# Presentation: 574159

## Relativity

- Physics 2C

## Chapter 36

- The Theory of Relativity

## The idea of relativity

- When doing experiments on a boat sailing at constant speed on a straight line on a smooth lake, the results are the _***same***_ as on shore!

- Without looking outside one cannot tell whether the ship is moving at all

- Velocity is  _***RELATIVE***_ to the reference frame

## Frames of reference

**A set of rods and rulers and clocks **
**that allow us to determine the time**
**of any event and the position of **
**any object with respect to a **
**reference point**

**Reference point**

**object**

## An inertial reference frame is a reference frame where isolated bodies are seen to move in straight lines at constant velocity.

## The arena where

- Absolute space in its own nature, without relation to anything external, remains always similar and immovable.

**The arena where**
**Nature occurs**

- Space according to Newton

## Is

- Time

**Is**
**Just**
**One**
**Thing**
**After**
**Another**

- Time according to Newton

- Absolute and mathematical time, of itself, and from its own nature, flows equally without relation to anything external

## Not all frames are inertial:

**Not all frames are inertial:**

- Roberta is in a_*** non-inertial***_ reference frame

- Ingrid is in an_*** inertial***_ reference frame

## Just shoot me

- target

**Just shoot me**

- Relative and absolute velocities

- And I claim everything , including light, will behave like that: *** absolute space and time imply ***_***all***_*** velocities (including c) are relative***

***v=***Speed of this bullet with respect to the target
***u= ***its*** ***speed with respect to the tank
***w=*** the speed of the tank
-               		***v=u+w***

## Just shoot me

- target

**Just shoot me**
**...****again**

**The motion of the source **
**and the speed of light**

- And _*I*_ claim the speed of light is the _***same***_ for all observers: _***c is absolute!***_

## The Michelson-Morley experiment

## Meet Einstein

**Hi**

## A lecture is the process by which

- the notes of the teacher
- become the notes of the students
- WITHOUT going through the minds of either

- The next results require
- an engaged and OPEN  mind

## The principle of relativity

- The Laws of Pysics

- are the same for all

- inertial observers

## Remember these?

- electric flux~charge

- Magnetic Gauss's law:
- magnetic flux=0

- Faraday's law:
- changing B generates an emf

- (Generalized) Ampere's law:
- Moving charges generate B

##  Remember this? – the wave eqn

## Electromagnetic waves 

- If we look at Maxwell’s eqns where there are no  charges or currents - after a bit of math we will get...

- the speed of light
- A constant!

## Maxwell’s equations: light  moves with speed c

**Maxwell’s equations are some of the laws of physics**
**If we accept the principle of relativity, **
**	****	*****light always moves with speed c***

**The speed of light is absolute**

- The speed of light

**By stating this Einstein also**
**implied that Newtonian**
**mechanics is flawed,**
** ****but Maxwell’s equations**
**are OK**

## The velocity of the source just adds to the velocity of the projectile...

**...*****even for light***

**The velocity of the source ****affects**** the velocity of the projectile...**
**But the effect is ****smaller and smaller**** as the projectile speed ****approaches c**
***The speed of light is unaffected by the motion of the source***

## The speed of light is independent of the speed of the source:

**The speed of light is *****independent *****of the speed of the source:**
**The speed of light is *****absolute***
**The speed of bullets *****depends *****on the motion of the source**
**The speed of bullets is *****relative***

**The faster a bullet is shot**
**the smaller the effect of the **
**motion of the gun**

## Time and Special Relativity

**Look first at a “light clock”. **
**We need:**

**Time is relative....**

## At rest with the mirrors

**At rest with the mirrors**

**t=0**

**t=1**

## Moving with respect to the mirrors

**Motion of mirrors**

## time

- Light **always** travels at speed ***c***

*time*
*dilation*

## Moving clocks slow down

**If you watch the clock move the up down trip takes *****more***** than 1 second**

**Moving clocks slow down**

## time is

- I’m moving with this clock. In ***my*** reference frame the trip takes ***T******0*** seconds

- He’s at rest with this mirror

*time is*
*relative*

## Length is relative too

**A puzzle:**
**John has an armed bomb with a 5 minute fuse**
**He is traveling at very high speed towards us**
**We know his (last) trip takes 6 minutes**
**Will we die?**

## I’m afraid so:  since he moves fast his clock is slow with respect to yours, and he cleverly arranged his speed for the bomb to take 6 minutes as measured in your clock to blow

- I’m afraid so:  since he moves fast his clock is slow with respect to yours, and he cleverly arranged his speed for the bomb to take 6 minutes *as measured in your clock* to blow
- Just enough time for him to reach you! Sorry...

- OK, but before we die: What does John see??
- Surely in *his* reference frame  the bomb blows after 5 minutes...if he is to kill us, how can
- he reach us in time?

- Well, since his bomb blows after 5 minutes and he does reach you...in his reference frame he will travel a *shorter distance*

## In the reference frame where we are at rest:

**boom**

**In the reference frame where we are at rest:**

## In the reference frame where John is at rest:

**boom**

**In the reference frame where John is at rest:**

## If the principle of relativity 

**In the reference frame where we are at rest:**

**In the reference frame where John is at rest:**

**If the principle of relativity **
**is correct**
**length is relative**

## The numerical calculations:

- In _**our reference frame:**_
*t = *fuse-time
*l = *distance traveled by John
*v = *John’s speed of approach

- In _**John’s reference frame:**_
*t’ = *fuse-time
*l’ = *distance traveled by us
*v’ = *our speed of approach

## Distances along

- the direction of motion
- are contracted

- Distances perpendicular
- the direction of motion
- are NOT contracted

## Exercise 9.3

- In a laboratory frame  of reference an observer notes that Newton’s 2nd law is valid (to the accuracy of the instruments).  Show that the same is true for an observer moving at constant speed with respect to the first.

## An astronomer on Earth observes a meteoroid approaching Earth at a speed of 0.8c. At the time of discovery it is 20 light years away. Find the Earth-time and meteoroid time for impact and the distance to Earth measured in the meteoroid frame of reference at time of discovery.  

- 1 light year ~ 1016m=1year*c

## Exercise 9.11

- A spacecraft with *proper *length of 300 m takes 0.75 s to pass an Earthly observer. What is the spacecraft speed with respect to Earth?

## A meter stick is moving along its long axis near the speed of light. A stationary observer will observe that the meter stick is
a. longer than one meter.
b. shorter than one meter.
c. one meter in length.
d. moving faster than the speed of light.
e. moving into the future.

- a. longer than one meter.
- b. shorter than one meter.
- c. one meter in length.
- d. moving faster than the speed of light.
- e. moving into the future.

## The addition of velocities

- If u=c, then u'=c

- v=velocity of reference frame
- u’=velocity of object in reference frame
- u=velocity on earth

## Exercise 

- A spacecraft moves at 0.8 c relative to Earth and fires a rocket in the forward direction moving at 0.9 c. What must be the rocket’s speed relative to the Earth?

## If the principle of relativity 

**E=mc****2**

**If the principle of relativity **
**is correct,**
**Energy and mass are equivalent**
**E=m c****2**

## Exercise 9.39

- The power output of the sun is 3.77 x 1026 W. How much  mass is converted into energy every second?

## In a nuclear power plant fuel rods last 3 years. During that time the plant produces 1 GW of power, what is the loss of mass in the rods?

## Slide 43

## Hiroshima:

** ****66,000 people died and 69,000 injured from the blast, **
** ****In a few weeks the number of dead had risen to 130,000**
** ****Then to 200,000 in 5 years**
**Nagasaki **
** ****Between 60,000 and 70,000 people died form the blast, **
** ****50,000 more died within 5 years. **
**The fate of more than 300,000 people was sealed in the fraction of a second it took these bombs to explode.**
**For comparison, there were about 620,000 casualties in the American civil war that lasted 5 years. **
**Current atomic weapons are roughly 100 times more potent than those dropped on Japan in 1945.**

- 1. What happens to the way a clock measures time as observed by a stationary observer as the clock increases its speed?
- a. It speeds up.
- b. It slows down.
- c. It stays the same.
- d. It stops.
- e. The hands move with simple harmonic motion.

## Which of the following is a postulate of relativity theory?
a. Space and time are invariant.
b. Mass and energy are equivalent.
c. The speed of light in a vacuum is the same for all observers no matter what the source velocity is.
d. Energy is conserved in elastic collisions.
e. Gravity can bend light.

- a. Space and time are invariant.
- b. Mass and energy are equivalent.
- c. The speed of light in a vacuum is the same for all observers no matter what the source velocity is.
- d. Energy is conserved in elastic collisions.
- e. Gravity can bend light.