The Problem of Relativity

When Copernicus proposed that the Earth went around the Sun, it was a great challenge to physicists because they had to deal with the problem of relative motion.

What does it mean to say something is standing still when it is actually on the surface of a planet moving at great speed through space?

Is there any such thing as ABSOLUTE REST? Can we ever say we are REALLY not moving, or can we only say, we’re not moving RELATIVE to the Earth, though we are moving RELATIVE to the Moon, the Sun and the stars.

Absolute Space

Beginning with Galileo and ending with Newton it was realized that certain kinds of motion, especially INERTIAL MOTION, meaning constant speed motion in a straight line, are equivalent to being at rest. If you are moving with constant velocity there is no experiment you which will tell you that you are REALLY moving.

Of course you can always look at the window.

Also, if you go around a corner then you can feel a mysterious centrifugal force pushing on you.

For this reason Newton insisted that there was an ABSOLUTE SPACE which defined a state of being ABSOLUTELY AT REST. Therefore as we travel around the Sun, we think we are rest, but we are REALLY moving, with respect to invisible space.

Measuring the Speed of Light.

Early measurements of the speed of light were hampered by the lack of a sufficiently precise clock. The use of the telescope in astronomy permitted the first reasonable estimate of the speed, by timing the motions of the Moons of Jupiter at different times of the year. When the Earth is farther from the Sun it take light longer to reach us from Jupiter, so the Moons appear to be “late” in their motions. It is not that they are any later, but that the messenger is delayed as a result of the fact that we, the observers, are moving.

In the 19th Century much more accurate measurements of the speed of light became possible when people realized they could take advantage of the wave nature of light. Light is itself a kind of clock, because it has a very regular period or frequency. One can use interference to compare the time it takes two different light rays to travel two different paths. If you measure the path lengths very carefully then the light itself provides the clock by which to measure the time take, which gives you the speed.

This is the basis of the INTERFEROMETER, invented by the great American physicist Albert Michelson.

Absolute Rest and the Luminiferous Ether

By the end of the 19th Century physicists though they had a way of proving that the Earth was REALLY in motion, with respect to Newton’s Absolute Space.

If light is a wave it must have a medium. 19th century physicists called it the Luminiferous (“light-bearing”) Ether, because the Ether was the “fifth element” of the ancient Greeks which made up Space.

If the Earth is moving through the Ether, then there ought to be an “Ether Wind” which would cause light to move more slowly when it is directed “into the wind.” It ought to be possible to measure a small difference in the speed of light when it is moving in different directions (about the size of v/c, where v is the speed of the Earth’s motion through the ether).

Relative Motion and Light

Suppose Light was made up of particles, as Newton thought. If you shine a laser light from your spaceship towards another spaceship, and if your spaceship is moving towards the other spaceship at speed v, what speed does the pilot of the other spaceship think the light is moving at? What speed do you (in your spaceship) think it is moving at?

a) YOU: c OTHER PILOT: c

b) YOU: c - v OTHER PILOT: c + v

c) YOU: c OTHER PILOT: c + v

d) YOU: c - v OTHER PILOT: c

Correct Answer: C – So in this case you think the light is moving at the same speed it always does. You can’t do an experiment on your own laser light to discover that you are REALLY moving. Only the guy on the other spaceship can do that, but he only discovers how fast you are moving RELATIVE to him.

What if Light is Wave?

Imagine you are on ship and you drop a rock into the water. The ship is moving through the water with velocity v. The water is moving in a current with velocity w (relative to the land). The waves move through the water with velocity c. What speed do you see the wave moving at? What speed does a landlubber on the shore see the wave moving at?

a) YOU: c LANDLUBBER: c

b) YOU: c - v LANDLUBBER: c

c) YOU: c + w LANDLUBBER: c + v

d) YOU: c LANDLUBBER: c + w

e) YOU: c - v LANDLUBBER: c + w

Correct Answer – E

Notice that your answer depends on the velocity at which you are moving through the water. If you measure the speed of the waves, then you will know how fast you are moving through the water, even if you are out of sight of land. The landlubber also can measure how fast he is “moving” with respect to the water, since he measures the speed to be c + w.

So if light is a wave, and the luminiferous ether is the sea, then we ought to be able to measure how fast the Earth is moving through this sea just by measuring the Ether Wind. Then we could assume that the Ether is Absolutely at Rest and we could prove that the Earth (and maybe the whole solar system) is REALLY in motion.

No Such Luck

Unfortunately despite the best efforts of Michelson and others no one was able to measure any difference in the speed of light in any direction on Earth.

So is the Earth really Absolutely at Rest, as the ancients believed? Modern Physicists didn’t believe this could be true.

So maybe light really doesn’t behave like a wave in this respect? Maybe if light is emitted like a particle then it has a speed equal to its usual speed, c, plus the speed of the object which emitted it.

Einstein proposed a different idea, which at first sight seems to make no sense. EVERYONE who measures the speed of light, no matter how they are moving, gets the same answer, c.

Einstein’s Axioms

Einstein proposed two axioms which lay at the heart of his Special Theory of Relativity

1. You cannot do any experiment to distinguish between INERTIAL MOTION and REST

2. Every observer who measures the velocity of light finds it to be c

Einstein’s Theory

So if we go back to the previous problem, in which you shone a laser light at an oncoming spaceship, what does Einstein’s theory say you and the other pilot should measure the speed of light as?

a) YOU: c OTHER PILOT: c

b) YOU: c + v OTHER PILOT: c + v

c) YOU: c OTHER PILOT: c + v

d) YOU: c + v OTHER PILOT: c

Correct Answer: A

So you both think that the laser light moves with speed c. How can this be? Suppose the other spaceship flies by incredibly fast, at a speed of 9/10 c. Shouldn’t it see the light moving at a speed of 1/10 c?

Why can’t the two of us agree to use similar clocks and measuring sticks to measure the speed of the light. Won’t we agree that it covered a given distance in a given time and that since the other spacecraft covered the same distance in slightly less time their relative speeds are less than c?

Einstein realized that the answer to this paradox lies in the fact that you and the other pilot actually won’t agree on how fast his clock his running, or even how long his meter stick is!

Relativity of Simultaneity

a) Einstein asked himself, what do we mean by time? Which of the following is true, as Einstein would have it?

b) Time is a thing which is measured by clocks (if time didn’t exist, we wouldn’t have clocks)

c) Time is a thing which is produced by clocks (if clocks didn’t exist, we wouldn’t have time)

Correct Answer – B

To Einstein time is simply the order in which events happen. A clock is simply a device which produces events. When we say that “Dan started the lecture at 12:30pm” we mean that Dan started talking when the little hand on the clock pointed towards 12 and the big hand pointed towards 6. When we measure time what we are actually talking about is taking note of a series of “coincidences.” When we don’t have manmade clocks we use naturally occurring events such as sunrise and sunset.

So time is measured by observing Simultaneous Events.

What Einstein realized is that observers who are in motion relative to each other will disagree about which events are actually Simultaneous.

Suppose I drop a glass, which breaks just as the clock, which is 10m away, strikes 1 o’clock. Meanwhile, a pilot is flying by in a spaceship moving at 1/10 c. What will the pilot see?

Clock MeRocket

a) The glass gets broken just before 1 o’clock

b) The glass gets broken at 1 o’clock

c) The glass gets broken just after 1 o’clock

Correct Answer – A

If the pilot had been standing still, the light from the clock would reach him first (the clock is closer to him), but he would know enough to allow for the time required to reach him, and could adjust to get the time the light left from the clock and the glass. He would decide the two events happened simultaneously. But since he is moving, he first receives the light from the clock, and then moves a measurable distance towards the glass before that light reaches him. Since that light moves at c regardless of how he moves, it takes a little less time to reach him then it would have had he been standing still. The result that when he takes his clock measurement he thinks the glass broke just before 1 o’clock because the light arrived a little earlier then he expected.

History Reversed?

So in Einstein’s Relativity Theory IF nothing can travel faster then light, two people can disagree about the order in which events can happen. Why did no one ever notice this before?

Because the speed of light is so fast, we have always assumed that we can compare two events which happen in very different places and see which happened first. We can do this, but ONLY if the time between the two events is greater then the time it takes light to travel between them. As long as this is true then everyone agrees on the order in which the events happen. Since light takes tiny fractions of a second to cross the Earth it was only when we got extremely accurate clocks that we could begin to notice knowing when things happen depends on getting information about them from wherever they took place.

Wierdness of Time and Space

Einstein’s two simple axioms lead to the conclusions that how you are moving affects how you measure distances and times. If you try to measure a distance as you are moving across it, it actually seems shorter then it did before you started traveling! It will take less time to go there then you thought. On the other hand someone left behind will still see the distance as being the larger value, but they will be convinced that your clocks are running slow. But everything on your spaceship is a kind of clock, including your body. You will actually age more slowly than the person you left behind, as you go on your trip. But you will only notice the difference if you travel at an appreciable fraction of the speed of light.