1- Relativity I

Question 1

Newton’s laws of motion only work correctly in…

Answer 1

inertial reference frames

frame that move with constant velocity to an inertial frame.

Question 2

“invariant”

(in the context of relativity)

Answer 2

unchanged

implication is that all inertial frames are equivalent–there is no special or favored inertial frame.

Question 3

c =

Answer 3

Question 4

In 19th Century, it was a widely held belief that electromagnetic radiation propagated through a medium called the…

Answer 4

ether / aether

Question 5

All waves that were known to 19th century scientists required a medium in order to propagate.

i.e.

Ocean Waves

Earthquake

Sound

The speed of the waves depends on the properties…

Answer 5

…of the medium and is derived relative to the medium,

Question 6

Michelson-Morley Experiment

Michelson interferometer

Answer 6

attempted to measure v²/c² by a diference measurement, using the interference property of the light waves as a sensitive “clock.”

purpose was to measure the speed of light relative to the interferometer (Earth), thereby detecting Earth’s motion through the ether and verifying its existence.

Question 7

Based on Maxwell’s equations and the experimental data presented by Maxwell (and others)…

Answer 7

…we must conclude that the speed of electromagnetic radiation is the same in all inertial reference systems, independent of the motion of the source relative to the observer.

Question 8

Einstein

on the elctrodynamics of moving bodies

Answer 8

postulated a more general principle of relativity that applied to both electrodynamics and mechanics.

a consequence of this postulate was that absolute motion cannot be detected.

Question 9

Einstein’s Postulates

Answer 9

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

The speed of light, c, is independent of the motion of the source and is constant in vacuum.

Question 10

Events simultaneous in one reference frame are…

Answer 10

… not, in general, simultaneous in any other inertial frame.

Question 11

Length contraction occurs in dimensions _______ to the motion

Answer 11

parallel

Question 12

Spacetime Intervals

Observers in inertial frames measure the same (Δs) between pairs of events in spacetime, where (Δs) =…

Answer 12

(Δs) =(cΔt)²-(Δx)²

Question 13

Spacetime Diagrams

Show “worldline” trajectories on a ___ vs. ___ graph

Answer 13

…a (c·t) vs. (x) graph

with slope Δct/Δx

Question 14

Maximum slope for worldline?

Minimum slope for worldline?

Answer 14

Max = 1

Min = -1

Question 15

As v approaches c…

time _____

and

length _____

Answer 15

time stretches

length contracts

Question 16

Einsteins Four Big 1905 Papers

Answer 16

1) Photoelectric effect
2) Brownian motion
3) Special relativity
4) Mass–energy equivalence

Question 17

The length of an object measured in the reference frame in which the object is at rest is called its ….

Answer 17

…proper length.

Question 18

The Spacetime Interval

Answer 18

(Δs)² = (cΔt)² - [Δx² + Δy² + Δz²]

(Δs)² = (cΔt)² - (Δx)²

[interval]² = [separation in time]² - [separation in space]²

The interval Ds is the only measurable quantity describing pairs of events in spacetime for which observers in all inertial frames will obtain the same numerical value.

Question 19

Twin Paradox

aka “the clock paradox”

Twins Homer and Ulysses; Homer travels to a star and returns at v–>c. Using the time transforms we get results that dont agree if we do the analasys from both brother’s points of views.

Answer 19

Ulysses’ spaceship does not remain in an inertial frame during the round trip; hence, it falls outside of the special theory, and no paradox arises.

Question 20

Pole and Barn Paradox:

Farmer watches runner with 10m pole dash into 5m long barn.

Answer 20

For the farmer, the front of the pole reaches the rear door of the barn simultaneously with the arrival of the back end of the pole at the front door; that is, at that instant in S the pole is entirely contained in the barn.

For the runner, the rear of the pole passes the back door and the front the pole lines up with the front door. The first of those two events occurs before the second, and the runner never sees the pole entirely contained in the barn. Once again, the relativity of simultaneity is the key— events simultaneous in one inertial frame are not necessarily simultaneous when viewed from another inertial frame.

In the case where the “back” door is armor plated steel and wont allow the runner to “punch through,” the instant the front of the pole “touches” the back it starts “sending the message” (an elastic shock wave, for example). However, that information is limited by the universal constant, c, and in the time it takes to convey the information the remaining portion of the pole is “in the barn.”

Question 21

c , the speed of light, is constant independent of the source motion.

the ___ of ______, however, does not adhere to this contraint.

Answer 21

…the direction of light…

Question 22

Headlight Effect

Answer 22

Approaching = more intense

Receding = less intense