Special Relativity

Question 1

Detection of Special Relativity

Answer 1

Muons are tiny particles
Enter the earths atmosphere at 0.997c
Muons have a half-life of aprrox 2.2(mew-seconds)

Question 2

Galilean Principle of Relativity

Answer 2

If you werent accelerating consistently, you would not be able to tell you’re moving without looking outside your frame of reference
Observers will disagree on certain things given their frame of reference

Question 3

Inertial Frame of Reference

Answer 3

One where there is no acceleration
In inertial FOR’s, there is constant velocity
In non - interial FOR’s, there is acceleration

Question 4

Frame of Reference

Answer 4

Defined by a physical object, the ‘reference body’ - its the POV of that object
Can be composite (made up of several parts or elements) such as using stars to study the solar system
Each object has its unique FOR

Question 5

Special Relativity

Answer 5

An object or something is moving if it is moving with respect to the POV of the reference body

Question 6

Coordinate System

Answer 6

Once a FOR is established, the motion can be measured accurately by setting up a coordinate system
Its a mathematical way of labelling the points in the FOR

Question 7

What is Special Relativity used for

Answer 7

Special Relativity is how to compare descriptions in different FORs
- Every physical object has its own description of whats occuring in the universe
- how each internally consistant FORs relate to each other
- what each individual frame agrees on

Question 8

Equations of Special Relativity

Answer 8

V (A relative to B) = V(A rel stationary observer) - V(B rel stationary observer)

V (Object in B) = V(Object in A) + V(A in B)

Question 9

Aether

Answer 9

• Prior to 1900’s, light was though tto travel from the Sun to the Earth through a medium called aether
• Aether ‘wind’ from Earth’s motion
• Light woudl travel at different speeds from different sides of the Earth (one faster than the other)

c + v , c - v

Question 10

Micheal - Morley Experiment

Answer 10

Experiment in 1887, using inferometers to determine if there was a measurable difference in light speed

• Light was measured to travel at the same speed

Question 11

Einstein’s Postulates of Special Relativity

Answer 11

1. The law of physics are the same in all inertial frame of references (There is no preferred FOR for it to be classified inertial; no law of physics can identify a state of absolute rest)
2. The speed of light in a vacuum has the same value, c, from all inertial FORs

Question 12

Before Einstein

Answer 12

Newton & Galileo (1600)
Without relationship to anything external
- there is absolute, true time
- there is absolute, true, immovable space

Einstein (1900)
Classical physics only hold in inertial FORs
No priveldged FOR - everything is relative Not true for light - evidenced by MM experiment

Question 13

Einsteins Gedanken Train

Answer 13

In the Gedanken Train, there are two individuals inside the train watching a light bulb hit the back and front of the train at the same time

An observer watching the train sees the light hit the back wall first as it moves forward that way

Question 14

Simultainety

Answer 14

Events simultaneous (occuring at once) in one FOR are not necessarily simultaneous for another

This situation is called simultaineity

It only occurs when objects are moving close or at the same speed as speed of light (Gendanken Train)

Question 15

Simultaneity Outcomes

Answer 15

Time is relative - it depens on the FOR on which it is measured

How far something travels is relative - it depends on the FOR on which it is measured

A 4D relationship must exist between the 3Ds of space and 1D of time - this is called spacetime

Question 16

Time Dilation - Derivation

Answer 16

Using a squared + b squared from two peopls views of a passing high-speed cart

Question 17

Proper Time and Relativistic Time

Answer 17

T = t0 / square root of 1 - v2/c2
Proper time - the time interval measured in the FOR which the event is occuring (or where the event/object is at rest)
Realtivistic time - the time interval measured in the FOR in which the object/event is in motion

Question 18

The Lorentz Factor

Answer 18

Factor that proper time is mutiplied to give realitivistic time is given the symbol gamma, Y, so that:
t = t0y

Question 19

Length Contraction

Answer 19

Derived from time = distance/speed and gendanken train
L = L0 square root of 1- v2/c2
Proper length - Length measured in the FOR in which the object is at rest
Realtivistic Length - Length measured in the FOR in which the object is in motion

Question 20

Realtivistic Mass

Answer 20

M = m0 / square root of 1 - v2/c2
m0 is the rest mass
m is the realitivistically connected mass
Rest Mass: the mass of an object when measured in the same FOR as the event
As v increases, m increases to infinity (think of Lorentz factor curve)

Question 21

Realtivistic Momentum

Answer 21

p = mv
p0 = gamma x m0 x v
p = p0/square root of 1 - v2/c2
Realitivistic momentum of an object when measured in the FOR in which the object is in motion

Question 22

Realitivistic KE

Answer 22

Ek = Total - Rest
Ek = mc2 - m0c2
Total = m0yc2
Ek = (y - 1) m0c2

Question 23

The Ultimate Speed Limit

Answer 23

v -> c, m -> infinity
For a particle with mass to travel at c, it would have infinite mass. Would require inifnte energy to move. Impractical reality

Hence, no object can travel at the speed of light

Question 24

The Twins Paradox

Answer 24

When you change from a moving perspective to non moving, change of perspective is called a Lorentz Factor

Travelling twin is accelerating with two different paths
Non - inertial path is younger
Travelling twin has two different perspectives between them and is accelerating betwen them

Question 25

Ladder and Barn Paradox