped at the same time from identical heights, both bricks accelerate towards floor equally. Now, imagine identical situation in space, FAR from any effects of gravity, what is the result of dropping bricks? Repeat experiment, but now accelerate ship in the direction of ceiling…how does result change from previous scenario? LAUNCH PAD Gravity vs Acceleration Equivalence Principle GRAVITY & TIME Consider a high speed rotating platform with three clocks positioned as shown. Clocks 2 & 3 are rotating and clock 1 is at rest on ground. 2 3 1 GROUND 2 3 1 GROUND What will clock 1 say about the movement of clock 2 What will clock 1 say about the movement of clock 3? What will clock 1 say about the TIME of clock 2? What will clock 1 say about the TIME of clock 3? 3 2 1 GROUND What will clock 2 say about time of clock 1? Therefore, what MUST clock 2 say about time of clock 3? Gravitational Time Dilation This was first measured by Pound and Rebka at Harvard in 1960 in the physics building which was 74 feet high. They compared times between the basement and the top floor. GPS again… Recall that atomic clocks on GPS satellites are affected by their high speed above the earth (STOR). Twin Paradox revisited We showed that Twin who took space journey: 1)Was younger by using flashes of light 2)Space twin experienced acceleration, therefore could not make claims as to earth twin being younger since space twin was not in inertial frame But what if ship accelerates Imagine 2 people freely floating in space far from towards gravitational effects. One ceiling? Gravity and Light person is outside the ship and the other is inside. If light is shone through a window, it is seen by observer inside the ship to be a straight line, entering and striking the opposite side and the same height it entered. How come we don’t notice light falling/bending like a cannonball shot from cannon? Recall how far objects will fall in 1second here on Earth. |y|= ½ gt2…y = 4.9m In one second, how far will light fall? How far will it travel horizontally in 1 second? We are able to see star at times when sun is not in front of it, so we know its true position. When Sun is blocking star, we can see the apparent position of star during an eclipse. This apparent position is due to how our brains perceive light, illusions. Need eclipse to see apparent position. Einstein predicts the bending of star light! Need solar eclipse to prove this. May 29, 1919, British scientists confirm Einstein’s prediction during solar eclipse. He becomes an instant celebrity. Revisit gravitational time dilation: Consider 2 rays of light on a wavefront which are bent as they pass near a massive object. A and B are in phase (moving together). Large mass Black Hole If a large enough star collapses due to its nuclear fuel being spent and gravity taking over, there will be a critical distance (Event Horizon) from the collapsed star where the gravitational field is so strong that the path of the light is bent so severely that it returns to the star itself. Approaching a black hole First, as you approach the black hole Earth RF would never see you cross the event horizon. WHY? Einstein redefines Gravity Einstein rejects 250yrs of Newtonian gravity. Gravity & Space Re-interpret gravity as geometry – Space and space-time are not rigid arenas in which events take place. They are influenced by the matter and energy content of the universe. 1) Mass & energy 2) Curved space Orbit of Mercury, 1st test of GR A long-standing problem in the study of the Solar System was that the orbit of Mercury did not behave as required by Newton's equations. As it orbits the Sun, it follows an ellipse. However, it is found that the point of closest approach of Mercury to the sun does not always occur at the same place, rather it slowly moves around the sun. This rotation of the orbit is called a precession. The precession of the orbit is not peculiar to Mercury, all the planetary orbits precess. In fact, Newton's theory predicts these effects, as being produced by the pull of the planets on one another. However, this discrepancy cannot be accounted for using Newton's laws. At one time, they proposed there was an undiscovered planet called Vulcan that was causing this. In contrast, Einstein was able to predict, without any adjustments whatsoever, that the orbit of Mercury should precess by an extra 43 seconds of arc per century. This is due to the fact that spacetime is more affected that close to the sun versus the other planets, it is a very tiny difference. Simply stated: Why star light BENDS • Light actually follows the curve in space created by massive objects like the Sun. More to follow… How light ‘bends’ or is attracted by ‘gravity’ • Photons are affected by gravitational fields not because photons have mass, • The photons are Gravitational Lensing When light travels curved paths around massive objects, we call this Gravitational Lensing. This can lead to multiple images and even rings if the geometry of the situation is just right. Example: A planet with a mass lower than that of Neptune has been detected as its gravity bent the light from a remote star. This lensing technique adds to our arsenal for spotting small planets outside the Solar System. The famous "Einstein Cross" is a case where a single object is seen four times. In this image, a single object appears as four objects. A very distant quasar is thought to be positioned behind a massive galaxy. The gravitational effect of the galaxy has created multiple images through gravitational lensing on the light from the quasar. warp of spacetime again 2:30 • The Einstein Gravitational Field Equation is shown below. This equation states that the spacetime curvature of anyplace in the universe (left-hand side of the equation) must be equal to the distribution of matter and energy in that part of the universe (righthand side of the equation). It is this equation that was 50 years ahead of its time when Einstein proposed it. Each subscript refers to each dimension of spacetime…so what looks like 1 equation is actually 16 eqns! (4x4)