• Special Theory (Einstein, 1905)
• uniform motion (constant velocities, no acceleration)
• General Theory (Einstein, 1916)
• accelerated motion, gravity, curvature of space

• In 19th century scientists thought that all space was filled with the ether (shades of Aristotle!).
• The ether was the medium through which EM waves such as light propagated.
• Everything (stars, sun, earth, etc.) moved through the mass-less, odorless, tasteless, etc. ether.

• James Clerk Maxwell - 19th cent. physicist did for light and EM radiation what Newton did for gravity.
• He showed that light is an EM wave that has to travel at speed c through the ether.
• Implication: The ether would be the physics equivalent of the holy grail - an absolute reference frame.

• At age 16 in 1895 a "thought" experiment
• Newtonian mechanics does not forbid any speed, even greater than c.
• If observer travels at c Maxwell implies that she will see light as a stationary wave.
• This is impossible - contradicts Newton or Maxwell: speed of light = c, a constant = ratio of EM and electrostatic units of charge

• "Wrong" in sense of finding limits to applicability (high speed for Newton; c maybe not a constant for Maxwell).
• Perhaps c depends on speed of observer (good for Newton, not so good for Maxwell).

• Experiment of firing a projectile from a moving railroad car (discussed in class)
• What happens if we do this with a spaceship traveling at close to the speed of light?
• If we shine a flashlight in the direction of travel, do the photons travel at 2c?

• Is the speed of light constant in a vacuum or does it depend on speed of observer and/or emitter?
• If it is constant, does it provide and absolute frame of reference against which all motion can be measured?

• This was pointed out after Einstein had presented special relativity.
• Consider double star with edge-on orbit
• Speed of star moving towards us very different from that moving away from us.
• Will observed speed of light change as well?

• Consider a binary-star system distance D from the Earth.
• Time light takes to reach us is:

Light-Travel Time from Star

• Star is in circular orbit with constant speed, V
• From top position:

• From bottom position:

• Difference in travel time to Earth:

or

• Numerical example:
• D = 10 light years = 9.4 x 10¹⁸ cm
• V = 30 km/sec = 3.0 x 10⁶ cm/s

A discrepancy this large would be easily measured and noticed.

• Conclusion: Speed of light is indeed constant through the ether as Maxwell said.
• Implication: Can you measure the Earth’s motion through the ether (2nd question)?
• An analogy: For c, take a jet moving at constant air speed; for Earth moving through ether causing "ether wind" take a jet stream blowing due east at 300 km/hr.

• Jet 1 goes from La La Land (a.k.a Los Angeles, LAX) to Dallas (DFW) & back
• Jet 2 goes from LAX to Calgary (YYC) and back.
• The distances are equal.

The Details

• The jets have air speeds exactly = 500 km/hr
• The jet stream is blowing due east at exactly 300 km/hr.
• DFW is due East of LAX 1600 km
• YYC is due North of LAX 1600 km
• Distances are the same

• LAX -> DFW: ground speed is

500 + 300 = 800 km/hr.
• DFW-> LAX : ground speed is

500 - 300 = 200 km/hr
• Conclude: flight takes 2+8=10 hours
• 

• LAX -> YYC: ground speed is 400 km/hr
• YYC-> LAX : ground speed is 400 km/hr
• Conclude: flight takes 4+4=8 hours, or 4/5 as long as the east-west flight.
• 

• For the jet stream substitute the Earth moving through the ether.
• For the two jets substitute two beams of light. From moving Earth you should measure two different speeds for light: one in direction of Earth’s motion, the other perpendicular to it.
• They used principle of interference.

• If the Earth were moving through the ether, the times for the light to come from the two mirrors would differ just like the plane and the jet stream.
• They didn’t differ. Implied that speed of light had to be independent of uniform motion of source or observer.

• Had to be very accurate because v/c =1/30,000 while for jets it was 3/5.
• For numbers very close to one, the difference in time will be like 0.5(v/c)² or one part in 200,000,000.
• They found: NO DIFFERENCE IN SPEED OF LIGHT IN TWO DIRECTIONS.

• No special frame of reference - a generalization of Newton and Galileo’s principles of relativity.
• Think of a sound wave: it moves at constant speed through air once it leaves source. But an observer can move at different speeds relative to sound.

• The Principle of Relativity: The description of all phenomena provided by any two observers in uniform relative motion are equally valid; the laws of physics are the same for both of them.
• The absoluteness of the speed of light in a vacuum: it is the same for any two observers in uniform motion.

• If c is an absolute constant we might expect some strange consequences because we observe the world via light.
• Our knowledge or perception of the world can travel no faster than the speed of light
• Consider measurements of time and distance.

For the triangle I show in class, we have:

Do some algebra to solve for t' in terms of t and V:

Solve this equation to get the time measured by the observer t'   in terms of the time measured by the light clock t .

The Lorentz factor appears in many of the equations of special relativity.  It is a measure of how much physical quantities differ when measured by two observers in uniform motion with respect to one another.  It is usually called "gamma":

• In 1880s FitzGerald proposed that moving objects will contract in their direction of motion by same amount.
• This was proposed as an explanation of the M-M experiment.
• Did not have physical basis.

• Conclusion:
• Observer in the rest frame measures time interval t.
• Observer who observes the clock moving at velocity V measures a longer time interval for the same event:

• The observer sees the light clock run slow when the clock is in motion.
• Moving clocks appear to run slow.
• This is called time dilation.
• Complete symmetry as to what is seen by two observers in uniform motion

• Two bolts of lightning strike "simultaneously" at A and B says observer O standing on grass.
• Observer O’ on train moving with velocity V says that flash at B (and B’) hit before flash at A and A’.
• Einstein concluded: concept of simultaneity is relative to the coordinate system in which it is measured. No absolute physical significance for events at different places.

Quantity	Rest  Frame	Observer's Frame	Phenomenon
Time	t		Time Dilation
Length	L		Lorentz Contraction
Mass	m0		no special name

• You can derive mass transformation equation from consider of conservation of angular momentum in two moving frames.
• By considering conservation of energy in a closed system you can show:
• E= mc² = gm₀ c² = m₀ c² + Kinetic Energy

• As V approaches c, g approaches ¥ , so it takes an infinite amount of energy to accelerate matter to the speed of light!
• Bad news for interstellar travelers!

• "Equivalence Principle": Observers cannot distinguish between inertial forces due to acceleration and uniform gravitational forces due to a massive body.
• Consequence: Gravity, inertia, and acceleration are related to the curvature of space-time.

• Precession of Mercury’s perihelion.
• GR accounts for 43"/century missed by Newtonian gravity
• Gravitational lensing
• Starlight deflected by the Sun and other massive objects
• Gravitational redshift
• Photons lose energy leaving a gravitational field

(Example of throwing a ball up in the air - it looses energy)

Back to Cosmology/Relativity Home Page