# Special Relativity vs. General Relativity

by IndustriaL
Tags: relativity, special
 P: 13 What is the difference between Special Relativity and General Relativity?
 Sci Advisor HW Helper PF Gold P: 4,108 The modern view [used by working relativists] is that General Relativity works with a spacetime consisting of an arbitrary 4-manifold $$M$$ with a lorentzian metric tensor field $$g_{ab}$$, whereas Special Relativity is the special case where the spacetime is the Minkowski spacetime consisting of $$R^4$$ and the [flat] Minkowski metric $$\eta_{ab}$$.
 Sci Advisor HW Helper P: 11,863 Take a look the the axioms for each of them.You'll then see that the geometry of space-time depends on the mathematical interpretation of one postulate in each theory. You may draw a comparison with QM and its first postulate. Daniel.
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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.
 Sci Advisor HW Helper P: 11,863 Nonetheless,special relativity deals very well with the problem of a pointlike particle moving through space-time with a constant acceleration "a". Daniel.
HW Helper
PF Gold
P: 4,108
 Quote by dextercioby Nonetheless,special relativity deals very well with the problem of a pointlike particle moving through space-time with a constant acceleration "a". Daniel.
Yes, indeed!... even with non-constant acceleration! The standard twin paradox situation is a non-constant acceleration problem.

 Quote by mathman 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.
As used here, "special relativity" really refers to "application of the Lorentz Transformations".

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.
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 Quote by IndustriaL What is the difference between Special Relativity and General Relativity?
Special relativity applies only to coordinate systems which correspond to inertial frames while general relativity applies to all coordinate systems.

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

Pete
 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.
 Sci Advisor HW Helper PF Gold P: 4,108 εllipse, Your statement reminds me of something called the "Bronstein Cube" which this first link attributes to Penrose http://www.physik.fu-berlin.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.
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 Quote by εllipse To put it in even simpler, very generic terms. Special relativity is the theory of what happens at very fast speeds, ...
No. That is a misconception. Special relativity was created in part to explain things happing at low speeds. Even at low speeds Lorentz contractions play a role in the electric field of a slowly moving wire. To determine the seperation of events in spacetime as measured in a moving frame you can't neglect relativity if the events have a large spatial seperation.
 ...while general relativity is the theory of what happens with very dense masses.
GR addresses all sorts of motion. In fact, according to Einstein, you can have a flat spacetime - change frames of reference and you "produce" a gravitational field. In this case the only mass working here is the mass of the "distance stars."

Pete
P: 2,955
 Quote by robphy εllipse, Your statement reminds me of something called the "Bronstein Cube" which this first link attributes to Penrose http://www.physik.fu-berlin.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.
Thanks for the link Rob. Please note that Stachel does not adhere to the "The modern view [used by working relativists] ..." comment you made. He adhere's to Einstein's views on GR and not to the view found in, say, Wald. Remind me in the future to e-mail his article on this point to you.

Pete
P: 195
 Quote by pmb_phy No. That is a misconception. Special relativity was created in part to explain things happing at low speeds. Even at low speeds Lorentz contractions play a role in the electric field of a slowly moving wire. To determine the seperation of events in spacetime as measured in a moving frame you can't neglect relativity if the events have a large spatial seperation. GR addresses all sorts of motion. In fact, according to Einstein, you can have a flat spacetime - change frames of reference and you "produce" a gravitational field. In this case the only mass working here is the mass of the "distance stars." Pete
Do you think someone asking what the difference in SR and GR is will know what Lorentz contractions are? I posted an answer in words anyone could understand.
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 Quote by εllipse Do you think someone asking what the difference in SR and GR is will know what Lorentz contractions are? I posted an answer in words anyone could understand.
Do you think the same person would understand Rob's post?

The main fact I'm pointing out is that SR is not just for high speed motion. That was pretty clear in my post
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PF Gold
P: 4,108
While it's been argued that this part is in accurate:
 Quote by εllipse 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.
I think we can agree that this part of the εllipse's description is fine:
 Quote by εllipse 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.

Quote by pmb_phy

 Quote by εllipse Do you think someone asking what the difference in SR and GR is will know what Lorentz contractions are? I posted an answer in words anyone could understand.
Do you think the same person would understand Rob's post?

The main fact I'm pointing out is that SR is not just for high speed motion. That was pretty clear in my post
Without much context on what the original poster already knows, it is my preference to first give a precise though-possibly-advanced answer (which can be simplified with clarifications as needed) rather than give an imprecise and possibly-misleading answer that has to be cleaned-up or thrown out later.

[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.]
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 Quote by robphy Without much context on what the original poster already knows, it is my preference to first give a precise though-possibly-advanced answer (which can be simplified with clarifications as needed) rather than give an imprecise and possibly-misleading answer that has to be cleaned-up or thrown out later. [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.]
Please don't get me wrong Rob. I see nothing with your post. I think its nice to have different people here posting different views at different levels. A discussion works best that way here. I was unable to determine the level of sophistication of the poster but he seems to read alot about physics and relativity from his profile so it seems he'd at least have heard of the Lorentz transformation.

I think different definitions give different answers. E.g. I think some would say that no Riemann -> No g-field while others would say no $\Gamma$ -> no g-field. 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 e-mail if you wish as always.

Pete
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PF Gold
P: 4,108
 Quote by pmb_phy 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 e-mail if you wish as always. Pete
Here is part of a quote I like from J.L. Synge:
 To understand a subject, one must tear it apart and reconstruct it in a form intellectually satisfying to oneself, and that (in the view of the differences between individual minds) is likely to be different from the original form. This new synthesis is of course not an individual effort; it is the result of much reading and of countless informal discussions, but for it one must in the end take individual responsibility. Therefore, I apologise, if apology is necessary, for departing from certain traditional approaches which seemed to me unclear, and for insisting that the time has come in relativity to abandon an historical order and to present the subject as a completed whole, completed, that is, in its essentials. In this age of specialisation, history is best left to the historians. - J.L. Synge in Relativity: The Special Theory (1956), p. vii
The history of SR/GR is interesting... there's some good stories in there and there is stuff to learn from it.

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
P: 2,955
Rob - That is not what I meant. Speaking of the practicing scientist referring to the historian, Einstein said
 He will, however, be grateful to the historian if the later can convincingly correct such views of purely intuitive origin.
A great example is to be found in the American Journal of Physics. With so many people saying "Gravity is a curvature in spacetime" some people take that to mean that a uniform gravitational field will have spacetime curvature. There is an article in AJP by someone who assumes the Riemann tensor must be zero for such a field and when he gets a non-zero value he is pleased with himself. The problem was that "uniform gravitational field" means "zero Riemann tensor." His lack of knowledge and relying on such ideas as "Gravity is a curvature in spacetime" and ignoring what a gravitational field really is (as Einstein knew all too well) led him to make this serious error in his article. The author, the editor and the referees all got it wrong since it was published.

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 1121-1125

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, 169-191, (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 stress-energy-momentum 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

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
P: 308
 Quote by pmb_phy With so many people saying "Gravity is a curvature in spacetime" some people take that to mean that a uniform gravitational field will have spacetime curvature.
Agreed. Such quotes are an example of how many sources on GR make the subject way more complicated than it is. I use the following definitions, which are simplified from a cross section of books:

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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