Gravity: real force or artefact of acceleration?

[pmb_phy]

I take the point of view in this discussion that "real" implies something objective, independent of a particular observer, and independent of the choice of coordinates.

That seems to imply that you believe that potential energy and kinetic enrgy are not real. That's fine but I don't think you'd have a problem defining them, right?

However, "the electric field observed by observer A" is real since, once observer-A has been distinguished, (E_{\mbox{\small seen by A}})_{a}=F_{ab}(v_{\mbox{\small A}})^b is agreed by all observers. Similarly,
"the x-component of a vector with the usual axes parallel to the sides of this post" is real.

It is always implied that inertial forces are observer dependant. That's something that should never be needed to say. So why would you assert that "the electric field observed by observer A" is okay but not "the gravitational field observed by observer A" not be? By the way. That definition you gave for the E field applies to only one point in spacetime whereas the gravitational field g_uv applies throughout spacetime as does the gravitational force.

I took a closer look at Wald. He says something weird. On page 67 he writes "...that we cannot in principle - even by complicated procedures - construct inertial observers in the sense of special relativity and measure a gravitational force."

That comment makes no sense since that is exactly how the gravitational force is seen to work. I.e. when you're in an inertial frame then you have transformed the gravitational force away! His further comments about geodesics is merely a description of what happens, not an explanation. He seems to want to geometerize the gravitational field like everybody else. That's fine. But that is his opinion and he, like most other GRists, are entitled to that. But I've have to go with Einstein and Weingberg when they say otherwise. That is part of the source of my opinion. And it is just that, an opinion, just as you and others have their opinion. This subject is juust as subjective as many otherones we've discussed.

Note: You don't have to respond to my last PMs. I was just uncertain if you were getting/reading them. Now that I know that you are then there's no need.

Pete

 

[robphy]

That seems to imply that you believe that potential energy and kinetic enrgy are not real. That's fine but I don't think you'd have a problem defining them, right?

I wouldn't say that the notions of "potential energy" and of "kinetic energy" aren't real.

For example:
"The [particular value of the] potential energy of a ball" has no objective reality.
"The [particular value of the] potential energy of a ball with respect to the ground" does.
As we often say, the value of the potential energy is not really physically meaningful... but the "difference in potential energy between two positions" is.

Similarly, as you know
"the [particular value of the] kinetic energy" depends on the frame of reference.
A ball on a jet has more kinetic energy with respect to the ground that with respect to the jet itself.

This is all classically speaking, of course.

So, this is consistent with my electric field example earlier... the notion of an electric field exists... but its value (i.e. magnitude and direction) is observer-dependent... so, it does not make sense to refer to it as "the electric field"... unless you say "the electric field observed by observer-A".

 

[pmb_phy]

For example:
"The [particular value of the] potential energy of a ball" has no objective reality.
"The [particular value of the] potential energy of a ball with respect to the ground" does.
As we often say, the value of the potential energy is not really physically meaningful... but the "difference in potential energy between two positions" is.

Similarly, as you know
"the [particular value of the] kinetic energy" depends on the frame of reference.
A ball on a jet has more kinetic energy with respect to the ground that with respect to the jet itself.

I assume you know that this is the reason I gave those examples? I.e. that there are quantities which by their very nature are observer dependant, just like inertial forces. Because I don't use the word "observer A" it should be understood that there is a particulate observer in mind since we already agree (I hope?) that there is an implied observer in mind.

This is all classically speaking, of course.

So, this is consistent with my electric field example earlier... the notion of an electric field exists... but its value (i.e. magnitude and direction) is observer-dependent... so, it does not make sense to refer to it as "the electric field"... unless you say "the electric field observed by observer-A".

Do you agree that a non-inertial observer would detect a particle, whose 4-velocity is zero (i.e. a "free-particle"), is, in general, accelerating moving with respect to the observer? Seems to me that one can apply the same reasoning to gravitational acceleration as you did above within the scope of relativity. Whether a 4-vector can be created from it is another story. I suspect that it's possible, but not easy. It would be defined by the deviation of the world lines, one of which is a geodesic (the free-particle) and the other is not. The observer would consist of the observers 4-velocity which is on a non-geodesic world line.

Edit:

It just occurred to me that my idea above would only work locally since a displacement 4-vetor only has meaning locally. I guess that's why define the gravity field/force according to the Christoffel symbols! In any case I want to make it clear that when I use the term "inertial force" then you should traslate it in your mind to mean "fictitious force." It seems to me that people might not understand what the term "inertial force" means, i.e. that it is a term which people use for "fictious forces" when they don't want people to get any idea of a negative conotation when the term "fictious " is used. Of course this was all explained in that web page I posted so anyone who actuall read the definition should already know this. Here is that link again for your convinience http://www.geocities.com/physics_world/gr/inertial_force.htm

Please note that this page is currently in flux since I've been trying to get it right without referencing gravity at the same time. I'm so used to the Equivalence Principle that its hard for me to not think of it when discussing only inertial forces.

Pete

 

[mendocino]

Gravity: real force or artefact of acceleration?

Following quote of California Institute of Technology theoretical physicist and 2004 Nobel laureate David Politzer

http://www.sciam.com/askexpert_question.cfm?articleID=ABE57453-E7F2-99DF-32538FF7C7B37F20

With general relativity, Einstein managed to blur forever the distinction between real and fictitious forces. General relativity is his theory of gravity, and gravity is certainly the paradigmatic example of a "real" force. The cornerstone of Einstein's theory, however, is the proposition that gravity is itself a fictitious force (or, rather, that it is indistinguishable from a fictitious force). Now, some 90 years later, we have innumerable and daily confirmations that his theory appears to be correct.

 

[Chris Hillman]

When is popsci too oversimplified?

Hi, mendocino,

I hope you noticed that Politzer was writing for a popular science organ (Scientific American). His statement is an oversimplified reference to the Equivalence Principle (c.f. "elevator experiment"), which is indeed one of the insights which guided AE on the path towards gtr, but gtr in fact treats gravitation rather differently from the impression which might be left by his statement read in isolation.

See for example the popular book by Robert M. Wald, Space, time, and gravity : the theory of the big bang and black holes, University of Chicago Press, 1977. Wald is a specialist in gtr and IMO this little book paints a much more faithful picture for general audiences of how gtr treats gravitational phenomena and how its predictions differ from Newtonian gravitation.

You might also try various recent posts by myself in which I tried to clear up a common confusion concerning how "acceleration" is treated in gtr, as compared to how the effects of a "gravitational field" on the motion of small objects is treated. See [post=1494972]this[/post], [post=1498288]this[/post], and [post=1482542]this[/post], plus older posts collected in my current sig.

 

[robphy]

Indeed... It's best to learn modern general relativity from a modern expert in general relativity.
A Nobel or Fields Medal prize winner is not necessarily such an expert in modern GR.
A Caltech or Harvard professor is not necessarily such an expert in modern GR.
An early researcher in relativity is not necessarily such an expert in modern GR.

 

[pmb_phy]

The cornerstone of Einstein's theory, however, is the proposition that gravity is itself a fictitious force (or, rather, that it is indistinguishable from a fictitious force).

I disagree. What Einstein said was that the force of gravity cannot be distinguished from inertial forces (aka "fictitious" forces) and as such what used to be referred to as "fictitious" forces can just as easily be taken as "real".

I got into this much deeper in a new web page I created which is located at

http://www.geocities.com/physics_world/gr/inertial_force.htm

Notice Einstein's comments in the February 17, 1921 issue of Nature [28]

Can gravitation and inertia be identical? This question leads directly to the General Theory of Relativity. Is it not possible for me to regard the Earth as free from rotation, if I conceive of the centrifugal force, which acts on all bodies at rest relatively to the earth, as being a "real" gravitational field of gravitation, or part of such a field? If this idea can be carried out, then we shall have proved in very truth the identity of gravitation and inertia. For the same property which is regarded as inertia from the point of view of a system not taking part of the rotation can be interpreted as gravitation when considered with respect to a system that shares this rotation. According to Newton, this interpretation is impossible, because in Newton's theory there is no "real" field of the "Coriolis-field" type. But perhaps Newton's law of field could be replaced by another that fits in with the field which holds with respect to a "rotating" system of co-ordinates? My conviction of the identity of inertial and gravitational mass aroused within me the feeling of absolute confidence in the correctness of this interpretation.

Pete

 

[mendocino]

Hi, mendocino,

I hope you noticed that Politzer was writing for a popular science organ (Scientific American). His statement is an oversimplified reference to the Equivalence Principle (c.f. "elevator experiment"), which is indeed one of the insights which guided AE on the path towards gtr, but gtr in fact treats gravitation rather differently from the impression which might be left by his statement read in isolation.

See for example the popular book by Robert M. Wald, Space, time, and gravity : the theory of the big bang and black holes, University of Chicago Press, 1977. Wald is a specialist in gtr and IMO this little book paints a much more faithful picture for general audiences of how gtr treats gravitational phenomena and how its predictions differ from Newtonian gravitation.

You might also try various recent posts by myself in which I tried to clear up a common confusion concerning how "acceleration" is treated in gtr, as compared to how the effects of a "gravitational field" on the motion of small objects is treated. See [post=1494972]this[/post], [post=1498288]this[/post], and [post=1482542]this[/post], plus older posts collected in my current sig.

What's so different?
Could you elaborate the following statement?

>>> gtr in fact treats gravitation rather differently from the impression which might be left by his statement read in isolation.

 

[Chris Hillman]

Ftfl!

Could you elaborate the following statement?

I have done so in the past few days; please see the posts I cited.

 

[mendocino]

Can you tell me the following link is what you referred to?
https://www.physicsforums.com/showthread.php?t=196359
If not, where can I find it?
Thanks...

 

[Chris Hillman]

The links I mentioned were the links I mentioned.

 

[mendocino]

What's "modern General Relativity"?

Indeed... It's best to learn modern general relativity from a modern expert in general relativity.
A Nobel or Fields Medal prize winner is not necessarily such an expert in modern GR.
A Caltech or Harvard professor is not necessarily such an expert in modern GR.
An early researcher in relativity is not necessarily such an expert in modern GR.

Can you tell me what's this "modern general relativity"?
What's the difference between Einstein's GR and so called "modern GR"?

 

[robphy]

In my opinion,
I would describe "modern general relativity" as the geometrical formulations of relativity as found in modern textbooks like Wald and Hawking&Ellis. These texts [based on modern research in relativity, starting from, say, from 1956 (Synge's relativity text)] represent the attempt to capture physical ideas with precise mathematical structures that model them. With such precision, it becomes easier to discuss, analyze, and make predictions of the physics.

I'm not sure how Einstein would react to the formalism...
...but one might look to his initial reaction to Minkowski's reformulation
...then his eventual acceptance and extension of it.

 

[Chris Hillman]

I Hope You Aren't Just Playing Word Games...

What's the difference between Einstein's GR and so called "modern GR"?

For quite a few years after Einstein introduced gtr, physicists (including AE) had great difficulty disentangling geometric phenomena from artifacts of a particular coordinate chart. It took many decades before most physicists working on gravitation finally understood such a basic point as the fact that according to gtr, a gravitational wave consists of ripples in curvature. During these difficult years, mathematicians--- working in part to fill the need for simple computational tools--- introduced and popularized methods which focused attention on geometrical phenomena. During the Golden Age of Relativity, c. 1960-1970, many major advances where made due to adoption by the leading researchers of the new methods. A well known example is the kinematic decomposition of a timelike congruence in a Lorentzian manifold into acceleration and vorticity vectors and expansion tensor. One might also mention the optical scalars and various decompositions of the Riemann tensor.

These techniques were not discussed in the earliest textbooks on gtr because they were not yet available when those books were written. In 1973, two landmark books appeared: the monograph by Hawking and Ellis and the textbook by Misner, Thorne, and Wheeler. These finally made available the geometric viewpoint widely avaible to students and nonspecialists.

So roughly speaking, gtr textbooks published after 1973 are modern; those published before are premodern.