Relativity

●Albert Einstein

●Special Theory of Relativity

–Speed of light

●General Theory of Relativity

–Special relativity + gravity

●Newton's Theory of Gravity

–Deals with low speeds

–Einstein's special relativity reduces to Newton's theory of gravity at low speeds

Newton's World of Velocities

●You are in a car going v=100 km/hr

●You fire a bullet forward with v=1000 km/hr from the open window of the car

●Your friend is on the sidewalk

●What does your friend measure for the speed of the ball?

Addition of Velocities

●v(bullet)=1100 km/hr

●v(light)=c

●Fig. MP22-1a

Measurement of Speed of Light

●Michelson-Morley Experiment

●They measured the speed of light

●The speed of light is independent of the motion of the observer or the source of the light

●Speed of light (in vacuum) is always c

●When speeds are near c, they are termed relativistic speeds

Thought Experiment

●Albert Einstein's Thought Experiment

●A person is in a totally enclosed elevator, no windows, in the middle of outer space.

●The person is weightless

●Then, suddenly the person feels like he has weight

●Fig. MP22-1b

Thought Experiment Cont.

●On left, a person has weight because a planet has passed nearby providing a downward force on the person

●On right, a person has weight because the elevator is moving upward, creating a force against his feet, which feels like weight

●If you are the person in the elevator how do you tell which situation is occurring?

●Fig. MP22-1b

General Relativity

●A person in the elevator cannot tell the difference between the 2 situations

●Thus gravity behaves just like acceleration

●Gravity can be treated as a general acceleration of all particles

●Fig. MP22-1b

Space-Time

●Newton described gravitational "fields" to explain gravity

●Einstein describes gravity as space-time

●According to Einstein, mass causes space-time to warp!

2_D Example of Space-Time

●(a) 2-D space

●(b) 2-D space deformed by presence of mass

●Fig. 22-14

Tests of General Relativity

●General relativity is harder to measure than special

●Need large gravitational fields to measure effects (when orbit speeds and escape velocities become relativistic)

●Deflection of light by mass (aberration of starlight)

●Precession of Mercury's perihelion

●Gravitational redshift

Aberration (Deflection) of Starlight

●The path of light is affected by mass, just like particles with mass

●Maximum deflection 1.75''

●1919 solar eclipse- deflection observed

●Fig. MP22-2a

Precession of Perihelion

●General relativity predicts that orbits of planets should deviate from Keplerian orbits (Fig. MP 22-2a)

●Effect is strongest closest to Sun- Mercury

●Rotation rate of Mercury's orbit is 574''/ century- most due to perturbations from other planets

●43''/ century due to relativity is predicted and seen

Gravitational Redshift

●A photon loses energy moving out of a gravitational well

●(Fig. MP 22-2b)

●E=hf

●So the frequency of an outgoing photon will be redshifted

Relativity- Continued

"Everything should be as simple as possible- but not simpler."

Albert Einstein

Space Warping

●When space-time warps, it takes more energy to send a photon to be received due to gravitational redshift (Fig. 22.15)

●In (d) the space-time is so warped that the photon loses all energy before it leaves the gravitational well

Curvature of Space-Time

●We on Earth usually use Euclidean geometry- flat space (Fig. MP 26-1)

●But in reality, the Earth is a sphere, we need to use Riemannian geometry

●On a sphere, the shortest distance between two points is an arc=great circle, not a line

Different Curvatures in Space

●Earth is positively curved

●Universe could be:

–Positively curved: Sum of angles in triangle >180°

–Negatively curved: Sum of angles in triangle >180°

–Flat: Sum of angles in triangle =180°

Wormholes

●If a tunnel existed between different regions of curved spacetime, one could theoretically travel there faster than normal

●Some speculate that an attempt to travel in a wormhole, would close the wormhole and destroy the traveler

●Fig. 57-16 (Safko)

Matter and Spacetime

●Relativity states that the laws of physics must be the same in all inertial frames

●John Wheeler: "Matter tells spacetime how to bend and spacetime returns the complement by telling matter how to move."

●Notes and Figures for the following slides are adapted from John Safko

●

Light Cone

●Light cone is defined by the speed of light and how far it travels for an observer

●Distance traveled by light is: d=ct

●Events within cone are past or future events

●Events outside of cone will never be realized/experienced by an observer

Reference Frames

●Reference frame defines the origin and coordinate system used to measure position and time

●An inertial frame is a reference frame that is not accelerating

●Master clock is in white

●Fig. 56-1 (Safko, Taken from Wheeler and Taylor "Spacetime Physics")

Reference Frames

●Reference frame defines the origin and coordinate system used to measure position and time

^●Distance between (1,2,1) and (0,0,0) is (1² + 2² +1²)^1/2

●If light is sent from origin to (1,2,1) it will take time=distance/velocity

●t=(1² + 2² +1²)^1/2/c

●The speed of light is c in all inertial reference frames

●Fig. 56-2 (Safko, Taken from Wheeler and Taylor "Spacetime Physics")

Simultaneity

●2 lightning strikes hit opposite ends of a moving train

●Person B on the ground would say both lightning bolts struck at the same time- simultaneous

●Person A on the train says the lightning bolt on the right struck first

●Simultaneous events depend on the reference frame

●Fig. 56-3 (Copyright Safko)

Time Dilation

●To dilate is to expand or stretch

●Proper time (T₀), defined as an interval between 2 events, is measured by a single clock located in one place, that is at rest (not moving)

●An observer who is in motion will always measure a longer time interval

●Time dilation is real and is simply due to the nature of time, it has nothing to do with the inner mechanisms of clocks

Length Contraction

●Proper length (L₀ ) is the length of an object measured at rest

●To get the proper length of an object you must measure both ends simultaneously

●If object is moving, you will measure a shorter length than L₀, the proper length

Twin "Paradox"

●Consider a twin on Earth and his astronaut brother

The Pole-Barn Paradox

●Consider a man running through a barn with a pole