Special Relativity vs. General Relativity

**IndustriaL** · Jun6-05, 03:36 PM

What is the difference between Special Relativity and General Relativity?

**robphy** · Jun6-05, 03:50 PM

The modern view [used by working relativists] is that General Relativity works with a spacetime consisting of an arbitrary 4-manifold

with a lorentzian metric tensor field $LaTeX Code: g_{ab}$ , whereas Special Relativity is the special case where the spacetime is the Minkowski spacetime consisting of

and the [flat] Minkowski metric $LaTeX Code: \\eta_{ab}$ .

**dextercioby** · Jun6-05, 04:29 PM

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.

**mathman** · Jun6-05, 04:40 PM

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.

**dextercioby** · Jun6-05, 04:44 PM

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

Daniel.

**robphy** · Jun6-05, 05:02 PM

Originally Posted 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.

Originally Posted 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.

~~pmb_phy~~ · Jun6-05, 05:22 PM

Originally Posted 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

**εllipse** · Jun6-05, 11:24 PM

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.

**robphy** · Jun6-05, 11:54 PM

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.

~~pmb_phy~~ · Jun7-05, 05:06 AM

Originally Posted 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

~~pmb_phy~~ · Jun7-05, 05:10 AM

Originally Posted 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

**εllipse** · Jun7-05, 02:11 PM

Originally Posted 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.

~~pmb_phy~~ · Jun7-05, 03:22 PM

Originally Posted 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

**robphy** · Jun7-05, 07:28 PM

While it's been argued that this part is in accurate:

Originally Posted 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:

Originally Posted 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.

Originally Posted by pmb_phy

Originally Posted 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.]

~~pmb_phy~~ · Jun7-05, 08:29 PM

Originally Posted 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 $LaTeX Code: \\Gamma$ -> 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

**robphy** · Jun7-05, 09:00 PM

Originally Posted 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