Relativityby

Albert EinsteinPrepared by:

Sir Antonio Salvador Jr.

The Relativity Principle

Galileo Galilei 1564 - 1642

The Ptolemaic Model

The Copernican Model

Problem: If the earth were moving wouldn’t we feel it?

A coordinate system moving at a constant velocity is called an inertial

reference frame. The Galilean Relativity Principle: All physical laws are the same in all inertial reference frames.

Other Examples:

As long as you move at constant velocity you are in an inertial reference frame.

Galilean Relativity

– “Relativity” refers in general to the way physical measurements made in a given inertial frame are related to measurements in another frame.

– An inertial observer is one whose rest frame is inertial.

– A quantity is invariant if all inertial observers obtain the same value.

– Under Galilean relativity, measurements are transformed simply by adding or subtracting the velocity difference between frames:

– vball(measured on ground)=vtrain (measured on ground)+vball(measured

on train) 12 m/s = 10m/s + 2 m/s– Vball(measured on train)=vground(measured on train)+ vball(measured on

ground) 2 m/s = 10m/s + 12 m/s10 m/s

2 m/s

12 m/s

ElectromagnetismA wave solution traveling at the speed of light

c = 3.00 x 108 m/s

Maxwell: Light is an EM wave!

Problem: The equations don’t tell what light is traveling with respect to

James Clerk Maxwell 1831 - 1879

Einstein’s Approach to Physics

Albert Einstein 1879 - 1955

1. (Thought) Experiments

E.g., if we could travel next to a light wave, what would we see?

2. “The Einstein Principle”:

If two phenomena are indistinguishable by experiments then they are the same thing.

Einstein’s Approach to Physics2. “The Einstein Principle”:

If two phenomena are indistinguishable by experiments then they are the same thing.

A magnet moving A coil moving towards a magnet

Both produce the same currentImplies that they are the same phenomenon

towards a coil

Albert Einstein 1879 - 1955

current

current

Einstein’s Approach to Physics1. Gedanken (Thought) Experiments

E.g., if we could travel next to a light wave, what would we see?

c

c

We would see an EM wave frozen in space next to usProblem: EM equations don’t predict stationary waves

Albert Einstein 1879 - 1955

ElectromagnetismAnother Problem: Every experiment measured the speed of light to be c regardless of motion

The observer on the ground should measure the speed of this wave as c + 15 m/s

Both observers actually measure the speed of this wave as c!

Special Relativity Postulates

• The Relativity Postulate: The laws of physics are the same in every inertial reference frame.

• The Speed of Light Postulate: The speed of light in vacuum, measured in any inertial reference frame, always has the same value of c.

Einstein: Start with 2 assumptions & deduce all else

This is a literal interpretation of the EM equations

Special Relativity PostulatesLooking through Einstein’s eyes:

Both observers (by the postulates) should measure the speed of this wave as c

Consequences:

• Time behaves very differently than expected

• Space behaves very differently than expected

Einstein’s Special Relativity

1,000,000 ms-1

0 ms-1

300,000,000 ms-1

Both spacemen measure the speed of the approaching ray of light. How fast do they measure the speed of light to be?

Einstein’s Special Relativity

• Stationary man– 300,000,000 ms-1

• Man travelling at 1,000,000 ms-1

– 301,000,000 ms-1?– Wrong!

• The Speed of Light is the same for all observers

Three effects• 3 strange effects of special

relativity

– Lorentz Transformations

– Relativistic Doppler Effect

– Headlight Effect

Lorentz Transformations

■ Light from the top of the bar has further to travel.

■ It therefore takes longer to reach the eye.

■ So, the bar appears bent.

■ Weird!

Doppler Effect• The pitch of the siren:

– Rises as the ambulance approaches– Falls once the ambulance has passed.

• The same applies to light!– Approaching objects appear blue (Blue-

shift)– Receding objects appear red (Red-shift)

Headlight effect

• Beam becomes focused.• Same amount of light concentrated in a

smaller area• Torch appears brighter!

V

Warp• Program used to visualise the three

effects

Demo . . .

Fun stuff

• Website:http://www.adamauton.com/warp/

Eiffel Tower Stonehenge

Time DilationOne consequence: Time Changes

Equipment needed: a light clock and a fast space ship.

Time DilationIn Bob’s reference frame the time between A & B is Δt0

Sallyon earth

Bob

Beginning Event A

Ending Event B

cDt 2

0

D

Δt0

Bob

Time DilationIn Sally’s reference frame the time between A & B is Δt

Bob

A BSallyon earth

22 2 22 2 2

2v ts D L D

Length of path for the light ray:

cst 2

and

Δt

Time Dilation2

2 2 22 2 22

v ts D L D

Length of path for the light ray:

cst 2

and

Solve for Δt:22 /1

/2

cv

cDt

cDt /20

Time measured by Bob

220

/1 cv

tt

Time Dilation

220

/1 cv

tt

Δt0 = the time between A & B measured by Bob

Δt = the time between A & B measured by Sally

v = the speed of one observer relative to the other

Time Dilation = Moving clocks slow down

If Δt0 = 1s, v = .999 c then: s 500999.1s 1

2

t

Time Dilation

• Bob’s watch always displays his proper time

• Sally’s watch always displays her proper time

How do we define time?

The flow of time each observer experiences is measured by their watch – we call this the proper time

• If they are moving relative to each other they will not agree

Time DilationA Real Life Example: Lifetime of muons

Muon’s rest lifetime = 2.2x10-6 seconds

Many muons in the upper atmosphere (or in the laboratory) travel at high speed.

If v = 0.999 c. What will be its average lifetime as seen by an observer at rest?

s 101.1999.1

s 102.2/1

3

2

6

220

cv

tt

Length ContractionBob’s reference frame:

The distance measured by the spacecraft is shorterSally’s reference frame:

Sally

Bob

0

0

LLvt t

The relative speed v is the same for both observers:

220

/1 cv

tt

220 /1 cvLL

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