[Help]whatis the relationship between general and special relativity

silver

whatis the relationship between general and special relativity?

i know the general idea,but i don't understand how they relate to each other... please tell me...

chroot

Special relativity deals only with relative motion of two observers, in the absence of gravitational "fields."

General relativity includes gravitation, and is significantly more complex than special relativity. However, in the limit of low masses and low gravitational "field" strengths, general relativity reduces to special relativity.

Furthermore, in the limit of both low velocities and low "field" strengths, special relativity reduces to Galilean relativity.

- Warren

Chi Meson

We could go on and on with this one.

One of the shortest relationships that I have come up with is as follows: both SR and GR are about the "fabric" space and time, known as spacetime.

Special relativity is the "special" condition of the effects that are caused by traveling at speeds close to the speed of light (the effects happen at slower speeds too, but they can't be noticed).

General relativity looks at the effects of acceleration, which is essentially changing the configuaration of spacetime. GR also examines the problem of gravitation since Newtonian gravitation has a fatal flaw if SR is correct. With GR, gravity is determined to be a "pucker" (or warp or dimple or whatever) in spacetime causing an effect that appears to be an acceleration.

chroot

Or.. well.. we can nitpick anyway. [:D]
Try not to use the term 'fabric' when explaining relativity to newbies -- it tends to produce all sorts of visceral ideas about the nature of spacetime that aren't really correct.
Special relativity is special because it does not include gravitation. It is a special case of general relativity, and is aptly named.
Special relativity can actually deal quite well with acceleration in many cases. The only thing it doesn't include is a theory of gravitation.

- Warren

Ambitwistor

This is a case where historical nomenclature is at odds with modern nomenclature.

Originally, special relativity was used to refer to physics in a global inertial frame, and general relativity to physics in either a global inertial frame or a non-inertial coordinate system.

Nowadays, special relativity refers to physics in flat, Minkowski spacetime, and general relativity refers to physics in either flat or curved spacetime.

So, according to the older term, special relativity in an accelerating coordinate system would have been called "general relativity". However, this came to be regarded as peculiar: we don't refer to Newton's laws in a non-inertial frame as being a different theory as Newton's laws in an inertial frame. From the laws in an inertial frame, we can find the laws in a non-inertial frame without changing any of the axioms of the theory; thus, they should be considered the same theory. Likewise, we say that special relativity can handle physics in inertial or non-inertial frames equally well. But to incorporate curved spacetime, we do have to change the axioms of the theory, to obtain general relativity.

pmb

As mentioned above - special relativity is physics in an inertial frame of referance. general relativity is relativity applied to general frames of referance and those include accelerating (non-inertial) frames of referance.

This article describes it quite nicely. See

"Introduction to Differential Geometry and General Relativity," Stefan Waner

people.hofstra.edu/faculty/Stefan_Waner/RealWorld/pdfs/DiffGeom.pdf


Strictly speaking - A gravitational field exists if there is a non-zero gravitational force acting on a test particle. Gravitational forces are identical in nature to inertial forces (e.g. Coriolis force etc.). If the frame of referance is not an inertial one then there is a gravitational field. If we change to an inertial frame the gravitational field has now vanished.

From page 102 of the above URL doc
When Eisntein realized this he refered to that idea as He wrote
A few years ago there was a course at MIT called Exploring Black Holes. They had an general relativity expert/historian there for a seminar. Some of that lecture is on the internet.

See Einstein's Equivalence Principle, by John Stachel
arcturus.mit.edu/8.224/Seminars/SemReptWk3.pdf
Pete

Chi Meson

Chroot

Picky-Picky!

I don't disagree with you. I actually thought I beat you to the first post this time, but you posted while I was writing! I agree with the "fabric" opinion. I never liked it myself, but you find that these catch phrases sneak in when trying to make short explanations.

But I stand behind the rest as being good enough for starters without being too wrong. Still, your short response was better than mine.

chroot

And Ambitwistor beat us both!

- Warren

Chi Meson

OK, now I'll have to qualify my position. I did some review on Minkowski. I was certain that dealing with acceleration was originally in the realm of GR due to Minkowski's mathematical "fixing" of SR. I remembered that there was something wrong with it. I found a good webstie that not only cleasrs up my confusion, but also clearly states that I have been propagating an error (just as Chroot said).

http://math.ucr.edu/home/baez/physic...eleration.html

Ambitwistor

It originally was in the realm of GR. Then the physics community changed the definition of what GR is, for the reason described above.

pmb

That is incorrect. Gravitational acceleration does not require any kind of "pucker" (i.e. spacetime curvature) at all. Gravitational acceleration/force is a first order effect whereas spacetime curvature is a second order effect. The metric tensor is the quantity which is refered to as the gravitational field. The presences of a g-field in a frame of referance is reflected in the spacetime variablity of the components of the metric when expressed in Minkowski coordinates. For details see

"Einstein's gravitational field" - arxiv.org/abs/physics/0204044

Pete

Ambitwistor

Actually, most relativists today say that there is no such thing as a "gravitational force" at all, in either flat or curved spacetime. And to pre-empt any quixotic exchange you might be inclined to have over it, I will just have my final word right now, and then you can say whatever you want:

First, I know that this is the common modern usage because I speak with gravitational physicists every day, go to conferences, and read the literature.

As to the physics: you can always choose a frame in which a body has a coordinate acceleration, but this does not necessarily represent the action of "a gravitational force". As I said before, accelerated motion in flat spacetime is considered today to be the purview of special relativity, and not implying the existence of a gravitational interaction. The reason why speaking of a "gravitational force" has fallen out of favor is because gravitational motion is inertial, and a straight line in spacetime, and people like to follow Newton in saying that bodies that move inertially in straight lines are not under the influence of an external force.

Once again, it is a matter of terminology. Not that you've said this, but just so we're clear: if someone asks you about gravity and you tell them that in general relativity, gravity is a force, that's fine. But if someone else tells them that it isn't, that's also fine: they're not wrong, they're using a different definition of "gravitational force".

As for Chi Meson's statement, it is not incorrect, it is just vague. In SR, a body in inertial motion appears to accelerate, relatively speaking, if the observer moves non-inertially. This is true in GR too; it accounts for why an apple accelerates relative to me if I drop it. But in GR, the curvature of spacetime is responsible for gravitational effects involving relative accelerations that can't occur in SR. SR can't account for how an observer on the surface of the Earth can see an inertially-moving apple accelerate relatively, if the observer himself is static on the surface of the Earth. (cf Wald, explaining "how does this viewpoint that there is no such thing as gravitational force square with the well-known `fact' that there is a gravitational force field at the surface of the Earth of 980 cm s^-1") SR can't account for how two inertially-moving bodies can accelerate relative to each other, e.g. the Earth orbiting from the Sun's perspective. These are inarguably gravitational effects arising directly from spacetime curvature.

pmb

So? Do you love to vote on these things all the time? You seem obsessed with how many people think what. You actually seemed more interested in how many people have an opinion than you do as to the correctness of that opinion.
Yes yes yes. I know you claim to go to conferences. Big deal. As far as the literature - that is what I'm refering to. Namely Hans C. Ohanian, John A. Peacock, John Stachel, Richard A. Mould etc.
If the 4-force on a paritlce is zero and there is a non-zero coordinate acceleration then, by definition, there is a gravitational force on the particle.
That claim is incorrect.
That is why Einstein concluded that the gravitational force is an inertial force and it is also the reason why Einstein concluded that inertial forces should be considered real forces
(1) GR is about gravity, SR is not (2) If an observer is at rest with respect to a the source of gravitational field and observers and an object in free-fall accelerates relative to him then he cannot concude from that fact that the spacetime is curved. The field might be uniform (i.e. flat spacetime). And in a uniform gravitational field particles will accelerate gravitationally but there is an absense of tidal forces (Riemman = 0). If the field is not uniform then the field can't be completely transformed away (i.e. it's not "permanent" as Tolman would say)
Nobody claimed that SR applies globally in a curved spacetime. In a curved spacetime then SR applies in a locally inertial frame.

Please make an attempt to post without your usual condescending remarks. i.e. to pre-empt any quixotic exchange you might be inclined to have over it - have you learned nothing from the moderator's warnings? If you think that you need to make those statments then do what Integral suggests - us the PM buttom below. Since you seem only want to make those statements publicly then please don't make them again.

chroot

pmb & Ambi,

Your arguments are always about notation and convention. Please, be aware that you're free to use your terms in whatever way you wish, so long as you clearly let other people know what the meanings are.

It's fine to debate the rationale for using or not using terms like "gravitational field," but please -- don't attack each other personally anymore to promote your own set of definitions. Threads like this have promise, and could be very useful to people confused about the way physicists throw around technical words -- but if they just degenerate into name-calling and assertions that "my way is better than yours," it'll just end up locked.

- Warren

Ambitwistor

Pmb, there is no such thing as "correctness of opinion" when it comes to terminology. When you go around "correcting" people's use of terminology, in a thread that is about terminology, I think it is worth pointing out that your terminology is neither universal nor even a majority.

In any case, you appear not to have understood what I said.

Not if you are speaking of 4-force, or proper force, which is the point. All the other interactions exert a nonzero 4-force, with a nonzero proper force, on a body with the appropriate type of charge; gravity never does.

How do you know?

If you don't believe me, go argue with other people who disagree with you, like Wald disagrees with you. Or survey the literature, i.e. papers, which most currently reflect the physics community. E-mail a randomly-selected sample of leading gravitational physicists. Whatever floats your boat, since you seem to care so much. I would be interested to hear the results, actually.

What Einstein said has nothing to do with the fact that terminology changes, or the fact that other people reached other conclusions.

I never said that the existence of relative acceleration implies curved spacetime. In fact, I said that relative acceleration occurs in both SR and GR. You seemed to have missed the point: not everybody considers an accelerating observer in a flat spacetime to experience a gravitational field or see particles "accelerate gravitationally".

Ambitwistor

That was my entire point.

chroot

[moderator hat]
Okay.. just keep it civil. You too, pmb. [:)]
[/moderator hat]

- Warren