PH 103 Dr. Cecilia Vogel Lecture 13

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

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.

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

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

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)

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 )

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.

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…

Electricity and Magnetism - review  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?  Laws of E & M determine the speed of light in vacuum.

Conundrum If classical relativity were true:  v 13 = v 12 + v 23 would hold  sunlight relative to the sun moves at c  but relative to spaceship, sunlight would move at c+v 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 Can’t both be true!

Einstein’s Second Postulate  The speed of light in a vacuum  is the same (c = 3X10 8 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.)

Evidence for 2 nd 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.

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: v AB = -v BA  of another object. Pattern: v 13 = v 12 + v 23 Quantities crossed out are only true for v<<c, not generally true.

You Can Hide But You Can’t Run  Speed of Light is Measured to be c=3X10 8 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.

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

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 accel forward  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 down at g  as if there were no grav or accel at all!