Schrödinger's Cormorant

2.3 There’s Something Funny about the Speed of Light

Light in a vacuum always has the same velocity - even if the observer is moving relative to the source. Evidence from binary stars.

Now you’re playing a game with Nefertiti. She is riding on a merry-go-round, while you stand some distance away and watch. During each rotation she throws two sardines at you: one as the rotation is taking her away from you and the other as she’s coming round towards you again. You use your cool digital watch to measure how long it takes from the moment Nefertiti releases each fish to the moment it hits you. Here’s a diagram and a question:

Figure II-ii

Question 2-2

Nefertiti enjoys the sardine throwing and decides to turn it into a project. She muses that, if the merry-go-round rotated fast enough, she could exactly compensate the shorter flight time of the sardine whose velocity is boosted by the rotation with the time taken for a half-turn of the merry-go-round, so that two sardines, released from opposite sides of the merry-go-round, will hit you simultaneously.

Here's what Nefertiti has in mind:

She will first throw the blue fish, when the velocity relative to you will be most decreased by the clockwise rotation.

After half a turn she will throw the red fish; its velocity relative to you will be increased by the rotation. It will catch up with the blue one and strike you at the same moment.

Question 2-3

Boosted by this reinforcement of your understanding of the additivity of velocities, you all adjourn to the pub and Nefertiti muses that that you could repeat the experiment in the dark, with her flashing at you (with a torch, she clarifies hastily) instead of throwing a sardine. You would measure the time taken for the flash of light to reach you each time, confident now that the light would take longer when Nefertiti was moving away from you, just as it did with the fish. Even as you are disputing the (numerous) technical difficulties inherent in this experiment, one of the many long-dead Dutch cosmologists who haunt your pub introduces himself: “Goedenavond. Allow me to introduce myself: Willem de Sitter, at your service”. It turns out he was way ahead of you with this idea but being a cosmologist he thought of binary stars, rather than merry-go-rounds. The same principles ought to apply, though.

We can think of a binary star – in a very approximate way which will upset Sir Isaac, so don’t tell him - as one star moving around another in a circular orbit. By analogy with the merry-go-round, we would expect that light from the orbiting star should have a greater velocity when this star is moving towards you than when it is moving away. Because the star is a long way off, even a small velocity difference would have a significant effect on the time taken for the light to arrive at your retina as you gaze into the night sky. The consequence is that all kinds of weird effects are predicted – just one of which is explored in Question 2-4, below:

Question 2-4

Depending on the orbital period and the distance from Earth, other odd effects might be observed (multiple images, strange variations in apparent speed) but what Willem wants us to know is that, although hundreds of binary stars can be resolved with the help of telescopes, none of these things has ever actually been seen: binary stars always behave visually just as Sir Isaac - who knew all about orbiting things – would predict. So what does this mean? Well, according to the late mynheer it means that it is light that is weird: photons are not well modelled by sardines. Light always travels at the same velocity, regardless of the motion of its source relative to the observer, so that it always takes the same amount of time to reach the Earth, regardless of what the star that emits it is doing in its orbit.

Since Willem pointed this out in 1913, a lot of people have raised awkward questions about his evidence – for example, the effects of interactions with molecules encountered en route - but more recent experiments which avoid these difficulties by looking at x-ray images point to the same conclusion. This was a clever bit of thinking by the Dutchman – clever but not random. He did all this because in 1905 Albert Einstein had used the invariance of the speed of light as the key foundation of what we now call special relativity and Willem wanted to test the postulate. And why did Einstein come up with this idea? Because odd though it is, it is inherent in James Clerk Maxwell’s equations which successfully describe electromagnetism. Einstein was a big fan of Maxwell and he wanted to heal what he saw as a rift between Maxwell’s electromagnetism and Newton’s mechanics. So we have a key point to take on board:

The speed of light is always the same, regardless of how its point of origin may be moving relative to its observer.

(Note that, by this, we mean the speed of light in a vacuum: flirting with molecules slows light down – which is what gives rise to refraction, for example – but that’s not our issue at the moment).

This is seriously counter-intuitive. Our everyday experience tells our brains: "that can't be right". But the thing is that our everyday experience doesn't include things moving at these incredibly high speeds. We are going to explore how Uncle Albert, with a little help from his friends, had to rewrite the laws that govern space and time, in order to accommodate this strangely invariant speed of light. The new physics that resulted from this is called the Special Theory of Relativity. Special relativity can sometimes seem like a strange and wonderful but possibly fictitious world – a mathematical Middle Earth – but every time that doubt starts to nag, you can call on Willem de Sitter to remind you: it’s real.

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