Thread: Differentiating between gravity and the General Theory of Relativity

Greetings all,
I'm new to all this, and this is my first post. Please pardon me for mistakes both in a grammatical and scientific sense....

I have read a few news articles on black holes, dark matter, etc. In basically all of them, they use gravity and the General Theory of Relativity interchangeably. Now, I have learned that for the General Theory of Relativity to be true; gravity cannot exist. If mass bends space (I'm using the general form I have learned) then there is no force pulling cosmic objects into orbit; mass (e.g. the sun) bends space causing objects (e.g. the planets) to be moved off of their straight line of constant motion and pulled (sorry, I could only think of the word pulled) into an elliptical orbit.

For gravity to exist, there is a pull on all the cosmic objects which puts them into an elliptical orbit around a large body of mass that has a great gravitational pull. For this to happen, (I have learned) the General Theory of Relativity cannot be true.

Now that I've probably bored you with my shabby knowledge of gravity and the General Theory of Relativity; here is my question:
For either gravity or the General Theory of Relativity to exist/to be true, do they require for the other to not exist?

There we go; I hope that all didn't bore you, thanks for reading!

I hope I don't over reach myself. I don't think general relativity states that gravity does not exist. Gravity is an observed effect. Rather it explains this effect differently than Newtonian physics. What is more, Newtonian physics still works fine for normal objects, it becomes inaddequate when dealing with extaordinary objects at the extremes of size, ie sub atomic and more massive than normal stars.

General Relativity is the theory of gravity.

Perhaps what is confusing you is this. In popular explanations regarding gravity it is described as a force comparable with electromagnetism, the strong nuclear force and the weak nuclear force. In General Relativity it is regarded as an artifact of the gemoetry of space time and not as a 'true' force. But, as AlexG says General Relativity is the mpst popular theory of gravity.

Ah, that explains it. Thanks to everyone who took the time to reply!

Originally Posted by John Galt

{gravity} is described as a force comparable with electromagnetism

Yes. The General Theory was published in 1915. Sometime in 1911 Einstein concluded that the gravitational field and the electromagnetic field are coupled (which even at the time he realised was bonkers - the former is static by assumption whereas the latter is quite definitely not).

Notwithstanding, this led him to the conclusion that, if the energy of the EM field contributes to the gravitational field, then so must the energy of the gravitational field "contribute to itself", so to say.

This quite obviously (I hope) requires a non-linear model of gravitation, which, for Einstein, starts with Riemann geometry and ends with the gravitational field equations as we have known them for close on 100 years

The history of this, in so far as it gives an insight into Einstein's genius (it was no less, in my view), is fascinating.

I could ramble on this for hours...days....weeks....

Wow, this is a lot more than I could've asked for, thanks Guitarist!

General Relativity (at least parts of it) can be applied to objects that are accelerating for reasons other than gravity. In a sense, any acceleration is "bending of space-time".

I'm not sure I understand why gravity is considered special in this respect. Rocket thrusters also bend space-time with respect to a rocket. As near as I can tell, all accelerated motion is curved when you look at it in 4 dimensions.

I am not sure I understand your point.

In its original form, the equivalence principle states that gravitation and acceleration are entirely equivalent.

I trust you all will humour my interest in the history of GR. In 1907, Einstein realised that a body falling under the influence of a gravitational field doesn't "feel its own weight" and is therefore entitled to consider itself in a field-free environment. A gravity-rooted observer knows otherwise - the body is accelerating under the influence of gravity.

Let these two bodies disagree as to what is the "reality" of the situation, and suppose we now reverse the process: the body that denies the existence of a gravitational field (i.e the falling one) is accelerated back to where it came. Even though this guy denies the existence of a gravitational field, it experiences a force that is entirely consistent (under suitable conditions) with the experience of the gravity-bound body.

It is a clever argument, given he had no experience of fast cars and aircraft taking off.

But, at the time about which I spoke earlier, namely 1911, he was forced to modify the equivalence principle to the claim that it holds "only locally", by which he seems to mean for very short light paths.

What I was wondering was why, if all accelerated motion is curved space-time, then why we see gravity being "curvature of space time" as an explanation for gravity. If acceleration and "curvature of space time" are the same thing, then saying that gravity is "curvature of space time" would be the same as saying gravity is "acceleration".

And if that's all we're saying, then we're still right back where Newton put us as far as understanding what gravity is. The only difference is that now we're applying relativistic effects to the acceleration (which would apply no matter what was causing it.)

Originally Posted by Guitarist

I trust you all will humour my interest in the history of GR. In 1907, Einstein realised that a body falling under the influence of a gravitational field doesn't "feel its own weight" and is therefore entitled to consider itself in a field-free environment. A gravity-rooted observer knows otherwise - the body is accelerating under the influence of gravity.

I guess that answers my question. A body accelerated by rocket thrusters definitely feels its own weight. That's a difference, I guess.

If you take a look at the wiki article on Newtonian gravitational potential you can see a "plot of a two-dimensional slice of the gravitational potential in and around a uniform spherical body". It looks like an upturned hat and is reminiscent of the bowling-ball analogy, where the curvature you can see equates to Riemann curvature or "tidal force". The force of gravity at some location relates to the gradient in the potential. If there was no detectable tidal force the upturned hat would resemble a cone, which you can simplify to a V. There's no Riemann curvature, but a horizontal light beam does still curve towards the ground. This is essentially the situation in your accelerating rocket*. Overall it isn't exactly equivalent to a real gravitational field (Einstein used the word "special"), but provided you limit yourself to a small region, it is.

There seems to be some ambiguity about what "curved spacetime" is. I always thought it was the Riemann curvature rather than the curved light beam. It might be interesting to ask around about that and see what answers you get.

* There's also something called Born rigidity, but best leave that for another day.

Originally Posted by Farsight

Riemann curvature ........... There's no Riemann curvature,

Hmm. Just remind us in what way "Riemann" curvature differs from the common-or-garden variety of curvature.

Overall {added my me: ie. globally} it isn't exactly equivalent to a real gravitational field but provided you limit yourself to a small region, it is.

Now isn't that exactly what I said in post #9?

Originally Posted by me

But, at the time about which I spoke earlier, namely 1911, he was forced to modify the equivalence principle to the claim that it holds "only locally"

Farsight, I seriously doubt the depth of your understanding of the geometry of spacetime as it relates to GR

How can we calculate the gravitational potential (potential energy) per unit mass? i mean on what basis we can calculate it. as i am new to this forum please anyone let me know this.