Talk:Equivalence principle/Archive 1

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A few problems (july 2004)

A few problems

There is lack of distinction in the article between active gravitational mass that causes gravitational effects through whatever mechanism, and passive gravitational mass that responds to whatever the agent of this mechanism is doing, the mass that is equal to the inertial mass making all the bodies fall with the same acceleration. So basically the mentioned in second paragraph principle of equivalence of masses refers only to passive gravitational mass being equal to inertial mass. An old Newtonian principle.

(William M. Connolley 20:26, 26 Jul 2004 (UTC)) Agreed.

It is stated in the article that the equivalence principle explains equivalence of (passive) gravitational mass and inertial mass. It only shifts the "explanation" to a different level (makes responsible for its validity the principle of general relativity). It would have left it unexplained hadn't the gravitational time dilation been confirmed experimentally. Before that it was just a result of the following chain of predictions: principle of general relativity $\rightarrow$ principle of equivalence of gravity and acceleration $\rightarrow$ gravitational time dilation $\rightarrow$ non existence of "attractive gravitational force" (objects take geodesics in spacetime so the "gravitational attracttion" is superfluous) $\rightarrow$ non existence of "passive gravitational mass" (nothing to attract if there is no attraction). Only at the end of this chain we see how the puzzle why the (passive) gravitational mass is equal to the inertial mass is "explained" (there is no such thing as the passive gravitational mass and so the puzzle disappears: "is explained"). However it is only an apparent explanation hanging on validity of the first link in the chain. Now, the time dilation has been confirmed experimantally so all the links from gravitational time dilation in the chain become facts. So they don't need principles to relay on. This way the "principle" of equivalence of (passive) gravitational mass and inertial mass is not a "principle" any more but just a fact resulting from experimental data that say that there is no "gravitational attraction".

(William M. Connolley 20:26, 26 Jul 2004 (UTC)) Partially agreed. It does shift it to a different level. I guess what I meant was that it shifts it from something puzzling with no particular reason to expect it to be true; to something that seems plausible and coherent. Thats not a very good formulation either. Hmm.

Someone might want to put an abbreviation of the above into the article because otherwise it is a little bit misleading. I'm not sure of my own literary abilities. I guess I'm talking too much (not to mention bad grammar and typos). Jim 20:15, 26 Jul 2004 (UTC)

Major revision ready

I have just completed a major revision of this article. The revision is at User:Ems57fcva/sandbox/Equivalence_Principle. My objections to the current version are as follows:

This article uses the Strong Equivalence Principle (SEP) instead of the Weak Equivalence Principle (WEP). The SEP is not true for the reasons stated in the revision.
This article brings up a lot of GR-related details which are superfluous to the Equivalence Principle:
- The fact that the Sun bends light rays passing near its surface by 1.75" is due to the full metric treatment of GR. Only the bending of light in a generic sense is due to the Equivalence Principle. (The original 1911 article predicting the bending of light was off by a factor of 2 in the amount of the bending!)
- Inertial movement ocurring along geodesics of spacetime, while an important aspect of GR itself, is not relevant to the Equivalence Principle. To describe geodesics, you need a metric of spacetime, but the Equivalence Principle is independent of any metric.

Comments will be appreciated. I intend to do the replacement soon.

--EMS 05:25, 30 Mar 2005 (UTC)

Changes made

The revision is now in place.

--EMS 16:24, 31 Mar 2005 (UTC)

Reasons for reverting changes

I am removing the following changes for the reasons stated in the more indented text:

... One way of stating a fundamental principle of general relativity is to say that gravitational mass is identical to inertial mass.

This is another way of expressing of the Equivalence Principle. It is not a seperate principle of GR.

Experiments performed in a uniformly accelerating reference frame with acceleration a are indistinguishable from the same experiments performed in a non-accelerating reference frame which is situated in a gravitational field where the acceleration of gravity = g = -a = intensity of gravity field.

My objections are as follows:

This is a poor attempt to state the strong equivalence principle, which as I state later in the page is not true and is not the currently accepted version of the Equivalence Principle.
A reference from where an acceleration due to gravity is locally detectable is not "non-accelerating" at all. That is the point of the Equivalence Principle.

One of the implications of the principle is that since photons have momentum and therefore must be attributed an inertial mass, they must also have a gravitational mass. Thus photons should be deflected by gravity.

Photons are massless. Their deflection is a gravitational field is due to the frame of reference being accelerated, therby making their path look curved (since for an inertial observer it is not curved).

They should also be impeded in their escape from a gravity field, leading to the gravitational red shift and the concept of a black hole. It also leads to gravitational lens effects.

Acceleration is enough to explain the red shifting of light, as I mention later in the article. Also, black holes and gravitational lenses are irrelevant to the Equivalence Effect, and are best not mentioned here at all.

I will retain the spelling corrections and added links.

--EMS 03:15, 4 Apr 2005 (UTC)

History of the equivalence principle

In the article it is stated:

The Equivalence Principle was introduced by Albert Einstein in 1907. An that time, he made the observation that the acceleration of bodies towards the center of the Earth at 1g is equivalent to the acceleration of inertially moving bodies that one would observe if one was on a rocket in free space being accelerated at a rate of 1g.

I think it is better to say that Einstein reinterpreted this centuries old observation. Newton could calculate the orbits of the planets without knowing their mass. Newton had assumed that gravitational mass is exactly equal in magnitude to inertial mass, and the subsequent succes of the theory in describing planetary motion was confirmation of the validity of that assumption.

Einstein saw an opportunity for unification. On Earth, the Earth's surface exerts a force on anything standing on it, thus maintaining a situation. In an accelerating space-ship the "floor" of the spaceship exerts a force on anything standing on it, maintaining it in co-accelerating motion with the space-ship. Einstein conjectured that in both situations the same physics is taking place (in the limit of infinitisimally small volumes of space.)

The only way that the same physics can be taking place is when gravitation alters the rate of time: gravitational time dilation. --Cleon Teunissen | Talk 10:05, 4 Apr 2005 (UTC)

Maybe I could present this better, but some thought is advised. The equivalence of intertial mass and gravitational mass is long standing as noted, but that is not the point of the Equivalence Principle. What is different about the Equivalence Principle is its interpretation of that observation. (The equivalence of gravitation and being in an accelerated rocket had been noted previously, but the conclusion that this means that freefall is the real intertial motion quite escaped most of Einstein's predescessors. Also, those whom it did not escape were quickly left with a contradiction that only the advent of non-linear geometry and the concept of spacetime permitted Einstein to resolve.)

--EMS 19:27, 5 Apr 2005 (UTC)

new version

I noticed that there were a number of errors in the last rewrite, particularly that the strong equivalence principle is incorrect (it has never been shown to be violated) and I thought the treatment of the weak equivalence principle was unclear. I was out of town while the update was in User:Ems57fcva's sandbox, and didn't get a chance to point this out.

I tried to revise things and make it clear the difference between the three versions of the equivalence principle and the ways in which they can each be tested. My article is a little lacking in discussing the tests of the Einstein and strong equivalence principles, other than looking for variation of the dimensionless fundamental "constants." In particular it would be good to add something about the limits placed by solar system tests of the strong EP and red-shift tests of the Einstein EP. --Joke137 23:54, 4 Apr 2005 (UTC)

Reverting to previous edition

I am reverting this page to my previous edition, for the following reasons:

That which is being presented as the "strong equivalence principle" is in fact the general principle of relativity. Indeed, it has not been refuted, but it is not the equivalence principle.
The point of the equivalence principle is that you are in an accelerated frame of reference when you are standing on the surface of the Earth. That has been lost.

It is indeed the equivalence principle.

What you presented in not the SEP. I very much assure you of that.

The weak equivalence principle (EP) is commonly called the universality of free fall. It is not transparent that this is what it means in your version, particularly for the reader who only knows a little physics. I tried to state clearly in the section on the relation to Newtonian physics that an observer standing on the surface of earth does experience a net force and is in an accelerated frame of reference.

That is at least a statement of the WEP, and your criticism is worthy of some discussion. I will not claim perfection in my writing, but I failed to see how you achieved the goals of clarity and accessibility any more than I did. Besides, you brought in so much else that I cannot abide by that I felt obligated to revert the version.

The material I brought in, on tests of the EP, is important and should be in the article. I think my version was clearer, if only because I stated the weak EP in the way most people hear it most often: free fall is universal, i.e. things all fall the same way, regardless of their constitution. --Joke137 17:35, 6 Apr 2005 (UTC)

The EP or Einstein EP is, simply put, nongravitational physics is the same in all local Lorentz frames.

That is not the EP. Instead it is the special principle of relativity, one of the foundatation principles of SR.

All the references I pointed you to confirm that this is the EP. If you disagree, or think I have selected some obscure references that happen to confirm my perspective, then I encourage you to explore arxiv to see what other authors have to say. Damour and Uzan, in particular, have both written extensively on the EP and are authorities on the subject. See also:

T. Damour and A. M. Polyakov, "The String dilaton and a least coupling principle," Nucl. Phys. B 423, 532 (1994) [arXiv:hep-th/9401069], which has been cited almost 300 times according to spires.
G. Adelberger, B. R. Heckel, G. Smith, Y. Su and H. E. Swanson, "Eotvos Experiments, Lunar Ranging And The Strong Equivalence Principle," Nature 347, 261 (1990).
J. D. Anderson, M. Gross, E. L. Lau, K. L. Nordtvedt and S. G. Turyshev, "Testing the Strong Equivalence Principle with Mars Ranging Data," arXiv:astro-ph/9510157.

--Joke137 17:35, 6 Apr 2005 (UTC)

The strong EP is a tricker and less frequently discussed principle that tightly constrains gravity. It says, essentially, that all physics is the same in local Lorentz frames,

That is the principle of Local Lorentz Invariance, an extension of SR that is one of the foundation principles of GR.

Lorentz invariant theories can still violate the EP by introducing new gravitational strength interactions.

in particular that the gravitational field of an object does not depend on its constitution

That is a Newtonian concept, is irrelevant to the EP (which deals with the effects of the gravitational field instead of its source) and does completely not hold true in GR. (A charged object will have a different gravitational field than an uncharged one, for example.)

(i.e. it seems to imply that gravity is mediated by a massless symmetric spin-2 particle).

The Hilbert action is what calls for spin-2 gravitions, not the EP.

No, gravitational-strength scalar interactions violate the strong EP by generating "fifth forces." That's why Brans-Dicke theory does not satisfy the strong EP, and why all these papers I'm referring you to are looking for scalar interactions. Alternatively, they place limits on the parameterized post-Newtonian formalism. The gravitational field of an object can still be discussed in GR, at least in the weak-field limit. --Joke137 17:35, 6 Apr 2005 (UTC)

I offer you the following references for my definitions:

C. M. Will, Theory and Experiment in Gravitational Physics', Cambridge U., 1993. (Discusses all three forms of the EP and is probably the standard reference for experimental tests of relativity.)
Misner, Thorne and Wheeler, Gravitation (discusses both the weak and Einstein EPs),
J. P. Uzan, "The fundamental constants and their variation: Observational status and theoretical motivations," Rev. Mod. Phys. 75, 403 (2003) [arXiv:hep-ph/0205340]. (Restates the weak and Einstein EPs)
T. Damour, "Questioning the equivalence principle," arXiv:gr-qc/0109063. (Discusses the strong EP.)
V. Boucher, J. M. Gerard, P. Vandergheynst and Y. Wiaux, "Primordial constraint on the spatial dependence of the Newton constant," arXiv:astro-ph/0407508; V. Boucher, J. M. Gerard, P. Vandergheynst and Y. Wiaux, "Cosmic microwave background constraints on the strong equivalence principle," Phys. Rev. D 70, 103528 (2004) [arXiv:astro-ph/0407208]. (Discuss recent Nordtvedt effect tests of the strong EP.)

If you still think that my understanding of the strong EP is incorrect, then please show me where I can see it defined otherwise.

--Joke137 22:32, 5 Apr 2005 (UTC)

I will check the arXiv sources ASAP, and see what I can quote. Checking MTW will be a bit harder since I lack a copy. (MTW is now outdated, although it was for a long time the "bible" of GR.) My reference to Ohanian's book is my source.

--EMS 02:04, 6 Apr 2005 (UTC)

I have now looked at the Arxiv papers. One states the SEP in terms of always getting the same result in free-fall, which is false due to tidal effects. However, all are looking for violations of the equivalence of inertial and gravitational mass due to scalar field interactions. To me, what is being tested in the Einstein Field Equations and not the EP, but if it is being called the SEP and does so in a peer-reviewed journal (and one of those articles is published in a peer-reviewed journal) then it needs to be dealt with as such under the rules of Wikipedia.

My request is to give me some time (like a week or two) to stare at those articles and reduce their SEP variations to something managable. I will work on this in my sandbox. The input is good, although I wonder how accepted this SEP is.

--EMS 03:11, 6 Apr 2005 (UTC)

Authority

Also, I included the following as a comment at the beginning of my "source" of this page:

PLEASE PLEASE do not edit without first discussing changes on the discussion page.

I meant that!

I know that the changes are sincere and well meaning, but unless you have taken graduate level GR courses (and I have), then you should not be editting this page.

I will soon add in a "Misconceptions" section which will include use of the General Principle of Relativity as one of those misconceptions.

--EMS 18:49, 5 Apr 2005 (UTC)

I didn't think arguments from authority were supposed to hold much weight on Wikipedia. I think my edits stand for themselves without listing my credentials. Wikipedia is supposed to encourage constructive edits, and I did my best to corrent what I think are errors in the page and add useful new content. --Joke137 22:32, 5 Apr 2005 (UTC)

The effort is acknowledged and appreciated. However if Wikipedia is to be a useful source it much contain accurate information. As for authority: I do think that for the sake of the resource you should defer to it, but with caution. (After all, you do not know me or my reputation.) Just give me some time to fix the page up more. For now I need to control it, but I must also learn from people like you even as I also ask you to learn from me. Within a few weeks (if not sooner) I will need to loosen up. For now I wish to get the page to the point where it at least can defend itself against well-meaning but relatively uninformed editors like yourself.

--EMS 02:04, 6 Apr 2005 (UTC)

Likewise, you do not know me or my reputation. That is not the issue here, but I can't really see how I sound uninformed.

I have added a disputed tag to the article. Please see Wikipedia:Disputed_statement. In particular, Wikipedia encourages users to immediately correct inaccurate information when they see it. The cool thing about Wikipedia is that it is in a constant state of flux, and nobody "owns" any article, not even for a week. Of course, there are articles that some people pay attention to and try and keep in a good shape, and such efforts are important, particularly for articles like the EP, which would be hard for someone without specialized knowledge to write. --Joke137 16:58, 6 Apr 2005 (UTC)

I will back off a little on the above comments, as my request to not edit without discussion was not present in the version that was editted. Even so, I did people the favor of requesting comments on my revision before I posted them, and feel that any such revision should never be done without prior discussion for any page.

Beyond that, there is the issue that the new version was seriously in error.

I am willing to work with people on this page, but there is a definite and limited meaning to the equivalence principle, and I will enforce it.

--EMS 20:33, 5 Apr 2005 (UTC)

The world of wiki wiki

Also, I included the following as a comment at the beginning of my "source" of this page:
Please do not edit without first discussing changes on the discussion page.
I meant that --EMS 18:49, 5 Apr 2005 (UTC)

Hi EMS, may I please remind you of the following wikiwiki instruction:

If you do not want your writing to be edited mercilessly and redistributed at will, do not submit it.

Preferably wikipedians should propose changes first and only implement them after discussion, but that is not mandatory. In fact, wikipedians are encouraged to be bold. I know you made your request because you care a lot, but there is just a thin line between caring a lot and being possessive.

Generally phycisists agree about the mathematics of their craft, but when it comes to interpretation what the mathematics represents, physicists can sometimes find they they disagree to the bone. Interpretation of physics is very much not an exact science. I suspect that it is not possible to reach consensus in the case of the Principle of Equivalence. I think only a staff of editors working under the responsibility of a chief-editor can write such an article, with the chief-editor making a judgement call if the editors cannot reach agreement. --Cleon Teunissen | Talk 20:24, 5 Apr 2005 (UTC)

I need to be possessive at this time, but that obviously must be short-lived. In the end, this page has to defend itself, and the Wiki community as a whole will need to defend it. Joke137's version is a common misconception about the EQ, and so I must address that. In that way some good has been done.

On the other hand the ability of people to completely revise a page that they disagree with is a problem. Unless there is some way of having some control for a page like this one, the usefullness of Wikipedia will be quite impaired. I know that Joke137's revisions were sincere, but they are not proper. (I will not make the obvious pun. Joke137 put some serious work into the changes, and this is worthy of some respect whether or not I can abide by the changes themselves.)

--EMS 20:44, 5 Apr 2005 (UTC)

Two independent spectrums of weak vs strong

I get the impression that EMS is discussing a spectrum of the volume of space in which the Principle of Equivalence is seen to hold. Weak Principle of Equivalence is then that it only holds in the limit of infinitisimally small volumes of space. (Fortunately, mathematics provides the tools to handle infinitisimals, integrating them back to reality.) A bit stronger assertion of the Principle of equivalence is that it holds in human-sized volumes of space. Formally it doesn't, by reasonable approximation it does. The strongest assertion is that the Principle of Equivalence holds throughout the universe, which is obviously untenable. --Cleon Teunissen | Talk 08:24, 6 Apr 2005 (UTC)

General relativity is usually introduced by describing how objects are moving, it is usually introduced as a theory of motion, motion of objects. However, just like special relativity, general relativity asserts that all the physics that is going will follow the local space-time geometry. Special relativity states that electrodynamics displays the same invariance as motions of objects.

I had always assumed automatically that whatever holds in special relativity holds in general relativity too.

A weaker form of the Principle of Equivalence would be that it only holds for material objects, but not for say, electrodynamics. Or not for some nuclear interaction. As far as known, there is no known physical process that is affected stronger or less strong by the magnitude of space-time curvature. All physical processes, such as radio-active decay, are affected in exactly the same proportion by say, gravitatonal time dilation, so all co-moving clocks, no matter their operating principle, remain in sync. --Cleon Teunissen | Talk 10:03, 6 Apr 2005 (UTC)

Ohanian

What I've written below is in line with what User:Cleon_Teunissen has said above, and I think it resolves the misunderstanding. I picked up Ohanian at the library. He states:

Local experiments can distinguish between a reference frame at rest in a gravitational field and an accelerated reference frame far away from all gravitational fields. Gravitational effects are not equivalent to the effects arising from an observer's acceleration.

He adds in a footnote:

It would seem that a perfectly homogeneous gravitational field (zero tidal force) cannot be distinguished from the pseudo-force field of uniform acceleration. This is true, but not very relevant: perfectly homogeneous gravitational fields can only exist under extremely exceptional and unrealistic conditions. It can be shown that uniform fields are only possible in regions (cavities) completely surrounded by a continuous distribution of mass.

Ohnian's statment of the strong EP is:

All laws of physics [are] the same in a laboratory freely falling in a graviational field, and in another laboratory far away from any field.

And he states, correctly, that it is wrong, because the observer can detect the presence of tidal forces, or, equivalently a curved geometry of space. But he is using the wrong definition of local. The strong EP is restricted to local experiments, where local in this sense means the dimensions of the experiment are much smaller than the curvature radius of spacetime. In Will, section 3.3:

In any metric theory of gravity, matter and nongravitational field respond only to the spacetime metric g. In principle, however, there could exist other gravitational fields besides the metric, such as scalar fields, vector fields, and so on. If matter does not couple to these fields what can their role in gravitation theory be? Their role must be that of mediating the method by which matter and nongravitational fields generate gravitational fields and produce the metric. Once determined, however, the metric alone interacts with matter as prescribed by EEP.

He goes on:

Consider a local, freely falling frame in any metric theory of gravity. Let this frame be small enough that inhomogeneities in the external gravitational fields can be neglected throughout its volume. [i.e. a local experiment] However, let the frame be large enough to encompass a system of gravitating matter and its associated gravitational fields. The system could be a star, a black hole, the solar system, or a Cavendish experiment. Call this frame a "quasilocal Lorentz frame". To determine the behavior of the system we must calculate the metric. The computation proceeds in two stagves. First, we determine the external behavior of the metric and gravitational fields, thereby establishing boundary values for the fields generated by the local system, at a boundary of the quasilocal frame "far" from the local system. Second, we solve for the fields generated by the local system. But because the metric is coupled directly or indirectly to the other fields of the theory, its structure and evolution will be influence by those fields, particularly by the boundary values taken on by those fields far from the local system. This will be true even if we work in a coordinate system in which the asymptotic form of

g_{\mu \nu }

in the boundary region between the local system and the external world is that of the Minkowski metric. Thus, the gravitational environment in which the local gravitating system resides can influence the metric generated by the local system via the boundary values of the auxiliary fields. [i.e. the vector or scalar fields described in the preceding quotation] Consequently, the results of local gravitational experiments may depend on the location and velocity of the frame relative to the external environment. Of course, local nongravitational experiments are unaffected since the graviational fields they generated are assumed to be negligible, and since those experiments couple only to the metric whose form can always be made locally Minkowskian. Local gravitational experiments might include Cavendish experiments, measurements of the acceleration of massive bodies, studies of the structure of stars and planets, and so on.

Finally, he defines the strong EP:

(i) WEP is valid for self-gravitating bodies as well as for test bodies (GWEP), (ii) the outcome of any local test experiment is independent of the velocity of the (freely falling) apparatus, and (iii) the outcome of any local test experiment is independent of where and when in the universe it is performed. The distinction between SEP and EEP is the inclusion of bodies with self-gravitational interactions (planets, stars) and of experiments involving gravitational forces (Cavendish experiments, gravimeter measurements).

This is the definition used nearly universally in the literature, as I've demonstrated above. Sorry I had to use such extensive quotation, although I think it qualifies as fair use. --Joke137 18:11, 6 Apr 2005 (UTC)

Where to go from here

I have considered all of evidence gathered, and now have some sense of where I want to go with the Equivalance Principle, but am still considering how to get there.

First things first: I think I need to at least act as an editor-in-chief at this point, admitedly self-appointed but as I see it I either do that job responsibly or the community will "boot" me out of it soon enough.

Next: We are dealing with two different beasts here in the weak and strong EPs. The WEP is pretty much as I have descibed: A rule for determining whether one's self is in an accelerated frame of reference. SEP is something else, being not just an extension of the WEP but also a more stringent version of the general principle of relativity. The SEP also seems to suffer from having multiple versions. In one form the SEP calls for the all physical constants (not just the value of $c$ ) to be the same everywhere and everywhen in the universe, which is of some value. Another version calls for all inertial/freefall experiments to come out the same in all cases, which is Ohanian's and Synge's (whom Ohanian quotes in his putting down of this experimental SEP) straw man.

So how do we handle these? One way is to section off the EP page appropriately. However, I am currently leaning towards turning the current EP page into a disambiguation page, which will breifly describe the WEP and SEP while linking to the pages covering each. On this count I am seeking comment and opinions: I am not calling for a vote per se, but will work with those interested to determing what is the best course of action at this point and will assist in implementing it.

Beyond that, my priorities for this effort are to achieve the following in these articles:

Accuracy - This is useless unless what we present in correct and (within reason) complete.
Brevity - What is said should be kept as short and to the point as possible. To paraphrase Einstein: These articles should be short as possible, but no shorter.
Clarity - It should be reasonably obvious as to what is being said and why. (This is not as easy as it sounds. I often find that I know what I am saying, but if noone else does that is a problem.)
Accessibity - Making this as informative as possible to as many people as possible: I don't think that we should even try to make this subject understandable to a village idiot, but neither should a Ph.D. be required to understand it either. Instead an interested party with some reasonable prerequisite knowledge should be our audience.
Faithfulness to the other stated goals of Wikipedia, including the NPOV.

So let's make some decisions on the format and run with them. Joke137 - I will let you at least draft the SEP stuff in either case. I figure I can trust you with the content, and I can then edit your work as needed. Cleon - Feel free to comment, but let me see any propsed edits before you impose them: There are still nuances about frames of reference that escape you. Then again, this is GR stuff, and GR is something else.

--EMS 02:43, 7 Apr 2005 (UTC)

(William M. Connolley 10:38, 7 Apr 2005 (UTC)) I'm not a physicist but I have an interst in this. Can I add to your list of criteria:

Consistency with textbooks (I think all this stuff is old enough that it should be sourceable from textbooks rather than research papers)
References to said books.

I consider the "Consistency ... " criteria to be covered by accuracy, and the "References ..." criteria to be covered by accessibility and faithfulness. So let's not get too detailed here, since the big picture is what needs to handled. OTOH we should not lose sight of deatils such as there. BTW - Your consistency goal may be a little hard to achieve, since I am not sure that even the textbooks 100% agree on what the SEP is. As I noted before, this may be more a matter of reporting on what the more common variants are instead of saying "this is the SEP". -- I have already made the mistake of saying "this is the EP" and been shown wrong on it. So let's not head down that road again.

--EMS 12:48, 7 Apr 2005 (UTC)

(William M. Connolley 14:57, 7 Apr 2005 (UTC)) Formally, they may be covered, but I think its worth making them explicit. But no, excess deatil is not needed, they have been mentioned, thats all that is needed. As I think you've noted, there is some variation on what the SEP is said to be (I don't speak from my own knowledge here) and I think you are right that the common variants should be reported: this might well help avoid arguments.

Upwards? Or downwards?

In the opening of the current article it is stated:

Whenever an observer detects the local presence of a force that acts on all objects in direct proportion to the inertial mass of the object, that observer is in an accelerated frame of reference.

This description is ambiguous. It does not specify whether a force in upwards direction is meant, or a force in downwards direction.

It does not matter. For example, when you are on an upwards moving elevator that is slowing down to stop at a floor you may detect the presense of a temporary upwards "force" caused by the acceleration of the elevator. That is no more a real force than gravity is, and its nature can be diagnosed through the WEP just the same as with gravity. So what matters is the nature of the force, not its direction.

Only experts will know that probably a force in upwards direction is meant, since it is also stated in the article:

[...] the equivalence principle indicates that free-fall is actually inertial motion. In that case, there is only one force acting on a person standing on the surface of a massive object, and that is the upward force of the surface on that person.

If you are saying the I should amend the above to "... indicates that free-fall is not due to a downwards acting force but instead is actually ..." (added text emphasized), that sounds like a good idea to me.

These confusing statements in the current version of the article should be resolved. The logic of the Principle of equivalence is self-consistent and consistent with both everyday observation and scientific observation. The article should demonstrate that. --Cleon Teunissen | Talk 13:11, 7 Apr 2005 (UTC)

The WEP is not consistent with everyday experience, in which it is easiest to treat the surface of the Earth as a rest frame and gravity as being due to a force. Instead the article needs to make it clear that the everyday observations of gravity in fact are best explained by a the very non-intuitive notions of the WEP.

--EMS 15:49, 7 Apr 2005 (UTC)

Physics recognizes four fundamental interactions of Nature, capable of causing acceleration, capable of mediating momentum exchange: weak nuclear interaction, strong nuclear interaction, electromagnetic interaction, gravitatonal interaction.

An explanation of the Principle of Equivalence should demonstrate that it is consistent with all other physics, so it must meet the following conditions:

The status of gravtational interaction as one of the four fundamental Forces of Nature must be confirmed.
No forces other than the known fundamental forces of nature should be postulated.

--Cleon Teunissen | Talk 14:45, 7 Apr 2005 (UTC)

It is getting obvious that a proper treatment of the SEP will need to bring in theories regarding a 5th force and the like (as those will cause SEP violations). It is against the rules of Wikipedia to speculate on one's own. It is however demanded by Wikipedia's mission that speculations with some good standing in the literature be reported on. I also am loathe to confirm gravitation as a "Fundamental force" since it really is not a true force to begin with, nor do I see how such a confirmation would assist in describing either EP.

--EMS 15:49, 7 Apr 2005 (UTC)

What is a true force?

I also am loathe to confirm gravitation as a "Fundamental force" since it really is not a true force to begin with, --EMS 15:49, 7 Apr 2005 (UTC)

Now let me get this straight:

I gather you propose to state that gravitation is not a true force. Does that also imply that gravitational potential energy is not true energy?

It is stated in Physics textbooks that as matter condenses to a proto-sun, gravitational potential energy converts to heat, heating up that proto-sun so much that inside the proto-sun nuclear fusion starts. Gravitational potential energy is part and parcel of physics.

How do you reconcile that? If gravity is not a true force, how do you propose to give a consistent account of gravitational potential energy? --Cleon Teunissen | Talk 16:21, 7 Apr 2005 (UTC)

What is a true force? (2)

I also am loathe to confirm gravitation as a "Fundamental force" since it really is not a true force to begin with, --EMS 15:49, 7 Apr 2005 (UTC)

I suppose that electrostatic force and magnetic force are examples of true forces as you define true force. In general, all chemistry is electromagnetic interaction between the outer shell electrons of atoms. The electrostatic field is mathematically described as a vector field, and there is electrostatic potential energy. That are the characteristics of a force: you have an associated potential energy, and you need field equations to describe the nature of the mediator. In the case of gravitational interaction: there is an associated gravitational potential energy and mathematically you need tensor field equations describe the nature of the mediator.

What, according to you, does gravitational interaction lack to make you propose that is not a true force? --Cleon Teunissen | Talk 17:23, 7 Apr 2005 (UTC)

There are two ways of answering yoru question. First of all, the other three forces are mediated by an exchange of quanta. For EM, this is photons. For the weak nuclear force this guage bosons (W+, W-, and Z), and for the strong nuclear force it is gluons. Gravitation is not mediated by an exchange of quanta (gravitons) at all. Instead gravitons are only emitted when the curvature of spacetime is being changed.

Secondly, there is Newton's First Law of Motion (as amended): An object will follow a given timelike geodesic as parameterized by proper time unless it is acted on by an unbalanced force. In GR, gravitation is a result of objects following geodesics of spacetime -- No force need apply nor is in operation.

As for potential energy: Let's go back to the EM view. For an electron to be removed from an atom, energy has to given to it to allow in to overcome the attaction of the positively charged nucleus. This energy allows it to resist acceleration due to EM. Similarly in an accelerated frame of reference energy has to be given to something to allow it to move against the acceleration due to gravitation. So because of how we view gravitation, potential energy is quite real to us. In fact, an object at a lower potential has less rest mass than the same object at a higher potential, courtesy of

E=mc^{2}

. (Note however, that if you are moving inertially, there is no potential energy due to gravitation at your location. But if you look at objects near you in a curved spacetime, you will be able to infer the existance of tidal "forces/potentials" that do affect how objects move with respect to you.)

--EMS 18:33, 7 Apr 2005 (UTC)

P.S. The term "gravitation" is used in GR instead of "gravity" since gravity is defined as being a force, while gravitation is the natural tendency of objects to attract one another due to how they curve spacetime.

--EMS 19:38, 7 Apr 2005 (UTC)

[...] the other three forces are mediated by an exchange of quanta. For EM, this is photons. For the weak nuclear force this guage bosons (W+, W-, and Z), and for the strong nuclear force it is gluons. Gravitation is not mediated by an exchange of quanta (gravitons) at all. Instead gravitons are only emitted when the curvature of spacetime is being changed.

Secondly, there is Newton's First Law of Motion (as amended): An object will follow a given timelike geodesic as parameterized by proper time unless it is acted on by an unbalanced force. In GR, gravitation is a result of objects following geodesics of spacetime -- No force need apply nor is in operation. --EMS 18:33, 7 Apr 2005 (UTC)

Cleon Teunissen | Talk 06:54, 9 Apr 2005 (UTC) Among the four fundamental interactions of nature, gravitational interaction does stand out. I prefer the interpretation that gravitational interaction is more fundamental than the other three. For example: as far as known, the other three are subject to gravitatonal time dilation in exactly the same proportion. The fact that it is currently not known how to reconcile gravitation with the other three should not result in reluctance to see gravitation as 'one of the four fundamental interactions of nature'.

[...] No force need apply nor is in operation. --EMS 18:33, 7 Apr 2005 (UTC)

I prefer the following interpretation. I define 'interaction between objects' as 'objects exchanging momentum'. For example: in astrophysics it is known (albeit from computersimulations) that a three-body system is unstable. Sooner or later one of the three bodies will be ejected.

In the case of a three body system, each body is influencing the motions of the other two bodies, not directly, but by curving space-time. Each body's motion is influenced by the (moving) space-time curvature of the other two bodies.

I prefer the interpretation that no matter the nature of the mediator of the interaction, this is a physical interaction, and momentum is being exchanged. At some point in time, the motions of the space-time curvatures of the three massive objects happen to interact in such a way that one object is ejected from the system via a slingshot mechanism.

In shifting one's thinking to General Relativity, familiar concepts need to be redefined to a meaning that is consistent in the context of the new paradigm. The choice of definition is at the same time the choice of how to understand the physics that is going on. I can see the motivation of choosing to define force as: quanta of a force-mediating field are exchanged, but I think that definition is unnecessarily restrictive. I choose to accept any nature of the mediator of the interaction. In my view, space-time curvature is a mediator of physical interaction, simply because it is obvious that it is actually mediating interaction.

I agree that the word 'gravity' is much associated with the newtonian inheritence of seeing gravity as a 'force just like other forces'. Generally I use the more abstract word 'interaction', rather than the word 'force'. --Cleon Teunissen | Talk 06:54, 9 Apr 2005 (UTC)

My thoughts

As I see it, there are three main versions of the equivalence principle in use by physicists. In order of their strength:

the weak equivalence principle (WEP) or the universality of free fall (UFF)
the Einstein equivalence principle (EEP) or simply the equivalence principle
the strong equivalence principle (SEP)

I think the article should be kept as one, even if it gets long, because all the principles are so closely related. It's better to have one really good article than six confusing articles on closely related subjects. However, the WEP is clearly the most important, and I think it is the principle that should be stated prominently in the introduction to the article and discussed first. I would also like to see discussions of tests of the EP.

WEP: I think we agree on what the WEP is, but perhaps not how it ought to be stated. I can see that UFF implies the WEP as presently stated in the article, but I'm a little uncomfortable with how it is stated: to test the WEP you don't even have to know what force, inertial mass or an accelerated frame of reference are. You don't have to know anything about physics, really, you just need to drop different objects and see what happens.

One of your references included the quote from Einstein that "we will now assume the physical equivalence of the gravitational field and an accelerated frame of reference". To me, that is the essense of the WEP. The UFF can be confirmed by observation, but WEP is a very non-obvious concept which is essential to GR. To leave out references to frames of reference is IMO to lose what WEP is all about.

It should also be stated in the simplest possible form: the gravitational motion of objects depends only on their initial position and velocity, not on their constitution, and give an example, perhaps from Galileo. We should note, that the object must be small (compared to the radius of curvature of the gravitational field), light (does not appreciably perturb the gravitational field), and uncharged (i.e. not interacting through other forces).

I would like to cover this in the History section.

This is the most important, and probably the most profound form of the EP, because in Newtonian mechanics it seems like a miracle that inertial and gravitational mass are the same.

Incidentally, although it has been said above that gravity is not a force, it depends largely on your definition. In GR, perhaps not, but a particle physicist would certainly call gravity a force: it has a coupling constant and is mediated by the graviton.

See my response to Cleon - Gravitions are not emitted by static or oscillating masses, whereas photons are emitted by static and oscillating charges. Gravitons seem to mediate curvature change, not gravitation itself.

EEP: This is the statement that in addition to the WEP, non-gravitational physics in local Lorentz frames is independent of your velocity and location. People do not often consider theories that depend on your velocity (these are called prior geometric theories, and are not Lorentz invariant) but theories may depend on your position, usually through variation of the fundamental "constants" (i.e. the marginal detection of the variation of the fine-structure constant of electromagnetism) and variation of particle mass ratios.

Schiff's conjecture says that WEP imples EEP. It is not proven, but seems credible. Nonetheless, this equivalence is not obvious, plenty of theories that violate both the EEP and WEP are most easily tested by looking for variations of the fine-structure constant.

SEP: The SEP is the least-often considered principle, because it is used to differentiate between theories of gravity, and most people believe Einstein's theory is the correct one. However, new theories of particle physics have plenty of light scalar fields which, if not stabilized, result in long-range, gravitational-strength forces which would manifest themselves as violations of the SEP or EEP. The unfortunate thing about Ohanian is that he is completely dismissive of these ideas and doesn't seem to see why they're worth bothering with. After all, he correctly points out that the idea of a uniform gravitational field is a mathematical idealization, and doesn't seem to worry that it holds with extraordinary accuracy over most of the universe. The book was written at just the right time, before the discovery of dark energy and dark matter, and before the rise of string theory and its menagerie of friends.

Of course, SEP implies EEP but the converse is false. Brans-Dicke theory has a varying gravitational constant, for example. The SEP is tested by fifth-force experiments (i.e. looking for Yukawa-type deviations from the inverse square law of gravity), by looking for specific deviations in celestial orbits with rangefinding experiments (the Nordtvedt effect) or by looking for cosmological variation in Newton's constant G.

I think the literature is consistent on what the statement of the SEP is, except that Ohanian and Synge disagree about what local means. Since there is considerable interest in this principle, including a number of important and expensive experiments to test it, I would like to focus on the common version, although we should also mention that there has been disagreement about what exactly the principle is.

Joke137 19:27, 7 Apr 2005 (UTC)

I think that overall we have a game plan here. If you are happy to work within a single article, then so am I. As I see it, we can break it up later if that is needed. My focus then will be the WEP, along with the intro and the history. You can take care of the EEP and SEP. Also, I think I want Ohanian's straw-man to be covered since his point is valid even if his dismissal of the SEP using it is not. BTW - I think that the EEP is covered by the WEP if the special principle of relativity is assummed.

--EMS 20:00, 7 Apr 2005 (UTC)

How the Principle of Equivalence ought to be stated

Joke137 I think we agree on what the WEP is, but perhaps not how it ought to be stated. I can see that UFF implies the WEP as presently stated in the article, but I'm a little uncomfortable with how it is stated: to test the WEP you don't even have to know what force, inertial mass or an accelerated frame of reference are. You don't have to know anything about physics, really, you just need to drop different objects and see what happens. Joke137 19:27, 7 Apr 2005 (UTC)

I think this is a very important issue. There are many ways to state the Principle of Equivalence, and each of them carries hidden assumptions of its own. I favor a formulation that requires (in the reader of the article) as little as possible prior familiarity with the conventions of the subject:

Inside a space-capsule situated on the surface of a gravitating body the same physics is taking place as inside a space-capsule that is being accelerated linearly by the force of thrusters. Locally, all measurable aspects of physics are affected in the same way in both situations.

Sufficiently sensitive devices will detect whether there are tidal forces, wich are second order effects of gravitation, but other than that there is no difference in physics taking place to detect.

I recommend against using the expression 'frame of reference'. First, I think it there is no necessity to use it. Second, I think that the concept of a 'frame of reference, being an abstraction, brings "luggage" with it. I favor phrasing the EEP in terms of concrete objects, concrete observations, to be as free as possible from being committed to a particular interpretation from the outset.

Terrestrial experiments are an indirect test of the Principle of Equivalence, they do not test the space-ship end of the principle, but I think the space-ship end is equally important. I favor a statement of the EEP that explicitly mentions a space-ship. For instance: you can release an object to free-fall/free-floating; the principle asserts that both on-the-surface-of-a-planet and accelerating-in-space the same physics is taking place. --Cleon Teunissen | Talk 14:31, 9 Apr 2005 (UTC)

Another sandbox version of the article

I have also written a sandbox version of the 'Principle of Equivalence' article.
User:Cleon_Teunissen/sandbox/Equivalence_Principle
For the time being, I have no intention to replace the wikipedia version of the article with my sandbox version.

The mathematics of a theory is exact science. On the other hand, there is often room for a multiplicity of interpretations of what the theory means. In quantum physics there is agreement on the mathematics, and there are several mutually incompatible interpretations: The Copenhagen interpretation, the Many-worlds interpretation, Quantum decoherence interpretation. Each of these interpretations is self-consistent and consistent with the observations. -

The corpus of observations that a theory is inferred from can be presented in a form that is as interpretation-free as possible. Beyond that I think that the ideal of a canonical interpretation of the theory must be relinquished, much as a wishful ideal like 'absolute space' had to be relinquished. ---Cleon Teunissen | Talk 11:53, 11 Apr 2005 (UTC)

Have updated this article in my sandbox

I finally have an edit avaialable in user:ems57fcva/sandbox/Equivalence_Principle. Please feel free to comment. Hopefully this will be a fairly non-controversial product that can be used as a basis for continued improvement by those interested over time.

(In any case, I see the "disputed" tag as being joke137's to remove. Hopefully this edit will be adequate for that.)

--EMS 19:29, 11 Apr 2005 (UTC)

The crucial importance of tidal effects

Source:
arxiv.org/abs/physics/0204044
Physics, abstract physics/0204044
Einstein's gravitational field
Authors: Peter M. Brown
Subj-class: General Physics

There exists some confusion, as evidenced in the literature, regarding the nature of the gravitational field in Einstein's General Theory of Relativity. It is argued here the this confusion is a result of a change in interpretation of the gravitational field. Einstein identified the existence of gravity with the inertial motion of accelerating bodies (i.e. bodies in free-fall) whereas contemporary physicists identify the existence of gravity with space-time curvature (i.e. tidal forces). The interpretation of gravity as a curvature in space-time is an interpretation Einstein did not agree with.

[quote from the article]
Another example of a gravitational field with zero space-time curvature is that of a vacuum domain wall. A domain wall is two a dimensional structure characterized by a fixed energy per unit area $\sigma$ . A surface tension equal to $\sigma$ (in appropriate units) is required in order for $\sigma$ to remain constant.
[end quote]

Cleon Teunissen | Talk 07:05, 12 Apr 2005 (UTC)
As EMS has pointed out, the presence or non-presence of tidal forces is a very important distinction. Gravitational acceleration/force is a first order effect whereas spacetime curvature is a second order effect.

In the limit of infinitisimally small space-time intervals, the only thing that affects the physics of a test mass is the first order effect, the incline in space-time geometry. Over a larger stretch of time, the second order effect, the space-time curvature, is relevant as well.

The fact that there are no tidal forces present in the case of uniform acceleration of a space-ship in gravitation-free space distinguishes it from gravitation. In the case of uniform accceleration there is only the first order effect, the incline in space-time geometry. In the case of gravitation, there is always both first order and second order effect.

Historically, Einstein concentrated on gravitational time dilation first. Initially, he predicted a bending of lightrays passing close to the Sun at half the actual angle. Later considerations made him decide to add curvature of space to the theory (doubling the predicted angle) and he obtained the angle of deflection that was later seen to correspond to measurement. --Cleon Teunissen | Talk 07:05, 12 Apr 2005 (UTC)

Degrees of asymmetry of space-time geometry

Minkowski space-time geometry is perfectly symmetrical.
Uniform acceleration corresponds with a first order asymmetry: an incline, a slope in space-time geometry.
Gravitational stress on space-time geometry corresponds with a second order asymmetry: curvature of space-time; a gradient in the space-time geometry.

--Cleon Teunissen | Talk 08:03, 12 Apr 2005 (UTC)

I think that you have misspoken here somewhat. Curvature is more than just a gradient. In your first example, uniform acceleration, there is a gradient of gravitational potential (at least for the accelerated observer). In the second case, that also exists.

The difference instead is in the existance (or lack) of curvature itself, and that is defined by equations which involve more than just the gradient(s) for the metric.

(Admitedly I am nitpicking on this one, but I felt that some clarification was needed. Overall, this is not a bad set of postings -- You are starting to get it.) :--EMS 19:19, 12 Apr 2005 (UTC)

Yes, describing space-time curvature as a gradient is short of the mark, as the equations allow for 10 different gravitational potentials. Gradient is a property of a vector field and space-time curvature is described as a tensor field.

The following Einstein quote in the article by Peter M,. Brown intrigues me:

The breakthrough came suddenly one day. I was sitting on a chair in my patent office in Bern. Suddenly the thought struck me: If a man falls freely, he would not feel his own weight. I was taken aback. [...] A falling man does not feel his weight because in his reference frame there is a new gravitational field, which cancels the gravitational field due to the Earth. In the accelerated frame of reference, we need a new gravitational field. (Translation of a talk that Einstein had given in Japan in 1922, published in the aug.1982 issue of Physics Today, p. 45-47)

The nature of the equivalence is such that the asymmetry corresponding to acceleration can largely cancel the asymmetry of space-time curvature (only the tidal effects remain). I needed a word to describe the asymmetry corresponding to acceleration and I decided on slope, which to me seems to slot in well with the geometrical character of GR. --Cleon Teunissen | Talk 19:57, 12 Apr 2005 (UTC)

Replaced article, again

I took the liberty of replacing the article with the version from User:Ems57fcva's sandbox, and edited it, merging in changes from my old version in the hope that we can reach some sort of consensus. I am pretty happy with this version, although I believe it could still do with a lot of work. Feel free to update it and/or remove the disputed tag. I hope we can accept this version as at least the "working draft" from which to make changes from.

I've been quite busy at work these past few days, and unfortunately haven't had much time to visit the talk page, but I wanted to put this version on the main page to get the ball rolling. --Joke137 21:48, 12 Apr 2005 (UTC)

You beat me to the punch. I was getting ready to move the sandbox version over, but this is what I am looking for for the most part. At the least, it is an improvement over the sandbox draft.

I also am busy. I will review the article as I can. I have a few issues with it, but nothing major.

One issue is the treatment of tidal forces. You can never completely get rid of them in a curved spacetime -- That is the point of Synge and Ohanian. Also, you wrote "other than masses and Newton's gravitational constant" for the EEP while my understanding of this is that it will include both. (A change in $G$ will affect the $\kappa$ of the EFE, while a change in the electron mass will affect the fine structure constant $\alpha$ amongst other things.)

I also scratch my head over the inverse-square business in discussing the tests of GR, but I think that the fact the GR itself predicts deviations from the inverse-square law for strong gravitational fields may be overly esoteric.

--EMS 15:38, 13 Apr 2005 (UTC)

I have tried to clarify the treatment of tidal forces, but it could probably still use some work. I also changed the inverse square business, because the inverse square law is somehow replaced by Birkhoff's theorem (which is a sort of analogue to Gauss's theorem for general relativity).

The EEP requires that dimensionless, non-gravitational constants cannot evolve, such as the fine-structure constant or ratios of masses. However, if all the particle masses increased by the same factor, or if Newton's constant increased by a factor, that would be consistent with the EEP, because non-gravitational physics will stay the same (e.g. the spectral lines of hydrogen will not be affected).--Joke137 18:48, 14 Apr 2005 (UTC)

I think that you have missed the boat on the EEP somewhat: The EEP only says that fundamental physical quantities cannot be dependent on the velocity of the laboratory. OTOH, it permits (by default) the constants to vary by location in and age of the universe. Also, it applies locally to all physical constants, not just dimensionless values (which often are not fundamental at all). Things like the fine structure constant and the magnetic moment of the electron are used in research since any changes in them will reveal the presense of changes in the real fundamental constants. The SEP then extends the EEP to apply locally throughout all of spacetime.

--EMS 05:08, 15 Apr 2005 (UTC)

I disagree. From Will (p. 22),

The Einstein Equivalence Principle then states: (i) WEP is valid, (ii) the outcome of any local nongravitational test experiment is independent of the velocity of the (freely falling) apparatus, and (iii) the outcome of any local nongravitational test experiment is independent of where and when in the universe it is performed.

It looks like you agree with the first two parts, but disagree with the third. The second condition is really a very weak condition, because it is satisfied by any Lorentz invariant theory of gravity. The review on variation of the constants by Uzan uses the same definition (p.4).

The problem with measuring the fundamental constants, like the speed of light, is you can never really be sure what it means for such a constant to vary except as expressed by dimensionless quantities. This is because we could simply define out units differently at each point in space time, and claim that the fundamental "constants" were varying. The numerical values of dimensionful fundamental constants are more a matter of convention than anything else, and it is the dimensionless constants in which real physical changes will show up (e.g. the fine structure constant is the perturbation parameter in quantum electrodynamics, and reducing it will affect different processes, such as Thomson scattering). Particle physicists often avoid this issue entirely with Planck units.

The strong equivalence principle measures variation of the (dimensionful) gravitational constant. What is really being looked for is the change in the ratio of particle masses to the Planck mass. --Joke137 19:12, 15 Apr 2005 (UTC)

Clarity

In the article it is stated:

Whenever an observer detects the local presence of a force that acts on all objects in direct proportion to the inertial mass of the object, that observer is in an accelerated frame of reference.

I call this: statement 1

In this statement a number of objects are involved, each with a different mass. Let us say that the objects are distributed over the floor of a cabin. All the objects are being accelerated in unison, they are being co-accelerated. In order for the objects to be co-accelerating the force must be proportional to the inertial mass, otherwise they wouldn't co-accelerate; a=F/m. So why the apparently superfluous mention that 'the force is in direct proportion to mass'. It has to be proportional anyway, otherwise no unison in acceleration.

I have made no reference to there being a unison of acceleration in that statement. Instead the unison is demanded by it. In this business, you have to start somewhere. I choose to start with gravitation being a d'Almbertian force like centrifugal force is. However, instead of getting highly technical and expecting people to understand how d'Almbert's work anticipated the WEP, I simply cut it down to it's bare essense.

I also badly need that statement in that spot, since I am trying to find the time to rework the GR page itself, and that statement of the WEP is essential for gaining an understanding of what GR is about. That

M_{g}=M_{i}

means that gravity is not a real force is essential to comprehending GR. Focussing on the UFF instead obscures that very, very important insight.

--EMS 05:39, 15 Apr 2005 (UTC)

I infer that in statement 1 two logically independent statements are combined:

When objects rest on weighing scales the weight that the scales indicate is always in direct proportion to the ineritial mass.
Whenever the weight that is measured is non-zero, the objects are in a frame of reference that is being accelerated by a mechanical force.

Positioning the objects on top of weighing scales is how the observer measures how much force is being exerted.

I think it is odd that such an important matter is only hinted at in a roundabout way in statement 1. I recommend to not vaguely imply things, but to mention explicitly what is meant. --Cleon Teunissen | Talk 21:11, 13 Apr 2005 (UTC)

This is more fundamental than placing stuff on scales. You are proposing a specific detection method here, but there are plenty of ways to determine the local presense of a d'Almbertian force. The issue is what is being detected, not how.

If you want to propose a change to "statement 1", you may do so in this discussion page, and I will comment on it. But before you do so, go back to Einstein's original gedanken and reconsider it's underlying question: How do you know when you are in an inertial frame of reference or not?

--EMS 05:39, 15 Apr 2005 (UTC)

interpretations of General relativity

In this business, you have to start somewhere. I choose to start with gravitation being a d'Almbertian force like centrifugal force is. --EMS 05:39, 15 Apr 2005 (UTC)

I agree that the choice of starting point is not straightforward. The concepts of relativistic physics do not lend themselves to be presented in a hierarchical manner, an ordering in which deductions can be made.

There are striking similarities between gravitaton and the inertial forces such as centrifugal manifestation of inertia, and differences. The similarities are such that the principle of equivalence is justified, with the severe restriction that it is justified only in the limit of infinitisemally small intervals of space-time. The differences are such that gravitation is recognized as one of the four fundamental interactions of nature. (Inertia seems to be regarded as something that needs to be assumed in order to frame a theory. There seems to be no consensus as to explaining the origin of inertia. External link: A brief summary of the 1953 paper by Dennis Sciama 'on the origin of inertia')

arxiv.org/abs/physics/0204044 In this article, the author, Peter M. Brown, documents a shift in interpretation of the theory of general relativity. The vintage 1916 Einstein interpretation of GR is that the inertial forces like centrifugal force should be seen as equally real as gravitation (or equally unreal, whichever is preferred).

The modern interpretation of Geometrodynamics is that gravitation is confirmed as one of the four fundamental interactions of nature. Gravitation is mediated by curvature of space-time. On the other hand, centrifugal manifestation of inertia is one of the ways manifestation of inertia can occur. Manifestation of inertia is a property of space-time that is equally valid for curved space-time and flat space-time: to be accelerated by a mechanical force is to deviate from moving along a geodesic. In order to accelerate a mechanical force is required.

There are (at least) two mutually exclusive interpretations of GR around. It appears you follow the 1916 vintage interpretation, I think the article should present the modern interpretation of geometrodynamics. --Cleon Teunissen | Talk 08:18, 15 Apr 2005 (UTC)

With regards to geometrodynamics, please see http://www.physicsdaily.com/physics/Geometrodynamics. Suffice it to say that I see little value in gravitation being confirmed as a fundamental interaction by a dead theory.

OTOH, you are using the word "interaction" instead of "force", and it is acceptable to me to call gravitation an interaction. In that case, gravitation being fundamental seems kind of obvious (at least until it is proven to be otherwise).

Beyond that, you are tripping over the semantics of GR. Gravity is what is being treated as an "inertial force" in GR. As you correctly note, centrifugal force can create a "gravitational field" comparable to the gravitational field of gravity. OTOH, gravitation is the tendency of objects to be affected be each other due to how they curve spacetime. So gravitation is specifically a curvature related term, while gravity and "gravitational field" are not. I think that this will account for your confusion. --EMS 20:58, 15 Apr 2005 (UTC)

General relativity and photons

Einstein's original gedanken and it's underlying question: How do you know when you are in an inertial frame of reference or not? --EMS 05:39, 15 Apr 2005 (UTC)

Indeed that is the key issue. Once more the following Einstein quote:

The breakthrough came suddenly one day. I was sitting on a chair in my patent office in Bern. Suddenly the thought struck me: If a man falls freely, he would not feel his own weight. I was taken aback. [...] A falling man does not feel his weight because in his reference frame there is a new gravitational field, which cancels the gravitational field due to the Earth. In the accelerated frame of reference, we need a new gravitational field. (Translation of a talk that Einstein had given in Japan in 1922, published in the aug.1982 issue of Physics Today, p. 45-47)

The weightlessness of astronauts in a space-station that is orbiting a planet is fundamentally different from the approximation to weighlessness that can be achieved with for example diamagnetism. Most atoms are diamagnetic and a uniform 20 Tesla magnetic field will levitate any object (unless it happens to be a non-diamagnetic material.)

Magnetic levitation is not wieghtlessness. Instead you have replaced the repulsion of the ground with a magnetic effect exerting the same force in a different manner. A magnetically levitated man will still feel his own weight.

But in the case of the space-station orbiting a planet the acceleration towards the planet truly cancels all gravitational effects (only tidal effects remain). I expect that if the Harvard tower experiment is performed onboard a space-station a null-result will be obtained. (The tower experiment in which Iron57 nuclei emitted and absorbed gamma-photons, confirming gravitational frequency shift of the gamma-radiation.)

Your basic point is correct. However, tidal effects can result in their being a small residual which a sensitive enough experiment could in principle detect.

The defining character of an inertial frame of reference is that the physics taking place is symmetrical in all aspects of geometry. --Cleon Teunissen | Talk 14:24, 15 Apr 2005 (UTC)

I'm not certain what that last line is supposed to mean. If you are saying that objects thrown up at least in the local are behave the same as objects thrown down, I will go along with that. However, on a larger scale that does not hold true in the topologies of GR. --EMS 16:44, 15 Apr 2005 (UTC)

Formulated more technically: a characteristic of an inertial frame of reference is that there is no anisotropy in the physics taking place. In the case of the Harvard tower experiment, conducted inside a space station orbiting Earth there are simultaneously two effects:

The experiment is conducted in curved space-time and the quantum behavior of the photons is affected by that space-time curvature.
The the experimental setup is accelerating due to the gravitation, and the fact that the setup is accelerating affects the outcome of the experiment.

The two effects largely cancel (only tidal effects remain), hence almost no anisotropy.
That is the difference between free-floating in gravitation-free space and free-falling in gravitationally altered space-time. --Cleon Teunissen | Talk 17:39, 15 Apr 2005 (UTC)

"The straight road to curved spacetime"

I have a copy of Clifford Will's "Was Einstein Right?" lying around, and started looking at it yesterday. On of the chapters is called "the straight road to curved spacetime", and it does a very good job of straightenning out the variations of the Equivalence Principle.

The first thing it did was to confirm something that I have gotten more and more suspiscious of: The EEP and SEP are in fact two names for the same thing.

Secondly, it gave a coherent (for me) definition of the SEP: The underlying laws of physics when written in covaraint form are the same in all inertial frames of reference. ("covariant form" refers to a type of tensor notation.) This is a saner statement that the "all experiments ..." one, which is obviously bogus: Not only can tidal effects be detected in curved spacetimes, but any experiment involving measurements of the cosmic microwave background will have results that vary based not only by where and when in the universe you are but also by on how you are moving with respect to other observers!

Finally, there is something that I have encountered elsewhere called Schiff's Conjecture. The gist of Schiff's Conjecture is that the WEP implies the SEP.

I will worry about editting this page a little later, but wanted this much to be known.

--EMS 18:30, 18 Apr 2005 (UTC)

This is very surprising to me, because I have a copy of Clifford Will's Theory and Experiment in Gravitational Physics, which I have extensively quoted from above. As far as I can tell, it is the standard reference for this subject. It clearly states that the EEP and SEP are two names for two manifestly different things. Brans-Dicke theory, for example, violates the SEP but not the EEP. It has a scalar field which generates Nordvedt-effect "polarized" orbits in the solar system and a time-varying gravitational constant. The theory, however, is perfectly covariant. The problem is that there are gravitational degrees of freedom other than the metric, the Brans-Dicke scalar field.

I agree that these statements about all experiments, laboratories etc are troublesome. The problem is that all the fine print is hidden in the word local, which implies that the experiment is not trying to measure anything external (such as the CMB, which sets a preferred frame for the universe) and that the experiment is small enough to be insensitive to tidal forces. But how do you separate something like the CMB from the Brans-Dicke scalar? It starts to get a bit philisophical, what you call gravity and what you don't.

I agree with your statement of Schiff's conjecture (see above). --Joke137 01:30, 19 Apr 2005 (UTC)

Then I may need to look around some more, and see what I can find. But I now have two sources that give as a definition for the EEP that which I though the SEP was. So if the SEP definition is the experimental one, then we are back to its being a bogus concept for the reasons listed.

I have dealt peripherally with the SEP for years, and now realize that I instinctively came to disregard it as being ill-defined and all but irrelevant. Much of its ground is covered by the general principle of relativity and the principle of general covariance. Now as I look around I find that some people describe an EEP but not an SEP. Others describe an SEP but not an EEP. Will in his on-line book now described both an EEF and a SEP, but is the only one that does so. (In his earlier book, he only described an EEP, and defines it as being what I thought the SEP was. I should have written his work indicated that the SEP and EEP are the same, BTW. He really never mentional SPE explicitly there.) Wald, in his book "general relativity" describes the WEP and ignores the EEP and SEP.

Right now, my thought is to document the EEP and SEP as described by Will, and make it obvious that Will is the source for it. I also very much want Ohanian's view documented, since it makes it clear that there are limits to the SEP even in Einstein's theory. I also think that the conjecture that the SEP means that only the metric g is responsible for gravitational interactions is important and needs to be mentioned.

One other thing: My most recent web search has resulted in my finding that other sites are already borrowing from Wikipedia, and therefore from our work. It makes me very antsy that this is already being treated as somehow being authoritative. At least we still have that "disputed" tag up.

--EMS 04:10, 19 Apr 2005 (UTC)

I think that physics literature has been relatively consistent in using Will's ideas about the strong equivalence principle. I don't think it's an option to think of the SEP as a bogus concept -- whether ill-defined or not, a lot of effort has gone into testing it.

There are two problems as I see it.

The problem, which occurs all over physics, of stating idealized thought experiments as principles that should hold in the real world. It is never possible to create perfectly ideal conditions for a real-world experiment. This is a problem even for the weak equivalence principle or the universality of free fall. I see this as being a more philisophical problem than anything: huge swathes of the universe are, to very high precision, free from tidal forces, for example.

The practical problem of determining whether to put a phenomenon in the gravity sector or the "matter" sector. With the CMB, even though it picks out a preferred frame for the universe, we don't view it as violating the Einstein equivalence principle. This seems reasonable, as it is an electromagnetic phenomenon. With, say, dark matter it seems a little ambiguous: after all, we have only detected it via its interaction with the metric. Nonetheless, physicists have taken the practical step of putting it in the matter sector, assuming it is a kind of particle that will eventually be detected.

I take a pragmatic view of these things. The statement of the various EPs may be problematical, but there are a clear list of things that would constitute a violation of each one, so clearly the definitions work operationally. It's like quantum mechanics: the philisophy of interpretations of quantum mechanics and the meaning of observation was worked out long after it was used successfuly in all kinds of different contexts, and had very little impact on the practice of physics, because the operational definition worked fine. --Joke137 16:39, 19 Apr 2005 (UTC)

I like the above analysis, even the part about its not being an option to treat SEP as bogus. I mostly just needed to vent in my last writeup above. The WEP is my focus here: It is what I need to have properly stated to support what I plan to do in the GR page. So the SEP is proving to be Pandora's Box for me. I don't really want or need it, but unfortunately it is a part of the "landscape" and dealing with it is part of the deal in working with this page.

What I need is to end up with are clear, coherent, defensible definitions of EEP and SEP: Something that can be stated in brief but technical terms, with accompanying explanations that make its content as accessible as possible to the average reader. I would much rather state things in terms of physical laws as experienced locally instead of this "experiments" business. As I it, there is nothing wrong with the underlying laws of physics always being the same but the result of applying them varying as functions of time, place, and/or velocity.

I think that we are getting there. It just will take some more time. I should probably try another edit soon, but I need to be sure I have an appropriate framework for it first. (Going off half-cocked just does not work in this environment.)

--EMS 21:31, 19 Apr 2005 (UTC)

The relevancy of general covariance

In Gravitation by Misner, Thorne and Wheeler, the following is stated about general covariance.

Section 12.5 (page 302)

"Every physical quantity must be describable by a (coordinate-free) geometric object, and the laws of physics must all be expressible as geometric relationships between these geometric objects." This view of physics, sometimes known as the "principle of general covariance", pervades twentieth-century thinking. But does it have any forcible content? No, not at all, according to one viewpoint that dates back to Kretschmann (1917). Any physical theory originally written in a special coordinate system can be recast in geometric, coordinate-free language. Newtonian theory is a good example, with its equivalent geometric and standard formulations. (Box 12.4). Hence, as a sieve for separating viable theories from nonviable theories, the principle of general covariance is useless.

I have found this information to be confirmed in multiple independent locations: general covariance is exclusively a property of how a theory is formulated.

The fact that the mathematical formulation of general relativity satisfies general covariance is irrelevant: only the physics content counts, and the physics content of general relativity meets the criterium of Lorentz invariance. External link: Symmetry, indistinguishability, and covariance
--Cleon Teunissen | Talk 20:05, 18 Apr 2005 (UTC)

Cleon - Using a bucket as a sieve normally does not work.

Coordinate independence is a highly desirable trait, and it is a real stregth of GR that it is at its most fundamental and elegant form when expressed in a coordinate-free fashion. However, having an ideal form should never be treated as any substitute for experimental verification.

--EMS 15:37, 19 Apr 2005 (UTC)

Clifford Will

EMS wrote:

Clifford Will:

The underlying laws of physics when written in covariant form are the same in all inertial frames of reference.

--EMS 18:30, 18 Apr 2005 (UTC)

The above statement only states the principle of relativity of Special Relativity, because it does not state which frames of reference are to be categorized as inertial frames of reference.

In a frame of reference that is co-moving with a free-falling test mass (free-falling in curved space-time) there will be tidal forces. So a decision needs to be made: does the presence of tidal forces imply that it is not to be categorized as an inertial frame of reference?

It should be stated explicitly: which frames of reference are to be understood as inertial frames of reference, and why they are to be understood as inertial frames of reference. --Cleon Teunissen | Talk 21:00, 18 Apr 2005 (UTC)

To identify an inertial frame of reference, just use the WEP. As for the EEP, I would just say that the underlying laws of physics are the same in all inertial frames of reference. Those laws permit tidal effects to appear in non-uniform gravitational fields.

--EMS 04:17, 19 Apr 2005 (UTC)

I hold the science of physics to be the following: the endeavour to account for the whole corpus of observations in a coherent mathematical framework. It all begins with observations, and observations should always be the final word.

Whenever a principle can be stated in a form that is not committed to any specific theory, it should be stated in that uncommitted form. The Equivalence principle is prime example of that.

The Harvard tower experiment indicates that there is no clash between quantumphysics and GR as far as measureable aspects of physics are concerned. At present the formal frameworks of the two theories cannot be reconciled, but the measurements agree.

The principle of relativity of special relativity can be formulated in a theory-committed form, but Einsteins choice of principle is best: in all frames of reference that are not measurably accelerated, measurement of the velocity of electromagnetic radiation will yield the same value. --Cleon Teunissen | Talk 06:30, 19 Apr 2005 (UTC)

The necessity to relinquish cherished assumptions

I would much rather state things in terms of physical laws as experienced locally instead of this "experiments" business. As I it, there is nothing wrong with the underlying laws of physics always being the same but the result of applying them varying as functions of time, place, and/or velocity. --EMS 21:31, 19 Apr 2005 (UTC)

Your philosophy of physics, it appears, is to move away from operational statements. I am in favor of making statements as operational as possible.

The starting point is the corpus of observations. Physicists infer certain abstractions from that corpus of observations, and these abstractions, these mathematical models, are the theories of physics.

There is no such thing as 'the underlying laws of physics', that's a myth. In quantumphysics calculations there is Erwin Schrödinger's wave equation approach to calculations, and there is Richard Feynman's sum-over-histories approach to calculations. Both yield the same outcomes, and these outcomes are in accordance with measurements. It is hard to see whether either of the two calculational approaches has physical meaning, possibly they don't have any physical meaning at all.

In the history of physics, physicists have been forced to relinguish all sorts of long cherished assumptions. Absolute space and absolute time had to go, etc, etc.

The following assumption is one of the hardest to relinguish: the assumption that a highly succesfull mathematical protocol is certain to have physical meaning. Quantumphysicists have had to let that one go. Quantumphysics is only operationally defined, and the Copenhagen interpretation asserts that is is useless to try and uncover a deeper level; there isn't any. Hence Feynman's summary of a widespread attitude among quantumphysicists: "Shut up and calculate." --Cleon Teunissen | Talk 08:29, 21 Apr 2005 (UTC)

Look again at QM: If there are not certain mathematical rules that underlie things, there is nothing to calculate. Schrödinger's Equation is an underlying physical law in my book, and Feynman's approach has been proven to be mathematically equivalent to Schrödinger's. As for whether the outcomes have physical meaning: If they did not, then how could they create measurable results?

So the successes of both GR and QM do come from the evaluation of underlying but also non-intuitive laws. The fact that people have not managed to come to a clear agreement on the meanings of the QM wave equations does not deprive them of their being physically relevant.

--EMS 15:28, 21 Apr 2005 (UTC)

I wasn't referring to relevancy, of course the calculations are relevant.

I'd like to explain how I see a distinction between 'relevancy' and 'meaning'. I define 'relevancy' as the question whether it works. I define 'meaning' as the question whether it provides a window on what is really physically going on.

I have noticed that in their efforts to make progress, physicists have found that they had to move the mathematics to ever higher levels of abstraction. The solutions to the most abstract equations are themselves vast 'solution-spaces'. It appears that physicists have had no choice but to move from laws to meta-laws.

I think that nature has constancy of properties, that experiments are repeatable. I think that the equations that physicists formulate are at best approximations to the versatility of nature, simplifications. I don't think that physicists can do any better, but I am doubtful that these meta-laws still provide a window on what is physically going on.

The fact that in QM there is no consensus about a "meaning" of the equations is not because of ineptitude or lack of interest on the part of the QM theorists. The Copenhagen interpretation asserts that no such thing as the meaning of the equations should be sought for, there isn't any. The Copenhagen interpretation asserts that the theory can fundamentally only be stated in operational terms, that the theory can only be stated in terms of observables. If you perform a double slit experiment you will get a particular distribution of photons hitting the screen, that's it.

We're getting sidetracked here. I hope I have been able to state my case for operational statements. --Cleon Teunissen | Talk 06:34, 22 Apr 2005 (UTC)

I will respond here not so much as to contest you but rather to record where I am coming from. I see there are being certain underlying concepts that present in this which need to be documented for the sake of completeness. At the least, those are the foundation of the concepts under discussion. However, those will need some elaboration to make them accessible to the average reader, and I am happy with those being "operational".

My issue with an overall operational focus is that this is proving to be misleading. There are exceptions to these "any experiment ..." rules. If instead you focus on such things as the physical constant being constant and such, then you can be running experiments what are not necessarily "local enough" but since they are not curvature-sensitive of course you expect the same result.

--EMS 15:43, 22 Apr 2005 (UTC)

Einstein did not propose the Weak Equivalence Principle

In his 1907 and 1911 papers, Einstein does not discuss kinematics. Instead Einstein offers calculations based on the assumption of complete validity of the equivalence principle. In his 1907 and 1911 papers, Einstein discusses the influence of gravitation on the propagation of light. Einstein assumes from the outset that it is all about the rate of time.

In his 1913 paper together with Grossmann, Einstein offers the following reasoning: in radio-active decay binding energy is released. The inertial mass of the nucleus of an atom is not just the addition of the inertial masses of the constituting particles, this binding energy contributes to inertial mass. Remarkably, the binding energy contributes equally to gravitational mass. That suggests a profound equivalence in the physical natures of acceleration and gravitation. Hence Einstein's wording:

[...}we shall therefore assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system.

External link: The genesis of general relativity
--Cleon Teunissen | Talk 08:08, 23 Apr 2005 (UTC)

It's the old problem: there are oodles of definitions of the WEP around, some of them mutually incompatible: One variation is: to define the WEP as the same as the equivalence of gravitiational/inertial mass.

It is important to note: the principle of equivalence of gravitational/inertial mass is independent of relativistic physics.

Newton needed to assume the principle of equivalence of gravitational/inertial mass in order to formulate his celestial mechanics. If different planets are differently affected by the force of gravity (that is, a different gravitational constant for each planet) then the computational task is much harder, if not insurmountable.

Another variation is: to define the WEP as being valid for kinematics only.

That is a silly definition of the WEP. The macroscopic behavior of matter is ultimately the result of the quantumbehavior of the individual atoms/quantumparticles. If the quantum behavior of the individual atoms would not be affected by gravitation, then large lumps of many atoms wouldn't be affected either. Probably, Einstein anticipated the coming of quantum mechanics even as early as 1907. His 1905 article about the interpretation of the photo-electric effect as a particle-type interaction of photons with matter indicates his preparedness to think in terms of particle/wave duality. It appears Einstein relied mostly on thinking about propagation of light as a guide in theoretical explorations.
--Cleon Teunissen | Talk 11:08, 23 Apr 2005 (UTC)

I have been reading the Clifford Will material that is online availabe at living reviews in relativity. section 2.1 of Clifford Will's article

It is clear that Clifford Will defines the WEP as the equalness of gravitational/inertial mass. In this definition the WEP has nothing to do with the relativistic equivalence principle.

In newtonian dynamics the gravitational/inertial mass equalness is assumed. (The success of theory indicates the assumption is justified.)

In relativistic dynamics the gravitational/inertial mass equalness is not assumed. As EMS has pointed out from the beginning, in relativistic dynamics it is a logical consequence of a much deeper assumption than gravitational/inertial mass equalness. Hence, general relativity is not based on the gravitational/inertial mass equalness (G/I mass eq.), meaning that there is no logical (deductive) path from G/I mass eq. to the relativistic equivalence principle.

Einstein mentions the gravitational/inertial mass equalness in passing, and moves on to hypothesizing the Relativistic Equivalence Principle, applying it to the propagation of light. --Cleon Teunissen | Talk 10:10, 24 Apr 2005 (UTC)

Hidden fine print

all the fine print is hidden in the word local, which implies that the experiment is not trying to measure anything external (such as the CMB, which sets a preferred frame for the universe) --Joke137 01:30, 19 Apr 2005 (UTC)

And there is yet another fine print aspect of the "only local measurment" restriction.

An experimental setup that is in free-fall in curved space-time will not detect any direction to be different from any other directon. The local inertial frame of reference will be indistinguishable from any other inertial frame of reference by way of local measurement.

When the measurements of two experimental setups are compared, one in close orbit around a gravitating mass, the other far away from that gravitating mass, then it will be seen that the rate of time for the two experimental setups is dissimilar. In the vicinity of a gravitating mass the rate of time is slower.

So, if the rate of time is dissimilar for different inertial frames of reference, are they different? A device that is sensitive to the CMB detects light that dates back to the moment in cosmological history of 'first light', that is measuring something from as far away as you can measure. But as Clifford Will notes, the clocks onboard the GPS-satellites do not run at the same rate as clocks on earth or clocks in close Earth orbit; the difference in the rate of time is a whopping 39 microseconds a day. --Cleon Teunissen | Talk 06:37, 25 Apr 2005 (UTC)

Rewrite of the article

I have decided to insert a version of the equivalence principle article. The main goal is to have an article that is in conformance with the wikipedia article on gravity. A lot of what I write is derived from that article. The basis of the equivalence principle is Einstein's 1907 vision that gravitational interaction is mediated by changing the rate of time, by curving space-time geometry. Then and only then can the effects of acceleration cancel the effects of gravitation. Everything else follows from that. Every interaction has a mediator. In the case of gravitation curvature of space-time is that mediator. --Cleon Teunissen | Talk 16:38, 25 Apr 2005 (UTC)

I am reverting this article back to the previous version. Your rewrite simply is not the direction that this article should go in.

My big complaint is the "unification" section. The Equivalence Principle is not about clocks and curvature. That is GR stuff, and the EP is not GR. Yes, it is an important part of the foundataion of GR and so some reference to GR and curvature are appropriate, but overall you are losing the reader in extraneous material with this.

You also express a goal of making this page consistent with the gravity page. I am not impressed by that page. The GR discussion in that page is overblown and in my opinion quite inaccurate. For example, it claims that gravitational potential energy can now be explained as being due to how the speed of light changes in a gravitational field. That is bogus at the outset: Potential energy exists as a result of resisting an accelerative condition, much as Newton described it. The observed changes in the speed of light in a gravitational field (which can be seen as due to the potential instead of causing it) are not and need not be a part of it. So I think that some work is needed on the gravity page instead.

--EMS 18:27, 25 Apr 2005 (UTC)