- #1
GordonFreechme
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So I am new to relativity, and without all the proper math analyzing the equation isn't easy. So I am stuck at this current point until I learn more math, for the most part trying to gain an understanding of how it works, through thought experiments and visualizations.
That being said I have run into a wall in my understanding.
From what I have read there was a wall that was hit in Special Relativity before Length Contraction was thought of, which had to do with the fact that as speed increases time dilates disproportionally. This was explained to me through a Michelson-Morley apparatus with the two sets of perpendicular mirrors traveling through time. Since one mirror (the one in the direction of motion) was moving away from the light as it traveled towards it and away as it moved away, this created an inconsistency. Time dilated in one direction with speed, but differently in another. To solve this length contraction was added, and it allowed time to dilate the same in all directions with speed.
Now when it comes to general relativity I understand that light follows the curves in space time created by the presence of energy. Why it distorts, and how it does it are things I am interested in, but they don't play a role in what I am asking, only the fact that it does curve, and light follows the curves matter for what I am asking. The other effects of the curvature may matter, I am not completely aware of the full effects, if I was I probably wouldn't be asking this question at all.
Now that all being said in the included image (assuming it shows up properly this is my first time on the site) I have set up a Michelson-Morley Apparatus similar to those diagrams I have seen relating to special Relativity, which to a large degree unlike general relativity I have a pretty good understanding of. In the diagram A and B are perpendicular to R and as such the light bends as it moves from A to B, it follows the bends in space created by the mass E. C and D are perfectly in line with R, I haven't labeled R in vector form because I am not the best at it, and because the direction of R doesn't matter so much for what I am asking. Now in this case light from A to B bends and thus it takes a longer path, causing our light clock in that direction to tick slower. However with CD wouldn't the light travel in a straight path? space is bend equally around it, why would it decide to curve in one way and not the other? If it doesn't curve then wouldn't its light path wouldn't be altered and it wouldn't experience the same time dilation as AB. This creates an inconsistently similar to the one first experience with Special Relativity.
I know this forum isn't supposed to be about proposing alternatives to the theory, I am not doing that. All I am asking for is an explanation of why this doesn't actually cause an inconsistency, and I ask because I haven't been able to find one through google searches (its probably labled as something which I am not aware of) and my Astro teacher, who claims to be a physicist as well had no explanation other than he thought my diagram seemed accurate. He actually said to tell him what I find on the matter, which I thought was cool, but it didn't help me at all.
What really makes this hard is almost no understanding of calculus or tensor analysis, it makes the equations really just look like a mess to me. I know I will need both to fully understand what is going on here, but a short simple explanation, with some math as long as it doesn't involve too much Calculus (if it does list it as well I may not know it know, but I could definitely use it later) would be great.
Oh and assume that the bars on top of the vertical lines, in the lower section of the diagram represent 1 second in relation to CD's light clock. Which is why the line in AB just stops, because by the time 1 CD second has passed it hasn't reach A again.
http://img812.imageshack.us/img812/258/xtmp.png [Broken]
That being said I have run into a wall in my understanding.
From what I have read there was a wall that was hit in Special Relativity before Length Contraction was thought of, which had to do with the fact that as speed increases time dilates disproportionally. This was explained to me through a Michelson-Morley apparatus with the two sets of perpendicular mirrors traveling through time. Since one mirror (the one in the direction of motion) was moving away from the light as it traveled towards it and away as it moved away, this created an inconsistency. Time dilated in one direction with speed, but differently in another. To solve this length contraction was added, and it allowed time to dilate the same in all directions with speed.
Now when it comes to general relativity I understand that light follows the curves in space time created by the presence of energy. Why it distorts, and how it does it are things I am interested in, but they don't play a role in what I am asking, only the fact that it does curve, and light follows the curves matter for what I am asking. The other effects of the curvature may matter, I am not completely aware of the full effects, if I was I probably wouldn't be asking this question at all.
Now that all being said in the included image (assuming it shows up properly this is my first time on the site) I have set up a Michelson-Morley Apparatus similar to those diagrams I have seen relating to special Relativity, which to a large degree unlike general relativity I have a pretty good understanding of. In the diagram A and B are perpendicular to R and as such the light bends as it moves from A to B, it follows the bends in space created by the mass E. C and D are perfectly in line with R, I haven't labeled R in vector form because I am not the best at it, and because the direction of R doesn't matter so much for what I am asking. Now in this case light from A to B bends and thus it takes a longer path, causing our light clock in that direction to tick slower. However with CD wouldn't the light travel in a straight path? space is bend equally around it, why would it decide to curve in one way and not the other? If it doesn't curve then wouldn't its light path wouldn't be altered and it wouldn't experience the same time dilation as AB. This creates an inconsistently similar to the one first experience with Special Relativity.
I know this forum isn't supposed to be about proposing alternatives to the theory, I am not doing that. All I am asking for is an explanation of why this doesn't actually cause an inconsistency, and I ask because I haven't been able to find one through google searches (its probably labled as something which I am not aware of) and my Astro teacher, who claims to be a physicist as well had no explanation other than he thought my diagram seemed accurate. He actually said to tell him what I find on the matter, which I thought was cool, but it didn't help me at all.
What really makes this hard is almost no understanding of calculus or tensor analysis, it makes the equations really just look like a mess to me. I know I will need both to fully understand what is going on here, but a short simple explanation, with some math as long as it doesn't involve too much Calculus (if it does list it as well I may not know it know, but I could definitely use it later) would be great.
Oh and assume that the bars on top of the vertical lines, in the lower section of the diagram represent 1 second in relation to CD's light clock. Which is why the line in AB just stops, because by the time 1 CD second has passed it hasn't reach A again.
http://img812.imageshack.us/img812/258/xtmp.png [Broken]
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