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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.