Gravity / equivalence principle

[jbusc]

This may be stupid question...

Equivalence principle - there is no experiment in a closed laboratory to determine if the lab is accelerating or at rest in a uniform gravitational field.

It seems, then, that it is a fundamental property of the universe that one can always consider themselves at rest, at the center of the universe, regardless of situation.

If gravitational fields did not exist, would it be difficult or impossible to make that statement, and one could always determine that they were accelerating and not at rest? That gravitational fields preserve the "general relativity" of the universe? thanks. :)

 

[Tzemach]

This is the basis of what Einstein said; there is no way to tell if you are accelerating or in a gravitational field - it is all relative.

 

[George Jones]

I would be a little more careful in attempting a statement of the equivalence principle. For example, I'm not sure what "at rest in a uniform gravitational field" means.

Possible statement of the equivalence principal: For any given experimental apparatus, there exists a spacetime region such that in this region, the apparatus cannot produce any results that show many difference from special relativity (including acceleration).

This still might not be a good enough statement.

Mathematically, a small neighbourhood of an element of a differntiable manifold "looks like" a small region of the tangent space at that element. For me, the statement of the equivalence principle has the flavour of an epsilon-delta definition of a limit.

It seems, then, that it is a fundamental property of the universe that one can always consider themselves at rest, at the center of the universe, regardless of situation.

Again, I'm not sure what either "at rest" or "at the centre of the universe" means. As robphy pointed out in another thread, another poster was using at rest to mean "inertial," but I don't think this is the meaning you intend.

You might want to look at https://www.physicsforums.com/showthread.php?t=119922" that I wrote a while ago, as well as other posts in the thread.

Keep posting - relativity is counter-intuitive and it take time an effort to build up intuition, and talking about it helps. Someone is bound to post something that makes sense to you.

 

[jbusc]

I would be a little more careful in attempting a statement of the equivalence principle. For example, I'm not sure what "at rest in a uniform gravitational field" means.

I'm quoting straight from Hartle's General Relativity text. He states (my understanding, at least) that the essence of the equivalence principle is that there is no experiment in a closed laboratory which can determine if the laboratory is undergoing uniform acceleration, or is at rest in a uniform gravitational field. "uniform gravitational field" is his words, not mine.

Personally, I interpret "at rest" to mean no fictitious forces are present, which means no accelerations.

I'm just trying to figure out, since in a universe without gravity the equivalence principle would not hold, therefore, not all reference frames can be claimed to be at rest. Gravity allows all closed-lab reference frames, non-inertial or not, to be equally able to be considered "at rest"

 

[George Jones]

I'm quoting straight from Hartle's General Relativity text. He states (my understanding, at least) that the essence of the equivalence principle is that there is no experiment in a closed laboratory which can determine if the laboratory is undergoing uniform acceleration, or is at rest in a uniform gravitational field. "uniform gravitational field" is his words, not mine.

Hartle does use the words "at rest" near the top of page 113, but not in the boxed statement on page 119, and not in the first sentence of section 7.4, which is close to what I wrote.

Personally, I interpret "at rest" to mean no fictitious forces are present, which means no accelerations.

If you mean zero 4-acceleration, then the terms "inertial" or "freely falling" are usually used. Again, I don't know if this is what you mean.

Hartle is not trying to be precise, and he's comparing someone standing on the Earth "at rest" in a (roughly) uniform gravitational field to someone acceleraring in a rocket acceleration in flat space. In both cases, the 4-acceleration is non-zero. In particular, the guy standing "at rest" on the Earth has non-zero acceleration.

I'm just trying to figure out, since in a universe without gravity the equivalence principle would not hold, therefore, not all reference frames can be claimed to be at rest. Gravity allows all closed-lab reference frames, non-inertial or not, to be equally able to be considered "at rest"

Sorry, I'm not trying to be difficult, but I'm having a bit of trouble understanding what you're trying to say.

I think my statement (and the 7.4 statement) of the equivalence principle holds trivially when there is no gravity.

As for "at rest" - any observer in GR or SR, accelerated or not accelerated, is at "rest" with respect to himself.

I hope that we're no talking past each other too much.

 

[jbusc]

It's ok, I appreciate you trying to interpret what I'm saying :)

It's just, while I like how Hartle lays things out, he can be really imprecise and informal at times and it's difficult to gain a real understanding of what is going on behind the scenes beyond just an intuitive guess. At times it seems like it's not much more than the "hollywood" popular science explanations produced for the general public.

I'm trying to prepare for a real GR class that uses Carroll as a textbook and my prof said that given my background (engineering, not physics) I might want to study Hartle before diving into Carroll.

 

[pmb_phy]

Equivalence principle - there is no experiment in a closed laboratory to determine if the lab is accelerating or at rest in a uniform gravitational field.

That is correct. What "at rest" means is pretty obvious. In fact the way you stated it is nearly identical to how Einstein stated it in his 1911 article Gravitation and Light and in his 1916 article The Foundation of the General Theory of Relativity.

For those who don't understand what Einstein means by "at rest in a gravitational field" then let me elaborate. The term "at rest at a point in a gravitational field" quite literally means that a particle which is moving inertial in frame K' will be accelerating as viewed from a system of reference K, which is itself accelerating relative to K'. The system K can (and is) said to be at rest in a gravitational field.


For the mathematically inclinded, no $\Gamma$'s means "no gravitational field."

If tidal forces are present then there is a stronger statement of the equivalence principle: The gravitational field at any point in space can be transformed away. However if these tidal forces present then, if your instruments for a particular experiment are incapable of detecting the tidal forces, then it is said that the gravitational field has be transformed away when one transforms to a system where all $\Gamma$'s vanish. However, in principle (not in practice), one can always detect the presence of a tidal forces (i.e. curved spacetime). There have been debates about this in the relativity literature as to the meaning of the equivalence principle.

Pete

 

[George Jones]

I'm trying to prepare for a real GR class that uses Carroll as a textbook and my prof said that given my background (engineering, not physics) I might want to study Hartle before diving into Carroll.

I like Hartle very much, and if I were to teach an undergarduate course on relativity, I think I would choose Hartle as the text. Put me in the same situation ten years ago (fantasizing that Hartle existed), and I would have been appalled at the thought of using Hartle!

At the University of Chicago last fall, Carroll http://http://cosmicvariance.com/2005/12/02/spacetime-and-black-holes/" , and he used Hartle!

Deciding how to teach a relativity course is a difficult task, even for someone like http://arxiv.org/abs/gr-qc/0511073" .

I think Hartle and Caroll complement each other nicely, and a joint review of Hartle and Carroll in the January 2005 issue of Physics Today comes to a similar conclusion.

One thing that I learned during my student and post-student years - different people learn differently. One size doesn't fit all. I'd be interested in hearing about any further opinions and experiences (the good, the bad, and the ugly) that you have about/with Hartle.

 

[robphy]

I like Hartle very much, and if I were to teach an undergarduate course on relativity, I think I would choose Hartle as the text. Put me in the same situation ten years ago (fantasizing that Hartle existed), and I would have been appalled at the thought of using Hartle!

At the University of Chicago last fall, Carroll http://http://cosmicvariance.com/2005/12/02/spacetime-and-black-holes/" , and he used Hartle!

Deciding how to teach a relativity course is a difficult task, even for someone like http://arxiv.org/abs/gr-qc/0511073" .

I think Hartle and Caroll complement each other nicely, and a joint review of Hartle and Carroll in the January 2005 issue of Physics Today comes to a similar conclusion.

One thing that I learned during my student and post-student years - different people learn differently. One size doesn't fit all. I'd be interested in hearing about any further opinions and experiences (the good, the bad, and the ugly) that you have about/with Hartle.

Just before this summer's AAPT national meeting in Syracuse, there is the
"AAPT Topical Conference: Teaching General Relativity to Undergraduates"
http://www.aapt.org/Events/topical_conference.cfm
http://www.aapt.org/Events/pdf/20060111ProgramPost.pdf

If anyone else is attending, let me know.

 

[jbusc]

I like hartle too, it's just that it seems like it's trapped halfway between a book suited to self-study and a book suited to supplement a lecture class. In some places it's a little vague and skips around too much.

I think, from what I've heard, when I get Carroll (I haven't purchased it yet) I will probably agree that Hartle and Carroll supplement each other. But since I am thinking of taking a grad-level GR course(using Carroll) with an engineering background - I was recommended starting with Hartle because of his "physics first" approach which would bring me up to speed on the various physics background I would need faster.

 

[pmb_phy]

I like hartle too, it's just that it seems like it's trapped halfway between a book suited to self-study and a book suited to supplement a lecture class. In some places it's a little vague and skips around too much.

I think, from what I've heard, when I get Carroll (I haven't purchased it yet) I will probably agree that Hartle and Carroll supplement each other. But since I am thinking of taking a grad-level GR course(using Carroll) with an engineering background - I was recommended starting with Hartle because of his "physics first" approach which would bring me up to speed on the various physics background I would need faster.

I would recommend that you spend the summer reading and becomming proficient in Geometrical Mathematical Physics by Bernhard F. Schutz. It will give you all the math that you'll need to understand Carrol. Carrol goes over this math lightly.

Pete