Yesterday I received an email with a very interesting question about Einstein’s lightclock. Why do we assume that light in a moving lightclock travels a longer distance than in a clock that stands still? If we throw a ball into the air in a moving train, it falls down vertically, right? Why is that different for a clock? This is a great question! It helps us realise what it actually means to say that things happen in absolute space (as Newton believed).
Newton’s view
In Newton’s view, everything in the universe happens in absolute space, which means that if you could take away all matter and energy, you would be left with an empty volume – space exists independently from that which it contains. So, from Newton’s point of view, when a ball is thrown up and falls down again in a moving train, the ball seems to be moving vertically by someone sitting in the train, but through absolute space it moves along a parabola (as observed by someone who stands still with respect to the train).
The problem with Newton’s view is that motion through absolute space is not observable. Think again about the ball moving up and down in the moving train, and now imagine that we remove the train, its tracks, the platform it passes, and everything else – leaving only the ball moving up and down in a universe that is empty except for the ball. In this situation, there would be no difference beween a ball moving up and down and a ball moving both up and down and sideways. Why do we make a distinction between a ball that moves only up and down, and one that follows a parabola through absolute space?
[In the thought-experiment about the train we know that the ball actually follows a parabola, because that is what is seen by an observer on a platform seeing the train pass by, but of a particle in an otherwise empty universe we know nothing.]
Einstein
Einstein proposed a theory in which space is not absolute: in which there is no such thing as motion through absolute space – all motion is relative. In a universe in which there is only one particle, Einstein’s theory makes no distinction between the particle standing still and the particle moving at a constant speed. To illustrate what that means for our concepts of space and time, we look at Einstein’s thought-experiment about a lightclock (see figure), in which he compares two clocks: one that is moving with respect to an observer, and one that is not. Each clock consists of two horizontal mirrors between which a light-particle (photon) bounces up and down. The path in the clock that stands still is vertical (left in the figure), and so it is shorter than the path of the light in the moving clock (think Pythagoras).
The clocks are the same, so in both clocks the equation $$x=v \times t$$ should hold. In one of the clocks $x$ has a larger value, while the speed of light is the same in both clocks, so $t$ must also become larger: it must be the case that time intervals in a moving clock, as seen by an observer at rest, become larger – moving clocks slow down.
Answer
The answer to the question we began with is that there is no difference – time slows down in both trains and lightclocks. More generally, time in any moving reference system slows down as seen by observers at rest. However, the effect is very small if the moving reference system (like the train) moves relatively slowly compared to the speed of light.
For example, when you travel in a train moving at 120 kilometers per hour [33.3 m/s] you’d be travelling at approximately one ten-millionth of the speed of light), and your watch would slow down with something like $10^{-15}$ seconds per second compared with someone you left at the train station.
Einstein’s theory has some strange consequences. Read here about the twin paradox.
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