Monday, 16 July 2018

And The Answer Is?

OK this is a great question, because it cuts right at the heart of what relativity really is, 

the important thing to understand about relativity is right in the name: it is relative. That is, for a massive object there is no such thing as having an objective, absolute speed that is agreed upon by all observers. A massive object cannot actually reach the speed of light, which will become apparent later on in this answer. But to roll with the question, let’s imagine a velocity that is just below the speed of light. So, if a spaceship is traveling past an observer (let’s say it’s moving past us on Earth) at nearly the speed of light, we see it moving by very fast. From the spaceship’s perspective, however, the ship is stationary. From the ship’s perspective, the Earth and the surrounding planets and stars are passing by the ship’s window at nearly the speed of light. That’s easy enough to visualize, but the following section is where things get weird, and you’ll see why it matters in a bit. The velocity of massive objects is relative to every observer, but the speed of light is always constant.

          From Earth, we see the high-beams shining from the spaceship moving at light speed, a number we refer to as c, as in E=mc^2, which happens to be 299,792,458 meters per second. Since the ship is moving at close to c relative to Earth, the high beams seem to us to be barely inching away from the ship—the ship is right on the light’s tail, so to speak. From the spaceship, they also understand that the light is beaming off into space ahead of them at the speed of light. Now here’s the counter-intuitive thing about the speed of light: remember that from the perspective of those on the ship, they are stationary and it is the surrounding universe that is passing by them through their window. So when they measure the speed of the light in their high-beams, the light isn’t barely inching away; it is also zooming off into the distance at c. They measure c in all directions as if they were stationary. In relativity, c stands for constant, because all observers witness it to be the same constant speed, no matter their own motion. No object with mass can reach or exceed c; light always seems to be moving towards you or away from you at c, in all directions.
            Next Lorenz contraction and time dilation, the nature of relativity was actually discovered based on this exact finding about the speed of light. Because the Earth is moving through space, scientists believed that light would seem to travel slower if they measured a beam pointed in the direction of the Earth’s movement (since Earth is chasing behind the light) as opposed to a beam shined perpendicular to the Earth’s movement. They ran an experiment and were amazed to find that light seemed to be going at exactly the same speed relative to their instruments, regardless of whether it was travelling along the Earth’s path or perpendicular to it. This was the famous inferometer experiment of 1897, and it was the finding that Albert Einstein eventually based his 1905 theory of special relativity on,  

        Now here’s where it applies to our question, because of this finding, in order for the wonky observations of various observers to be reconciled, two things must take place as the ship travels. One is Lorentz contraction: the ship seems squished, lengthwise, to the observer on Earth. If the people on the ship think the ship is 100 meters long, and the ship is moving about 99.5 percent of the speed of light, well, those of us on Earth see the ship as about 10 meters long (you can run the calculation for Lorentz contraction here). So the person on the ship thinks they’re running at 5 meters per second, but we on Earth would perceive them to be running at 0.5 meters per second—not accounting for time dilation, so of course the other component is time dilation. In addition to the discrepancy in distance, there is also a discrepancy in time. That is, the person on the ship runs from back to front in what they think is 20 seconds. To those of us on Earth, the people on the ship are moving in slow-motion, so we see the jogger taking 200 seconds to get from the back to the front of the ship (you can run the calculation for time dilation here), which compounds with the fact that the ship is only 10 meters long from our perspective. That means we on Earth see the runner travelling only 0.05 meters per second faster than the ship is traveling—not fast enough to close the gap and reach the speed of light. The effect of time dilation and Lorentz contraction increase as you go faster, approaching infinity at c, so they always overpower any attempt to reach c. 

         The observations are relative. Another really counter-intuitive aspect about relativity is that the observer on the ship has the exact same observations of us on Earth as we do about the person on the ship. Since the people on the ship think they’re stationary, they look at a Lorentz-contracted oval-shaped Earth that appears squished as it flies by them. The rest of the local universe is squished as well, with all the planets in oval-shaped orbits, and the stars in front of them seeming to be only 10 percent as distant (the stars on their left and right appear to be the same distance as they do to us on Earth). They also observe Earthlings moving in slow-motion.
An object with mass can never reach light speed. With all this in mind, it’s easier to see how reaching the speed of light is impossible. The more the people on the ship power their rockets and accelerate, the more they do accelerate—in the sense that the surrounding universe seems to contract more and more, making distances shorter and their progress through those distances increase dramatically. From the Earth, though, the ship appears to approach light speed (or c) more and more, but the closer they get to c, the more the ship’s length contacts and the less of a difference it makes when they try to accelerate. They will inevitably run out of fuel before they get to c. (The thrust of their rockets also appears to slow down as time slows. That’s not to be confused with their forward motion, which is still approaching c.), 

so if the ship were to actually reach light speed, three things would have to have happened: the surrounding universe would have had to become completely two-dimensional from the ship while the ship seems completely two-dimensional from Earth (impossible), the people on the ship would observe time for the surrounding universe to have completely stopped while people on Earth would observe time to have completely stopped on the ship (impossible), and the ship would have to have used an infinite amount of energy to get to c (impossible). The ship would also be said to have infinite mass, because anything that they hit would experience an infinite amount of energy on impact (impossible). Even a single atom they impact would cause an explosion of infinite energy that would destroy both the ship and the entire universe.
It would also violate the finding that c is constant; an observer travelling at c would stop observing light travelling at c, since they would be travelling at the same speed as the light. Light going in their direction would seemingly be frozen, which brings with it a host of other conceptual problems. Only things without mass can travel at c: light, gravity, electromagnetism and the strong nuclear force. These things can only travel through a vacuum at exactly the speed of light, never any slower, well I did say it was a long answer! and many thanks to Matt Pizzuti for answering it!

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