Theory of Relativity…My Brain Hurts

For some reason, I started thinking about Einstein’s Theory of Relativity. His theory came in two parts. The first was his Special Theory of Relativity (SR) which is what he had to settle on because he couldn’t figure out how to make his theories work when you throw in gravity. However, he did crack the code, and developed the General Theory of Relativity. Good for him. We’ll focus on SR.

My knowledge of SR until now composed of the following:

• Nothing goes faster than the speed of light
• The twin paradox – Twin brother Jack stays on earth and twin John heads out to space at .999x the speed of light. Upon return, Jack is much, much older than John (like grandpa age).
• Mass behaves strangely the closer it gets to the speed of light (c)

Well, I understood it in bits and pieces. The twin paradox is what confounds me the most. Time passes differently depending on one’s frame of reference.

The key is that the speed of light is constant everywhere in the universe. If Joe is standing in the middle of the street, and Sally is driving towards him from afar at 50 mph, and then she takes a slingshot and slings(?) a rock ahead of the car towards Joe at 30mph, what is going on here (must have been a nasty breakup, but that’s besides the point)?  To Sally, the rock is moving at 30mph relative to her position, but to Joe, the rock would appear to be coming at him at 80mph (50mph of the car + 30mph of the rock from the slingshot). In Newtonian physics, you can add up speeds to get a relative speed, savvy?

Well, when it comes to speeds approaching c, this all falls apart. If a spaceship going half the speed of light fires a laser gun at a distant point ahead of it, to an observer sitting still (also a relative concept) from a distance, the relative speed cannot appear to be 1.5x the speed of light (speed of ship + speed of laser), since c is the universe’s speed limit.

This is where I get lost. There are several ways that physicists try to illustrate how this works at high, near light speeds, but they are difficult to grasp. The big a-ha moment I got out of reading further is that if the speed of light doesn’t change, then something else must change. In SR, it’s the perception of time that changes.

The only illustration that I came across in my research that made any sense was this one below. In Figure 4, imagine this clock (shaped like a bullet) is on a space ship going somewhere near lightspeed.  Above the clock is a mirror that stretches across eternity (use your imagination). From the frame of reference of someone on the spaceship, let’s assume the roundtrip of a laser from the clock bouncing off the mirror directly above it and back (duh, definition of a roundtrip) takes 1 second, with the beam moving at the speed of light.

Now (stay with me), let’s change this from a spaceship to a train, and the arrows in figure 4 represent the path of a ball being tossed straight up in the air on the train. Figure 5 would be what that same action on the passing train looked like if the observer were standing on the platform. In both cases, from both locations (on the train, and on the platform), the ball would take the same amount of time to make the round trip up in the air and back; however, the ball would have a high lateral speed, from the perspective of the platform viewer. Got it?

Now, back to the spaceship. From afar, it would appear that the laser beam had to travel further in order to make the round trip (due to the lateral movement). In normal physics, this would be analogous to the train example. But, light always travels the same speed, regardless of frame of reference. That said, the laser beam is clearly covering more distance in figure 5. If it’s not going faster to cover that distance, then time must appear to shift (since the speed cannot). To the person viewing from afar, it may appear that the laser took 2 seconds to cover the round trip distance (since the light had to travel twice as far). However, to the person on the spaceship, the laser took only 1 second to make the round trip.

Thus the twin paradox. If this beam took 6 months from the perspective of the person from afar to travel the distance, then to the person on the spaceship, the time elapsed to that person would only be 3 months. Therefore, the guy on ship ages slower, and is effectively traveling into the future.

Holy cow, it hurts the brain.

Incidently, other effects of near light speed include an elongation of the object from the frame of reference of someone watching it from a ‘fixed’ point.

Now if only I could figure out how to do a load of laundry without shrinking the clothes, I wouldn’t mind my lack of knowledge in the area of relativity.

Feel free to correct me, or better express what I am trying to explain.