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Relativity

Special vs. General Relativity

- Special Relativity deals with non-accelerated

motion. Objects moving at a constant speed

relative to something else. - General Relativity deals with accelerated motion

and how it relates to observed gravity

Relative Motion

- Standard velocity addition
- Ex A friend throws a ball at 5 m/s toward you

from a vehicle moving 5 m/s toward you. - Ex If the vehicle were moving 5 m/s away from

you? - Video.
- Definition of a Frame of Reference Area in which

objects are at rest relative to each other.

Michelson-Morely Experiment

- Purpose Detect relative motion between the

Earth and the ether by detecting changes in the

speed of a light wave. - Demo Interferometer Experiment
- Outcome
- Possible conclusions?

Special Relativity

- First Postulate The laws of physics are the same

in all frames of reference. - Second Postulate Speed of Light is always

measured to be the same (3x108 m/s). Its

independent of the motion between observer and

the source.

Simultaneity

- Events that occur simultaneously in one reference

frame will not appear simultaneous in another

reference frame - When moving toward an event at high speed,

light from that event will reach you first.

Time Dilation

- Time Dilation Equation
- Derivation
- T T / v(1-v2/c2)
- Exs
- A space explorer goes on a high speed trip for 1

year at 99 the speed of light. How much time

passes by here on earth? - Evidence?
- Muon Decay, Atomic Clocks on airplanes, GPS

Examples of Time Dilation (?)

Practice Question

- Your parents go on a 6 month (.5 yr) space cruise

at a speed of 99.99 the speed of light. - How old will you be when they return?
- How will they be when they return?

Twin Trip

- If one twin travels at a high speed away from

earth and then returns. The traveled twin will

now be younger than a stay at home twin. - Twin Trip Simulation Web Site

Changes to Length and Mass

- Length of object will contract as observed from a

different reference frame. - L L x v(1-v2/c2)
- Mass will increase as well as observed from a

different reference frame. - M M / v(1-v2/c2)
- Mechanical Universe Video 42 Lorentz

Contraction

Energy Mass Equivalence

- Since nothing can go faster than the speed of

Light, then the energy transferred to a moving

object must increase the objects mass. - KE 1/2 m v2 , if v cant exceed c, then

energy must end up transferred to the mass - Evidence
- electrons in a accelerators and cyclotrons become

heavier as their speed increases. - Nuclear reactions
- E m c2
- Ex 1 kg is converted into how much energy?

Practice Questions

- A passenger on a rocket traveling at 98 the

speed of light says that his trip takes 5 days.

How long does it take from an outside reference

frame? - A meter stick (1 m) is contracted to 20 cm as

observed from an outside reference frame. How

fast is the meter stick going? - An object is lifted up so that it has 1000 Joules

of PE. How much mass is this PE equivalent to? - What evidence is there that supports Einsteins

theory of Special Relativity? - According to Special Relativity, why cant any

material object go faster than the speed of light?

General Relativity

- Principal of Equivalence (Animation)
- Observations made in an accelerating reference

frame are indistinguishable from those made in a

gravitational field. - Exs light falling in a rocket ship
- How far would light fall in one second here on

earth? - Space-Time
- We can replace our notion of Gravity with the

idea that mass warps space and time and all

objects follow the law of inertia

(4-Dimensionally) - http//www.ligo.caltech.edu/LIGO_web/aaas0203/curv

ature_lan.ram

3 Tests of General Relativity

- Perihelion shift of Mercurys orbit.
- Newtons Law of Gravitation and Keplers Laws

failed to explain why Mercurys elliptical orbit

rotated as observed. - Einsteins General Relativity accurately predicts

this shift to within 0.1 error. Not Bad!! - Light from a distant star should be bent by the

suns gravitational field - Tested and verified by Eddington in 1919
- Heavily publicized and made Einstein famous
- Gravitational Redshift
- Clocks in a stronger gravitational field should

run slower than in a weaker field. - Verified in 1960 with atomic clocks between the

top and bottom floors at a building at Harvard. - Re-verified in 1976 and confirmed Relativity

predictions to within 0.02! WOW!!

Gravitational Redshift

- Spinning Turntable Example
- Observers looking at clocks in a stronger

gravitational field will notices those clocks

running slower. - Ex If we could look at a clock near the sun

we would see it run slow. - Observers looking at clocks in a weaker

gravitational field will notice those clocks

running faster. - Ex Look at a clock that is on the moon it

will run faster. - Where do we age the fastest, on top of

skyscrapers or at street level? - Black hole effects?

Other Consequences of Gen. Relativity

- Black Holes
- Extremely dense objects will bend space-time to a

point of infinite curvature. - Radius of a Black Hole 2 GM/c2
- For our sun radius 2,900 m
- For earth (M 6 x 1024 kg) r ?
- Gravitational Waves or 2
- Accelerating masses should produce waves in

space-time. Two stars (or pulsars) rotating

around each other (or Binary pulsar) should emit

waves large enough to detect. - LIGO or LIGO

Misc.

- Thinking in 4-D is TOUGH!!
- Calculations using General Relativity require the

use of 4-D descriptors and operators known as

Tensors (kinda like matrices) - Gab (8pG)Tab !!
- In other words The rate at which a small ball of

freely falling test particles begins to shrink is

proportional to its volume times the energy

density at the center of the ball, plus the

pressure in the x direction at that point, plus

the pressure in the y direction, plus the

pressure in the z direction. - Therefore most illustrations and examples are

simplified to 2-D or 3-D - http//archive.ncsa.uiuc.edu/Cyberia/NumRel/Movies

Edge.htmlWormHolesToWhere?

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