Astronomy 162: Professor Barbara Ryden

``Common sense is the collection of prejudices acquired by age eighteen.''

- Albert Einstein

- All speeds are
**relative**, except for the speed of light, which is**absolute**.

Both the theory of Special Relativity and the theory of General Relativity were formulated by Albert Einstein (born 1879, died 1955). The theories of relativity have received the reputation of being incomprehensible. Actually, this is something of a bum rap. The theory of Special Relativity, in particular, is very simple from a mathematical viewpoint. Why, then, has Special Relativity attained a reputation for being incomprehensible? Mainly because it violates ``common sense''. In everyday life, we deal with objects moving much slower than the speed of light. Special relativity deals with objects moving at speeds close to the speed of light. It is not too surprising, then, that Special Relativity doesn't conform to the collection of prejudices that we have accumulated from our observations of slow-moving objects.

The theory of
**Special Relativity**, published by Einstein
in 1905 (when he was 26 years old), describes how objects
behave when they have a constant velocity. Ten years later,
in 1915, Einstein published his theory of **General
Relativity**, which describes how objects move
when they are accelerated by gravity. (General Relativity is the
subject of tomorrow's lecture;
today we'll stick to the
simpler case of Special Relativity.)

Special Relativity can be summed up in one brief sentence:

A concise sentence -- but what does it mean? Let's start
by examining what is mean by ``relative speed''.
A professor paces across a lecture platform.

Her speed **relative to platform**=

1 meter/second

Her speed **relative to center of Earth**=

360 meters/second

Her speed **relative to center of Sun**=

30,000 meters/second

Her speed **relative to center of Galaxy**=

220,000 meters/second

Which of the above speeds is the ``correct'' speed? They are all correct.
When you state the speed of a material object, like a professor or
a star, you are stating the speed relative to some other object.
For massive objects, **all speeds are relative**.

As another example of the

To summarize the situation:

Speed of car relative to bystander = v = 30 meters/second

Speed of bullet relative to car = u = 250 meters/second

To find the speed of the bullet relative to the bystander,
just add the speeds together:

Speed of bullet relative to bystander = v + u = 280 meters/second.

The question ``What is the speed of the bullet?'' doesn't
have a single answer. The speed of the bullet **relative
to the car** is 250 meters/second. The speed of the
bullet **relative to the bystander** is 280 meters/second.
For that matter, the speed of the bullet relative to the
center of the galaxy is 220,000 meters/second.

There is a critical caveat attached to the theory of Special Relativity: all speeds are relative,

As an example of the **absolute** nature of the
speed of light, consider the same criminal roaring down
High Street in his getaway car. Relative to a bystander,
the car has the same speed v = 30 meters/second. Now,
however, the criminal draws a laser
gun. A laser produces electromagnetic radiation, so relative
to the car, the laser beam will travel at the speed of light:
c = 300,000,000 meters/second.

To summarize the new situation:

Speed of car relative to bystander = v = 30 meters/second

Speed of light beam relative to car = c = 300,000,000 meters/second

What is the speed of the light beam relative to the bystander? A classical physicist, like Galileo or Newton, would say the speed is v+c = 300,000,030 meters/second. This, however, is WRONG. The correct answer, given by Einstein, is that the speed of the light beam relative to the bystander is c = 300,000,000.

The speed of light is absolute; that means it is the same seen by any observer, no matter how fast the observer is moving relative to the light source. THE OBSERVED SPEED OF LIGHT IN A VACUUM IS ALWAYS 299,792.459 KILOMETERS PER SECOND. (Parenthetical comments: it is necessary to add the qualification ``in a vacuum'' since interactions with matter can slow down a light beam. The exact value of the speed of light is usually rounded off to 300,000 km/sec for practical purposes. The speed of light is the speed of all electromagnetic radiation, from radio to gamma-rays.)

The fact that the speed of light is constant has been experimentally
verified, first by a pair of physicists in Cleveland in 1887.
The fact that the speed of light is absolute, while all other
speeds are relative, has some bizarre consequences. Suppose
I hand you a light bulb, and send you away from Earth with
a speed equal to 99% the speed of light. You say:

``The light bulb is stationary. The light
from the bulb is moving at a speed c.''

On the other hand, I say:

``The light bulb is moving at a speed 0.99c.
The light from the bulb is moving at a speed c.''

Two observers are moving at a speed 0.99c relative to each other. Each observer, using his own yardstick and clock, measures the speed of a particular beam of light to be the same. The only way the two observers to observe the same speed for the beam of light, Einstein concluded, is for odd things to be happening to the yardsticks and clocks with which they measure the speed of light.

Whose clock is correct? **Both** are correct. THERE
IS NO SUCH THING AS ABSOLUTE TIME. The rate at which time flows
is different for different observers.

Whose yardstick is correct? **Both** are correct.
THERE IS NO SUCH THING AS ABSOLUTE SPACE. The distance between
two points is different for different observers.

Please note that the relativistic effects mentioned above (time dilation and length contraction) are all very small unless the relative speed is close to the speed of light.

Suppose you accelerate an object by applying a constant force to it. As the speed of the object approaches the speed of light,

- its length (as measured by you) approaches zero
- the time between ticks of its clock (as measured by you) approaches infinity
- its acceleration (as measured by you) approaches zero
- and thus its mass (defined as force/acceleration) approaches infinity.

An insight of Einstein:

E = m c^{2}

Where E is energy, m is mass, and c is the speed of light. Since
the speed of light is large, a small amount of mass can
be converted to a large amount of energy.
One kilogram of matter is equivalent to 10^{17} joules,
or 25 billion kilowatt-hours.

Further insight of Einstein:

Prof. Barbara Ryden (ryden@astronomy.ohio-state.edu)

Updated: 2003 Feb 10

Copyright © 2003, Barbara Ryden