Why is the speed of light so special?
If you ask any well acclaimed physicist about what is the fastest speed you can travel at, they will happily answer the speed of light. The explanation for why one cannot go any faster than the speed of light is not simple however. It took the genius of Einstein to reformulate the meaning of space and time and thus establish this fundamental fact of nature.
Let’s break down this problem. According to our intuitive perception of nature, if we are in spaceship and we are going at a 100 kilometers per hour, unless something (or we ourselves) resists us, we will keep going at that speed. That’s just Newton’s First Law of Motion. Next we can claim, if we turn on our spaceship’s thrusters for a brief moment, we can probably get to 150 kilometers an hour. Correct! Building on to that argument, if we continue doing that (launching our thrusters), we can get near the speed of light, say 299,750 km/s — 42.5 km/s below the speed of light. All of this is allowed, given that there was enough fuel to start with. But the proposition is, no matter how much more fuel you have, you can never achieve that extra 42.5 km/s speed. Well you can say it’s just an additional speed of 42.5 km/s. The simple intuition that pushing something at slow speeds produces the same effect (in change of speed) as pushing something at high speeds, is flawed, and only becomes significant as we approach the speed of light. In other words, its very easy to get from 100 km/s to 101 km/s compared to getting from 299,750 km/s to 299,751 km/s. That’s relativity!
At the speed of 299,750 km/s, turning on the exhaust even for a very long time would not provide any significant increase in speed. Some people like to think that the spaceship gets heavy as it reaches higher and higher speed, and thus it takes more and more force (and energy) to add just a tiny speed. And very close to the speed of light, the amount of energy needed to get another bit close becomes almost infinity. Its like running a long-ass marathon. As you get closer and closer you, it requires much more effort to get even that extra-meter. However, unlike in a marathon, with nature you can never reach the finish line. Matter* will always see the speed of light as the mirage in a desert. You feel like you get closer and closer to it, and yet you can never catch it. Things like light themselves however know only one speed, the speed of light, they don’t go faster nor do they go slower*.
Most often the explanation ends here. But we go ahead and ask: Does the spaceship really get heavy? Does it really get hard because of an increased mass? The answer is actually no, but there is a catch. The spaceship actually does not get heavy, a constant in the equation of motions (called the gamma factor) gets significant at these speeds. This constant of motion whose value is very close to 1 for low speeds, suddenly becomes important enough that its effects are reflected in the fact that more and more energy is required to produce even tiny speed additions. Some people like to absorb the gamma factor in the mass itself to say that the mass of the spaceship itself increases. This argument does not really work because absorbing the gamma factor does not always remove it completely from the equations of motion. So physicists finally defined mass to be a constant. Turns out mass at the end of the day is just a definition!
*By matter we actually mean the hard stuff that has a non-zero mass.
*This case is for light in vacuum. In another medium, like glass, it travels with a different speed.
