The Validity of Force and Point Particles in Special Relativity

[pervect]

You may be implicitly switching between two views of "inertial forces" here. Strictly speaking, there is a key physical difference between "inertial forces" and "real forces": real forces are actually felt as acceleration; inertial forces are not. This is modeled in differential geometry as the covariant derivative of a worldline: it's zero for a body moving solely due to "inertial forces", but nonzero for a body subject to "real forces".

But often when we talk about "inertial forces", we forget that the actual "force" we feel is not due to the inertial force itself; it's due to the real force that is pushing us out of the geodesic path that the inertial force would have us follow. I feel a force sitting here on the surface of the Earth, and speaking loosely I might say this is the "force of gravity": but actually it's not, it's the force of the Earth pushing on me. A rock falling past me is moving due to the "force of gravity", but it feels no force. The principle of equivalence does not require me to say that I and the rock are equivalent; so IMO it doesn't require me to say that inertial forces and "real" forces are equivalent either.

In the Newtonian concept, in order to get forces to transform via the Galilean transformation, gravity has to be considered to be a force - you can't omit it and keep the tensor nature of forces. Taking the example of standing on the Earth, if your feet were pushing on you that hard, and there was no gravity, you'd be flung into the air. Let me stress again that this is the Newtonian viewpont I'm discussing.

The equivalence of gravitational and inertial mass in the Newtonian theory was noticed for a long time. I believe it's accurate to say that this equality between gravitational and inertial masses gave the equivalence principle it's very name, though I don't have a reference.

Now, the equivalence principle is vague enough where you could still take the position that this equivalence is some sort of happy accident, but if you start to believe it's not just a coincidence, I think you're more or less drawn to the position I mentioned. I.e. you start to think that inertial forces are the same gravitational forces, and you already know that the inertial forces don't transform properly, i.e. like tensors. As I mentioned, you also know that gravitational forces need to be included as "real" forces in the Newtonian viewpoint.

I suppose it is also self consistent to think of gravity as being a "curvature of space time" and in no ways a force, which seems to be your suggestion. So then you do get to keep all the other forces as tensors, and you insist that gravity is "not a force".

 

[PAllen]

The equivalence of gravitational and inertial mass in the Newtonian theory was noticed for a long time. I believe it's accurate to say that this equality between gravitational and inertial masses gave the equivalence principle it's very name, though I don't have a reference.

Now, the equivalence principle is vague enough where you could still take the position that this equivalence is some sort of happy accident, but if you start to believe it's not just a coincidence, I think you're more or less drawn to the position I mentioned. I.e. you start to think that inertial forces are the same gravitational forces, and you already know that the inertial forces don't transform properly, i.e. like tensors. As I mentioned, you also know that gravitational forces need to be included as "real" forces. I think you get into quite a muddle, until you take the position that none of the forces were tensors under the most general sorts of coordinate transformations, and you've been making them look like tensors by considering a restricted set of transformations. Which is OK and self-consistent and even traditional, but if you want to open up the playing field to treating all sorts of transformations equivalently, you need to sacrifice the idea that forces are tensors. And you also then sacrifice the notion of inertial frames being "special", but I think this later part is or less a plus, you have one less thing to worry about defining.

I disagree with these two paragraphs.

1) The equivalence of gravitational and inertial mass was noticed long ago. The equivalence principle was Einstein's huge generalization of it: that no local physics of any kind can distinguish free fall from inertial motion in 'empty space' with no significant mass around.

2) The conclusion I draw is almost the opposite of yours. It is that gravity is not a force at all, and there are no such thing as inertial forces. Then, forces are tensors and no coordinate systems are privileged in any way. You never need to worry about inertial frames if you don't want to. In any coordinates, it is unambiguous whether a world line is experiencing force or not.

 

[PeterDonis]

I suppose it is also self consistent to think of gravity as being a "curvature of space time" and in no ways a force, which seems to be your suggestion. So then you do get to keep all the other forces as tensors, and you insist that gravity is "not a force".

This is more or less my position, but my terminology may be a bit different. I would say that tidal gravity is curvature of spacetime. Gravity as whatever it is that makes a rock fall to Earth is not tidal gravity, though it is related to it. But I would agree that the latter type of gravity is still not a force, because the rock falling to Earth feels no force (its 4-acceleration is zero, neglecting air resistance). A force is something that causes a nonzero 4-acceleration; by this definition, yes, all forces are tensors.

 

[juanrga]

Pitts and Schieve seem to have no disagreement that gravity=spin 2. All the questions are about exactly what assumptions are needed to obtain uniqueness.

(GR ≠ spin-2 field)

They avoid the criticism cited here and merely repeat Deser, Feynman, and others mistakes

 

[atyy]

(GR ≠ spin-2 field)

They avoid the criticism cited here and merely repeat Deser, Feynman, and others mistakes

Dang, you are persistent! I thought by citing Schieve, some of whose work you had approved of, I could make you change your mind

 

[PAllen]

He avoids the criticism about (GR ≠ spin-2 field) cited here and only offers a partial dispute with Padmanabhan work also cited here

He doesn't ignore it. He rejects it completely as incorrect. I am not going to try to referee this debate among people who know enormously more than I, but there is no doubt what Deser thinks:

"In summary, I have annotated the steps involved in the non-geometric derivation [1] of
GR from special relativistic field theory as the unique consistent self-interacting system,
(13) extending the initial free massless spin 2."

In short, Deser remains convinced: GR=spin 2 field theory.

Truth is not determined by poll, but I would predict that Deser's position would handily win a poll of relevant experts. For example, I have seen a number of comments by Professor Steven Carlip endorsing this point of view.

 

[pervect]

I disagree with these two paragraphs.

1) The equivalence of gravitational and inertial mass was noticed long ago. The equivalence principle was Einstein's huge generalization of it: that no local physics of any kind can distinguish free fall from inertial motion in 'empty space' with no significant mass around.

2) The conclusion I draw is almost the opposite of yours. It is that gravity is not a force at all, and there are no such thing as inertial forces. Then, forces are tensors and no coordinate systems are privileged in any way. You never need to worry about inertial frames if you don't want to. In any coordinates, it is unambiguous whether a world line is experiencing force or not.

I was thinking about the topic as I wrote it You managed to respond to one of the earlier/earliest versions. You make some good points, I think. It's interesting that the final version I came up with (which was before I read this criticisms) almost seems as if I read your criticism (but at the time I finished my original, I didn't see the criticisms yet).

I'll agree that it is possible to view gravity as not being a force, but rather due to the curvature of the space-time. This way one gets to keep the traditional structure of "forces" mostly intact, having only to sacrifice the original Newtonian idea of gravity being a force with the replacement idea that "it's not really a force".

Then one can explain that curved space-time transforms as a tensor, but it's a rank 4 tensor, i.e. the Riemann, thus it has more degrees of freedom than any "force" concept allows.

I still don't think this approach is really in the true spirit of "general covariance", because one still has to single out inertial frames as being "special - and one has to be careful of what sort of transformations are allowed as well. But it's a reasonable way of looking at things nonetheless.

 

[juanrga]

Dang, you are persistent! I thought by citing Schieve, some of whose work you had approved of, I could make you change your mind

Then that is a strong difference between you and me. I do not cite authors, I cite specific works .

And as many others I am well aware that the same author can be completely right regarding some topics and completely wrong regarding others.

 

[juanrga]

He doesn't ignore it. He rejects it completely as incorrect. I am not going to try to referee this debate among people who know enormously more than I, but there is no doubt what Deser thinks:

"In summary, I have annotated the steps involved in the non-geometric derivation [1] of
GR from special relativistic field theory as the unique consistent self-interacting system,
(13) extending the initial free massless spin 2."

In short, Deser remains convinced: GR=spin 2 field theory.

Truth is not determined by poll, but I would predict that Deser's position would handily win a poll of relevant experts. For example, I have seen a number of comments by Professor Steven Carlip endorsing this point of view.

Deser only partially answers Padmanabhan work.

Deser completely ignores the rest of criticism to his derivation (nowhere Deser replies the criticism to his 'derivation' done in the section 3.3 of http://arxiv.org/abs/gr-qc/9912003

This reference shows conclusively that (GR ≠ spin 2 field theory).

Effectively, truth is not determined by poll, neither by appeal to authority. If you or some other want to rely on what some 'big' names say, you are welcomed. I prefer to check by myself the literature

 

[atyy]

Deser only partially answers Padmanabhan work.

Deser completely ignores the rest of criticism to his derivation (nowhere Deser replies the criticism to his 'derivation' done in the section 3.3 of http://arxiv.org/abs/gr-qc/9912003

This reference shows conclusively that (GR ≠ spin 2 field theory).

Effectively, truth is not determined by poll, neither by appeal to authority. If you or some other want to rely on what some 'big' names say, you are welcomed. I prefer to check by myself the literature

The reference only claims to show it for quantum GR in very strong gravity (eg. near spacetime singularities), for which it is agreed that GR may not be spin 2.

 

[juanrga]

The reference only claims to show it for quantum GR in very strong gravity (eg. near spacetime singularities), for which it is agreed that GR may not be spin 2.

You are completely confused.

One can read already from page 2 of the reference cited (bold font from mine):

There are many articles and books dealing with GR but only a few papers discuss FTG. Perhaps it is a consequence of wide-spread opinion that FTG is equivalent to GR and hence we need not spend time to study field gravity approach. [...] Indeed in papers of Thirring(1961) and Deser (1970) there were claims that field theory approach is identical with the geometrical one and there are no gravitational effects which could provide grounds to distinguish between them.
[...]
However, as it will be shown here, reality turns out to be much more complex and interesting. Actually GR and FTG are two alternative theories with different bases and different observational predictions. Of course, for the weak gravitational fields, which are available for experiments now, both theories give the same values of the classical
relativistic effects, but they profoundly different in the case of strong gravity, which will be obtainable in near future.

First, FTG and GR agree on weak gravity, are different for intermediate gravity and «profoundly different in the case of strong gravity»

Second, he writes about GR. Nowhere he writes about «quantum GR» as you pretend {*}.

Indeed, the section 3 of the paper is titled «Classical theory of tensor field». The interesting part for this thread is the subsection 3.3 «Thirring and Deser about identity of GR and FTG», where is shown why the previous claims by both about GR being equivalent or derivable from a classical field theory are incorrect.

The «Quantum theory of tensor field» is presented in section 4 {**}, but I repeat, the proof that GR (a classical theory) is not equivalent to the classical field theory of gravity is given before in section 3.

The 'derivations' presented here by Deser, Schieve, and other people are incorrect: GR is not equivalent to a field theory of gravity (FTG).

{*} Moreover, does not exist a consistent and accepted «quantum GR».

{**} There exists a classical FTG and a quantum FTG, somewhat as there exists a classical electrodynamics and a quantum electrodynamics.

 

[atyy]

You are completely confused.

One can read already from page 2 of the reference cited (bold font from mine):
First, FTG and GR agree on weak gravity, are different for intermediate gravity and «profoundly different in the case of strong gravity»

Second, he writes about GR. Nowhere he writes about «quantum GR» as you pretend {*}.

Indeed, the section 3 of the paper is titled «Classical theory of tensor field». The interesting part for this thread is the subsection 3.3 «Thirring and Deser about identity of GR and FTG», where is shown why the previous claims by both about GR being equivalent or derivable from a classical field theory are incorrect.

The «Quantum theory of tensor field» is presented in section 4 {**}, but I repeat, the proof that GR (a classical theory) is not equivalent to the classical field theory of gravity is given before in section 3.

The 'derivations' presented here by Deser, Schieve, and other people are incorrect: GR is not equivalent to a field theory of gravity (FTG).

{*} Moreover, does not exist a consistent and accepted «quantum GR».

{**} There exists a classical FTG and a quantum FTG, somewhat as there exists a classical electrodynamics and a quantum electrodynamics.

Yes, you are probably right about what Baryshev intends to claim, maybe not from this paper, but I looked at some of his other papers, and he says what you say he does pretty clearly. In http://arxiv.org/abs/0809.2323 Baryshev cites Straumann as providing caveats about the equivalence of GR and FTG. Straumann's caveats seem pretty standard. Is Baryshev saying anything that Straumann or eg. Ortin are not saying? As I understand, the major restriction for the equivalence of FTG and GR is that the GR spacetime needs a nice topology and can be covered by nice coordinates like harmonic coordinates

 

[juanrga]

Yes, you are probably right about what Baryshev intends to claim, maybe not from this paper, but I looked at some of his other papers, and he says what you say he does pretty clearly. In http://arxiv.org/abs/0809.2323 Baryshev cites Straumann as providing caveats about the equivalence of GR and FTG. Straumann's caveats seem pretty standard. Is Baryshev saying anything that Straumann or eg. Ortin are not saying? As I understand, the major restriction for the equivalence of FTG and GR is that the GR spacetime needs a nice topology and can be covered by nice coordinates like harmonic coordinates

Well it seems to me that the first paper cited before and the quotations given are pretty clear:

Actually GR and FTG are two alternative theories with different bases and different observational predictions

I cannot imagine how someone would misread that as «GR and FTG are the same theory».

Regarding the new preprint 0809 that you cite, the appeal to Straumann point is correct. Straumann point about BHs is close to the criticism done by Wald (in his famous textbook) against string theory. String theory starts from the incorrect supposition that (GR = spin-2 theory) but then defines causality (e.g. in the S-matrix) with regard to the original flat background instead of with regard to the GR real metric. Therefore it cannot be equivalent to GR.

However, the criticism done by Baryshev in the first paper cited before is more complete and applies beyond BHs.