Physics 10 UCSD General Relativity Einstein Upsets the
Physics 10 UCSD General Relativity Einstein Upsets the Applecart Physics 10 UCSD So Far, We Have Decided that constant velocity is the natural state of things Devised a natural philosophy in which acceleration is the result of forces Unified terrestrial and celestial mechanics & brought order to the Universe
Spring 2008 2 Physics 10 UCSD Frames of Reference This is all fine, but accelerating with respect to what?? Why the Earth, of course! Spring 2008 3
Physics 10 UCSD Science is Fraught with Assumptions The Earth is at the center of the universe... The Earth is at the center of the solar system... The world is flat... The geometry of the Universe is flat... The surface of the Earth is the natural reference frame... Time and space are independent concepts These assumptions can have a dramatic impact on our views of Nature Spring 2008 4 Physics 10
UCSD Recall the Rotating Drum Example An accelerating frame of reference feels a lot like gravity In fact, it feels exactly like gravity The essence of General Relativity is the recognition that gravitational force is an artifact of doing physics in a particular reference frame! Spring 2008 5 Physics 10
UCSD Imagine Being in a Car Windows are painted black Move the car to outer space Now imagine placing a few objects on the dashboard of this blacked-out car, still in outer space. If the car accelerates forward, what happens to these objects on the dashboard? (Why?) If you didnt know the car was accelerating, what would you infer about a force acting on the objects? How would that force depend on the masses of the objects? Spring 2008 6
Physics 10 UCSD Gravity vs. Acceleration Can you tell the difference between forward acceleration and gravity from a star being brought up behind the car? Spring 2008 7 UCSD Physics 10 Can you tell the difference between
gravity and acceleration? Spring 2008 8 Physics 10 UCSD Constant Velocity Elevator Accelerating Elevator Spring 2008
9 Physics 10 UCSD An Exercise Changing Your Perspective Close your eyes and imagine youre being accelerated upwards by the room around us The natural (i.e. inertial) coordinate systems are falling past you at 9.8 m/s2! You are being accelerated upwards at 9.8 m/s2 by the normal force of the seat youre in. Spring 2008 10
Physics 10 UCSD A Conclusion: Doing Newtonian mechanics in a non-inertial frame of reference can force you to invoke fictitious-forces, really just unexpected forces, i.e., artifacts from doing physics in that frame. Since these fictitious-forces are invoked to explain what is actually an acceleration of the entire reference frame, they are necessarily proportional to mass. Do you understand why? Examples: Centrifugal force in rotating systems Actually an example of gravity in the theory of General Relativity
Gravity! Spring 2008 11 Physics 10 UCSD Einstein in an Elevator Film clip from Nova/PBS http://www.pbs.org/wgbh/nova/einstein/rela-i.html Spring 2008 12
Physics 10 UCSD Whats left?! If we blame gravity on our doing physics in the wrong reference frame, is all of gravitational physics wiped out? No! There is still an interaction there, just more subtle than Newton thought..... Newton couldnt explain what gravity was Thought of it as instantaneous action at a distance Whats wrong with action at a distance? Spring 2008
13 Physics 10 UCSD Mattress Example Imagine 2 bowling balls on a mattress, on earth As they roll around on the mattress, they make dimples in its surface If they get close to each other, they roll into each others dimples they are attracted to each other Spring 2008 14
Physics 10 UCSD Bowling Balls on a Mattress Spring 2008 15 Physics 10 UCSD Gravity = Geometrical Distortions Film clip from Nova/PBS http://www.pbs.org/wgbh/nova/einstein/rela-i.html
Spring 2008 16 Physics 10 UCSD A Geometrical Approach Mass tells space-time how to curve Space tells mass how to move This naturally explains the Universality of Free Fall Acceleration All objects move along the same geometrical distortions Gravity is a property of the geometry of spacetime Spring 2008
17 Physics 10 UCSD How fast are you moving? If time is a dimension like space, then how many meters long is one second: Answer: 300,000,000 meters: c = 300,000,000 m/s Then in each second, were traveling 300,000 km through the time dimension! Were all going at the speed of light! If we accelerate ourselves to a substantial speed through space, we give up some of our speed in the time dimension:
our clock runs slower compared to a stationary observer our total speed through spacetime is always c Spring 2008 18 Physics 10 UCSD Mass Tells Space-Time How to Curve The illustrations youve seen are what would occur if the world were 2-dimensional. This allows us to show the curvature in the 3rd dimension. In reality, gravity causes 3 spatial and 1 time dimensions to curve, which is tough to visualize!
Space Tells Mass How to Move Objects travel along straight lines in a curved spacetime. They dont accelerate due to gravity Spring 2008 19 Physics 10 UCSD Curvature in this room! Space (spacetime for that matter) seems flat to us Curvature is small Strength of relativity in this room is given by 2GM/(Rc2), roughly 1.410-9 Near sun, this is about 10-6
Actual radius of curvature on earth is about one lightyear Is there some way to measure curved space? Yes! Orbiting satellites with gyroscopes Spring 2008 20 Physics 10 UCSD The Curvature of Space is Real It has been measured: GR is right! How? a
a a Spring 2008 Northern latitude line Equator a 21 Physics 10 UCSD
Curved Space is Real (Part Deux) Orbiting gyroscope (Gravity probe B, and others) Tips because space is curved, just like the arrow before L Spring 2008 gyroscope axis rotates 22 Physics 10 UCSD
Quantifying curvature Lets take a projectile traveling straight up initial speed v (up) means hang time is t=2v/g height acquired is h = g(t/2)2 = v2/g in this time, we travel ct = 2vc/g meters through the time dimension If we drew an arc of height h and length 2vc/g, we would find that its radius was R = c2/g 1 light year note this is independent of initial velocity (could be a bullet or a superball) Spring 2008 space
time 23 Physics 10 UCSD A Contemporary View Curved Spacetime forms a stage on which other physics happens General Relativity (GR) is a very successful description of the interaction between spacetime and objects GPS wouldnt work without it Einsteins Field Equation: (just for fun) G = 8T +
Einstein Tensor describing how spacetime is curved Spring 2008 Cosmological Constant: Einsteins Biggest Blunder (resurrected as dark energy) Stress-Energy Tensor describing distribution of mass and energy 24 Physics 10 UCSD A Genuine Scientific Revolution The General Relativity view
Relegated gravity to the interaction between mass and spacetime Abolished the notion that the geometry of spacetime is everywhere flat Mixed the concepts of space and time GR does not mean everything is relative! The basic concept is that the equations/laws that describe physical systems should not depend on your reference frame. Coordinate Invariance would be a better term... Einstein wanted to call it The Theory of Invariants Spring 2008 25 Physics 10
UCSD References and Assignments References dmoz.org/Science/Physics/Relativity/Overviews/ especially links titled General Relativity Relativity Visualized, by L. C. Epstein great intuitive development, low math (low PC also) Assignments Read Hewitt Chapters 35 and 36 HW5: 9.R.13, 9.E.9, 9.E.14, 9.E.43, 9.P.7, 10.E.16, 35.R.27, 35.E.6, 35.E.19, 35.E.20, 35.E.37, 35.P.3, 35.P.10, 36.R.7, 36.E.2, 36.E.6 Spring 2008
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