Classical Relativity and Einstein's Postulates

1. PH 103 Dr. Cecilia Vogel Lecture 13

2. Review • Relativity • classical relativity • constants • velocity addition • Einstein’s postulates • inertial frames indistinguishable • constancy of speed of light • principle of equivalence (general relativity) Outline

3. Postulate of Classical Relativity Laws of Mechanics same in all inertial reference frames What is an inertial frame? One in which Newton’s first law holds When doesn’t it?! Accelerating frame Do objects at rest remain at rest when you stop, start, turn corner in your car? In practice, inertial frame moves at constant velocity.

4. Different but the Same Laws of Mechanics same in all inertial reference frames • Meaning 1: Same mechanics experiment repeated in two different reference frames will yield the same outcome. • Example: Throw a pretzel up and catch it • on Earth • on smoothly flying airplane • same result • Why smooth? -- no acceleration

5. Different but the Same Laws of Mechanics same in all inertial frames Meaning 2: Same mechanical process observed by observers in different reference frames will not look the same but will follow the same laws Example: Throw a pretzel up and catch it on an airplane in smooth flight as viewed on plane as viewed on Earth SAME law of gravity applies to both

6. Postulate of Classical Relativity Laws of Mechanics same in all inertial frames If all frames yield same laws, then how do you tell whether or not you are moving? you don’t – you are always at rest in your frame! If you wake up on an airplane with all the windows shuttered, how do you know whether you are flying smoothly or still on the runway? You don’t! No mechanics experiment will distinguish between inertial frames (i.e. there is no acceleration)

7. Postulate There is NO preferred frame No frame can claim to be at absolute rest. All are at rest relative to themselves. Relative to the trees, the cars are moving, but relative to the cars, the trees are moving. (Earth is a convenient reference frame for us, but it’s not special in the laws of physics)

8. Tempted to extend that rule If there really is no preferred reference frame, then ALL laws of physics should be same for all inertial observers That’s Einstein’s first postulate of special relativity.

9. Einstein’s First Postulate • ALL laws of physics are same for all inertial observers. • There is NO preferred frame • If you wake up on an airplane with all the windows shuttered, how do you know whether you are flying smoothly or on the runway? • You don’t! • No experiment of any kind will distinguish between inertial frames. • laws of mechanics, optics, electricity and magnetism, atomic and nuclear physics…

10. Electricity and Magnetism- review • Laws of E & M determine the speed of light in vacuum. • So if all laws of physics are the same for all inertial observers, then • the laws of E& M are the same, • and the speed of light in vacuum is the same. • How can that be?

11. Conundrum If Einstein’s postulate is true: • speed of light is same for all I. O. • sunlight relative to the sun moves at c • and relative to spaceship, sunlight moves at c, too If classical relativity were true: • v13 = v12 + v23 would hold • sunlight relative to the sun moves at c • but relative to spaceship, sunlight would move at c+v Can’t both be true!

12. Einstein’s Second Postulate • The speed of light in a vacuum • is the same (c = 3X108 m/s) • no matter the motion of the source of the light! • no matter the motion of the observer! (Note that this concept is not true of other waves. For example, sound travels faster with the wind than against it.)

13. Evidence for 2nd Postulate • Recall that if one of two coherent beams of light travels further than the other, • then it will get behind • and interfere with the other beam. • Also if one of two coherent beams of light travels slower than the other, • then it will get behind • and interfere with the other beam. • The first evidence that the speed of light in vacuum is same no matter what • used Michelson interferometer to see if one beam went slower.

14. What do we need to Throw Out? • We had for classical relativity: • True (or very close to true) when v<<c • Different observers measure same time interval • Different observers measure same length • Different observers measure different velocity • of each other. Pattern: vAB = -vBA • of another object. Pattern: v13 = v12 + v23 Quantities crossed out are only true for v<<c, not generally true.

15. You Can Hide But You Can’t Run • Speed of Light is Measured to be c=3X108 m/s by all. What does it mean?? • Can you run away? NO! No matter how fast you go, light still catches up by c. • you can’t even “buy time.” • Can you catch up? NO! No matter how fast you go, light still outruns you by c. • What if the source moves? A lamp coming at you (or away from you), light still reaches you at c.

16. Einstein’s Postulate of General Relativity Einstein’s postulates we’ve seen so far are called Special Relativity; hold for inertial frames NO acceleration, NO gravity. Einstein later developed General Relativity Postulate of general relativity: Acceleration is indistinguishable from a uniform gravitational field in the opposite direction to the acceleration

17. Equivalence • Artificial Gravity • rotating spaceship, with centrip accel = g • feels like home, earth’s grav • Virtual Reality • tilted chair has grav down and back • feels like grav down, and accelforward • Car accelerating forward • you pushed down and back in chair • fuzzy dice hang down and back • objects slide backward on the seat • all as if grav had a backward component • Freefall = accel down at g and grav downat g • as if there were no grav or accel at all!