My Relativistic Paradox

It’s been a really long time since I’ve posted something on the blog. Blogger tells me my last post was 28^th May. That’s nearly 5 months back. As you can guess, a lot has changed in 5 months. NO. I still don’t like my college, but now at least I’m comfortable around some of my classmates. Secondly, I am sort of forced to conclude that I am better off than some of my friends as well, who deserved more but got less, and more importantly who deserved less and got more but still aren’t happy. (Evil Laugh).

Of all the teachers in the college (or university, if that matters), the most cool teacher I find is our physics professor. Well, it’s also possible that I find him cool only because of physics, but anyhow. As many of you may know, the first semester studies include basic engineering level physics. Thus, so far, I’ve studied LASER, optical fibers, mathematical derivations of Maxwell’s equations (ugh!) and of course, relativity. Things can get really interesting and peculiar, particularly if you go down on a very small scale, (quantum mechanics), or you go very fast (General relativity).

With quantum mechanics tackled (or maybe not, because you can never be sure! :P ), I started to focus on the special and general theory of relativity. You all might have heard of the twin sister paradox, where one of them travels through space time and upon returning finds that she has aged less than her twin sister who stayed on earth. Basically implying that time moves slowly for anything moving with any speed. This also implies that someone living on say 4^th floor will live longer than someone living on ground floor. The difference perhaps may be less than a nanosecond. As you move faster and faster in space, you end up moving slower and slower in time. For someone moving at the speed of light, time will simply pause. This is the time dilation area of general relativity.

                                  Stephen Hawking on the Grandfather paradox

Then there are two other aspects of relativity, one is length contraction, where a rod of length 1 meter(say) will look shorter and shorter as it gains velocity, until it becomes a point when it reaches c, the speed of light. The other aspect is relativistic mass, where the object gains mass as it gains energy, specifically kinetic energy. Any object moving at the speed of light will have infinite mass. I’m not posting the equations here, as I find them boring.

All these results were obtained by Einstein using a simple postulate that speed of light is independent of the frame of reference that is irrespective of the motion of the source of light. In noob-y words, velocities cannot be added or subtracted to light. Still confused?

Assume you are in a car, moving at 40kmph. You throw a ball forward at 10kmph relative to yourself. To a person standing on the ground, the ball will have a velocity of 50kmph. This is Newtonian mechanics. Simple and intuitive.
Now, measure the velocity of light escaping from the headlamps, and ask the stationary observer to do the same.

Irrespective of the direction of motion of car, and irrespective of the velocity of the car, the speed of the photons emerging from the headlamp will be 3x10^8 m/sec. That’s weird. But that’s nothing.

Assume that there is a train, moving at just 1m/sec less than the speed of light, (.999c, or something like that). What about the light from the engine in front?

I asked the same question to my professor. According to him, since light is independent of other velocities, the light would be there as usual. But according to my view, the light would not be behaving the usual way. If the light is mounted3 meter above the ground, then it would take 3 seconds or less to reach the ground itself, and once it bounces back from the tracks, it will take minimum another second to catch back to the front of the engine, which has already passed over. Another interesting thing may happen if someone on this train sneezes. Since nothing can travel faster than speed of light, the air and the saliva droplets and everything lese would just end up floating in midair. The person might not be able to sneeze at all!

Then my Prof. said that screw the speed being 1m/s less than c. Even if the speed is equal to c, then also light will be visible from the front.

Erm, no. AFAIK, once the train reaches c velocity, time will cease to exist. This has multiple implications. Firstly no one will be able to actually turn the light on. Since doing so would require a certain amount of time, which as I’ve said, just isn’t there. Even if we assume the light was on before the train hit the c velocity, won’t make much difference. Think at a basic level. Bulb glows when current passes through it. Current is basically the flow of electrons. To observe something flowing, you need time. Since you no longer have time, you no longer have electron flow, you no longer have current and thus you will no longer have a glowing light bulb. So this means you won’t see light up front. Right? WRONG!

If you had the light turned on before you hit the speed of light. You will still perhaps see the bulb glowing. Everything will come to a halt. Your heartbeat, your brain, everything. Hence if your brain was seeing light before, it will continue to do so. Photos may keep on hitting you retina, but they won’t be absorbed, because again that requires time, which just isn’t there. I think perhaps that’s not good for health as well. Leaving a paused heart aside, all the photos will tend to accumulate inside your eye ready to be absorbed by retina, as soon as they get the time. Now if the train slows down a bit, time starts flowing again and all the photons will be absorbed directly. Damaging your eyes. Or there is another possibility of photons destructively interfering with each other to produce a null effect.

To someone on the ground, Doppler Effect of light will be observed to the extreme. I’m not going into that partly because this post has already become too complex for many people and partly because I still don’t understand what all can happen.

All this also taught me another lesson. It simply doesn’t matter where you are getting education now. If you have interest and internet (ofc) then everything else just ceases to have value. Perhaps my college isn’t that bad after all. But again, I just don’t care.