I've always been intrigued by the theory of relativity, but I really have a hard time wrapping my head around the whole concept. I'd like to think I'm smart enough to understand it, but after ten minutes of thinking about it, I start to feel like that famous railroad worker that had a tamping rod driven through his skull. I understand how it all works to some degree, but I don't understand why. I know that the discovery that light travels at a constant rate irregardless of the velocity of the source emitting or reflecting the light contributed to Einstein's development of the theory in some way. I know all about the time dilation and the Twin Paradox and everything. I just can't quite grasp the way it all works. I've tried to devise a kind of thought experiment to help me understand, but I think I'm clearly missing something.
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| Figure 1. |
Alright, so you have these two houses. They are both separated by a distance of one light year (figure 1). It's 2010 at both houses, but because of the time it takes for the light to reach each neighbor, when they look out at each other they're both seeing the state that each existed in back in 2009.
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| Figure 2 |
Okay, so now let's say that in 2010 the guy in house B decides to visit the guy in house A. He gets into his spaceship and travels at as near the speed of light as it's possible to get (figure 2). Since the distance is one light year, it will take him just over a year to make the trip. So he'll arrive at house A in 2011. Okay, now let's say that the guy in house A has been standing at his window watching all this. Again, since it takes a year for the light to travel, the guy in house A doesn't see his neighbor in house B pull his spaceship out of his garage until 2011. Then, a mere few minutes later, he gets a knock at his door. His neighbor from house B has just arrived on his doorstep.
So doesn't it seem like the trip would seem nearly instantaneous to the guy in house A? Yet, everything I've ever heard about relativity seems to suggest the opposite. They say that if the guy in house A could see a clock aboard his neighbor's spaceship it would seem to slow down. If the guy from house B could see a clock in the living room of house A from aboard his ship, it would seem to race by. But it seems almost like it would be the other way around. House A would see the clock zip along, spinning through a year of days in a matter of seconds. Meanwhile, from the ship, the clock in house A would seem to slow down to compensate for the extra year. (Remember, that the guy in house B sees house A as it was in 2009 when he climbs aboard his ship.)
I don't know. The problem's obviously not with relativity, but rather with my understanding of it. There's either something fundamentally flawed or missing in my experiment, or my idea of relativity itself is completely backward. I don't get it.
I need some aspirin.
Interesting and innovative paradox u've stumbled upon!
ReplyDeleteLet's begin with a statement: At greater speeds, all processes go slower.
Practically witnessed in case of some unstable particles which have longer lifetimes when accelarated to higher speed i.e. their decay process slows down.
Acc to Relativity, the guy in the ship will not age a bit in the year while he's @ velocity of light. Aging process stopped(astonishing?) along with everything else - even molecular motion and fireworks.
Your paradox is based on position. The observer to whom the clock is stopped, is a stationary observer, irrespective of the fact that he can't practically observe it. It's something universal, and DOES NOT refer to light as carrier of information to observe etc.
So the problem of stationary guy is his medium of observation i.e. speed limitations of light, while witnessing a universal phenomena.
Can't prove it, but it's dere! :)
I don't really understand relativity either, so I'm not posting this in any authoratative sense, and so I could be completely mistaken. Anyway, this is how I see it:
ReplyDeleteTo summise, both men stand at their window in January 2010. Both men are seeing the other house as it looked in January 2009. The man from house B sets off in January 2010. Which means that the man in house A would, in real terms, still have to wait one year before the man in house B arrives - the exact same length of time it takes man B to travel to house A.
Yet the man in house A wouldn't actually SEE him leave house B until January 2011.
Ok, let's assume that if they can see eachother's house, they can also see everything inbetween. Or in other words, man A can see the journey that man B undertakes, and man B can see House A for the duration of his journey.
The closer they actually get to eachother, the less distance light has to travel, thus meaning that the time they are actually seeing eacother in the past decreases. (In simple terms, if they are 1/2 light year away from each other, then they are seeing eachother as they were 6 months ago.)
So, from man B's perspective, it takes man B 6 months to get to the half-way point in his journey. The date now is July 2010. Therefore, man B can see house A as looked 6 months ago (January 2010).
Yet six months ago, when man B set off on his journey, he could see Man A's house as it looked in January 2009. Which means that during Man B's six months of travel, the stationary object (House A) has (to man B) passed through 12 months of time. If Man B could see the clock inside house A, it would therefore appear to him at this point to be be going twice as quickly.
Now, for Man A, it's January 2011, and he sees man B leave. Yet because it's January 2011, the reality is that Man B has been travelling for one year. Anyway, let's say it's 8am, and man B is due to arrive a 9am. So that means that man A is watching the whole journey over the course of one hour. At 8am, he sees man B as he was one year ago. At 8.30am, man B is 6 months into his journey, thus man A is now seeing man B as he was 6 months ago. This means that the closer man B gets, the time into the past in which man A sees man B is decreasing. If man A could therefore see the clock inside man B's spaceship, it would appear to man A to be slowing down as it gets closer to him. It would continue to slow down until the point man B reaches man A's house, at which point the clock would now appear to passing by at exactly the same rate as man A's own clock.
Thank you, I'm glad to see someone can follow the scenario I've laid out :)
ReplyDeleteIf you read on to the next couple of parts, you'll see that I reached fairly similar conclusions, but I followed a slightly different path getting there. I posted part 4 the other day, and I think maybe I've made some real progress.