You board the CATA bus and it pulls away immediately as you walk towards the back to take a seat. The bus is moving at 25 mph as you walk at about 3 mph. Your speed relative to someone standing outside of the bus is only 22 mph. As your stop approaches you get out of your seat to move to the front. Now your speed relative to someone watching from the sidewalk is 28 mph since your walking speed of 3 mph is added to the bus’s 25 mph. Now instead of a CATA bus, let’s imagine that you are on a spacecraft that can travel at speeds approaching the speed of light.
Since most of us hate the metric system, we’ll stick with English units. The speed of light is 670 616 629 miles per hour. Since it is impossible to travel exactly that fast (you can travel 99.999% that speed but never reach it according to Einstein), we’ll be traveling on our spacecraft at only a couple miles per hour slower, 670 616 620 miles per hour. Now, since intergalactic travel is long and boring, the spacecraft has a gym, basketball court, and track for you to stay in shape. At the end of another uneventful day, you decide to go work out. Sprints seem like they’d be fun. You head to the track and do your sprints. You’re a pretty good sprinter so you peak at 14 miles per hour. All of this seems practical until you analyze the system from outside of the ship, as we did with the CATA bus. If you are sprinting in the direction opposite of the spacecraft’s motion, your relative speed is then 670 616 606 mph, which poses no problem. It is when you turn around and sprint back that everything falls apart. Adding the speed of the ship to your sprinting speed, you would be moving, relative to a stationary point outside of the ship, at 670 616 634 miles per hour…five miles per hours over the speed of light.
The speed of light is the intergalactic speed limit, so obviously something is terribly wrong with the above situation (other than the fact that you’re doing sprints on an intergalactic spacecraft moving at nearly the speed of light). The reason that you would not break the speed of light is because of time. Time is relative, as Einstein so brilliantly theorized. This means that time depends on those experiencing it. This is a very confusing topic but I’ll try to put it in perspective.
Everyone experiences time in the same way. As you are traveling through space close to the speed of light, time goes by as usual. A day feels like a day, a year like a year. While you’re on your trip, I am still back on Earth, where time carries on as usual. Everyday feels the same, every year the same as well. It is not until your return that we learn how time has changed between the two of us. Your trip was only a year long for you, but you find that decades have passed here on Earth while you were gone. This is because time slows down as you approach the speed of light, and it is because of this dilation of time that you do not break the intergalactic speed limit. While, from your perspective, you are sprinting at 14 mph, time is actually traveling a thousand times faster than it seems to you. The sprints only take a couple seconds from your perspective, but, from the perspective of time here on Earth, it takes you days to do one sprint; you may think that you are fast, but to us it would barely look like you’re even moving. It is this time compensation that prevents you from breaking the speed of light.
But does this make intergalactic travel impossible. Even if we could build such a spacecraft, even if it traveled at speeds hundreds of thousands of miles per hour less than the speed of light (still unfathomably fast), time would mess everything up. A trip to the nearby stars or even the center of the Milky Way would definitely be plausible with this kind of ship. Astronauts would reach the center of the galaxy in twenty some years – in their time. Upon returning to Earth after their 50 year round trip, somewhere in the tens of thousands of years would have passed on Earth. In the future, we may be able to develop ways to overcome the difficulties of building spacecraft to travel at the breakneck speeds approaching the speed of light, but we may never overcome the universe’s laws of time.