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Relativity, speed of light and stuff... 
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#55
Aug3008, 02:43 AM

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#56
Aug3008, 02:49 AM

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Maxwell's equations + Principle of Relativity = Principle of Relativity + constancy of speed of light 


#57
Aug3008, 08:15 AM

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#58
Aug3008, 10:05 AM

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#59
Aug3008, 07:01 PM

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Al 


#60
Aug3008, 07:25 PM

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#61
Aug3008, 07:37 PM

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1) What transformations are consistent with 2 invariant speeds (speed of light and something else). I suppose this us related to doubly special relativity. 2) Can light (and gravity) be usefully modelled as a medium? For light, it appears the answer is yes. For gravity, the answer is unknown, but there are several intriguing leads (http://arxiv.org/abs/0712.0427) 


#62
Aug3008, 07:50 PM

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2 invariant speeds?
it gets confusing since we are talking about sound but what we are really talking about is light. I never meant to say anything implying 2 invariant speeds. 


#63
Aug3008, 07:52 PM

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Chinese philosophers theorized that the division could be continued indefinitely, and hence that there were no elementary particles. Greek philosophers assumed that the division could not be continued indefinitely ... Those ultimate particles were called "atomos". He quotes the Dao De Jing (p11): The Dao that can be stated cannot be eternal Dao. The Name that can be named cannot be eternal Name. The Nameless is the origin of the universe. The Named is the mother of all matter. Which he mischievously translates as (footnote, p11): The physical theory that can be formulated cannot be the final ultimate theory. The classification that can be implemented cannot classify everything. The unformulable ultimate theory does exist and governs the creation of the universe. The formulated theories describe the matter we see everyday. Preface (pviii): we still know so little about the richness of nature. However, instead of being disappointed, I hope the readers are excited by our incomplete understanding. ... The human imagination is also boundless. ..... I wonder which will come out as a 'winner', the richness of nature or the boundlessness of the human imagination. 


#64
Aug3008, 07:57 PM

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Our vacuum is more like an ocean which is not empty. Light and fermions are collective excitations that correspond to certain patterns of 'water' motion. 


#65
Aug3008, 09:14 PM

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PF Gold
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#66
Aug3008, 09:45 PM

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#67
Aug3008, 10:49 PM

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If you think I am mistaken, please demonstrate how it explains the inverse square law. Or an even simpler question: How does GR get to the Newtonian limit. 


#68
Aug3008, 11:32 PM

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or maybe Sean Carroll does that here or here? i think they can derive the inversesquare relationship (or maybe it's a 1/r relationship for potential energy) for the flat spacetime limit. the constant of proportionality in the Einstein equation ([itex]8 \pi G[/itex]) does come about to be compatible with Newtonian gravitation. i can't actually do the math myself (i am ashamed to confess i never figured out tensors), but it appears that this is what they do. 


#69
Aug3108, 12:02 AM

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I tend to agree with Jennifer here. I can not see how a physicist isolated in a small spacestation that had never experienced gravity or even heard of it, would conclude from a knowledge of Special Relativity alone, that two particles would have to move towards each other, let alone that they accelerate towards each other with an acceleration inversely proportional to the distance separating them.
As far as I can tell General Relativity started with a knowledge that we experience "Newtonian gravity" and extrapolated or reverse engineered that knowledge to more extreme conditions than we normally experience. It is hardly surprising that Newtonian gravity is recovered from GR in the weak field limit because GR started with that assumption. lease do not get me wrong here. I am not saying there is anything wrong with GR, I am just saying that it does not fundementally explain or predict gravity and just provides a pretty good mathematical description of what we observe. Put it another way. In multiverse theories where there are any number of possible universes each with their own laws of nature, would a universe that obeys the laws of Special Relativity have to have an inverse square law of gravity in the weak field limit or come to that, any gravity at all? 


#70
Aug3108, 12:21 AM

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#71
Aug3108, 09:06 AM

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the electric field follows an inverse square law because space is 3 dimensional. aether theory explains this very well.



#72
Aug3108, 10:15 AM

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To Kev and MeJennifer, I would like to add a couple of things: I don't consider the way Einstein discovered SR and GR to be "derivations" of those theories. In both cases he wrote down a somewhat illdefined list of properties that he wanted the theory to have, and then searched for a theory that had those properties. The reason why I can't consider this method a "derivation" is that the "list of properties" was illdefined to begin with, and later made welldefined by the theory that was found. (E.g. we need Minkowski space to properly define the inertial frames in which the speed of light is supposed to be a constant). I understand that your opinion is that the fact that GR was found by looking only for theories that could reproduce the Newtonian limit means that GR can't be said to explain the inverse square law. That is a valid opinion (about the meaning of the word "explain") but I don't agree with it. There is no deeper form of understanding than having a theory that agrees with experiment, so if derivation from a theory that agrees with experiment can't be considered an explanation, nothing can. It makes no difference to me (at all) how the theory was found. All that matters to me is what range of phenomena it's capable of describing and how well it agrees with experiment. 


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