The fascinating story of the ultimate cosmic law
Where does the speed of light come from and why is it so tenacious?
NASA, ESA, CXC, SSC
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If you’ve taken a college-level physics course, you’ll have “good” memories of being asked to measure the speed of light and—if, over several hours, you could get your mirrors, lenses, and light source perfectly aligned—getting an answer of just under 300 million meters per second. This is a fundamental constant of physics, which is crucial to understand if you want to learn anything about the universe.
When we look at the cosmos, light is our only resource – well, not quite the only one, but gravitational waves are pretty limited in what they can show us at the moment, so forgive the slight exaggeration. Virtually all advances in astronomy and cosmology rely on the collection of light that has traveled millions or billions of years from the edge of reality. Even light from the closest star to our solar system traveled more than four years to reach us. The time it takes for light to travel is perhaps one of the most useful – and least intuitive – aspects of physics.
People have been arguing about the speed of light since before we had any idea what light actually is. For centuries, many of the brightest minds thought that light was actually emitted from your eyes like a kind of lantern, partly because of the way some animals’ eyes glow at certain angles in the dark. Despite this, they still argued about whether light was transmitted instantly or took time to propagate, and this was not properly tested until the 17th century.
Early attempts to quantify it involved setting up a lantern some distance from an observer and measuring the time difference between when the lantern was opened and when the observer saw its light. This didn’t work (Galileo and his contemporaries couldn’t get a conclusive measurement because the observers were too close to the lanterns), and scientists eventually opted for more complex and precise methods. The first one that actually worked was in 1675, when Ole Rømer was working to measure the orbital period of Jupiter’s moon Io. Rømer noticed that the period seemed to change as the distance between Earth and Jupiter changed over time, which made no sense: why would Io’s orbit have anything to do with Earth’s position? In fact, it only looks different because of the time it takes for light to travel from Io to Earth, which is shorter when the two are closer together. One of his colleagues, Christiaan Huygens, did the math and found that the speed of light was about 220,000,000 meters per second. It wasn’t entirely accurate, in part because we didn’t yet know the details of Earth’s movements, but it’s an approximation, and estimates improved as scientists developed more precise measurement techniques. Around the middle of the 18thth century, the measured values were within a few percent of the currently accepted figure of 299,792,458 meters per second for the speed of light in a vacuum.
This raises two questions: why is the speed of light such a random number, and why is there a speed limit? The first is easy to answer: it concerns our units, because meters and seconds (or miles and hours, or whatever other daily unit you want to use) were first defined in terms of human experience of the world – a mile was equivalent to a thousand steps, for example – which had nothing to do with fundamental constants. The second is more complicated and concerns special relativity.
We will find our answer in perhaps the most famous equation ever written: e=mc2. This has many implications, but at its lowest level it means that we can view energy and mass as interchangeable. When objects are moving at extraordinarily high, or relativistic, speeds, I like to think of them as simply having momentum, which is a combination of their mass and speed. If you want to speed up an object, you have to put more and more energy into it. A massive object moving at the speed of light would have infinite momentum, which you can think of as infinite energy or infinite mass. This is simply not possible: by the time the object approaches the speed of light, its mass would become so enormous that it would be impossible to accelerate it further. But light has no mass, so it easily avoids this problem.
Special relativity also means that a stationary outside observer would see something really wacky if they looked at this. When an object is moving at a relativistic speed, from the outside, time appears to slow down for that object. If I moved away from you at 99% the speed of light, you would see my aging slow down. This is called time dilation. The other part is called length contraction. If I walked away from you headfirst, Superman-style, you would also see me getting shorter and shorter as I accelerated. From my quick frame of reference, I wouldn’t feel time slowing down or myself shrinking, but from the outside, the closer I got to the speed of light, the smaller and more ageless I became.
This is a problem because if I ever reached the speed of light, an outside observer would see time stop completely for me when my size reached zero. I would disappear, with space-time traveling with me. Fortunately for me, the laws of physics don’t allow this. The only things that can reach this speed limit are massless: photons, gluons, the effects of gravity and that’s it. Nothing can travel faster through space-time.
Instead of being frustrated by this cosmic speed limit, we can rejoice, because the speed of light has a very important consequence: the very idea of consequences. All of physics, all of our understanding of everything, rests on a foundation of causality, the idea that effect always follows cause and never the other way around.
Think of it this way: as I approach the speed of light, you observe time slowing down for me. If I reached the speed of light, it would stop. And if I kept going even faster, it would start going in the opposite direction. By traveling faster than the speed of light, as observed from your frame of reference, I would move backward in time. If I sent you a signal that traveled faster than the speed of light, like some sort of physics-defying magical text message, you would receive it before I sent it. Without our universal speed limit, it would be impossible to tell which event caused which effect – everything about the universe would be almost incomprehensible.
This brings me to my final point, which I find both mind-blowing and fun to contemplate. If each signal takes time to propagate, and time moves differently in frames of reference that move at different speeds relative to each other, what does it mean for two events to occur “at the same time”? If I wink at myself in the mirror, the wink I see reflected actually happens just a tiny slice of time later than the wink I physically did, because the light had to bounce off my face, then off the mirror, then back to my eyes to perceive. If you say that two events happened at the same time in different places in space, I have to ask: “according to whom?” “. Depending on the distance between the two locations, it is possible that for one observer, event 1 happened first, and for another, event 2 preceded event 1. Objective simultaneity does not exist – no “same time” – and all because light has speed. Wild, right?
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