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Why We Can't Travel the Speed of Light

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I spent a decent amount of time browsing the internet for an answer on why we can't travel the speed of light, and have found many different answers contradicting each other. I'll try my best to explain them.

The first explanation I saw began with a reminder of equations: How force is proportional mass. In order to travel faster, you must accelerate an object in order to obtain a higher velocity. The main issue begins when the video I was watching started to explain that the faster you move, the more mass you have. This naturally went right over my head, but continued to explain how since the mass increases, the amount of force required to accelerate an object also increases. When scaled to nearing the speed of light, the amount of force required grows exponentially, essentially becoming infinite. This is just like an old problem: Somebody is standing a set distance from a wall, and moves toward the wall. Every time he moves, however, he can only move half of the distance to the wall. He will never reach the wall, but will get infinitely close to it, just like how an object can never reach the speed of light, but can get infinitely close to it.

The second explanation I saw was a roller coaster. I started to watch a video that began with somebody explaining some simple physics while in front of a chalkboard. Then, out of nowhere, they disappeared, and started displaying calming pictures with a new narrator with a soothing voice. It seemed strange at first, but I kept listening until I realized what they were trying to do: They tried to convince me that the reason we can never obtain the speed of light is because we're in a simulation. Naturally, I stopped to watch a different video.

The third explanation I saw was one I had never seen before, but was still interesting. They started by reminding us of simple 2-Dimensional motion. There's an x-axis, and a y-axis. If an object is moving along the x-axis, it is moving its entire velocity along the x-axis with no velocity along the y-axis, and vice versa. If that object is moving diagonal, however, it has a component on both the x-axis, and the y-axis. Then, he brought Relativity into play. He explained that in reality, every object in the universe is moving at the speed of light, just not along our traditional axis. He put space along the x-axis, and time along the y-axis, saying that we travel the speed of light through spacetime. If we're traveling vertically in this instance, then we travel through time at the speed of light, but not through space. In our eyes, we would be at rest. On the other hand, if we are traveling diagonally, we are traveling through both space and time, but both components at a slower rate than the speed of light. So if travelling through time at the speed of light is how we usually perceive time, then that means that the faster we travel, the slower we travel through time. This especially interests me because of an experiment where three atomic clocks were synchronized. One was kept stationary on the Earth's surface, and the other were flown around the Earth in planes in different directions. After two full revolutions around the Earth, the clocks were no longer synchronized, and supported relativity. Another thing that interests me with this theory is that it actually seems plausible to travel the speed of light through space, but it would have no component in time. This essentially means that you can travel the speed of light as long as you aren't travelling through time. Would that mean that you aren't travelling since displacement is proportional to time? Or would this mean that you would essentially teleport? Could you control it? Most importantly, how do I get my brain to stop hurting from all of this?

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