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=mc 2 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 Relativity Accepted the experimental work on the speed of light and the nature of electromagnetic waves Now the speed of light was absolute and time and space were relative

1 st 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

2 nd 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, km/sec Compared to everyday scales: 65 mph = km/sec = 9.3x10  8 c light travels across this room in ~30 nanosec Human Reflexes: ~0.1 sec (~10 8 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 Time A Thought Experiment Photon Path Length = 3 meters One “Tick” = Time of Flight = 3 meters  c = 10  seconds 1.5 meters Tick! Laser fires to a mirror 1.5m away Light bounces to a detector Detector Laser 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 Dick Jane

Jane’s clock as seen by Jane: Tick !! Photon Path = 3 meters

Jane’s clock as seen by Dick: 0.8c Photon Path = 5 meters Tick!

He Said, She Said... Jane’s Observations: Jane’s Speed = 0 Dick’s Speed = 0.8c Photon Speed = c Path Length = 3 m Tick = 3  c = 10  8 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 =5  c=1.67x10  8 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=mc 2 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 dilation Moving clocks run slow Length contraction Moving 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=mc 2

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 you lab = wavelength emitted by source v = speed of source (+ means receding) c= speed of light

How wrong? Consider a speed we see in planetary orbits: 30 km/s = c. 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.