Astronomy 1143 – Spring 2014

Lecture 18:Special Relativity

Framework

Postulates

Things assumed to be true about the Universe

Example: the speed of light is the same for all observers

Consequences

What happens when moving quickly or in strong gravitational fields

Example: time is different for observers who have relative motion

Framework

Tests

Observational proof

Example: the bending of light in the gravitational field of the Sun

Relevance

When special or general relativistic equations must be used

Example: Special Relativity – fast

General Relativity – strong gravity

Key Ideas: Special Relativity

Postulates:• The laws of physics are the same for all

uniformly moving observers.• The speed of light is the same for all observers.

Consequences:• Different observers measure different times,

lengths, and masses.• Only spacetime is observer independent.

Key Ideas: Special Relativity

Tests:• Michelson-Morley Experiment• Muon decays• E=mc2

• Many, many particle accelerator experiments

Relevance:• When an object is moving close to the speed of

light relative to you• When very accurate results are required

Waves

Waves on Earth travel in a medium

Water waves: water

Sound waves: air, etc.

Earthquakes: earth

No medium, no wave

Speed through the medium affects speed of wave

Motion through the “ether” would affect the speed of light.

Test: Michelson-Morley experiment

Michelson-Morley experiment showed that light is different

They attempted to measure the change in the speed of light as the Earth moved around the Sun

They found that the speed of light did not change

Experimental results helped lead to a new theory

On-Line demonstration of Michelson-Morley

Einstein’s Revolution

1905: Proposed his Theory of Special RelativityAccepted the experimental work on the speed of light and the nature of electromagnetic wavesNow the speed of light was absolute and time and space were relative

1st Postulate of Relativity

The laws of physics are the same for all uniformly moving observers.

(“Uniformly” = “with a constant velocity”)

Consequences:• No such thing as “absolute rest”.• Any uniformly moving observer can consider

themselves to be “at rest”.• Idea appears in the work of Galileo and Newton

Uniformly moving observers

Example:

A car moving at a constant velocity

Counterexample:

A car accelerating (faster or slower)

Laws of Physics are the same:

No experiment can tell you whether you are in the “stationary” or the “moving” frame

2nd Postulate of Relativity

The speed of light in a vacuum is the same for all observers, regardless of their motion.

Implications:• The speed of light is a Universal Constant.• We cannot send or receive information faster

than the speed of light.

Experimentally verified in all cases.

How fast is fast?

All information about the Universe is carried by light.

Speed of Light: c = 299,792.458 km/sec

Compared to everyday scales:• 65 mph = 0.028 km/sec = 9.3x108 c• light travels across this room in ~30 nanosec• Human Reflexes: ~0.1 sec (~108 nanosec)

Common Sense, But Incorrect, Ideas

Time is absolute: The time between two events is independent of the observer. Events are always in the same order.

Space is absolute: The distance between two events is independent of the observer.

Speeds are relative: How fast something is moving depends on how fast you are moving

Essential Relativity

Two observers moving relative to each other experience the world differently:

• Both measure the same speed of light• Both find the same physical laws relating

distance, time, mass, etc.

But, both measure different distances, times, masses, etc. when applying those laws.

Observers can calculate what other observers see from the laws of physics

Consider a simple photon clock:

Consequence: The Relativity of TimeA Thought Experiment

Photon Path Length = 3 meters

One “Tick” = Time of Flight

= 3 meters c

= 10 seconds

1.5

m

ete

rs

Tick!

• Laser fires to a mirror 1.5m away

• Light bounces to a detector

DetectorLaser

Mirror

Dick & Jane fly past each other in rockets:• Constant Relative Speed = 0.8 c• Jane is carrying a photon clock• Each measures how long it takes between “ticks

” of Jane’s photon clock.

What do they see?

Relativity with Dick & Jane

DickJane

Jane’s clock as seen by Jane:

Tick!!

Photon Path = 3 meters

Jane’s clock as seen by Dick:

0.8c

Photon Path = 5 metersTick!

He Said, She Said...

Jane’s Observations:

• Jane’s Speed = 0

• Dick’s Speed = 0.8c

• Photon Speed = c

• Path Length = 3 m

• Tick = 3c = 108 s

“My Clock Runs OK”

Dick’s Observations:

• Jane’s Speed = 0.8c

• Dick’s Speed = 0

• Photon Speed = c

• Path Length = 5 m

• Tick =5c=1.67x108 s

“Your Clock runs slow”

Relative Time

This result is true for all kinds of clocks.

Conclusion: There is no absolute time.• Times passes at different rates for observers

moving relative to each other.• At speeds small compared to c, the difference is

very small.

Verified experimentally using atomic clocks on airplanes and satellites.

Consequences of Relativity

Observers moving relative to each other:• Do not measure the same times.• Disagree on what events occur simultaneously• Do not measure the same lengths.• Do not measure the same masses.

Other Consequences:• Mass and Energy are equivalent: E=mc2

• Massless particles must move at speed of light

Spacetime

Common sense View:• Space & Time are separate and absolute.• Universe looks the same to all observers.

Einstein’s View:• Space & Time are relative.• United by light into Spacetime.

Only spacetime has an absolute reality independent of the observer.

Consequences: Time & Space

The speed of light is a constant. It cannot be changed. Only the length and time we observe can be changed.

• Time dilationMoving clocks run slow

• Length contractionMoving objects are shorter

Tests of Special Relativity

Einstein’s Theory of Special Relativity did not receive instant acceptance

Needed experimental confirmation

Examples:

Nuclear fusion E=mc2

Test: Muon Decay Times

Muons are elementary particles. They can be created by energetic protons slamming into the Earth’s atmosphere and starting “particle showers”

Half-life of 1.5 microseconds

Test: Muon Decay Times

Non-relativistic view• About 1 millisecond to

travel through the Earth’s atmosphere

• This time is the same both in the muon’s frame and to an observer on the ground

• No muons would survive to reach Earth’s surface

Relativistic view• Muons are traveling at

speeds up to 0.99 c• They experience time

more slowly according to an observer on the ground

• 1 microsecond in observer frame = 1 millisecond in muon frame

• Many survive

Test: Muon Decay Times

Relevance: Fast relative motion

Example: Doppler shift

Non-relativistic formula

Relativistic formula

obs = wavelength

observed by youlab = wavelength

emitted by sourcev = speed of source (+ means receding)c= speed of light

How wrong?Consider a speed we see in planetary orbits:

30 km/s = 0.0001c. The source emits light at 500nm

Non-relativistic:

Relativistic:

Consider a much higher speed: 0.8c. The source emits light at 500nm

Non-relativistic:

Relativistic:

How good is the instrument? Can I even measure that?

Yikes!Egads!Doh!

What about Gravity?

Special Relativity is restricted to uniformly moving (unaccelerated) observers.

But, objects are accelerated by gravity. (Newton: “They feel a gravitational force.”)

It took Einstein another 8 years to generalize relativity.

Led to a completely new theory of gravity.