Unit 1B: Special Relativity Motion through space is related to motion in time.

Newton and others thought of space as an infinite expanse in which all things exist. Einstein theorized both space and time exist only within the universe. There is no time or space “outside.” Einstein reasoned that space and time are two parts of one whole called space-time. Space-Time special theory of relativity: time is affected by motion at constant velocity; mass and energy are related

You are moving through time at 24 hr/day. This is only half the story. Instead, think “moving through space-time.” Space-Time At rest, you travel only through time. In motion, you travel through space, but mostly still through time.

Light travels only through space and is timeless. A photon moving at light speed, takes no time to travel! Space-Time If you could travel the speed of light… c = 3 x 10 8 m/s

If at rest, you are traveling at the maximum rate through time: 24 hr/day Space-Time If in motion at the maximum rate through space: c (time would stand still)

Whenever we move through space, we alter our rate of moving into the future (time). Space-Time time dilation: stretching of time caused by motion in space Stationary Clock Moving Clock 0.87c (87% speed of light)

Einstein reasoned all motion is relative and there is no one absolute frame of reference. The First Postulate of Special Relativity Which is at rest? Which is moving? A spaceship cannot measure its speed alone, but only relative to other objects.

2 nd Postulate of S.R.: speed of light is constant regardless of the speed of the flashlight or observer. The Second Postulate of Special Relativity

The fixed speed of light is what unifies space and time. For any motion through space, there is a corresponding passage of time. The ratio of space to time for light is the same for all who measure it. The Second Postulate of Special Relativity

Consider a “light clock”: empty tube with a mirror at each end flash of light bounces between parallel mirrors flash bounces indefinitely “ticks off” equal intervals of time Time Dilation

A moving ship contains a light clock. a.An observer moving with the spaceship observes the light flash moving vertically. b.An observer who is passed by the moving ship observes the flash moving along a diagonal path. Time Dilation

Recall the 2 nd Postulate of S.R. : “speed of light measured by any observer as c.” since the speed of light can not increase, we must measure more time between bounces! Time Dilation more distance more time less distance less time = c = same c

Time Dilation From outside, one tick of the clock takes longer than inside the spaceship. The spaceship’s clock has slowed down. BUT, for observers inside the spaceship, it has not slowed.

Time Dilation The Twin Trip

If a twin travels at 50% c for 1 yr, 1.15 yrs will have elapsed on Earth. If the twin travels at 87% c for a yr, 2 yrs will have elapsed on Earth. Time Dilation At 99.5% c, 10 Earth yrs would pass in 1 yr. At this speed, the traveling twin would age only 1 yr while the stay-at-home twin ages 10 yrs.

At 87% c, a meter stick appears to be 0.5 m At 99.5% c, it appears to you to be 0.1 m As speed approaches the speed of light, the measured length of an object contracts closer and closer to zero. Length Contraction

The contraction of speeding objects is the contraction of space itself. Space contracts in only one direction, the direction of motion. Lengths along the direction perpendicular to this motion are the same.

One of the most celebrated outcomes of special relativity is the discovery that mass and energy are one and the same thing— as described by E = mc 2.

Momentum equals mass times velocity: p = mv To Newton, infinite momentum would mean infinite speed. Einstein showed that a new definition of momentum is required: v = velocity of an object c = speed of light Mass and Momentum in Relativity

When a particle is pushed close to the speed of light, it acts as if its mass were increasing, because its momentum increases more than its speed increases. rest mass: (m) is a constant property of an object no matter what speed it has Mass and Momentum in Relativity rest energy: (E) according to E = mc 2, a piece of matter has an “energy of being” Mass is a kind of potential energy.

If a new theory is to be valid, it must account for the verified results of the old theory. correspondence principle: new theory and old theory must overlap and agree where the results of the old theory have been fully verified. The Correspondence Principle NewtonEinstein p = mv