# [Help]whatis the relationship between general and special relativity

• silver
In summary, general relativity includes gravity, 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. Additionally, in the limit of both low velocities and low "field" strengths, special relativity reduces to Galilean relativity.f

#### 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...

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

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.

Originally posted by Chi Meson
We could go on and on with this one.
Or.. well.. we can nitpick anyway.
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.
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 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).
Special relativity is special because it does not include gravitation. It is a special case of general relativity, and is aptly named.
General relativity looks at the effects of acceleration
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

Originally posted by silver
whatis the relationship between general and special relativity?

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.

Originally posted by 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...

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.

"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
All this is telling us is that an inertial frame in a gravitational field is one in which a particle experiences no force. That is, it is a “freely falling” frame. To experience one, try bungee jumping off the top of a tall building. As you fall, you experience no gravitational force—as though you were in outer space with no gravity present. This is not, however, the situation we are studying here. We want to be in a frame where the metric is not locally constant. so it would defeat the purpose to choose an inertial frame.
When Eisntein realized this he referred to that idea as
The happiest thought of my life.
He wrote
The gravitational field has only a relative existence... Because for an observer freely falling from the roof of a house - at least in his immediate surroundings - there exists no gravitational field.
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
Like the electric field generated by electromagnetic induction, --- the gravitational field has only a relative existence." ... The similarity between the inertio-gravitational field is quite clear: What is absolute (i.e. independant of the inertial frame of referance) is the presence of the inertio-gravitational field. What is relative (i.e. dependant on the individual frame of reference) is the division of this field into inertial and gravitational components. ... At any time and at any point you can take a frame of referance that makes the gravitational field go away ... you can always say "I'm at rest look, I perform my experiments in my local frame and everything looks like its ar rest ..." if you look at observers nearby [however] they are either accelerating towards you or away from you ... relative acceleration is a thing that cannot be transformed away ... this is a deeper meaning of curvature ... the curvature tensor is just a way of measuring relative acceleration.

Pete

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.

Originally posted by Chi Meson
Still, your short response was better than mine.
And Ambitwistor beat us both!

- Warren

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/physics/Relativity/SR/acceleration.html

Originally posted by Chi Meson
I was certain that dealing with acceleration was originally in the realm of GR due to Minkowski's mathematical "fixing" of SR.

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

Originally posted by Chi Meson
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.
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 referred 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

Originally posted by 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.

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.

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Originally posted by Ambitwistor
Actually, most relativists today say that there is no such thing as a "gravitational force" ..
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.
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.
Yes yes yes. I know you claim to go to conferences. Big deal. As far as the literature - that is what I'm referring to. Namely Hans C. Ohanian, John A. Peacock, John Stachel, Richard A. Mould etc.
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".
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.
As I said before, accelerated motion in flat spacetime is considered today to be the purview of special relativity,
That claim is incorrect.
... because gravitational motion is inertial,..
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
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.
(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)
SR can't account for how two inertially-moving bodies can accelerate relative to each other
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 statements 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.

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

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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.

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.

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.

That claim is incorrect.

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.

That is why Einstein concluded that the gravitational force is an inertial force and its also the reason why Einstein concluded that inertial forces should be considered real forces

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

(1) GR is about gravity, SR is not (2) If an observer is at rest with respect to a massive body and observers an object in free-fall accelerate 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 g-field particles will accelerate gravitationally but there is an absense of tidal forces (Riemman = 0)

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".

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Originally posted by chroot
pmb & Ambi,

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.

That was my entire point.

Originally posted by Ambitwistor
That was my entire point.
[moderator hat]
Okay.. just keep it civil. You too, pmb.
[/moderator hat]

- Warren

Originally posted by Ambitwistor
Pmb, there is no such thing as "correctness of opinion" when it comes to terminology.
Not if you are speaking of 4-force, or proper force, which is the point.
That is incorrect. The gravitational force is not a 4-force.
How do you know?
Claims such as is considered today means that the entire community holds such an opinion. That is clearly not the case. In fact the most authoritative GR expert that I know of, i.e. John Stachel, holds otherwise.

Or survey the literature, i.e. papers, which most currently reflect the physics community.
Your forcing definition - i.e. you're insunutating that modern physics text should not be included in the literature you refer to.

...not everybody considers an accelerating observer in a flat spacetime to experience a gravitational field or see particles "accelerate gravitationally".
Not everybody considers 1 + 1 to be equal to 2 either. So what?

re - e-mailing people. Don't give advice that you would never take. I've given that advice to you before and you've always ignored it.

General Relativity and Gravitation, Proceedings of the 11th International Conference on General Relativity and Gravitation, (Stockholm,Cambridge University Press, Jul 6-12, 1986), "How Einstein Discovered General Relativity: A Historical Tale With Some Contemporary Morals," J.J. Stachel

This paper reflects Stachels opinion on how gravity should be defined, i.e. according to Einstein's definition rather than the (inorrect) way that Von Laue suggested.

As far as how "SR" is defined one simply has to look in Schutz's text or most other modern physics texts.

Originally posted by pmb

Then what was the point of your remark concerning the correctness of opinions?

That is incorrect. The gravitational force is not a 4-force.

That's what is said by those who say that gravity is a force. The whole point is that other people do not say that.

Claims such as is considered today means that the entire community holds such an opinion.

No, it doesn't, and I specifically said that there are those who use the other definition.

In fact the most authoritative GR expert that I know of, i.e. John Stachel, holds otherwise.

You pick your experts and I'll pick mine.

Your forcing definition - i.e. you're insunutating that modern physics text should not be included in the literature you refer to.

As I've said more than once, papers are much more current when it comes to describing the state of the active physics community. Or just go out and just talk to people. Sheesh. You are never going to learn what the physics community thinks if you are outside of it.

Not everybody considers 1 + 1 to be equal to 2 either. So what?

re - e-mailing people. Don't give advice that you would never take.

Huh? Why? I'm not interested in collecting statistics, but since you care so much, I thought you might be.

This paper reflects Stachels opinion on how gravity should be defined,

What Einstein thinks, or what Stachel thinks, isn't the point of the discussion.

i.e. according to Einstein's definition rather than the (inorrect) way that Von Laue suggested.

If people decide to define a word differently, they can do that. It happens all the time. Just because it disagrees with Einstein's definition doesn't mean it's "incorrect". It's just different.

As far as how "SR" is defined one simply has to look in Schutz's text or most other modern physics texts.

Or Wald's text, or any of the others that you appear to ignore.

I have to weigh in here about the facts (though I'll decline to state my opinion).

Wald's book (which is really an excellent text, and is highly respected) does indeed use the label "special relativity" to describe any physics (including accelerations) in Minkowski spacetime. It is also the most modern text I know of in its tensor notation.

- Warren

Schutz's text is also quite an excellant text. Schutz states
Although the concept of relativity is old, it is customary to refer to Einstein's theory simlply as 'relativity'. The adjective 'special' is applied in order to distinguish it from Einstein's theory of gravitation, which acquired the name 'general relativity' because it permits one to describe physics from the point of view of both accelerated and inertial observers and is in that respect a more general form of relativity. But the real distinction between these two theories is that special relativity (SR) is capable of descrinbing physics only in the absense of gravitational fields, while general relativity (GR) extends SR to describe gravitation itself. One can only wish that an earlier generation of physicists had chosen appropriate names for these theories.
The difference comes into what one means by "gravity." and most GRists never knew that "gravity = curvature" was not Einstein's view.

Pete

I like Schutz's text too; it is probably the best single technical introduction to GR for someone with no exposure to the theory, and he does a good job of summarizing the historical point of view. I don't know if it's the case that "most GRists never knew" Einstein's view; if you read his papers, he clearly concentrates on the Christoffel symbols (as derived from the metric) when describing the gravitational field.

You actually run into this issue in non-gravitational areas of physics, too; in electromagnetism, for example, people sometimes argue over whether A or F (analogous to the GR &Gamma; or R) is "the electromagnetic field"; clearly, A has a physical effect (e.g. Aharanov-Bohm), but it has been also common to refer to "electric fields" and "magnetic fields" as components of F. Once again, it is a matter of definition.

Arguing as to whether A or F is the EM field is equivanent to argueing as to whether the metric tensor if the Christoffel symbols is the g-field. A is a potential where F is defined in terms of the derivative of A. GR is no diffferent in Einstein's view - The Christoffel symbols are the derivative of the components of the metric. That's why those components are referred to as the gravitational potentials. In Newtonian gravity its the same as arguing as to whether the gravitational acceleration or the gravitational potential is the field - however the curvaure interpretation is similar to a Newtonian arguing that its the Newtonian tidal force tensor which is the g-field.

http://www.geocities.com/physics_world/tidal_force_tensor.htm

The thing about the Christoffel symbols is that they aren't tensors, and so equations in Christoffel symbols aren't generally covariant; a C. symbold can be 0 in one coordinate frame and non zero in another. But when you combine them into the curvature tensor you get something that is generally covariant, at the equation level; if the curvature tensor is zero in one frame it is zero in all frames..

Originally posted by pmb
Arguing as to whether A or F is the EM field is equivanent to argueing as to whether the metric tensor if the Christoffel symbols is the g-field.

No, I think it is more analogous to arguing whether the Levi-Civita connection (or its components upon choosing the standard fiducial connection, which are the Christoffel symbols) or the Riemann tensor is the field; the latter is the curvature of the former, just as F is the curvature of A in Yang-Mills theory. The people who say that the vanishing of the Riemann tensor means an absence of the gravitational interaction are typically those who say that the vanishing of the electric and magnetic field vectors (or the electromagnetic field tensor) means an absence of the electromagnetic interaction.

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Originally posted by Ambitwistor
The people who say that the vanishing of the Riemann tensor means an absence of the gravitational interaction are typically those who say that the vanishing of the electric and magnetic field vectors (or the electromagnetic field tensor) means an absence of the electromagnetic interaction.

Those who say Reimman = 0 means no g-field are the same people who say F = 0 means no EM field