Space, Time and Einstein
J. B. Kennedy
PART I – Einstein’s revolution
Faster speeds, longer hours
Someone might mistakenly think that the constancy of the speed of light leads to contradictions, and therefore cannot be true. For example, suppose there are two rockets travelling through space in the same direction but at different speeds, and that there is a ray of light racing out ahead of them. Someone might think that light cannot travel 300,000 kilometres per second faster than each rocket, because the light beam would then have two speeds. But that would be a con- tradiction – light cannot have two different speeds. What is wrong with this reasoning?
Einstein was able to remove the appearance of contradiction by profoundly altering our view of time. To understand this, we must carefully reconsider what a contradiction would be. Plato and Aristotle were apparently the first to state what is, perhaps, the most fundamental idea in philosophy: The law of non-contradiction: Opposite properties do not belong to one and the same thing in the same respect and at the same time.
According to this law, a positive integer is never both even and odd. A newspaper can be “black and white and red all over”, but not “in the same respect”. It can be black here and white there and “read” throughout. It cannot be black and white at the same point since these colours are opposites. (Lukasiewicz calls this the “ontological” version of Aristotle’s law: it is about properties and things. Other versions of the law concern true sentences or psychological states like belief.) In a move of breathtaking audacity, Einstein reasoned that, since there were no real contradictions, and therefore a light beam cannot have two speeds in the same respect and at the same time, the two rockets above must have different times. That is, the rockets each measure the same relative speed for the light beam because time flows differently for each rocket.
A little story will help make this more concrete. Suppose that Jill is an astronaut flying overhead through the starry night. Jack is earth- bound and working in mission control, and it is his job to monitor Jill and her spaceship carefully through a large telescope. As Jill’s spaceship approaches the speed of light, Jack observes something marvellous. Jill and everything in the spaceship move in slow motion, like a film in the cinema shown at a slowed rate. The hands on Jill’s
wristwatch begin to crawl around the clock face. She seems to be wading through molasses. The half-hour programme she is watching on her television takes 45 minutes.
Jack is not surprised because Einstein predicted all this. As the rocket speeds up, its time flows more slowly than here on Earth. An hour on the rocket is longer than an hour on Earth. This is now called time dilation (to dilate is to become wider or longer), and there is a simple formula to predict how much Jill’s time will slow when her rocket has a particular speed (see Appendix C).
Reasoning from the constancy of the speed of light, Einstein concluded that there was no single, universal passage of time. Rather, the flow of time depends on speeds. Faster speeds mean longer hours.
Each body moving through space experiences the flow of time at a different rate.
This astonishing conclusion was confirmed by many experiments.
One experiment by Hafele and Keating in 1971 used very accurate atomic clocks, which were carried on around-the-world flights in Boeing jets. Although the jets flew much more slowly than the speed of light, there was still a measurable time dilation. The clocks were slightly behind other clocks that remained in the laboratory, just as Einstein’s theory predicted.
This can be tested at home. For example, time dilation can be used to delay getting the wrinkled hands that accompany ageing. If both hands are simply flapped up and down continuously at nearly the speed of light, they will remain young while the rest of your body ages.
Many studying relativity for the first time assume these effects are some kind of illusion that arise because of the way fast-moving objects are observed. That is, they believe that durations are really constant and merely appear to vary with speeds because they must be observed from far away. Some believe it is the lag time – the time it takes for light to travel from the object to the measurement device – that produces an illusion.
This is easy to refute, and cannot be correct. For example, when the travelling atomic clocks were returned to the laboratory bench, the slight discrepancy between them and stay-at- home clocks could be read off immediately. No fancy apparatus or fast-moving objects were involved. Indeed, human observers are unnecessary. A computer could have registered and printed out the difference. Similar examples of relativistic effects are widespread in the daily work of experimental physicists. Almost everyone in the present debate agrees that the effects cannot be simple illusions.
Likewise, some beginners mistakenly believe that time dilation is just a consequence of using different units of measurement. A measurement assigns a number to a distance or duration. A tennis court is 24 metres or 78 feet long; a tennis match may last 3 hours or 180 minutes. These numbers obviously depend on conventional units of measurement: on, say, whether metres or feet are used. When international organizations change the definitions of the units, the numbers assigned to bodies change too. But time dilation occurs even when everyone agrees on and uses the same units of measurement.
Jack and Jill compare their rulers and synchronize their watches before the spaceship leaves Earth. Even so, Jill’s watch will run more slowly relative to Jack’s when she increases her speed. In short, time dilation is a real effect, and is neither an illusion nor a difference in the choice of measurement units. The flow of time depends on speeds.
If two rockets flying at different speeds are chasing the same light beam, the light will indeed travel 300,000 kilometres per second faster than each of the ships. But there is no contradiction. The light beam has opposite properties but not “at the same time”; each ship has its own time.
Time dilation was inferred from the constancy of the speed of light and other assumptions in order to avoid contradictions, and was later confirmed by many experiments.