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Member (Idle past 4874 days) Posts: 624 From: Pittsburgh, PA, USA Joined: |
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Author | Topic: Speed of Light Barrier | |||||||||||||||||||||||||||
Ben! Member (Idle past 1429 days) Posts: 1161 From: Hayward, CA Joined: |
I've followed this thread up to the current post... I'm studying special relativity with a physics buddy of mine, who's putting together some ConcepTests for Special Relativity (as well as the basics of quantum). It's cool stuff he's doing, I'm excited about it.
Anyway, I still have this nagging question that I can't resolve, given this picture. JustinC reiterated the same question I think, after reading your explanation here. I'll post two versions of the question; the longer version is more correct, but it's good to try and summarize what you want to say in just a few words. For evidence of that, please review the mess I've made of these last two paragraphs Short version: Why is the length of the vector equal to (or related) to 3X10^8m/s? Long version:In your explanation, light travels such that the vector has no time component. If that's true, then I don't understand why light has the actual velocity that we measure it to be. Why couldn't that velocity be 3m/s? Why not 3X10^88m/s? How does the actual measured velocity of the speed of light relate to the fact that light has no time component? In this view, does it fall out directly from the hyperbolic relationship between spatial coordinates and time coordinates? I don't think that would answer it either... I just can't understand why this vector would have one length, as opposed to any other. OK, thanks again for all your willingness to entertain questions. I'm really enjoying your posts. So you have my heartiest "Welcome to EVCForum!" Ben This message has been edited by Ben, Saturday, 2005/07/16 09:57 AM
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
In this view, does it fall out directly from the hyperbolic relationship between spatial coordinates and time coordinates? Exactly... as to its value: Very short answer: it just is Short answer: if it was much different to 3x10^8m/s you wouldn't be here to ask the question It's one of the constants that you hope will drop out of whatever TOE happens to be your favourite. Just one point:
light travels such that the vector has no time component Be careful here. A photon's 4-velocity certainly has a time component, but it also has an "equal" space component. It's the magnitude of the vector that is zero.
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Son Goku Inactive Member |
The reason light has that speed is more to do with human measurements than anything else.
In special relativity light moves equally in space and time, so for every 1m light covers in time, it covers 1m in space. So it's speed is: 1m/1m = 1. Similarly for every 300,000,000 meters in time light covers it covers 300,000,000 meters in space.So again this is: 300,000,000m/300,000,000m However, because of the way we see the world, humans call 300,000,000 meters in time 1 second. So this speed becomes 300,000,000m/1s = 3x10^8 m/s. It isn't that light's speed is arbitrary or "without reason" it's because us humans don't measure time and space equally.Our time measurement, the second, is way too big compared with our space measurement. There is a similar reason for all the constants.
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JustinC Member (Idle past 4874 days) Posts: 624 From: Pittsburgh, PA, USA Joined: |
quote:Can you explain this a little further. From your vector "analogy", it seems that if something is travelling through space at c, it won't be traveling through time. Thanks for answering these questions, and feel free to stop anytime. I can go asking questions ad infinitum. Even better than this, do you recommend any books on general and special relativity?
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
However, because of the way we see the world, humans call 300,000,000 meters in time 1 second. Yes, and the whole question is why is the number 3x10^8 and not say 2x10^8. The units are a given, it's the magitude that is of interest.
There is a similar reason for all the constants. If you mean, why they have their given dimensions, then this is obvious. Their magnitudes are not obvious.
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
From your vector "analogy", it seems that if something is travelling through space at c, it won't be traveling through time. It's time for you to start answering your own questons clue: which frame are you talking about? Do you see light rays travelling through time... or not? Even better than this, do you recommend any books on general and special relativity? If you mean textbooks, then there's always Misner Thorne and Wheeler's Gravitation... the bedrock of relativity... literally given its size. But I do like Ray D'Inverno's Introduction to General Relativity. And the book I mentioned earlier, Penrose's "The Road to Reality" is a great bridge between layman and graduate textbook. If you mean layman's guide... then no, cause I haven't written mine yet Seriously, I have yet to find a decent guide. These days everyone's so desperate to rush into explaining string/M-theory that they miss out any deoth in relativity. Seriously, all this talk of branes is deadly dull compared to a good talk through of Reisnner-Nordstrom or Kerr geometry (electrically charged black hole and rotating black hole respectively)
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
From your vector "analogy", it seems that if something is travelling through space at c, it won't be traveling through time. Sorry, I was being a little unfair there. Understand that there are two very different things: the time dimension, and elasped time. The latter we call "proper time" and is essentially how much time you experience. But this has little to do with the time dimension unless you always move such that v<
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Son Goku Inactive Member |
quote: For the reason I stated.We humans simply invented a measurement of time called the second and a measurement of space called the meter. The only reason there is a "speed of light" is because the temporal measurement is so mismatched from the spatial one. That is the explanation of the magnitude, our disproportionate measurement system. quote:No also their magnitudes, for instance G only comes about because our unit of mass is so small compared with our unit of space and extremely small compared with our unit of time. i.e. kg < meter < second. The constants are there because of errors in the formulation of our measurement system.
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Brad McFall Member (Idle past 5063 days) Posts: 3428 From: Ithaca,NY, USA Joined: |
If I understand the concept of the "ordertype" (Cantor's)then it seems (as to if one had "seen" light rays, calculations on photons interacting with matter etc...)iT provides an "alternative" (possible (If tHe phyiscs was done etc. etc etc., to the analytic geometry involved or invovlable et. al.)from a/the 'magnitude' of a vector (the scalar part) and the infinity that might be cardinally organizaed could be devolved on the imaginary plane could it (ordinally) not else one is speaking of an idol or else*** things humanely measured faster than said quantification recorded for all to read?
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JustinC Member (Idle past 4874 days) Posts: 624 From: Pittsburgh, PA, USA Joined: |
quote:Sorry for the delay. This is how I analyze the situation with light. From my perspective (and I guess all reference frames besides light's), light is travelling at c. This would mean that a photon would have infinite length contraction and infinite time dilation. From the photon's reference frame, I am moving at c. Therefore, my reference frame has infinite length contraction and infinite time dilation. So for a photon, it travels a distance of zero when going from the sun to my eyes. Do I see light rays travelling through time? I think so. I kindof get caught up when trying to think of light as an electromagnetic disturbance or as a particle (photon). But if it takes light 8 minutes to get from the sun to the earth, I guess it would have to be travelling through time. This message has been edited by JustinC, 07-18-2005 04:32 PM
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Ben! Member (Idle past 1429 days) Posts: 1161 From: Hayward, CA Joined: |
Son Goku,
Thanks for your reply. I find your answer to be insightful and I see how you're thinking about my question. But my intended question requires a bit of a different answer; I think cavediver sees that, and has addressed my question as I intended it to be read. Let me try and restate it.
Son Goku writes: We humans simply invented a measurement of time called the second and a measurement of space called the meter.The only reason there is a "speed of light" is because the temporal measurement is so mismatched from the spatial one. That is the explanation of the magnitude, our disproportionate measurement system. Your argument is that we could have defined different units, in order to get "the speed of light" to be any number we want, and of course that's right. But if measure in meters and seconds, we always get the speed of light to be 3x10^8m/s. This has to do with the relationship between space and time. My question is, why do we find THIS relationship between space and time? What is it that makes us measure the speed of light to be 3x10^8m/s, and not 1m/s. Because, although it's possible to measure the speed of light as 1(length unit "A")/(time unit "B"), it's impossible (theoretically) or never-been-done (experimentally) to measure the speed of light, in m/s, as anything but 3x10^8m/s. Something has fixed the relationship between space and time to be very specific, and I want to know what is fixing it that way. Bah, that didn't help at all I think. Well, if not, then I'll drop it; I'm satisfied with cavediver's previous answer (thanks for that). Ben
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Percy Member Posts: 22506 From: New Hampshire Joined: Member Rating: 5.4 |
I read a good analogy in Brian Greene's Fabric of Space and Time. The analogy is only useful for drawing a helpful image, it isn't really analogous to reality.
He likened space and time to a two dimensional space, with space being one orthogonal axis and time the other. Imagine you're moving at a constant speed. When you're moving parallel to the time axis you're not moving through space at all, and so you proceed through time at the normal rate. But the more your direction of motion becomes parallel to the space axis, in other words, the faster you move through space, the more slowly you move through time. Hope this is relevant, I didn't read the whole thread. --Percy
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
I didn't read the whole thread. Obviously
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Ben! Member (Idle past 1429 days) Posts: 1161 From: Hayward, CA Joined: |
Thanks Percy. Try Message 8 or Message 5; they both mention Greene.
I think I get the idea of a space/time vector of static length which rotates (knowing, and possibly understanding the fudging cavediver mentioned about hyperbolic sin/cos). What I don't get is why the length of that vector is the length that it is. Or another way to restate the same question (I think) is, why does OUR space-time necessitate a "c" of 3x10^8m/s in order forthe space-time interval to be invariant? Why doesn't "c" just have some other arbitrary value? All that means is that space and time need to be mixed in different proportions in order to get an invariant. Why did we get THESE proportions of space and time which mix together to give us an invariant? I doubt I'm saying this correctly. I studied space/time invariance 8 years ago, and refreshed it in 3 minutes on the web. Ben Edited to fix message link formatting This message has been edited by Ben, Tuesday, 2005/07/19 07:53 AM
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Percy Member Posts: 22506 From: New Hampshire Joined: Member Rating: 5.4 |
Your question could be asked about any of the fundamental constants, and in fact, the speed of light is thought to be a function of a more fundamental constant called the fine structure constant, probably already mentioned in this thread.
Physicists working on the theory of everything are disturbed most by their inability to derive the fundamental constants from first principles. For the most part, the constants have to be measured and cannot be derived. The current best hope is that superstring theory provides the foundation for eventually doing this. My favorite question is, "Why something instead of nothing?" The question isn't original with me, I forget who asked it first. --Percy
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