Announcements

•Exam 3 is Monday April 13. Will cover the rest of Chapter 4, all of Chapters 5, 6, 7 & 8. New Sample Questions that include Chapter 8 are posted.

The basic postulates of Special Relativity

• The laws of physics are the same in all inertial reference frames.

• The speed of light in a vacuum is the same in all inertial reference frames

The “special” of special relativity is that it only applies if the relatives velocities are constants. There must be no acceleration.

Time Dilation: Time is not absolute

Observers always see the other guy’s clock as moving slow. No one ever sees the other guy’s clock as fast (at least not in Special Relativity).

Length ContractionConsider a round trip to Alpha Centauri at 99.99% the speed of light. For the person making the trip it takes a few months but for someone left on Earth it takes a little more than 8 years. Since nothing can move faster than the speed of light, the distance to Alpha Centauri to the person making the trip is only a few light months. The distance in the direction of motion shrinks.Play with King’s Special Relativity apps on Length Contraction and Appearance of Relativistic Objects

2

21

cvLL p

Five Minute EssayThe Wyle E. Coyote trap a relativistic train caper

Tunnel doors courtesy of the Acme Corp.

The main equations of special relativity

Time Dilation:

Length Contraction:2

21

cvLL p

2

21

restttvc

A bit about terminologyProper Time: time measured stationary relative to the “event”

Your watch always tells proper time for you

Proper length: length measured stationary relative to the “event”A meter stick you carry always measures the properlength of objects that are stationary with respect to you

Rest mass: mass measured stationary with respect to the objectA scale you carry always measures the rest mass ofobjects that are stationary with respect to you

Boost factor (G) from the Lorentz transformation.

2

21

1

cv

Check out links on Special Relativity at http://www.apsu.edu/astronomy/cosmology-links-and-applets

Other Equations of RelativityRelativistic Momentum Relativistic Mass

Relativistic Energy

2mcE

002

21

m vp mv m v

vc

0

02

21

mm m

vc

220

02

21

m cE m c

vc

2

2

1

1vc

The Classic Doppler Effect

The classical Doppler Effect is only radial: only motion away or towards the observer affect the observed frequency

The Relativistic Doppler Effect

1

1

1

1

1

2

2

z

cucu

cucu

obs

The relativistic Doppler Effect includes the stretching or contracting of waves due to relative motion and time dilation due to the relative motion.

The relativistic Doppler Effect occurs even perpendicular to the direction of motion

Space-time DiagramsAnything inside your light cone could influence you (below you) or you could influence it (above you). Anything outside your light cone cannot affect you

The Space-time Interval is invariant. i.e.: it is the same for all

inertial reference frames222 xtcs

Note the minus sign difference from the Pythagorean theorem. This means Ds2 can be negative (space-like)

Play with Applets on Special Relativity

The Twin Paradox. The paradox goes away if you

consider that the traveler is in two different inertial

reference framesTerence stays at home while Stella makes a trip to Alpha Centauri. See the Twin Paradox Website

The “Special” of Special Relativity was constant velocity

How do we deal with situations where there isn’t constant velocity? What about near the surface of the Earth where there is gravity? What about the general case?

It took Einstein 10 years to figure out General Relativity

The problem with Newton’s gravity: the anomalous precession of the

perihelion of MercuryThe observed precession is 5600 arcseconds per century. 5025 arcseconds is due to the Precession of the Equinoxes of Earth, 532 is due to the effects of Venus, Earth, Jupiter and all the other planets on Mercury. That leaves 43 arcseconds per century unaccounted for by Newtonian gravitation and mechanics.

Newton’s Universal Gravity is a force law with no propagation speed

rr

mmGF ˆ

221

There is nothing in the force equation that says how fast it is transmitted. In fact, it assumes an instantaneous transmission of the force.

An instantaneous transmission is in direct violation of Special Relativity

Special Relativity was for “inertial” reference frames. What about

accelerating reference frames?

The Weak Equivalence Principle

Any acceleration is indistinguishable from gravity

Is “freefall” an inertial reference frame?

On Earth’s surface we are not in an inertial reference frame

The two “fictitious” forces we feel are the Coriolis force and the

centrifugal force

The fictitious forces are invoked to explain the observed accelerations when we are in a non-inertial reference frame

The Strong Equivalence Principle

All inertial and freely falling reference frames are equivalent

Recall from Special Relativity: All laws of physics are the same in all inertial reference frames

A consequence of the equivalence principle is the

bending of light by massive objects

Time is changed by gravity

Gravity slows time. The stronger the gravity, the slower time flows. Unlike Special Relativity, you can tell whose clock is slow. The one that is deeper in the gravity well is the slower one.

Gravitational Redshift is another

consequence of equivalence

Light loses energy as it “climbs” out of a gravity well. This results in the light being redshifted by gravity.

General Relativity deals with geometry