Is the equivalence principle good for anything?

[CuriousKid]

I heard that there is now consensus in literature that a charged particle will take a DIFFERENT path around a neutral object than an uncharged particle. The reason is that the charged particle will radiate.

I have even heard physicists try to wave this away as "well a charged particle needs to carry its "fields" around with it" so that is not a local object. If you take that stance, then the equivalence principle is completely worthless except for interactions which are purely point/contact interactions ... of which there are none. All four known fundamental forces can be described with fields.

So what good is the equivalence principle?

Alternative phrasing to make this more constructive:
Can anyone completely mathematically/rigorously define the equivalence principle, and NOT have it be violated by the differring trajectories of a charged and neutral particle?

EDIT: Just checked. According to the definitions in wikipedia, this would indeed violate the equivalence principle.

 

[jfy4]

I heard that there is now consensus in literature that a charged particle will take a DIFFERENT path around a neutral object than an uncharged particle. The reason is that the charged particle will radiate.

I have even heard physicists try to wave this away as "well a charged particle needs to carry its "fields" around with it" so that is not a local object. If you take that stance, then the equivalence principle is completely worthless except for interactions which are purely point/contact interactions ... of which there are none. All four known fundamental forces can be described with fields.

So what good is the equivalence principle?

Alternative phrasing to make this more constructive:
Can anyone completely mathematically/rigorously define the equivalence principle, and NOT have it be violated by the differring trajectories of a charged and neutral particle?

EDIT: Just checked. According to the definitions in wikipedia, this would indeed violate the equivalence principle.

I don't understand what the violation is? or where the equivilence principle fails?

why should a charged and neutral particle have the same paths?

please state it for the forum and me .

 

[atyy]

All four known fundamental forces can be described with fields.

Aren't all the particles described by fields too? So if you have no more particles, do you still have a problem?

The EP only applies to freely falling particles. A particle in its own field is acted on by its own field, so it is not freely falling.

The EP suggests that gravity is geometric. Newton's theory obeys an EP, and can be reformulated as geometry (Newton-Cartan theory). Nordstrom's theory, which was the first relativistic theory of gravity can also be reformulated as geometry. General relativity is also in some sense a geometric theory.

The EP suggests a simple way of generalizing special relativistic laws to general relativistic laws (minimal coupling or the "comma goes to semi-colon rule").

When all is said and done, the EP is neither a single principle nor a logical necessity. Chapter 24 of Blandford and Thorne has an amusing discussion of when the EP fails.

 

[bcrowell]

Keep in mind that even if you think of this as violating the EP (which is partly a matter of interpretation), the violation is ridiculously small -- way too small to be measured in any practical experiment.

 

[TcheQ]

I have even heard physicists try to wave this away as "well a charged particle needs to carry its "fields" around with it" so that is not a local object.

Who were these physicists, and how many papers have they had published in refereed journals?

 

[CuriousKid]

Keep in mind that even if you think of this as violating the EP (which is partly a matter of interpretation)

How is it a matter of interpretation? Or better yet, how can a mathematical principle even be left to interpretation: is the EP really defined that poorly?
These are not rhetorical questions, I really am asking and really am confused.

jfy4,
in answer to your question, here is the definition of the weak EP from wikipedia
The trajectory of a point mass in a gravitational field depends only on its initial position and velocity, and is independent of its composition.

That is why I would expect a neutral particle and charged particle to have the same trajectory around a neutral gravitating body. But the EP misleads us here (as is why apparently there was disagreement in literature for awhile), as the two will not have the same trajectory.

Aren't all the particles described by fields too? So if you have no more particles, do you still have a problem?

I'm not sure what you are suggesting here. Is the point that the EP can never be used?

The EP only applies to freely falling particles. A particle in its own field is acted on by its own field, so it is not freely falling.

The point is that a free falling frame is supposed to be locally equivalent to an inertial frame.

Can a particle at rest in an inertial frame feel a proper force due to its field? No. So I would expect the same from a free falling field. That fact that it isn't confuses me deeply. I don't even understand how this can be violated since I though the EP along with some other conditions could be used to derive GR.

When all is said and done, the EP is neither a single principle nor a logical necessity. Chapter 24 of Blandford and Thorne has an amusing discussion of when the EP fails.

I don't have that book. But from people's comments here, it is sounding like there is no real equivalence principle in any rigorous sense. It is just a thought that is useful, but hard to define, like "inertia"?

 

[CuriousKid]

Who were these physicists, and how many papers have they had published in refereed journals?

Was that a really non-mainstream opinion? Why I am being asked to provide references?

I'm new here, so I'm sorry if I was supposed to supply references for comments (other questions didn't seem to, so I thought it was okay).

Parrott
Found.Phys. 32 (2002) 407-440.
"since the field extends throughout all spacetime, no measurements on the particle can
be considered truly local"
http://arxiv.org/pdf/gr-qc/9303025
To be fair, the full quote shows that he is quoting yet other physicists, and it references another published article. I couldn't find a free copy of the other article.

But I've heard that "non-local due to fields" comment from other physicists in person (I'm a student at a large research university), and yes they are well published. So I thought it was, at the least, a not-unheard-of-opinion.

Basically it looks like the EP fails for electrodynamics, and this is a reason some people give.

 

[TcheQ]

Was that a really non-mainstream opinion? Why I am being asked to provide references?

I'm new here, so I'm sorry if I was supposed to supply references for comments (other questions didn't seem to, so I thought it was okay).

Parrott
Found.Phys. 32 (2002) 407-440.
"since the field extends throughout all spacetime, no measurements on the particle can
be considered truly local"
http://arxiv.org/pdf/gr-qc/9303025
To be fair, the full quote shows that he is quoting yet other physicists, and it references another published article. I couldn't find a free copy of the other article.

But I've heard that "non-local due to fields" comment from other physicists in person (I'm a student at a large research university), and yes they are well published. So I thought it was, at the least, a not-unheard-of-opinion.

Basically it looks like the EP fails for electrodynamics, and this is a reason some people give.

You're adept at quoting and researching your sources, just keep in mind that when you quote something from an old source, it is your imperative to make sure that it hasn't been re-researched of refuted in the meantime.

The reason I brought this up is that the phrase "carries it's fields" implies the person who wrote that line doesn't understand what they talk about (which is common when you try to describe Quantum mechanics using classic physics).

So for your question "what good is the equivalence principle", we would say "because it allows us to conduct experiments with acceleration as simulating gravitational fields"

I am unsure where the confusion is also... charged particles have different mass and charge than neutral particles...so we would expect them to behave differently.

 

[Altabeh]

Keep in mind that even if you think of this as violating the EP (which is partly a matter of interpretation), the violation is ridiculously small -- way too small to be measured in any practical experiment.

Proving every spacetime is locally flat does completely rely on a mathematical basis (see for example Schutz B. A first course in general relativity, p.p. 158-160 or Weyl H. Space-Time-Matter, 1922, p. 80.) So it's not a matter of interpretation at all!

But the EP misleads us here (as is why apparently there was disagreement in literature for awhile), as the two will not have the same trajectory.

I don't know why EP confuses and misleads you that much! EP is purely geometrical and as atty said, it only occurs for those fields that can curve spacetime, including gravitational field and very small affects of electromagnetic field (which are neglected if gravity is strong enough to make their affect be ruled out). EP does always happen to exist for freely falling particles having mass or being point masses! But the charged particles don't follow any kind of geodesics, though $$d\tau^2>0$$ for them and this of course does not make EP worthless to rest on it for support because there are so many particles that have no charge but we can apply them to EP as test particles for simplicity of calculations (here the testing properties let us ignore all measuring aspects of particles [except photons or neutrinos]
such as mass, charge which can be assumed zero, and size.) Nevertheless, even if we take a particle to have electron's mass and be of its size but uncharged, yet the geodesic equations around any gravitating mass are still valid because we are just trying to study gravitational affect on particles that don't experience any force but gravitational so if charge was involved, then one would expect other perturbative forces acting on particle due to an electrical field it carries along so that this stuff is not GR anymore!

AB

 

[Ich]

is the EP really defined that poorly?

I think so.
But I think you already formulated the resolution:

The point is that a free falling frame is supposed to be locally equivalent to an inertial frame.

Can a particle at rest in an inertial frame feel a proper force due to its field? No.

You omitted "locally" in your second statement. Include it, and everything is fine again.
The EP is valid locally, that means, if there is some backreacktion with the field from inside the region you are considering, that's ok. You just make the region smaller if you want less deviation, and it goes to zero for a point like region. If you include backreaction from large distance, well, that's not local, so it doesn't concern the EP.

I am unsure where the confusion is also... charged particles have different mass and charge than neutral particles...so we would expect them to behave differently.

We would expect so, if gravity were a force. It's the whole point of the EP that all objects behave exactly the same way, independent of composition. That the gravitational mass of the internal EM field energy is exactly the same as the inertial mass.
But you mustn't include any influence whatsoever from the outside world, be it self-made or not. You have to restrict yourself to truly local penomena.

 

[atyy]

http://relativity.livingreviews.org/Articles/lrr-2004-6/
"In the scalar and electromagnetic cases, the picture of a particle interacting with a radiative field removes any tension between the nongeodesic motion of the charge and the principle of equivalence."

http://www.pma.caltech.edu/Courses/ph136/yr2006/text.html
"What is the minimum amount of nonlocality that can produce curvature-coupling modifications in physical laws? As a rough rule of thumb, the minimum amount is double gradients:"

http://nedwww.ipac.caltech.edu/level5/March01/Carroll3/Carroll4.html
"In fact, let us be honest about the principle of equivalence: it serves as a useful guideline, but it does not deserve to be treated as a fundamental principle of nature. From the modern point of view, we do not expect the EEP to be rigorously true."

http://relativity.livingreviews.org/Articles/lrr-2006-3/
"Empirically it has been found that almost every metric theory other than GR introduces auxiliary gravitational fields, either dynamical or prior geometric, and thus predicts violations of SEP at some level (here we ignore quantum-theory inspired modifications to GR involving “R2” terms). The one exception is Nordström’s 1913 conformally-flat scalar theory [195], which can be written purely in terms of the metric; the theory satisfies SEP, but unfortunately violates experiment by predicting no deflection of light."

http://arxiv.org/abs/0707.2748
"There is no precise definition of “gravitational” and “non-gravitational” field. One could say that a field non-minimally coupled to the metric is gravitational whereas the rest are matter fields. This definition does not appear to be rigorous or sufficient and it is shown in the following that it strongly depends on the perspective and the terminology one chooses. ... following Will’s book one can argue that the EEP can only be satisfied if there exists some metric and the matter fields are coupled to it not necessarily minimally but through a non-constant scalar"

 

[Altabeh]

The EP is valid locally, that means, if there is some backreacktion with the field from inside the region you are considering, that's ok. You just make the region smaller if you want less deviation, and it goes to zero for a point like region. If you include backreaction from large distance, well, that's not local, so it doesn't concern the EP.

No it is not okay! Even in small regions, one can't make a charged particle obey the general geodesic equations so in GR they use something like a test particle to ignore qualities like charge and large sizes of particles to make the theory geometrically compatible with EP and taking the particle to have charge, due to Coulomb' law, would impose a very large electrical force compared to Newtonian gravitational force (if we are, for instance, freely falling towards Earth's surface) which leads to a large deviation from the path described by the geodesic equations around the target gravitating body! The general definition of EP only applies to particles idealized in some way so as to get the theory to work well while keeping things in agreement with empirical viewpoints! From this loophole, I'd also be tempted to say that EP is not well defined in the context of physics!

 

[Altabeh]

Atty, those links are amazing! Thanks.

AB

 

[Mentz114]

I think this is a storm in a tea-cup. I have always understood that the EP applies only to gravitational phenomena. It starts with the equivalence of inertial and gravitational mass which means we can say that the effect of a gravitational field on a body is independent of the mass and composition of the body ( not test particles only, anything ).

The difference between gravitational fields and EM is that there is free-fall in gravity but not in EM. So it's blindingly obvious that electrodynamics has no equivalent of the gravitational EP !

It isn't possible to invoke the EP in situations where force fields are present and it's bound to lead to the confusion that is apparent in this thread.

[edit : I just noticed the references given by atyy. I will check them but I can see at least one solecism in the the summaries. I suspect there's at least some hot-air in there.]

 

[Altabeh]

It isn't possible to invoke the EP in situations where force fields are present and it's bound to lead to the confusion that is apparent in this thread.

Unfortunately you are (sort of) wrong! Charged particles carry electric fields which can affect their motion along a path if in particular this path is a geodesic and the deviation is not negligible at all; then they won't follow geodesic and so the definition of "freely falling bodies" is not applicable in which case where charge is also involved unless you omit the field blindly! Though EP has a completely gravitational origin and thus geometrical, this doesn't mean it is in a completely safe zone when it comes to the charged particles involved in the situation! But I think you are also correct, if a comparison of EM and gravitation is considered when studying EP! In such easygoing case, where mostly photons are involved, EP isn't damaged unless the electromagnetic force is also dominant so it can curve the photon's path! I don't think this has a very influential impact on EP as in small regions such deviation due to EM could be safely neglected!

AB

 

[Ich]

No it is not okay!

Of course it is ok. Maybe you overlooked "from inside the region you are considering".
As an example: The EP would predict a capacitor to fall at the same rate, whether it's charged or not. But only as long as there are no stray fields that reach beyond the finite region that you consider, there's no additional error. There is some error of course due to the finite extension of the region.

The difference between gravitational fields and EM is that there is free-fall in gravity but not in EM. So it's blindingly obvious that electrodynamics has no equivalent of the gravitational EP !

??
Are you saying that a treatment of EM in inertial (=free falling) frames is invalid? Or that acceleration in an EM field is not free fall (true, of course)?
The EP includes of course all conceivable interactions - but only locally. When the fields go through the whole universe, well, that's not exactly local.

 

[Mentz114]

Unfortunately you are (sort of) wrong! Charged particles carry electric fields which can affect their motion along a path if in particular this path is a geodesic and the deviation is not negligible at all; then they won't follow geodesic and so the definition of "freely falling bodies" is not applicable in which case where charge is also involved unless you omit the field blindly! Though EP has a completely gravitational origin and thus geometrical, this doesn't mean it is in a completely safe zone when it comes to the charged particles involved in the situation! But I think you are also correct, if a comparison of EM and gravitation is considered when studying EP! In such easygoing case, where mostly photons are involved, EP isn't damaged unless the electromagnetic force is also dominant so it can curve the photon's path! I don't think this has a very influential impact on EP as in small regions such deviation due to EM could be safely neglected!

AB

I think you've missed my point completely. Applying the gravitational EP ( what other kind is there ? ) to any situation where force fields are acting is not even wrong ! The EP has nothing to say about 'deviations from geodesics due to EM forces' ! Electrodynamics is written entirely in terms of inertial mass - so how can the EP have any relevance since it is concerned with the equality /non-equality of inertial and gravitational mass. The latter concept is missing entirely from electrodynamics.

The EP includes of course all conceivable interactions - but only locally. When the fields go through the whole universe, well, that's not exactly local.

No it doesn't. It is only applicable to gravitational fields.

 

[Ich]

No it doesn't. It is only applicable to gravitational fields.

I can't make sense of this statement. Could you please answer my request for clarification?

Are you saying that a treatment of EM in inertial (=free falling) frames is invalid? Or that acceleration in an EM field is not free fall (true, of course)?

 

[Mentz114]

Are you saying that a treatment of EM in inertial (=free falling) frames is invalid?

Only the parts that depend on the ratio of gravitational mass to inertial mass.

Or that acceleration in an EM field is not free fall (true, of course)?

What does that mean ? Of course it's not free fall.

 

[Ich]

Hmm, didn't help either.

I mean, it's obvious that the presence of external fields may lead to a force on the test particle, therefore it's no longer free falling.
It's less obvious when we consider the (charged) test particles own field. Still, if the field extends far longer than the region around the test particle that we regard as "pointlike" in the context of the experiment, there may be deviations from a geodesic, too.
But if all fields of the test particle are constrained to said "pointlike" region around it, and there are no external fields, the EP predicts the particle to move on a geodesic. This prediction is nontrivial, it is what is meant by "independent of the constitution of the test particle".

Agreed?

 

[Mentz114]

Hi Ich,

I mean, it's obvious that the presence of external fields may lead to a force on the test particle, therefore it's no longer free falling.

Yes, but the EP has nothing to say about this. The test particle is experiencing proper acceleration while moving in curved spacetime. The covariant curl ( wedge derivative) of the potential is identical to the flat space curl, so the two effects are completely independent. I believe that interaction betweem EM and gravity have almost been ruled out by experiment ( I may be mis-remembering this ).

... it is what is meant by "independent of the constitution of the test particle".

Hmmm. I think this is where we part company. I don't think that statement was intended to include anything other than mass. Charge does not have mass, or rather it is not mass, so it does not gravitate per se ( I'm sticking my neck out here because obviously some energy gravitates ...).

1. For these reasons I conjecture that in the absence of other fields, a charged particle will follow the same geodesic as an uncharged particle.
2. a charged body freely falling in the absence of any other fields will not radiate.

Are we getting anywhere ?

 

[Ich]

Charge does not have mass, or rather it is not mass, so it does not gravitate per se

EM fields have energy content, thus mass. Same with the strong force. Eötvös-type experiments check different materials where - mostly on the nucleon level - a different part of the mass is contributed by the different fields. So that's exactly what the EP means.

Are we getting anywhere ?

I think so.

 

[Mentz114]

EM fields have energy content, thus mass. Same with the strong force. Eötvös-type experiments check different materials where - mostly on the nucleon level - a different part of the mass is contributed by the different fields. So that's exactly what the EP means.

The binding energy that holds bodies together may be taken as part of the gravitational and inertial mass. But if we have an isolated charged body, does the field that permeates the space around have mass ? I think not.

I seem to remember now that there is an argument that some kind of energy will contribute to the gravitational mass but not to inertia ( or vice-versa), which would violate the EP, but those arguments are not supportable. I think the references atyy gave are of those type.

I think I've made my position clear, but I have to take a break now.

I'll be back.

 

[bcrowell]

Keep in mind that even if you think of this as violating the EP (which is partly a matter of interpretation)

How is it a matter of interpretation? Or better yet, how can a mathematical principle even be left to interpretation: is the EP really defined that poorly?

Yes, it really is defined that poorly. It's not a mathematically well defined principle. It's more like a guiding philosophical precept for evaluating candidate theories of gravity.

The classic paper on the topic of the free-falling charge and the e.p. is: C. Morette-DeWitt and B.S. DeWitt, "Falling Charges," Physics, 1,3-20 (1964). It's available here: http://www.physics.princeton.edu/~mcdonald/examples/EM/dewitt_physics_1_3_64.pdf Note the last sentence of the abstract, where they point out that the effect is "far too small to be detected experimentally." When they say far too small, they really mean it. For a calculation of just how small it is, see ch. 1, problem #7 in this book http://www.lightandmatter.com/genrel/ . The solution is given in the back of the book. For a proton and a neutron orbiting the earth, the relative violation of the e.p. (difference in acceleration divided by acceleration) turns out to be $10^{-34}$.

Proving every spacetime is locally flat does completely rely on a mathematical basis (see for example Schutz B. A first course in general relativity, p.p. 158-160 or Weyl H. Space-Time-Matter, 1922, p. 80.) So it's not a matter of interpretation at all!

There are various versions of the equivalence principle. For a detailed discussion of why the e.p. is not a single, mathematically well defined statement, see this paper: "Theory of gravitation theories: a no-progress report," Thomas P Sotiriou, Valerio Faraoni, Stefano Liberati, http://arxiv.org/abs/0707.2748 On p. 3, they lay out various versions of the e.p. (WEP, EEP, SEP). Your characterization of the e.p. as a statement of local flatness is one that you often hear stated loosely, but if you take a look at the forms of the e.p. given in the Sotiriou paper, you'll see that it's not one of them. I think the basic reason for that is that local flatness only works as a way of characterizing the e.p. within GR. The real answer to the OP's question ("Is the equivalence principle good for anything?") is that it's useful for comparing candidate theories of gravity.

If all you want to do is work within GR, then you could certainly throw away the e.p. and never mention it again. To the extent that the e.p. holds in GR, you don't need it because the results of GR calculations will obey they e.p., whether or not you explicitly know or invoke the e.p. To the extent that the e.p. fails in GR (e.g., very weak violations for charged particles), you don't want the e.p. because it gives the wrong answer.

If you want to use the e.p. for the one thing that it's really useful for, which is testing competing theories of gravity, then just saying that it's equivalent to local flatness is not useful. It's only within GR that it's (approximately) equivalent to local flatness. I think this is the reason that the Sotiriou paper's statements of three versions of the e.p. all refer to actual experiments. Unless you talk about actual measurements, you can't state the e.p. in a model-independent way.

 

[bcrowell]

I have even heard physicists try to wave this away as "well a charged particle needs to carry its "fields" around with it" so that is not a local object.

Yes, that's a good way of looking at it.

Who were these physicists, and how many papers have they had published in refereed journals?

C. Morette-DeWitt and B.S. DeWitt, "Falling Charges," Physics, 1,3-20 (1964), http://www.physics.princeton.edu/~mcdonald/examples/EM/dewitt_physics_1_3_64.pdf

Parrott, http://arxiv.org/abs/gr-qc/9303025

Harpaz and Soker, http://arxiv.org/abs/physics/9910019

Gralla, Harte, and Wald, http://arxiv.org/abs/0905.2391

Grøn and Næss, http://arxiv.org/abs/0806.0464

Bryce DeWitt and Wald are both extremely well known relativists. I know that Grøn is also a well known relativist who publishes frequently in refereed journals. I'm not as familiar with the reputations of the others, but I think they're all mainstream physicists. If you read this sequence of papers, I think you'll see very clearly that although there are some disagreements, what they're all clarly agreeing on as the topic of discussion is exactly the issue that CuriousKid pinpointed.

I think this is a storm in a tea-cup. I have always understood that the EP applies only to gravitational phenomena. It starts with the equivalence of inertial and gravitational mass which means we can say that the effect of a gravitational field on a body is independent of the mass and composition of the body ( not test particles only, anything ).

The difference between gravitational fields and EM is that there is free-fall in gravity but not in EM. So it's blindingly obvious that electrodynamics has no equivalent of the gravitational EP !

It isn't possible to invoke the EP in situations where force fields are present and it's bound to lead to the confusion that is apparent in this thread.

I don't think this attempt to sidestep the problem really works. The e.p. violation we're talking about is not a violation due to an externally applied field, it's a violation due to radiation. The big picture of GR is that it's a geometrical theory of spacetime, and it's perfectly happy to be coupled to any matter field you like. You tell it, "Hey, I want you to tell me about the gravitational field of a cloud of axions," and it says, "Sir, yes, sir!" The whole reason it's been such a useful and durable foundational theory is that it's completely agnostic about what sources are creating the stress-energy tensor. The e.p. is an important part of the interpretation of GR, and the ability to insert any matter fields you like is an important feature of GR. The fact that you can't have both of these things at once is actually a potentially important issue. It just turns out to be a numerically negligible effect for practical cases, like a neutron and a proton orbiting the earth.

Applying the gravitational EP ( what other kind is there ? ) to any situation where force fields are acting is not even wrong ! The EP has nothing to say about 'deviations from geodesics due to EM forces' !

I think the problem with this statement is that you need to add the important distinction made in Ich's #16. For example, see the statement of the Weak Equivalence Principle on p. 3 of this paper http://arxiv.org/abs/0707.2748 :

If an uncharged test body is placed at an initial event in spacetime and given an initial velocity there, then its subsequent trajectory will be independent of its internal structure and composition.

The qualifier "uncharged" is equivalent to Ich's statement that the object's field can't extend far away (as in his example of the capacitor). This is the distinction that needs to be made, not something stronger or weaker. If you strengthen it by forbidding electromagnetic phenomena completely, then, e.g., every test of the e.p. done by the EotWash group in the last decade is useless, because they used material objects that were held together by electromagnetic interactions. If you weaken it by allowing test bodies with nonzero net charge, then you get the extremely small violations of the e.p. that are too small to measure, but possibly philosophically important.

 

[Mentz114]

I agree with BCrowell's answers to the OP except for this

To the extent that the e.p. fails in GR (e.g., very weak violations for charged particles), you don't want the e.p. because it gives the wrong answer.

The EP cannot fail in GR, because as you've said it is implicit. If the EP were to fail then the whole theory goes belly up because you would need a different set of Christoffel symbols for every 'geodesic', because they would depend on the composition and starting conditions for every motion I can provide a reference for this ). Obviously there would no such thing as free-fall or inertial frames.

Now, in order for the EP to fail because of some field, there must be a coupling between the field and the sources of the gravitational field. No such field has been found except some things in string-theory which are entirely theoretical ( dilatons ?).

[edit: this was added while I was posting]

every test of the e.p. done by the EotWash group in the last decade is useless, because they used material objects that were held together by electromagnetic interactions.

All material bodies are held together by a combination of EM and nuclear forces so how can that statement be relevant. The binding energy of the bodies gravitates like mass, I'm not denying that but it has nothing to do with charged bodies radiating and violating the EP.

If you weaken it by allowing test bodies with nonzero net charge, then you get the extremely small violations of the e.p. that are too small to measure, but possibly philosophically important.

Without a coupling between EM and gravity, there will be no radiation or violation

If you strengthen it by forbidding electromagnetic phenomena completely, then, e.g.,

I don't need to strengthen it, it already forbids EM because there is no interaction between EM and gravity.

 

[Altabeh]

I think you've missed my point completely. Applying the gravitational EP ( what other kind is there ? ) to any situation where force fields are acting is not even wrong ! The EP has nothing to say about 'deviations from geodesics due to EM forces’! Electrodynamics is written entirely in terms of inertial mass - so how can the EP have any relevance since it is concerned with the equality /non-equality of inertial and gravitational mass. The latter concept is missing entirely from electrodynamics.

You seem to be missing the whole thing! The question is if particles were charged, then would it be possible to take them as freely falling particles when being put in a gravitational field around a gravitating body e.g. Earth? EP only applies to particles which have no charge and it is obvious why such a conditional situation has to be defined in GR to exclude charge:

Charged particles carry electric fields which can affect their motion along a path...

No it doesn't. It is only applicable to gravitational fields.

This is right in case the OP had not asked about particles having charge and moving around gravitational bodies! He simply said to us something like if a test particle is replaced by an electron or a charged particle, explain why in such cases EP doesn't work or IF it works, argue why and how it is possible! Do you see something strange here?

Of course it is ok. Maybe you overlooked "from inside the region you are considering".

It is not! We don't know precisely how large the "inside" of the region in which EP is guaranteed is! This may be so much large compared to the implication of ‘epsilon-neighborhood’ of mathematicians so we can't be sure about the smallness of deviation from geodesics! On the otehr hand, interaction of charged particles in small distances would also lead to sizable electric forces according to Coulomb's' law which of course exceeds the Newtonian gravitational force!

The EP would predict a capacitor to fall at the same rate, whether it's charged or not. But only as long as there are no stray fields that reach beyond the finite region that you consider, there's no additional error. There is some error of course due to the finite extension of the region

EP can also predict a sack of capacitors to fall at the same rate as g around Earth, but we are not talking about predictions here! EP is itself not extremely stable in its definitions, let alone void predictions! Until now, there have just been fundamentally uncharged particles accepted by EP to fall at the same rate. Most well-known charged particles including electron and proton have spin and spinning charged particles would in general deviate from geodesics according to Papapetrou and Frenkel:

1-A. Papapetrou, Spinning test-particles in general relativity, I, Proc. Roy. Soc.
London A209, 248-258 (1951).

2- J. Frenkel, Z. fur Physik 37, 243 (1926).

(I didn't find the available papers on the Internet. But there may be other papers or books covering their works.)

I mean, it's obvious that the presence of external fields may lead to a force on the test particle, therefore it's no longer free falling.
It's less obvious when we consider the (charged) test particles own field. Still, if the field extends far longer than the region around the test particle that we regard as "pointlike" in the context of the experiment, there may be deviations from a geodesic, too.
But if all fields of the test particle are constrained to said "pointlike" region around it, and there are no external fields, the EP predicts the particle to move on a geodesic. This prediction is nontrivial, it is what is meant by "independent of the constitution of the test particle".

The point is we don't consider those external fileds to be present when discussing EP because if we do, then

therefore it's no longer free falling.

The region in which EP is assumed to be true is not "pointlike": it may be "sufficiently small" so that the local flatness is guaranteed! Furthermore, if it is looked as a point, then it has no length to be prolongated (I don't mean you are saying it is a point. Just for more clarification.) The region EP offers for particles to be indeed freely falling is not obvious, but according to the fact that local flatness implies EP and vice versa, what is known is that the region of EP is not pointlike because local flatness happens to be defined around a point at which the spacetime is made Minkowski! We do have something like 'deviation' from a point if considered EP to occur in one single point but this is not the case.

AB

 

[turin]

All four known fundamental forces can be described with fields.

Yes, but also they can (and oftern should) be described by other means. In particular, the EP suggests that gravitation isn't even a force, so that there are only three fundamental forces. I emphasize that this is not dictated by shear math/logic, but rather by experiment (beginning with Galileo, and continuing to this day). For example, a perfectly mathematical/logical equation for the motion of a particle under the influence of gravity can include terms (derived from the metric alone) that represent "genuine" gravitational force (i.e. violating EP, because the particle would not obey the geodesic equation). However, no such force term has been observed (so far as I am aware).

Can anyone completely mathematically/rigorously define the equivalence principle, and NOT have it be violated by the differring trajectories of a charged and neutral particle?

What do you mean by "completely mathematically/rigorously define"? Can you give an example of a mathematical definition that is not complete and/or rigorous (of the EP or anything else), so that we have an idea what you would like to avoid? For instance, what is wrong with this statement of the Einstein EP from An Introduction to General Relativity Spacetime and Geometry by Sean M. Carroll, Sec. 2.1, p. 50:

It is impossible to detect the existence of a gravitational field by means of local experiments.

Charged particles may behave differently than neutral particles; the Einstein EP makes no statement regarding this difference. The issue of the EP is whether a given particle, charged or not, behaves differently in a kinematically accelerating frame compared to a gravitational frame. Can a scientist do an experiment on the charged particle to determine that he/she is in a gravitational field rather than an accelerating rocketship?

However, I will admit this particular quote from the same source as above, Sec. 4.7, p. 177:

... the Principle of Equivalence is not a sacred physical law, nor is it even a mathematically rigorous statement;

But so what? That does not make it worthless. (For instance, that same author decided to write an entire textbook devoted to the consequences of the EP.)

The EP only applies to freely falling particles. A particle in its own field is acted on by its own field, so it is not freely falling.

No, this is not the issue (nor is it a correct statement, but freely falling particles probably do provide the most straightforward demonstration of the EP.)

General relativity is also in some sense a geometric theory.

In what sense is it not? My impression of GR is that of an extremely geometrical theory; the ultimate geometrical theory. It says, in essence, that a completely geometrical principle (the Bianchi identity) is equivalent to a completely physical principle (conservation of energy and momentum).

How is it a matter of interpretation? Or better yet, how can a mathematical principle even be left to interpretation: is the EP really defined that poorly?

Why are you asking about a mathematical principle? What mathematical principle? The EP is not a mathematical principle, it is a physical principle. Even if you did conjure up some mathematical principle that you would call the EP, you cannot avoid the necessity of interpretation.

math ≠ physics

... here is the definition of the weak EP from wikipedia
The trajectory of a point mass in a gravitational field depends only on its initial position and velocity, and is independent of its composition.

That is why I would expect a neutral particle and charged particle to have the same trajectory around a neutral gravitating body. But the EP misleads us here ...

Again, I don't know about the difference between the charged particle trajectory compared to the neutral particle trajectory, but it is not the EP that is misleading, it is wikipedia. I am aware of no form of the EP that compares two different objects. The weak EP imposes a proportionality between the inertial mass and gravitational response (gravitational mass) of the same object. The Einstein EP imposes an equivalence between special relativity (Minkowski spacetime) and "small enough" regions of spacetime (that include gravity). The srong EP imposes an equivalence between gravitational energy and all other forms of energy. None of these principles imply a comparison between two different particles.

The point is that a free falling frame is supposed to be locally equivalent to an inertial frame.

Do not underplay the "local" aspect. Radiation is not a local phenomenon (as I understand it), and I would argue that neither is a trajectory, only a tangent vector to a trajectory.

Basically it looks like the EP fails for electrodynamics, and this is a reason some people give.

NO! I think that you are very confused by reading wikipedia. I love wikipedia; don't get me wrong. But, don't base your entire understanding on it, especially not of physics. I am not an expert, so I don't want to bluntly say, "wikipedia is wrong." But, I hope that some expert will chime in and say that, because the "EP" that you quoted from wikipedia is worthless, in my opinion. It does not even mention locality, and it is restricted to a very small class of phenomena (in which I would declare the EP to be trivial).

... if charge was involved, then one would expect other perturbative forces acting on particle due to an electrical field it carries along so that this stuff is not GR anymore!

I don't think that you know what GR is. To suggest that E&M precludes GR is absurd. GR accommodates E&M quite well (e.g. by almost trivial use of the "comma to semicolon" rule that atyy aluded to in Post #3).

If you include backreaction from large distance, well, that's not local, so it doesn't concern the EP.

Backreaction has always confused me. Are you talking about the Abraham-Lorentz force? Can you explain why it is nonlocal?

It's the whole point of the EP that all objects behave exactly the same way, independent of composition.

That is not my understanding of the EP at all. My understanding is that the EP regards the (lack of) experimental distinction between gravity and acceleration. The EP only marginally refers to objects and compositions (i.e. regarding the most straighforward way to flasify the EP).

Even in small regions, one can't make a charged particle obey the general geodesic equations ...

What are you talking about? Are you just saying that a charged particle cannot be a free particle? That may be true, but it has nothing to do with the EP.

... so in GR they use something like a test particle to ignore qualities like charge and large sizes of particles to make the theory geometrically compatible with EP ...

They do not try to do this; it has been done, and now the result is GR. The EP was basically empirical, and GR was designed in order to accommodate this factual observation. There is nothing invalid about this; would you rather that a theory disagree with observation?

The test particles that you describe are still used in GR experiments, not in order to make GR compatible with the EP, but rather because the experimenters want a clean test of GR. (Yes, GR is still being tested.) Why would you want to complicate an experiment with undesirable influences that you know how to remove?

... taking the particle to have charge, due to Coulomb' law, would impose a very large electrical force compared to Newtonian gravitational force (if we are, for instance, freely falling towards Earth's surface) which leads to a large deviation from the path described by the geodesic equations around the target gravitating body!

You are contradicting yourself. An object that experiences "a very large electrical force compared to ... gravitational force" is, by definition, not freely falling in the first place (not even approximately).

The general definition of EP only applies to particles idealized in some way ...

You have the issue quite backward. The general definition of the EP has absolutely nothing to do with particles, but rather with very general laws of physics. Only specific consideration of the EP (such as in this thread) regard particles.

I have always understood that the EP applies only to gravitational phenomena.

The weak and Einstein EPs apply to all phenomena except gravity! The strong EP includes gravity. However, that may be a bit confusing (in light of your following statements). To clarify, the EP regards any possible distinction that can be made by way of otherwise non-gravitational experiments if a gravitational field is replaced by an "equivalent" acceleration (or vice versa). This means that things like freefall are not phenomena to be tested under the weak or Einstein EP. Alternately things like gravitational waves can be considered under the strong EP, but not the weak nor Einstein EP I think.

It starts with the equivalence of inertial and gravitational mass which means we can say that the effect of a gravitational field on a body is independent of the mass and composition of the body ( not test particles only, anything ).

Yes, that's the idea! (of the weak EP)

The difference between gravitational fields and EM is that there is free-fall in gravity but not in EM. So it's blindingly obvious that electrodynamics has no equivalent of the gravitational EP !

This is very confusing. I don't understand what you are getting at. That's not the difference (from a modern perspective), but it is certainly a very important difference (from a historical perspective).

It isn't possible to invoke the EP in situations where force fields are present ...

This is backwards. If no forces are present, then the EP is trivial (i.e. regards a comparison of flat empty space to itself).

... which can affect their motion along a path if in particular this path is a geodesic and the deviation is not negligible at all; then they won't follow geodesic ...

You are contradicting yourself again. If the path is a geodesic then it won't be a geodesic? What?

... EP has a completely gravitational origin and thus geometrical, ...

No, it does not. EP has a completely empirical origin (see weak EP). It developed into a geometrical idea (GR).

... where mostly photons are involved, EP isn't damaged unless the electromagnetic force is also dominant so it can curve the photon's path!

Please explain how an electromagnetic force can curve a photon's path. I am unfamiliar with this concept.

The EP has nothing to say about 'deviations from geodesics due to EM forces' !

On the contrary, this is exactly the kind of situation to which the EP applies (nontrivially).

Electrodynamics is written entirely in terms of inertial mass - so how can the EP have any relevance since it is concerned with the equality /non-equality of inertial and gravitational mass. The latter concept is missing entirely from electrodynamics.

Electrodynamics is written entirely without regard to mass at all. E&M could care less what kind of mass it is.

... if we have an isolated charged body, does the field that permeates the space around have mass ? I think not.

I think so, but I cannot prove this to you (I can't think of an experiment that would test this in a satisfactorily pure form). The energy of the electric field is an abstraction in E&M that seems to be consistent with cases that can be observed (such as the energy in the field of two separated charges, or the energy stored in the electric field of a capacitor). Then, use the famous E=mc² to relate this energy to (inertial!) mass.

I seem to remember now that there is an argument that some kind of energy will contribute to the gravitational mass but not to inertia ( or vice-versa), which would violate the EP, but those arguments are not supportable. I think the references atyy gave are of those type.

You are probably thinking of gravitational binding energy. The srong EP regards this. I have read that such a result would remain compatible with the far more popular "weak" and "Einstein" versions of the EP, but I appologize for my lack of reference on that.

Your characterization of the e.p. as a statement of local flatness is one that you often hear stated loosely, but if you take a look at the forms of the e.p. given in the Sotiriou paper, you'll see that it's not one of them.

What is the difference between that conception and the Einstein EP? Sorry, I haven't read the paper that you cited yet, so maybe my question is answered there. I'll give it a look.

If you want to use the e.p. for the one thing that it's really useful for, which is testing competing theories of gravity, ...

Which EP? For instance, the weak EP is certainly useful in simple freshman physics calculations where the mass "cancels out". I suppose that, where it is "useful", it is simply not recognized, but just taken for granted. Are you only considering a usefulness as it applies to cutting-edge physics (and probably not even the weak EP at all)?

Unless you talk about actual measurements, you can't state the e.p. in a model-independent way.

Well said. This pronounces the distinction between an "absolute rigorous mathematical definition" (i.e. clever tautology that still requires an ambiguous interpretation in order to be made useful) and a useful physical definition.

The EP cannot fail in GR, because as you've said it is implicit. If the EP were to fail then the whole theory goes belly up ... Obviously there would no such thing as free-fall or inertial frames.

I basically agree with this. However, wouldn't we just call the new theory, with the modified geodesic equation, "GR"?

... you would need a different set of Christoffel symbols for every 'geodesic', ...

This is not necessarily true. For instance, you can modify the trajectories by introducing contractions between the tangent vector and the Riemann tensor (i.e. add them to the geodesic equation).

Without a coupling between EM and gravity, there will be no radiation or violation

I think that you have it backwards here, according to my interpretation of your punctuation. The "coupling" between E&M and gravity (in GR) is that gravity acts like an accelerating frame. Accelerating charge radiates. So, I claim that it is precisely this "coupling" that saves, rather than violates, the EP. If, for instance, an accelerating charge radiates, but a charge in a gravitational field does not, then that would provide an experimental distinction between the accelerating frame and the gravitational frame, and thus violate the EP.

However, I do remain confused by the very concept of radiation in curved spacetime.

 

[cesiumfrog]

a charged particle will take a DIFFERENT path around a neutral object than an uncharged particle. The reason is that the charged particle will radiate.

I hope we can assume you're not mistaking the emission (or not) of radiation for an observer independent fact..

"well a charged particle needs to carry its "fields" around with it" so that is not a local object. If you take that stance, then the equivalence principle is completely worthless except for interactions which are purely point/contact interactions ... of which there are none. [..] So what good is the equivalence principle?

Obviously the EP does not apply to me if I intend to use my telescope, a network of radar telemetry beacons, and a rocket pack, to alter my course depending on whether or not I determine myself to be in the presence of a gravitating mass. But it feels like cheating - the EP isn't intended to override non-local interactions, and the same goes for the phenomena of the retarded influence on charged particles by their own gravitational self-images. Anyway, might such exceptions be avoided just by limiting our attention to gravitational distortions that are sufficiently large in scale, or placing the test charge in an opaque conductive box?

..you're probably also going to be interested in the paths of neutral spinning test masses.

 

[Altabeh]

Well, everybody himself tries to correct the answers given to him by turin who accidently hit this thread with a long list of misunderstandings:

I don't think that you know what GR is. To suggest that E&M precludes GR is absurd. GR accommodates E&M quite well (e.g. by almost trivial use of the "comma to semicolon" rule that atyy aluded to in Post #3).

If your weird E&M is shorthand for electromagnetism, to save my time, I just cite two papers that deal with the problem of "how can EP be compatible with EM in GR?":

1- http://linkinghub.elsevier.com/retrieve/pii/S1873198808000042
2- http://arxiv.org/abs/0705.3422

As is discussed in the second paper, it takes you to answer some fundamental question regarding a spacetime relation in order to probably provide a framework within it EP can be compatible in the presence of EM. So giving us some primary ideas about the rule of "comma and semicolon" which of course has nothing to do with this stuff does not make me not know what GR is! If you studied Gravitoelectromagnetism (GEM ) and how B. Mashhoon et. al (see. e.g. http://arxiv.org/pdf/gr-qc/0311030) derive the "analogous" equations of electromagnetism in the context of GR, then you would ask yourself: Do all these calculations consider EP to hold for example, for an electron moving around a gravitating body? They bring up a gravitational version of the Larmor Theorem of Electrodynamics to establish Einstein's EP within the GEM framework but in a very limited case involving a test particle of inertial mass $$m$$ whose gravitoelectric charge is $$q_E = -m$$ and its gravitomagnetic charge being $$q_B = -2m.$$ A similar assumption is made for a rotating gravitational source with mass $$M.$$ This is like a matching condition to get a spin-1 field e.g. the field of Maxwell's theory. Most importantly, the equations do not include the aspect of "spin" itself which would of course lead to a deviation from the geodesic equations if was considered (see my last post)!

What are you talking about? Are you just saying that a charged particle cannot be a free particle? I suppose that's true, but it has nothing to do with the EP.

You seem to be just seeing posts partially and then there you start making conclusions\statements that aren't at all what the OP and people here are seeking out!

Btw, your answer here contradicts the one you gave above: if EM and GR are like two brothers, how come such a deep dissension exists? We assumed EP is consistent with charged test particles of EM so according to EP they must follow geodesics! What happened?

They do not try to do this; it has been done, and now the result is GR. The EP was basically empirical, and GR was designed in order to accommodate this factual observation. There is nothing invalid about this; would you rather that a theory disagree with observation?

The test particles that you describe are still used in GR experiments, not in order to make GR compatible with the EP, but rather because the experimenters want a clean test of GR. (Yes, GR is still being tested.) Why would you want to complicate an experiment with undesirable influences that you know how to remove?

Which EP? There are lots of them and you must specify what exactly you mean by 'EP'. Our EP is actually EEP and I guess yours is this, too! But we have been mostly talking about the quality of "charge" which is a diamond in the rough when it comes to EP and about mass, of course the more particle has mass the more it has deviation from being freely falling! So two qualities along with the size of particles which gets larger as particle gains more mass than before, offer to use test particles whose mass and charge are set equal to zero and it is considered to be a point mass in essence to better match the conditions EP lives with! And retrieving mass and size wouldn't be as troubling as the resurgence of the implication of "charged test particles" is! No such thing as EP has ever been observed for charged test particles! If there had been some sort of evidence to stand for this thing empirically, all of us would have stopped giving ideas up to the post #5.

You are contradicting yourself. An object that experiences "a very large electrical force compared to ... gravitational force" is, by definition, not freely falling in the first place.

I don't think there is a contradiction in my sentences. I invite you to take another look:

...taking the particle to have charge, due to Coulomb' law, would impose a very large electrical force compared to Newtonian gravitational force (if we are, for instance, freely falling towards Earth's surface) which leads to a large deviation from the path described by the geodesic equations around the target gravitating body!

Btw., you just left abandoned the idea of GR + EM and rather started groping around for contradictions which have no relevance to the points made to get the OP closer to the understanding of why EP doesn't work for charged particles! If you are insisting a GR version of EM exists that is unified not analogous (so every facet and basis of GR including EPs is consistent with EM), why are you pushing us away from knowing what is behind that theory which bothers you to make a reference to?

No. You have the issue quite backward. The general definition of the EP has absolutely nothing to do with particles.

The point is that particles in GR have a vivid and limpid definition when the issue is about a gravitating body plus the motion of particles around it: particle = test particle which has no charge but may have size and mass! No one has ever seen they use the famous geodesic equations not only for charged particles but for spinning ones which also drags into the discussion another quality of a particle the so-called spin!

In GR we don't have anything to do with charge in general except the cases where the efforts are all made to make the charge involved in equations somehow!

Where? In their hands?

I think you've got the wrong thread; to have some fun visit the forum "General Discussions"!

You are contradicting yourself again. If the path is a geodesic then it won't be a geodesic? What?

If it is a contradiction, you got to worry then: you talked about some theory that sorts out all these contradictions (!) and stuff! In your theory, charged particles are following geodesics so they won't deviate but here you are saying...

No, it does not. EP has a completely empirical origin (see weak EP). It developed into a geometrical idea (GR).

Please explain how an electromagnetic force can curve a photon's path. I am unfamiliar with this concept.

The Photon-Photon interactions would have an effect on the trajectory of photons but I'm not so familiar with this stuff. You can consult Google and QFT books!

AB

 

[jfy4]

I heard that there is now consensus in literature that a charged particle will take a DIFFERENT path around a neutral object than an uncharged particle. The reason is that the charged particle will radiate.

I have even heard physicists try to wave this away as "well a charged particle needs to carry its "fields" around with it" so that is not a local object. If you take that stance, then the equivalence principle is completely worthless except for interactions which are purely point/contact interactions ... of which there are none. All four known fundamental forces can be described with fields.

So what good is the equivalence principle?

Alternative phrasing to make this more constructive:
Can anyone completely mathematically/rigorously define the equivalence principle, and NOT have it be violated by the differring trajectories of a charged and neutral particle?

EDIT: Just checked. According to the definitions in wikipedia, this would indeed violate the equivalence principle.

Is the EP saying that two particles, charged and uncharged, accelerating through space-time with the charge particle being acted on by a force and the uncharged one not, should have the same "trajectories"?

That doesn't sound like the EP to me... but maybe i miss understand it...

 

[Altabeh]

Is the EP saying that two particles, charged and uncharged, accelerating through space-time with the charge particle being acted on by a force and the uncharged one not, should have the same "trajectories"?
That doesn't sound like the EP to me... but maybe i miss understand it...

In the presence of an electromagnetic field, the motion of a test particle is characterized by

$$d^2x^{\mu}/ds^2+\Gamma^{\mu}_{\alpha \beta}(dx^{\alpha}/ds)(dx^{\beta}/ds) + e/{m_0}F^{\mu}_{\alpha}(dx^{\alpha}/ds)=0,$$

where $$s$$ is the affine parameter of the curve along which the particle with charge $$e$$ is travelling, $$m_0$$ is the rest mass of particle and $$F_{\alpha}^{\mu} = g_{\alpha\beta}F^{\mu\beta}$$ is the electromagnetic field tensor. This of cource isn't a geodesic equation so charged particles won't freely fall unless we neglect their charge or take the electromagnetic field tensor to be zero.

AB

 

[turin]

1- http://linkinghub.elsevier.com/retrieve/pii/S1873198808000042

I don't understand what that first paper has to do with the discussion.

... giving us some primary ideas about the rule of "comma and semicolon" which of course has nothing to do with this stuff ...

The EM equations dictate how charge moves. The partial derivatives in the EM equations should be replaced by covariant derivatives in GR. So it has everything to do with "this stuff" (meaning this thread).

If you studied Gravitoelectromagnetism (GEM ) and how B. Mashhoon et. al (see. e.g. http://arxiv.org/pdf/gr-qc/0311030) derive the "analogous" equations of electromagnetism in the context of GR, then you would ask yourself: Do all these calculations consider EP to hold for example, for an electron moving around a gravitating body?

No, I would not, I would take it for granted.

Most importantly, the equations do not include the aspect of "spin" itself which would of course lead to a deviation from the geodesic equations if was considered (see my last post)!

I will admit that I do not know how spin (I presume you refer here to intrinsic angular momentum of fundamental particles) would modify the geodesic equation. However, the OP mentioned a concern due to charge, not spin. Even neutral particles have spin, so spin is a separate issue that is unrelated to the charge, and so unrelated to this thread.

... if EM and GR are like two brothers, how come such a deep dissension exists?

What? Why are EM and GR "like two brothers"? Where does that come from?

We assumed EP is consistent with charged test particles of EM so according to EP they must follow geodesics!

No, the EP does not require charged test particles to follow geodeiscs. If it did, then it would certainly be violated.

... we have been mostly talking about the quality of "charge" which is a diamond in the rough when it comes to EP and about mass,

I have no idea what this is supposed to mean.

... of course the more particle has mass the more it has deviation from being freely falling!

I disagree. The amount of mass of a particle and the condition of freefall are completely independent.

... you just left abandoned the idea of GR + EM ...

No, I didn't. GR accommodates EM perfectly well. What else do you want me to say about it?

... to get the OP closer to the understanding of why EP doesn't work for charged particles!

Keep in mind that we have different agenda's in this respect. I am trying to help the OP understand that the EP does work for charged particles.

If you are insisting a GR version of EM exists ...

What are you talking about? When did I say this? I believe that you must have misunderstood me. GR is a framework in which EM can be formulated. That does not mean that "a GR version of EM exists".

... why are you pushing us away from knowing what is behind that theory which bothers you to make a reference to?

I have no idea what you're talking about here. The theories that bother me have nothing to do with this thread.

No one has ever seen they use the famous geodesic equations not only for charged particles but for spinning ones which also drags into the discussion another quality of a particle the so-called spin!

The issue raised in the OP is charged vs. neutral; not scalar vs. spinor. I think that you need to start a new thread to address the spin issue.

... you talked about some theory that sorts out all these contradictions (!) and stuff! In your theory, charged particles are following geodesics so they won't deviate ...

How did you get this impression? The only two theories that I talked about (I think) were GR and EM. Both of these theories are mainstream, and neither one of them addresses your contradictions; I personally addressed your contradictions.

 

[jfy4]

In the presence of an electromagnetic field, the motion of a test particle is characterized by

$$d^2x^{\mu}/ds^2+\Gamma^{\mu}_{\alpha \beta}(dx^{\alpha}/ds)(dx^{\beta}/ds) + e/{m_0}F^{\mu}_{\alpha}(dx^{\alpha}/ds)=0,$$

where $$s$$ is the affine parameter of the curve along which the particle with charge $$e$$ is travelling, $$m_0$$ is the rest mass of particle and $$F_{\alpha}^{\mu} = g_{\alpha\beta}F^{\mu\beta}$$ is the electromagnetic field tensor. This of cource isn't a geodesic equation so charged particles won't freely fall unless we neglect their charge or take the electromagnetic field tensor to be zero.

AB

Great, then i don't think there is any violation of the EP then. i guess you guys have wrapped this up right?

 

[atyy]

I think the basic reason for that is that local flatness only works as a way of characterizing the e.p. within GR.

I think even within GR, local flatness is not enough (local flatness being that the metric can have Minkowski form at a point). The EP also requires that the GR laws reduce to the SR laws at that point in curved spacetime. I think roughly speaking that first derivative laws do reduce (eg. including "fundamental laws" like Maxwell's equations), but second derivative laws do not necessarily do so (eg. the "derived" law for radiation) unless spacetime is flat.

On thinking further, I guess local flatness is that spacetime can look locally flat, provided one does not measure second derivatives of spacetime. So additional requirement for the EP to hold is that the laws of physics should not allow one to measure spacetime curvature. So actually, it is very closely related to local flatness after all. So although it is not mathematically true, by common sense, we can think of second derivatives as "non-local". So the EP is true provided we do not use non-local laws of physics to measure non-local properties of spacetime.