Astronomy 162: Introduction to Stars, Galaxies, & the Universe Prof. Richard Pogge, MTWThF 9:30

Lecture 31: A Tale of Two World Views:
Special Relativity

"Common sense is the collection of prejudices acquired by age eighteen."
Albert Einstein (1952)

"It will seem difficult at first, but everything is difficult at first."
Miyamoto Musashi [Book of Five Rings 1645]

Key Ideas

Central Postulates of Relativity:

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.

Newton's Universe

• The universe keeps absolute time.
• Objects move through absolute space.
• Universe looks the same to all observers, regardless of how they move through it.

The result was a set of laws formulated from the perspective of an absolute "God's Eye View" of the Universe.

Einstein's Challenge

• We cannot take a "God's eye view" of the Universe.
• We can only compare our view with that of other observers.
• All information we have is carried by light.
• But, light moves at a finite speed.

Result is an irreducible relativity of our physical perspective.

Seeing the World

Speed of Light: c = 300,000 km/sec

Compared to everyday scales:

• 65 mph = 0.028 km/sec = 9.3x10^-8 c
• light travel time in the lecture hall (front-to-back) = ~30 nanoseconds
• Human Reflex Time = ~0.1 sec (~10⁸ nanoseconds)

Our everyday experience of the world is with phenomena at speeds much slower than the speed of light.

1st Postulate of Relativity

"Uniformly" = "with a constant velocity"

Implications:

• No such thing as "absolute rest".
• Any uniformly moving observer can consider themselves to be "at rest".

2nd Postulate of Relativity

Implications:

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

This has been experimentally verified in all cases.

Essential Relativity

• 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. applying those laws.

The key is the role of light.

The Relativity of Time: A Thought Experiment

• Laser fires to a mirror 1.5 meters away
• Light bounces to a detector
• Photon Path Length = 3 meters
• One "Tick" = Time of Flight = 3 meters / c = 10^-8 seconds

Relativity with Dick & Jane

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?

Jane's clock as seen by Jane:

Jane's clock as seen by Dick:

He Said, She Said...

Jane's Observations:

• Jane's Speed = 0
• Dick's Speed = 0.8c
• Photon Speed = c
• Path Length = 3 m
• 1 Tick = 10^-8 sec
• Jane says: "My Clock is running correctly"

Dick's Observations:

• Jane's Speed = 0.8c
• Dick's Speed = 0
• Photon Speed = c
• Path Length = 5 m
• 1 Tick = 1.67x10^-8 sec
• Dick says: "Your Clock is running slow."

Relative Time

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.

This has been verified experimentally using atomic clocks on airplanes and satellites.

Consequences of Relativity

• Do not measure the same times.
• Disagree on what events occur simultaneously.
• Do not measure the same lengths of objects.
• Do not measure the same masses for objects.

Other Consequences:

• Mass and Energy are equivalent: E=mc²
• Massless particles must move at speed = c.

Spacetime

• 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.

Light the Unifier

• All uniformly moving observers see the same physical laws.
• All observers measure the same speed of light.

We must unify otherwise disparate ideas:

• Space and Time are unified into Spacetime.
• Matter and Energy are Equivalent (E=mc²)

What about Gravity?

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

Einstein took 8 years to generalize relativity.

This effort was to lead to the formulation of a completely new theory of gravity.

A Final Thought:

"The principles of special relativity are remarkably simple. They are very much simpler than the axioms of Euclid or the principles of operating an automobile. Yet both Euclid and the automobile have been mastered - perhaps with insufficient surprize - by generations of ordinary people. Some of the best minds of the twentieth century struggled with the concepts of relativity, not because nature is obscure, but simply because man finds it difficult to outgrow established ways of looking at nature. For us the battle has already been won. The concepts of relativity can now be expressed simply enough to make it easy to think correctly - thus "making the bad difficult and the good easy."[*] The problem of understanding relativity is no longer one of learning but one of intuition - a practiced way of seeing. When seen with this intuition, a remarkable number of otherwise incomprehensible experimental results are revealed to be perfectly natural."

[*] Quote is from Einstein, in a similar connection, in a letter to the architect Le Corbusier.