Topic 5

Topic 5 – Relativity

In the exam you are expected to:

Describe the Principle of the Michelson-Morley interferometer;
Outline the experiment as a means of detecting absolute motion;
Describe significance of the failure to detect absolute motion;
Describe the invariance of the speed of light;

Basic Relativity

When we measure movement, we do so against a fixed reference point. A car travelling at 30 m/s is moving at 30 m/s relative to the road. Suppose we have two cars, A travelling at 30 m/s and B travelling at 20 m/s.

Relative to B, car A is travelling 10 m/s faster, i.e. +10 m/s;
Relative to A, car B is travelling 10 m/s slower, i.e. –10 m/s.

We can use any of these frames of reference:

The road;
Car A;
Car B.

Another example is an aeroplane flying at 90^o to the wind:

The plane is heading due North at 75 m/s and the wind is blowing from West to East at 15 m/s. We can easily work out the resultant velocity to be 76.5 m/s.

There can be three frames of reference on the ground:

The speed is 75 m/s heading due North;
Or 15 m/s due East
Or a resultant velocity of 76.5 m/s at 11.5^o east of north.

The question that bothered physicists was whether there was an absolute fixed point relative to which all speeds could be measured.

A Boat Race

Both boats, X and Y have a speed of 5 m/s. Boat X has to cross the river from A to B and back to A, while Boat Y has to travel from A to C and back again.

Question 1

(a) What is the velocity of X relative to the river bed (Use a vector diagram)?

(b) What is the time for X to travel from A to B to A?

(d) What is the velocity of the boat Y going from C to A and its time?

(e) Which boat wins and by how much?

ANSWER

Inertial Frame of Reference

Question 2 Write down Newton’s First Law of Motion. ANSWER

An inertial frame of reference is one in which Newton I is valid. If you are in a train travelling at constant speed, all objects behave as if they were stationary in the stationary train. The train is travelling at 60 m/s, the passengers and their luggage are all travelling at 60 m/s.

Suppose now that you are in an aeroplane. Against all airline regulations, there is a drinks trolley free (not secured) in the central aisle. The aeroplane accelerates down the runway. From within the plane the trolley appears to accelerate towards the black of the plane.

From the ground, the trolley obeys Newton I since there is zero force acting on it, hence zero movement.
From within the plane, an accelerating frame of reference, the trolley appears to accelerate, which is not consistent with Newton I.

Question 3 Why is it not consistent with Newton I? ANSWER

Now consider this situation. A person is standing at the centre of a roundabout. He has a gun. A target is placed outside the roundabout as shown

When the roundabout is stationary, it is easy to see that the path of the bullet is straight. What about when the roundabout is turning?

For an observer on the ground the path of the bullet will be a straight line. For the person on the roundabout, the path will appear curved.

Question 4 Why is this not consistent with Newton I? ANSWER

Question 5 What kind of frame of reference is the roundabout? Explain your answer.

ANSWER

The Michelson-Morley Experiment

In order to explain wave phenomena such as light waves, the late nineteenth century physicists depended on a medium called ether. (It is nothing to do with diethyl ether, an explosively flammable compound used in organic chemistry.) Ether was a mass-less and non-viscous material that was needed to carry waves. Ether is used nowadays as a poetical word to describe radio-broadcasting.

If ether permeated the whole of space, then it would provide a perfect frame of reference to determine absolute motion. The experiment was carried out by Albert Abraham Michelson (1852 – 1931) and Edward Williams Morley (1838 – 1923). Their idea was to measure the speed of light parallel to the Earth’s motion with the speed of light perpendicular to it. It would be rather like the boat race example we saw above.

They used the physics of optical interference in a set up like this:

Light is split into two perpendicular beams.
They travel to the mirrors and superpose as they return to give interference fringes.
If the distance between the half-silvered mirror and m1 is the same as the distance between the half silvered mirror and m2, the time taken would be different.
This would indicate a shift in the expected interference pattern.
The experiment was repeated with the equipment set at 90^o to the orientation of the first experiment, so that the motion in the ether would be observed in two different directions.
It was repeated at different times of the year in case the sun at one point or another was moving in the same frame of reference.

The results were the most important null (nothing) result of the time:

There was no difference in the speed of light whichever way the experiment was done, or whatever the time of year;
There was no absolute reference point;
There was no such thing as ether.

Although the Earth orbits about the Sun, and is technically an accelerating frame of reference, we can generally treat it as an inertial frame of reference.

The measurement of the speed of light foxed the early physicists. Galileo tried it, but his results were inconclusive.

Question 6 Why was it so hard to measure the speed of light? ANSWER

In 1926 Michelson gave the first accurate measurement of the speed of light using a system of concave mirrors and a rotating octagonal mirror. He established that the speed of light is 299 792 458 m/s. The quoted figure of 3.0 ´ 10⁸ m/s is quite good enough for most purposes.

In a school physics lab it is possible to get a reasonable estimate of the speed of light by sending a pulse up a length of fibre optic cable to a receiver. The transmitted and received pulses are displayed on a CRO. The time period between the pulses is measured, and the length of the fibre optic cable is measured, so it’s possible to measure the speed.

Question 7 Would this give the speed of light quoted above? ANSWER

Summary

Objects move relative to a frame of reference

In an inertial frame of reference, Newton I is obeyed.

In an accelerating frame of reference Newton I is not obeyed.

There is no absolute frame of reference.

Light travels at 3.0 ´ 10⁸ m/s in a vacuum.

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