Where does the speed of light come from and why is it so stubborn?
NASA, ESA, CXC, SSC
The following is an excerpt from our newsletter, Lost in Spacetime. Every month we dive into fascinating ideas from across the universe. You can register for Lost in Spacetime here.
If you've taken a physics course at university level, you'll have “fond” memories of being asked to measure the speed of light and – if within a few hours you managed to get the mirrors, lenses and light source just right – getting an answer of just under 300 million meters per second. This is a fundamental constant in physics that is very important to understand if you want to know anything at all about the Universe.
When we look into space, light is our only resource – well, not exactly our only resource, but gravitational waves are pretty limited in what they can show us right now, so please forgive the slight exaggeration. Almost every breakthrough in astronomy and cosmology is based on the collection of light that has traveled millions or billions of years from the edges of reality. Even the light from the star closest to our solar system took more than four years to travel to us. The time it takes light to travel may be one of the most useful—and least intuitive—parts of physics.
People were arguing about the speed of light long before we had any idea what light actually was. Over the centuries, many of the brightest minds have thought that light actually shines from your eyes, like a kind of lantern, partly due to the way some animals' eyes glow in the dark at certain angles. Despite this, they still debated whether light was transmitted instantly or took time to travel, and this was not properly tested until the 17th century.
The earliest attempts at quantification involved placing a lantern at some distance from the observer and measuring the difference in time between the lantern being opened and the observer seeing its light. This did not work (Galileo and his contemporaries were unable to obtain conclusive measurements because the observers were too close to the lanterns), and eventually scientists moved on to more complex and accurate methods. The first one that actually worked came in 1675, when Ole Römer was working on measuring the orbital period of Jupiter's moon Io. Roemer noticed that the period seemed to change as the distance between Earth and Jupiter shifted over time, which didn't make sense at all – why should Io's orbit have anything to do with Earth's position? In fact, it only seemed different because of the time it takes light to travel from Io to Earth, which is shorter when they are closer together. One of his colleagues, Christiaan Huygens, carried out mathematical calculations and found that the speed of light is about 220,000,000 meters per second. This wasn't entirely true, partly because we didn't yet know the details of the Earth's motion, but it's about right, and estimates have gotten better as scientists have developed more precise measurement methods. By mid 18th 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 at all? The first is easy to answer: it has to do with our units of measurement, because meters and seconds (or miles and hours, or whatever everyday units you want to use) were first defined in terms of human experience of the world (a mile, for example, was a thousand steps), which had nothing to do with fundamental constants. The second is more complicated and is related to the special theory of relativity.
We will find the answer in perhaps the most famous equation ever written: e=mc.2. This has many implications, but at the most basic level it means that we can think of energy and mass as interchangeable concepts. When objects are moving at extremely high, or relativistic, speeds, I like to think of them simply as having momentum, which is a combination of their mass and speed. If you want to speed up an object, you will have to put more and more energy into it. A massive object moving at the speed of light will have infinite momentum, which can be thought of as infinite energy or infinite mass. This is simply impossible: by the time an object approaches the speed of light, its mass will be so enormous that further acceleration will become impossible. But light has no mass, so it easily avoids this problem.
Special relativity also means that an outside stationary observer would see something really strange when watching it. When an object moves at a relativistic speed, time appears to slow down for that object from the outside. If I were moving away from you at 99 percent the speed of light, you would see my aging slowing down. This is called time dilation. Another point is called length contraction: if I were flying away from you head first, Superman style, you would also see me getting shorter and shorter as I get faster. In my fast frame of reference I wouldn't feel time slowing down or being compressed, but on the outside, the closer I got to the speed of light, the shorter and ageless I became.
This is a problem because if I ever reached the speed of light, an outside observer would see that time stopped completely for me when my height reached zero. I will disappear with space-time traveling with me. Luckily for me, the laws of physics don't allow this. The only things that can reach this speed limit have no mass: photons, gluons, the effects of gravity, that's all. Nothing can travel through space-time faster.
Instead of being upset about this cosmic speed limit, we can rejoice because the speed of light has one very important consequence: the very idea of consequences. All of physics, our entire understanding of everything that exists is based on cause and effect, on the idea that the effect always follows the cause, and not vice versa.
Think of it this way: as I approach the speed of light, you watch time slow down for me. If I reached the speed of light, it would stop. And if I kept going even faster, he would start moving in the opposite direction. By traveling faster than the speed of light, as seen in your frame of reference, I would travel back in time. If I sent you a signal that traveled faster than the speed of light, like some magical text message that defies physics, you would have received it before I sent it. Without our universal speed limit, it would be impossible to tell which event caused which effect—everything in the universe would be virtually incomprehensible.
This brings me to my final point, which I find both mind-blowing and fun to think about. If every signal takes time to propagate, and time moves differently in reference frames that move at different speeds relative to each other, what does it mean for two events to occur “simultaneously”? If I wink at myself in the mirror, the wink I see in the reflection actually occurs only a small amount of time later than the wink I physically made, because the light had to bounce off my face, then off the mirror, and then back to my eyes to be perceived. If you say that two events in different places in space happened at the same time, I have to ask: “According to whom?” Depending on the distance between two points, it is possible that for one observer Event 1 will occur first, and for another, Event 2 will precede Event 1. There is no such thing as objective simultaneity – there is no such thing as “same time” – and this is because light has speed. Wild, right?
Topics:
