The tragedy of the question: “what if we could go faster than light?”
There’s nothing tragic about approaching the speed of light. There is, on the other hand, something tragic about the human mind, which is repeatedly compelled to ask naive questions of this form: Why does everybody, especially scientists, assume there is a cosmic speed limit and something unfathomably tragic will occur if a speed faster than that of light is achieved?.
The way the human mind works, we ordinarily only perceive and understand the world around us in terms of linear responses to sensations. We expect, through our considerable experiences and the programming of our neural networks, that if one of something is good, and two of something is better, that three of something might be as “better-er” as the difference between one and two of something. Or, we might understand that four of something is twice as good as two of something relative to how much “better-er” two of something is from one. These are all deeply “linear” responses- they deal with simple functions of addition and multiplication. Up until the past 100 years, the vast majority of humanity was utterly illiterate with regard to mathematics beyond simple linear functions, and that’s baked into a whole series of unfortunate occurrences.
For example, energy isn’t linear with velocity: kinetic energy rises with the square of velocity. So although you might be able to run perhaps ten miles an hour, and you might ordinarily understand that a collision at 10 miles per hour might hurt a lot, your brain isn’t capable of scaling up the difference between five and ten miles an hour to 10x or 100x. The energy involved in collisions as you go faster grows with the square of the velocity, so as you begin to go at faster velocities, 20, 40, 60, 80, 100 miles per hour, as we have begun to do only in the last 200 years or so, you begin to experience a scale of energy that isn’t in the million or so years of reptile-brain experience baked into our genes and our histories. The human mind begins to abstract it, and (in some cases) people begin to put increasingly outsized adjectives that don’t scale properly with the occurrences at those higher velocities.
When you need to go “one mile an hour” faster, as you go to higher and higher velocities the amount of energy needed to go that “one mile an hour faster” begins to grow, because you need to overcome inertia.
For example, the inertia at 100 miles per hour (44 meters per second) for a one-kilogram object is 0.968 kilojoules of energy. To go about one mile an hour faster, say 44.5 meters per second, you need to expend and additional 22 joules: the inertia at 44.5 m/s is 0.9 kJ.
Now, let’s compare that with 1000 miles per hour, say 440 meters per second. The inertia at that speed is 96.8 kilojoules. But to go one mile an hour quicker, to 440.5 meters per second, you must expend an additional 220 joules: the inertia at that 440.5m/s is 97.02 kJ.
At lower rates of speed, the power-law nature of this growth isn’t very obvious, particularly when there’s a lot of factors like friction, or efficiency, or how the gears in your engine are ratioed, but as you go to increasing levels of speed the effort to go even just a little bit faster, like as if you imagine a mile an hour might be “just a little bit”, becomes something that begins to scale outside of ordinary human experience.
Now, that’s just plain inertia, something that’s been around and well understood for centuries. We’re talking about relativity, and that adds an additional term which makes that “square power” even more dramatic. As you get closer and closer to the speed of light, the apparent mass of the body you are trying to push to a greater velocity begins to change. The speed of light is 299.8 million meters per second, where the apparent mass of anything goes to infinity. But let’s scale it back to about a tenth of that speed, say 44 million meter per second (inertia is now 9.839 x 10¹¹ kJ) and that tiny difference of “one mile an hour” now grows to somewhere around 2.22 x 10⁴ kJ: about 22.2 million joules in order to go “one mile an hour faster” when you’re travelling at 44 million meters per second, a tenth of the speed of light, an action that only took 22 joules at 100 miles an hour, and 220 joules at 1000 miles an hour. Relativity, at a tenth of the speed of light, is only beginning to take hold (a mere 1%), and yet the power differences to make that one tiny change are becoming “astronomical” in size.
Let’s push it even further: at 299.5 million meters per second, you are getting very close to the speed of light. At this point, the inertia is 1.95 x 10¹⁵ kilojoules. If you go one mile an hour faster, a mere 299.5000005 million meters per second, you need an additional 3.4 billion joules of energy to increase your velocity that merest one mile an hour additional. And again, that’s for an object merely 1 kilogram in mass: multiply that by millions of kilograms for a spaceship payload, and you begin to understand the scale of energy consumption required as you approach light speed.
There’s no big calamity when you get to the speed of light- you can’t get there. Every way we know how to go faster, every possible way to make something go faster, requires us to use a little bit more energy to push it to overcome its inertia. What we know from playing with extremely small amounts of matter, individual electrons or nuclei of atoms, things that don’t weigh a kilogram but weigh many millions of times less, is that these experimental observations hold true- when we try to accelerate an electron to one-tenth the speed of light, it takes not only as much as the calculations say, but even more energy. That their apparent mass doesn’t stay the same, but is an ever increasing factor that is scaled by one over the square root of the fraction of the velocity relative to the speed of light squared.
At some point, the energy required to go even just a tiny bit faster exceeds all the energy in the available known universe.
That’s why it’s a “speed limit”. It’s nothing like that sign on the side of the road, that says, “speed limit”. At a mere 100 miles per hour, it requires no more than a flick of your foot to exceed despite increasingly calamitous consequences associated with collisions as you begin to increase that speed. That’s what our “human scale” says, and yet we still routinely ignore speed limits as if they’re just a “roadside sign”, a mere hint or suggestion. But in reality, at light speed, you can’t press that accelerator any harder. The energies involved are off the scale of human, or indeed any, experience. There’s no calamity to be expected at light speed- the calamitous misuse of energy occurs at speeds well under that of light speed, speeds thousands of times smaller and before you ever reach the realm of relativity.
In order to go “faster than light”, you must first develop a method of going faster that doesn’t require as much energy as you would need to overcome inertia. You must find a way of getting to the going 100 miles per hour from 0 miles per hour that doesn’t first require you to go 50 miles per hour, or 10 miles per hour, at some point in that journey that you happened to go 100 miles per hour. Both of these things are impossibilities and have always been impossibilities since the dawn of time. They require instantaneous transportation without going through the intervening points, a possibility only hinted at in quantum mechanics and never observed in anything larger than an electron. Even for electrons, we don’t know how or why that happens, only that it can, for things electron-sized. While there may be physics which enables faster than light travel, none of this physics has ever been verified nor have there been any experiments that are even hopeful of such a physics. This is why it is a “speed limit”- there’s good reason to believe that all of the interesting physics challenges that remain- and there are a lot of them- are safely in the realm of sub-light physics.
There’s something about being told, “that’s impossible”, when we’re so used to miracles happening in science every day, that makes “impossible” seem like a cop out. Too often, though, “impossible” is a word used by people who aren’t qualified to understand what is or is not in the realm of possibility. While it is good to constantly question those limits, and explore the boundaries, it’s not as easy as a teenager just laying their foot a little more aggressively on a pedal. It’s hard work, and a bit more skepticism about the value of being ignorant of limits is warranted.
answer originally published on Quora: Why does everybody, especially scientists, assume there is a cosmic speed limit and something unfathomably tragic will occur if a speed faster than that of light is acheived?
matt harbowy is a scientist, activist, and data management expert. He is one of the founders of the non-profit Counter Culture Labs, working to bring fairness and egalitarian ideals to people interested in learning about science and biotechnology. He is also a top writer on the question and answer site, Quora.