Farewell to Reality (15 page)

Einstein was also something of a rebel, ready and willing to challenge prevailing opinions. He was at this time completely unknown to the academic establishment, and could therefore publish his outrageous ideas without fear of putting his (non-existent) academic reputation at risk.

In shaping his special theory of relativity, Einstein established two fundamental principles. The first, which became known as the principle of relativity, asserts that observers who find themselves in states of relative motion at different (but constant) speeds
must
observe precisely the same fundamental laws of physics.

This seems perfectly reasonable. For example, if an observer on earth makes a measurement to test Maxwell's equations and compares the result with that of another observer making the same measurement on board a distant spaceship moving away from the earth at high speed, then the conclusions from both sets of observations must be the same. There cannot be one set of Maxwell's equations for one observer and another set for space travellers.

We can turn this on its head. If the laws of physics are the same for all observers, then there is no measurement we can make which will tell us which observer is moving relative to the other. To all intents and purposes, the observer in the spaceship may actually be stationary, and it is the observer on earth who is moving away at high speed. We cannot tell the difference through physics.

The second of Einstein's principles concerns the speed of light. At the time he was working on special relativity, all attempts to find experimental or observational evidence for the ether — the universal medium that was supposed to fill the universe and support light waves — had failed. The most widely known of these attempts was conducted by American physicists Albert Michelson and Edward Morley. In 1887, they had made use of light interference effects in a device called an interferometer to search for small differences in the speed of light due to changes in the orientation of the earth relative to the ether, which was assumed to be stationary (and therefore absolute).

As the earth rotates on its axis and moves around the sun, a stationary ether would be expected to flow over and around it, creating an ‘ether wind' that would change direction with the time of day and the season. Light travelling in the direction of such an ether wind could be expected to be carried along a little faster, just as sound waves travel faster in a high wind. Light travelling against the ether wind could be expected to be carried a little more slowly. As Michelson and Morley rotated their interferometer through 360°, the changing orientation in relation to the ether wind would then be expected to manifest itself as a change in the measured speed of light. Any such differences in speed would be detected through subtle shifts in the observed interference fringes.

No differences could be detected. Within the accuracy of the measurements, the speed of light was found to be constant.

It seemed that the ether didn't exist after all. What's more, physicists had no choice but to conclude that the speed of light appears to be completely independent of the speed of the light source. If we measure the speed of the light emitted by a flashlight held stationary on earth,
³
then measure it again using the same flashlight on board a spaceship moving at high speed, we expect to get precisely the same answer.

Einstein concluded that he didn't need an ether. In his 1905 paper on special relativity he wrote: ‘The introduction of a “light ether” will prove to be superfluous, inasmuch as the view to be developed here will not require a “space at absolute rest” endowed with special properties …'
⁴

In a bold move touched by genius, he now elevated the constancy of the speed of light to the status of a fundamental principle. Instead of trying to figure out
why
the speed of light is independent of the speed of its source, he simply accepted this as an established fact. He assumed the speed of light to be a universal constant and proceeded to work out the consequences.

One immediate consequence is that there can be no such thing as absolute time.

Suppose you observe a remarkable occurrence. During a heavy thunderstorm, you see two bolts of lightning strike the ground simultaneously, at points you label A (a certain distance to your left) and B (to your right).

A passenger on a high-speed train also observes the lightning. From your perspective, the train is moving from left to right, passing first
point A and then point B. The lightning bolts strike as the passenger is passing through the midpoint of the distance between A and B.

The train is travelling
very
fast, at 100,000 miles per second, or about 54 per cent of the speed of light.
^*
What does the passenger see?

Let's further suppose that the vantage point of the passenger at the midpoint between A and B is half a mile from both points. It will take about three millionths of a second for the light from the lightning flash at point B to cover this distance. But in that time the train has moved about a third of a mile to the right,
towards
point B. The light from the lightning bolt at point A now has a little further to travel before it reaches the passenger, and because the speed of light is constant, this takes a little longer. Consequently, the passenger sees the lightning strike at point B before she sees it strike at point A.

Because the speed of light is fixed, you and the passenger have different experiences. You perceive the lightning strikes to be simultaneous. The moving passenger sees the lightning strike point B first, then point A. Are the strikes actually simultaneous or not? Who is right?

You are both right. The principle of relativity demands that the laws of physics must be the same irrespective of the relative motion of the observer, and you cannot use physics to tell whether it is you or the passenger who is in motion.

We are left to conclude that there is no such thing as absolute simultaneity — events perceived to be simultaneous by you are not perceived to be simultaneous by the passenger. And as our very understanding of time is itself based on the notion of simultaneity between events, there can be no ‘real' or absolute time. Something's got to give. You and the passenger perceive events differently because time is relative.

The dilation of time

Okay, so perhaps there's no such thing as absolute simultaneity and therefore no such thing as absolute time. But so what? All this business
with lightning flashes and speeding trains just means that different observers moving at different relative speeds
perceive
things differently. It doesn't mean that time is
actually
different. Does it?

Let's imagine that the passenger has set up a little experiment to measure the speed of light on board the train. A small light-emitting diode (LED) is fixed to the floor of the carriage. This flashes once, and the light is reflected from a small mirror on the ceiling, directly overhead. The reflected light is detected by a small photodiode placed on the floor alongside the LED. Both LED and photodiode are connected to an electronic box of tricks that allows the passenger to measure the time interval between the flash and its detection. The height of the carriage is accurately and precisely known. From the distance travelled and the time it takes, the passenger can calculate the speed of the light.

For the sake of argument, let's assume that the height of the carriage is 12 feet, and the passenger carries out her first experiment when the train is stationary. The light makes a round trip of 24 feet (0.0045 miles) from floor to ceiling and back again. The passenger determines that this takes about 24.1 billionths of a second. The round-trip distance divided by the time taken gives a speed of light of 186,722 miles per second. Not a bad estimate.

The train then accelerates to a constant speed of 100,000 miles per second. Now, from your perspective as a stationary observer watching from the platform, the light from the LED doesn't travel vertically up and down. In the time it takes for the light to travel upwards towards the ceiling, the train has moved forward. It continues to move forward as the light travels back down to the floor. From your perspective, the light path looks like a ‘Λ', a Greek capital lambda.

You therefore judge that the light now has further to travel, and the round trip takes longer. This could be compensated if the light were to move a little faster, covering the longer distance in the same time. But Einstein says that the speed of light is a constant, independent of the speed of its source. So, we use Pythagoras' theorem to work out that it now takes 28.6 billionths of a second for the light to make its round trip from floor to ceiling and back.
⁵

As far as the passenger is concerned, nothing has changed. How is this possible? There is only one conclusion. From your perspective as a stationary observer,
time slows down on the moving train.
This is not like
some optical illusion created by looking at identical figures against a changing perspective. The difference is not apparent, it is real. Muons in cosmic rays move at 99 per cent of light speed and decay five times more slowly than slow-moving muons created in the laboratory. When we put an atomic clock on board an aircraft and fly it from London to Washington DC and back, it loses 16 billionths of a second due to relativistic time dilation compared to an identical stationary atomic clock left behind at the UK's National Physical Laboratory.
⁶

Those looking for a more practical application of special relativity need look no further than the Global Positioning System (GPS), used to navigate from place to place on land, sea and through the air. The GPS receiver in your smartphone or car navigation system uses signals from a network of orbiting satellites to triangulate and pinpoint your position to within a range of five to ten metres in a matter of seconds. Atomic clocks on board each satellite keep time to within 20—30 billionths of a second.

The satellites travel around their orbits at speeds of the order of 14,000 kilometres per hour. Relativistic time dilation causes the atomic clocks to run slow when compared with stationary clocks on earth: they lose about seven thousandths of a second each day. If this effect were not anticipated and corrected, the error in position would accumulate at the rate of a couple of
kilometres
per day! A bit of a problem if you're trying to find the location of your next meeting or a good restaurant.
⁷

The contraction of length

What about space?

Let's now measure the length of the train. That's easy. Whilst it is stationary we calculate its length using the standard metre, made of platinum and iridium, which we borrow from the International Bureau of Weights and Measures in Sèvres, France. We find that the train is half a mile long.

But what if we now want to measure the length of the train as it moves along the track at a speed of 100,000 miles per second? We could try running alongside it with the standard metre, but this seems a bit impractical. Instead we ask our passenger to set up a different experiment. She now places the LED and photodiode detector at the
back of the train and the mirror at the front. The LED flashes, light travels the length of the train and is reflected back by the mirror. She measures the time it takes to make one complete round trip, multiplies this by the speed of light and thus calculates the length of the train.

Our passenger first checks that everything is in order by doing the experiment on the train as it sits, stationary, by the platform. While you're busy running along the outside with the standard metre, she's discovering that the total round-trip time for the light flash is about 5.4 millionths of a second. This is consistent with a total round-trip distance of one mile, which means that the train is half a mile long. Perfect.

Now she performs the experiment on the moving train. She finds nothing untoward. Once again, however, from your perspective as a stationary observer, you see something rather different. As the light travels from the LED to the front of the train, the train is moving forward. The light therefore has to travel a distance that is a little longer than the actual length of the train. This extra distance is the distance covered by the train in the time it takes for the light from the LED to reach the mirror, given by the speed of the train multiplied by the time taken.

As the light reflected from the mirror travels back down the train, the back of the train is also moving forward, so the light travels a distance that is a little shorter than the actual length of the train. This foreshortening is given by the distance covered by the train in the time it takes for the light from the mirror to reach the photodiode. This is again calculated by the speed of the train multiplied by the time taken.

Okay, so we relax. The extra distance that the light has to travel on its way to the mirror is compensated by the shorter distance it travels on its way back. But, I'm sure you won't be surprised to learn, it doesn't quite work out that way. When we do the maths, we discover that the length of the moving train as judged by a stationary observer is now
shorter
than the length of the stationary train. The length of the moving train contracts by about 16 per cent, to something like 0.42 miles.
⁸

This contraction in the lengths of objects in the direction of their motion is often called the Lorentz—FitzGerald contraction, named for Dutch physicist Hendrik Lorentz and Irish physicist George FitzGerald. They had both argued that the negative results of the Michelson—Morley experiment could be explained if the interferometer were physically contracting along its length in response to pressure from the ether wind,
by an amount that precisely compensates the change in the speed of light, such that the speed of light is always measured to be constant.

Einstein's special theory of relativity makes the contraction no less physical. But instead of the object's atoms or molecules getting pushed closer together by the ether wind acting on the object in absolute space, it is instead
relative
space — the relative distance between objects as judged by a stationary observer — that is contracting.