The Claim: Gravitation is acceleration.

1. Jun 9, 2007

Gulliver

The Claim: "Gravitation is acceleration."

Please help me understand. I'm struggling with this claim. I have a BA with a physics major (though 26 years ago), but I don't seem to be able win an argument about this claim. It's important to advancing our understanding, and I politely request your help.

I believe the claim is actually a foreshortened version of "In GR we understand that all gravitation is actually an acceleration." However, gravitation and acceleration cannot be used interchangeably. I've argued rotational acceleration, radioactive decay, and even his car braking.

Based on your answer, I either have some remediation to do and some better communication to deliver.

Last edited: Jun 10, 2007
2. Jun 9, 2007

yogi

The Gravitational Constant has units of volumetric acceleration: meters^3 per sec^2 per kgm. If you transform the volume integral to a surface integral via the divergence theorem, the isotropic divergence acceleration of the Hubble sphere of radius R is 2c^2/R.

Last edited: Jun 9, 2007
3. Jun 9, 2007

Gulliver

Okay. I agree, but ...

If that's an answer to my request, you haven't help me in the least.

4. Jun 9, 2007

yogi

Well, the answer is yes - gravity is an acceleration in the same sense that
a = F/m. But because the acceleration is isotropic, it is not as easy to formulate. A simple backward way to do it is from Friedmann's equation, you can start with the relationship for critical mass - and solve for G as has been done on these boards before. You then get the value of G in terms of factors that are easily identified with acceleration.

5. Jun 9, 2007

cesiumfrog

Perhaps give an example of why you think gravitational acceleration is something locally distinguishable from inertial acceleration?

(The underlying axiom of GR is the identification of these two local concepts, then the curved space-time manifold must be introduced to avoid global self-contradictions, next the Einstein equation is postulated as a quantitative relation between space-time curvature and mass-energy distribution, and the result has always tended to be verified in experiments.)

6. Jun 9, 2007

Gulliver

I'm not getting my question across. Do you agree with the claim "Gravitation is acceleration."? Is, for example, the "acceleration" of a beta particle and a thorium-234 away from the fission of a U-238 atom "gravitation". I say "no".

Thanks for putting up with my late night miscommunication! You've already helped (some).

7. Jun 10, 2007

yogi

They are both accelerations - but they are not both gravitationally driven. The mechanism producing the force can be something other than the attraction of a mass - the distortion of space by mass is only one example of a phenomena that results in a change in velocity

8. Jun 10, 2007

Gulliver

Thanks!

My heartfelt gratitude!

9. Jun 10, 2007

cesiumfrog

By "beta", I'll assume you mean "alpha"? I think this is a bad example (because it's basically a collision/explosion, we can't discuss an acceleration over any significant time-scale), so I'll use the car "breaking" (as you mentioned).

No, I would not say the forward-pulling force is "gravity". In this context, however, neither would I say the down-pulling force on an apple "hanging from a tree" is gravity. I would say the apple is dangling downward because the tree is accelerating upward. (In fact, I said just that in my honours thesis somewhere.) And I'd put it down to space-time curvature that, despite all this acceleration, this Australian (Batlow?) apple tree never gets any further away from the "oppositely" accelerating European orchards. In GR there is no gravitation, only acceleration (and space-time curvature, induced by presence of mass-energy).

Last edited: Jun 10, 2007
10. Jun 10, 2007

Gulliver

I stand corrected on the beta particle. I wonder if you left out a word in this sentence: "No, I would say the forward-pulling force is "gravity"." Thanks.

11. Jun 10, 2007

pmb_phy

I'll do the best I can.
Ah yes. The equivalence principle. That is not exacctly my understanding of it. Here is what I hold as being the equivalence principle.
That's about as close to Einstein's equivalence principle I can get I think.
I see no problem with either senario other than you can't replace a flat spacetime with a curved one. There are ways to generate a Coriolis field by using a rotating shell of matter. The spacetime inside the shell will be flat but there will be a gravitational field present.

Pete

12. Jun 10, 2007

Chris Hillman

Hope this helps

I think you've got this turned on it's head, and I'm surprised no-one said that!

My guess is you are misquoting one of the versions of the Equivalence Principle, which helped guide Einstein during his search for a relativistic field theory of gravitation c.1911-1916, according to which the effects of gravitation in a small lab can be mimicked in deep space (far from any massive objects) by a constant acceleration of the lab. (Aka the "elevator thought experiment".)

Or perhaps you are misquoting the assertion that tidal accelerations are associated, in gtr, with (part of) the curvature tensor of spacetime. Tidal accelerations also arise in Newtonian theory, e.g. when we compare the "gravitational acceleration" of small objects dropped at different heights above the surface of the Moon (an example chosen since it's easier to neglect atmospheric drag there), and find that the lower object draws ahead as the pair falls.

If you are saying that not all accelerations are due to gravitation, that is of course quite correct. If you are trying to distinguish, in the Equivalence Principle, between linear acceleration (e.g. pushing on a rod) and angular acceleration (e.g. spining up a disk), well, this quickly get's very technical, so let's try to clear up easier conceptual issues first.

Last edited: Jun 10, 2007
13. Jun 10, 2007

pmb_phy

There is an article in the American Journal of physics on this topic. The article is called What is the principle of equivalence?, Hans C. Ohanian, Am. J. Phys. 45(10)), October 1977*

The abstract is located at
http://www.geocities.com/physics_world/journal_articles/abstracts/Ohanian_1977_abstract.htm

I can e-mail the entire article to you but your e-mail provided must be able to handle single file transfers of 10Meg since the article, in PDF format, is slightly smaller than that.

I myself wrote an article on the subject and placed it on the internet. The article is at http://xxx.lanl.gov/abs/physics/0204044 Einstein's gravitational field, by Peter M. Brown

Best wishes

Pete

14. Jun 10, 2007

pervect

Staff Emeritus
Note that this article should not be regarded as being peer-reviewed, but simply as a fuller and more detailed exposition of PMB's personal views on the topic.

My personal \$.02 is that while I would agree that the view on the "gravitational field" may have evolved since Einstein's time, such evolution does not imply that the modern ideas are in any way inferior to Einstein's ideas. In fact, I would argue that the more evolved ideas are just that - more evolved.

15. Jun 10, 2007

Chris Hillman

The nature of gtr

Just to amplify pervect's point:

During the Golden Age of General Relativity (roughly 1965-1975), it became very clear that the true nature of gtr is in several crucial respects quite different from what Einstein anticipated when he laid down a complicated system of desiderata for the theory he was seeking in about 1913 (give or take a few years).

One of the many amazing things about gtr is that this theory satisfies essentially all of the well-formulated criteria Einstein wanted to satisfy. It turns out not to satisfy his most imprecise criterion, that the theory should in some sense realize Mach's notoriously murky ideas, however. (To make a very long story very short.) Still, when you consider the list of desiderata, gtr really seems to be a virtually miraculous creation. It's very difficult to create a self-consistent physical theory which is well-motivated; Einstein's success in creating a theory which also satisfies a sizeable list of criteria will forever stand as a landmark in intellectual history! In addition, gtr has won universal acclaim as one of the most beautiful physical theories ever devised, maybe even the most beautiful. And on top of all of these virtues, it has been one of the most successful theories of all time.

There was simply no possibility of anticipating c. 1913 very many of the profound implications the new theory would have, in part because the mathematical tools required to understand and develop gtr were then little known and themselves not yet highly developed. One of the interesting and perhaps little appreciated aspects of the history of gtr (little appreciated outside mathematics and physics, that is), is how many profound advances in 20th century mathematics occured partly in response to the technical challenges posed by gtr. One in particular, Cartanian geometry, may finally be coming into its own some eighty years after it was created. Recognition of the importance of distinguishing between local and global structure in geometric formulations of physical theories also owes much to gtr.

I've posted at great length in the distant past (in sci.physics.*) about the revolutionary advances in our understanding of gtr which occured during the Golden Age, so interested readers can Google for those expositions.

Last edited: Jun 10, 2007
16. Jun 11, 2007

Gulliver

That's the ticket!

Thank you, sir. A kind, accurate, and understanding response! I've taken the liberty of PMing my email address. Thanks again.

17. Jun 11, 2007

pmb_phy

Thank you kind Sir and you're most welcome. I didn't get a PM by the way. Perhaps you should try sending it again.

Pete

18. Jun 19, 2007

pmb_phy

There is very little, if any, of my personal opinion in this paper. It is an historical tracing of the term "gravitational field", defined by Christoffel symbols. I recommend reading a paper before you try to tell other people what the contents is about. Its not like this is an outlandish idea. Even John Stachel (Einstein expert and GR expert) at BU holds the same opinion as Einstein did. I'm not sure if I mentioned my personal opinion in it.

Tell me something. What part of my (historical outline) paper indicates that my opinion about anything is in there? In that paper I merely follow Einstein's views throughout his life on this topic as well as quote his own textbooks, expecially his The Meaning of Relativity.
Modern according to whom? Dr. Stachel is certainly a modern day physicist and he holds to Einstein's definition on this topic, i.e. Gravitational field = affine connection. Don't get me wrong though. Einstein's definition is rarely if ever seen used in modern GR textbooks. I wish these textbooks would at least mention the original definition so that people can better understand what he meant by the equivalence principle regarding a uniform g-field and a uniformly accelerating frame. MTW do state that sometimes the affine connection is identified as the g-field.

If you turn to MTW page 467 you will see this mentioned, i.e. they state "No Gamma's means no 'gravitational field'"

Pete

Last edited: Jun 19, 2007
19. Jun 20, 2007

pmb_phy

Why do you believe that? This article was sent to the American Journal of Physics for submission to be published in that journal. It was peer-reviewed and sent back to me. The reviwer's found no error in the paper. They didn't publish it because (1) they claim that they're not interested in publishing articles of an historical nature and (2) that they didn't think readers would care about the subject. But, again, they found no errors. So is it peer-reviewed or not. It sounds to me like you're associating the terms "peer-reviewed" and "published" as being the same thing, are you not?

Pete