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Special Relativity vs. General Relativity 
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#1
Jun605, 02:36 PM

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What is the difference between Special Relativity and General Relativity?



#2
Jun605, 02:50 PM

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The modern view [used by working relativists] is that General Relativity works with a spacetime consisting of an arbitrary 4manifold [tex]M[/tex] with a lorentzian metric tensor field [tex]g_{ab}[/tex], whereas Special Relativity is the special case where the spacetime is the Minkowski spacetime consisting of [tex]R^4[/tex] and the [flat] Minkowski metric [tex]\eta_{ab}[/tex].



#3
Jun605, 03:29 PM

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Take a look the the axioms for each of them.You'll then see that the geometry of spacetime depends on the mathematical interpretation of one postulate in each theory.
You may draw a comparison with QM and its first postulate. Daniel. 


#4
Jun605, 03:40 PM

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Special Relativity vs. General Relativity
From a layman's point of view, special relativity is concerned only with inertial systems (no acceleration), while general relativity does not have that restriction. In particular G.R. is a theory of gravity.



#5
Jun605, 03:44 PM

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Nonetheless,special relativity deals very well with the problem of a pointlike particle moving through spacetime with a constant acceleration "a".
Daniel. 


#6
Jun605, 04:02 PM

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Yes, G.R. is a theory of gravity. As such, the spacetime of GR is often said to be a dynamical one... the equations of motion being the Einstein Field Equations. 


#7
Jun605, 04:22 PM

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The special cases of the vacuum domain wall, straight cosmic string and uniform gfield make you really think about these ideas and why they became to be defined as such. Pete 


#8
Jun605, 10:24 PM

P: 195

To put it in even simpler, very generic terms. Special relativity is the theory of what happens at very fast speeds, while general relativity is the theory of what happens with very dense masses. To go further, special relativity solves the problems Newtonian physics has with high speeds; general relativity solves the problems Newtonian physics has with very large gravitational fields. Of course, this is a generalization. There are many more applications.



#9
Jun605, 10:54 PM

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εllipse,
Your statement reminds me of something called the "Bronstein Cube" which this first link attributes to Penrose http://www.physik.fuberlin.de/~lenz...nsteincube.gif I heard about this from lectures by Stachel http://physics.syr.edu/research/heth...k/stachel.html (click on the thumbnails with cubes) Essentially, this diagram suggests relationships between the different theoretical regimes using certain limits of fundamental constants. 


#10
Jun705, 04:06 AM

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Pete 


#11
Jun705, 04:10 AM

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Pete 


#12
Jun705, 01:11 PM

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#13
Jun705, 02:22 PM

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The main fact I'm pointing out is that SR is not just for high speed motion. That was pretty clear in my post 


#14
Jun705, 06:28 PM

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While it's been argued that this part is in accurate:
[I must also admit that one reason for that first answer I gave was to try to defeat misconceptions, particularly those stemming from the historical development of the subject, and to advocate the modern terminology and interpretations used in practice.] 


#15
Jun705, 07:29 PM

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I think different definitions give different answers. E.g. I think some would say that no Riemann > No gfield while others would say no [itex]\Gamma[/itex] > no gfield. The first comes from MTW while the second comes from MTW and Wald. This last part is, of course, confusing. To see the latter part see MTW page 467. Btw  what do you find wrong with historical matter if it works better for some people? In his text "Concepts of space," Max Jammer has an foreword by Einstein in which he discusses the importance of history in science. It is well worth your read. I can scan and email if you wish as always. Pete 


#16
Jun705, 08:00 PM

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However, today [in practice], a lot of the ideas have been formulated neatly with some precise definitions... let's use them! In teaching others, I feel we (as a whole) go further in understanding and advancing the subject by teaching the modern formulation (appropriately simplified for the audience) and building upon it rather than stumbling over the same mistakes made in the past. (Certainly, it may necessary to take folks through a few mistakes to get them to appreciate things... but I think we need to streamline the path somewhat.) my $0.02 


#17
Jun705, 09:29 PM

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Rob  That is not what I meant. Speaking of the practicing scientist referring to the historian, Einstein said
The article I refer to is Nonequivalence of a uniformly accelerating reference frame and a frame at rest in a uniform gravitational field, Edward A. Desloge, Am. J. Phys., Vol. 57, No. 12, Dec 1989, page 11211125 Einstein would roll over in his grave if he read that article! Of course other authors assume a vanishing Riemann tensor such as Principle of Equivalence, F. Rohrlich, Ann. Phys. 22, 169191, (1963), page 173 In my own experience it took me a very long time to learn that E does not always equal mc^2 (recall that stress contributes to momentum and thus to inertial mass aka "relativistic mass" = m = p/v). I should have read Rindler's text first. It would have saved me a LOT of time. I went back to Einstein's original papers and there it all was in his 1907 paper (or was it 1906?). What a genius Einstein was! But in all the dicussions over the last 7 years I've had on the concept of mass nobody ever mentioned these basic concepts. Probably because the stressenergymomentum tensor is never used in SR texts as applied to simple bodies such as a capacitor. But leave it to Rindler to do so! See http://www.geocities.com/physics_wor...rd_paradox.htm Another example is my current efforts to write a text (I'll be finished in about 40 years ). I want to start off by presenting a (an operational??) definition of "space," "time" and "spacetime." Not an easy task. One article I keep putting off is that regarding the Hopi Indians. In there language it is said that there is no concept of time. All good stuff. Hans Riechenbach has a great book called "The Philosophy of Space and Time" which I will be reading someday. I pick it up once and a while when I need to switch gears for a moment. Pete 


#18
Jun1005, 04:34 PM

P: 308

curved spacetime nonuniform gravitational field (see) flat spacetime uniform gravitational field (see) inertial frame A local frame in free fall local In a vicinity or having a volume throughout which the tidal force is negligible nonlocal In a vicinity or having a volume within which the tidal force is significant nonuniform gravitational field (curved spacetime) The gravitational field of a nonlocal frame tidal force The relative gravitational acceleration of two test particles in free fall uniform gravitational field (flat spacetime) The gravitational field of a local frame A region of flat spacetime as large as our observable universe, say, could be moving at relativistic velocity and accelerating toward and relative to some mass outside of it. The region can be deemed an inertial frame so long as the tidal force imparted by the mass is negligible throughout the region (i.e., the mass does not curve the region). The reason that inertial frames must be infinitesimal in GR is a technicality to guarantee that the tidal force within them is negligible; practically speaking there is no size limit. Once that is understood, it follows that flat spacetime is synonymous with a uniform gravitational field, and curved spacetime is synonymous with a nonuniform gravitational field. 


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