Talk:Mach's principle

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[edit] This article needs much improvement

This article needs to be entirely rewritten to

  • take account of the fact that many distinct ideas have been called "Mach's principle", leading to much confusion in the literature,
  • give an accurate account of how these are/are not validated in gtr and other major theories,
  • give pointers to the most useful references in the literature, especially recent volumes/reviews.

For now I have just added a few citations---CH (talk) 04:22, 18 August 2005 (UTC)

I just wrote a German Article (de:Machsches Prinzip) on this subject. It might be better or worse than this version. Maybe it could be a pointer. And thanks for comments on same. -- 217.230.58.97 08:08, 19 August 2006 (UTC)

[edit] Misattribution?

The article is currently very confused about whether the quote is due to Einstein or Mach himself. In fact I think it is probably due to Born! Whoever wrote this, please fix! TIA ---CH 21:33, 24 December 2005 (UTC)

[edit] Some Clarification

The central idea here is that a particle at a point P experiences two effects from a particle O at the origin. The first of these is a force which is proportional to the product of their masses, and inversely proportional to the square of the distance between them, and acts opposite to the position vector from O tp P. The second of these is proportional to the product of their masses and directly proportional to their relative acceleration, and acts opposite to the acceleration vector of P relative to O, regardless of the distance between them. Rather than defining inertial mass and gravitational mass and constants for each, we define the unit of force by F = MA and absorb everything else in to a single gravitational constant G in the formula for gravitational attraction.

The principle of Equivalence, which says that gravitational and inertial mass are equivalent then becomes the notion that the trajectory of a particle under gravitational influence is independent of composition, and GR satisfies this because the trajectories are geodesics, and don't depend on what the body is made of.

In any case, the degree to which a body resists accceleration relative to "everything else" is caused by the inertial interaction between that body and everything else in the Universe. In a universe without other matter, there would be no accelerated frames, and no inertial forces, because there would be no other material you could say you were accelerated relative to. If the universe had half the matter in it, inertial forces would be half as strong.

This interpretation is perfectly consistant with General Relativity. If someone subjects you to sudden acceleration, you will feel inertial forces. If you stand still, and someone subjects everything else in the universe to sudden acceleration, you will feel equivalent tidal forces from "mass at a distance." These are both descriptions of the same physics.

If you look at weak-field General Relativity, which is equivalent to Newtonian mechanics, you can see that the inertial interaction between matter in a region and the rest of the universe is modified by the second time derivative of mass-energy in the region. This means that inertial shielding occurs when the rate at which energy flows in or out of a region is time-varying. Sciama showed in 1953 that inertia could be understood as a gravitational effect in linearized General Relativity. James Woodward of California State University at Fullerton showed in 1991 that there was also a time-dependent term in addition to the acceleration-dependent term we associate with ordinary inertia. His paper is "Measurements of a Machian Transient Mass Fluctuation" and can be found in the 1991 Foundations of Physics Letters, Vol 4, pp. 407-423. Woodward showed that an object with a time-varying energy density will have a non-trivial variation in its inertial mass which depends on the second time derivative of the energy.

The canonical experiment to test Mach's Principle is to fasten a capacitor to a piezoelectric transducer, and drive the capacitor with alternating current, while driving the transducer at twice the frequency, phased so that the transducer pulls the capacitor in the same direction with maximum force during the two points in the cycle where the second time derivative of the energy flow in and out of the capacitor is maximized. This should result in some non-symmetrical acceleration of the whole contraption if inertial shielding is occurring at certain points in the capacitor's charge/discharge cycle.

Experiments continue to be done on such apparatus, including one for NASA's Breakthrough Propulsion Project. Whether real results have been achieved or not is currently a subject of debate in the scientific community.

So that's Mach's principle in a nutshell. Inertia is the result of a particle's interaction with all other matter in the universe. It's not incompatible with General Relativity, and it's not necessary to drag in scalar-tensor theories like Dicke-Brans-Jordan to incorporate it into ones understanding of gravitation.Hermitian 08:18, 12 January 2006 (UTC)

Tom Peters inserted the following comment after the paragraph in Hermitians comment which ends "These are both descriptions of the same physics". I moved Peters's comment to this location to help keep the attributions clear. ---CH 22:50, 1 February 2006 (UTC)
In another sense, the GTR is in direct opposition to Mach's principle. In Mach's universe, you cannot have a complete description of a body if you do not know the dynamics of everything else in the universe. In contrast, the GTR is a gauge theory which deals with a strictly local field. Fundamentally, it is hopeless to do physics with Mach's principle. The GTR saves the science of physics because you can give a complete description from local observations. In that sense the principle of relativity is a theory ABOUT physics rather than a theory OF physics. Tom Peters 20:28, 1 February 2006 (UTC)
Hermitian, you seem to be one of those commentators who believe with passionate conviction that he understands what "Mach's principle" [sic] really is and what role it plays in gravitation physics. Unfortunately, perusal of the literature soon shows that as a rule such commentators violently disagree with one another, and often do not even acknowlege the existence of alternative viewpoints. Such bibliographic oversights, in addition to internal inconsistencies and frequently loose reasoning, tends to make such statements appear based more upon stubborness and even ignorance than upon sound reasoning. In my view, the wisest thing one can say in a brief comment is this: it seems that no-one has yet proposed a "Mach principle" which is either fully well-defined in curved spacetimes, or fully acceptable to other researchers.
"Loose reasoning": you are not alone, unfortunately, in appealing without comment to noncovariant concepts, as if this requires no explanation in the context of curved spacetimes. For example, you mentioned "distance" above without any explanation of what definition of "distance" you have in mind or why this definition should be considered to be physically preferred to all others! According to Kate you have been an irregular contributor to the Wikipedia since April 2005, but in case you haven't studied the policy guidelines in detail, please note for future reference that in such a controversial context as a discussion of "Mach principles", writing "Sciama showed" rather than "Sciama argued", while acceptable in a talk page such as this, would probably not be considered sufficiently NPOV for a Wikipedia article.
I take it that you are not a gravitation physics newbie, but for the benefit of others, a good place to begin reading about this thorny topic might be Section D.2 of Lawrence Sklar's book Space, Time, and Spacetime. However, this is only the tip of vast iceberg. ---CH 23:29, 1 February 2006 (UTC)
One other thing: you wrote weak-field General Relativity ... is equivalent to Newtonian mechanics. You should know better than that! ---CH 23:31, 1 February 2006 (UTC)
To address your points in order. First of all, the notion that GR being a gauge theory is incompatible with Mach's principle's non-covariant terminology of instantaneous "mass at a distance" is misguided. Electromagnetism is a gauge theory as well, and one can choose a representation in which the electrostatic force propagates instantaneously, even through the notion of something happening instantaneously at all points in space is horribly un-covariant and anathema to correct relativistic thinking. Your perceived incompatibilty is a similar one of terminology and not one of physics.
I suppose that reformatting led you to attribute the remark on gauge theories to Hillman, but I brought that up. However, that is not my point, nor do I care much about instantaneous action. Mach's principle, like formulated on the main page, works from a "holistic" view that everything depends on everything else. My point is that it is impossible to even start doing physics from such a concept because prescience of the whole universe is impossible. In contrast, the TGR can describe things locally. Tom Peters 11:43, 7 February 2006 (UTC)
Everything DOES depend on everything else. The net motion of "mass at a distance" determines the asymptotic boundary conditions far away from you. A solution of GR subject to these boundary conditions determines your local geometry, which in turn determines the "forces" particles in your vicinity experience. The example given in the article, that GR doesn't explain the forces on a rotating earth if one picks a frame in which the earth stands still, and distant mass rotates around the earth, is just plain wrong. The entire idea behind GR is that the physics works with arbitrary coordinates.Hermitian 18:21, 7 February 2006 (UTC)
Fine, but in GRT you can take the local field for granted (or as an observational entity) without knowing in detail what generates it. Also there is a time lag: stuff beyond your light cone|observational horizon have had no effect (yet). I suspect that Mach's principle does not allow such local treatment. I fully agree with the "entire idea", but as a precept for doing physics: you should formulate your laws of physics in such a way that they are independent of the particular coordinate system you choose. Tom Peters 12:29, 8 February 2006 (UTC)
Your argument that claiming to "understand" Mach's principle indicates passionate conviction, rather than good physics, is a claim once made of GR as well, decades ago when it was perceived as much more arcane and understood by only a small number of people on the planet. Nowdays, we can teach much of it to undergraduates.
I am attempting to give a quick non-technical overview of stuff that wasn't covered in an article which doesn't really do a good job of describing Mach's principle. Going on and on about obtuse math on families of spacelike surfaces, while covariant, would not lend clarity to this explanation vis a vis the commonly used English terms for various things, like distance.
I think it is appropriate to use "showed" in lieu of "argued" for purely mathematical derivations that are not in dispute. One would not say that someone "argued" that quadratic equations are solved by the well-known formula most people can easily derive, as if there was an opposite point of view that needed to be presented. Sciama's ability to do tensor calculus correctly, and derive results from the equations of GR, is not in doubt. "Argued" is probably appropriate for Woodward's results, which have yet to be widely accepted.
For a quick non-technical overview of what's happened since Mach articulated his principle, I think equating linearized GR with Newtonian gravitation is perfectly acceptable.
Hermitian 08:53, 7 February 2006 (UTC)

Hermitian, I am finding this very difficult to follow because the attributions have become so munged, despite my efforts. Please, everyone, try to insert your comments at the bottom, and format all your paragraphs consistently to match your signature. This should make it much easier to see at a glance who wrote what. I would certainly not agree that hyperslices are irrelevant or constitute "obtuse math"! This is a key point: much of the incredible confusion in the literature (and discussions like these) is entirely preventable (and unenlightening, hence a waste of everyone's time) because commentators were too lazy (or ignorant) to make their thinking precise. You absolutely do need to use the language of mathematics because, for example, much of the "controversy" arises from various parties confusing mathematically distinct notions of things like "rotation" which are central to discussing Mach's ideas and suggested applications. In general, WikiProject GTR is trying to raise the bar (while also trying to make all these articles easier for technically challenged readers to get something useful from!), but in this case, there is a very strong case to be made for the neccessity of not trying to "save" readers from exposure to any higher mathematics.

I am glad that you do know that linearized GR =/= Newtonian gravitation. ---CH 02:59, 11 February 2006 (UTC)

[edit] Students beware

I extensively edit the August 2005 version of this article and had been monitoring it for bad edits, but I am leaving the WP and am now abandoning this article to its fate.

Just wanted to provide notice that I am only responsible (in part) for the last version I edited; see User:Hillman/Archive. I emphatically do not vouch for anything you might see in more recent versions.

Be aware that Mach principles (see the arXiv eprint by Hermann Bondi for the plurality of Mach principles), is one of the most contentious topics in gravitation physics. Unfortunately, several WP editors have attempted in the past to slant this and related articles to present their own idiosyncractic view as the only view, or have suppressed the fact that this topic is highly controversial (or have simply unbalanced coverage by presenting far more information about their particular view than about the dozens of alternative views).

Good luck in your search for information, regardless!---CH 01:57, 1 July 2006 (UTC)

[edit] Mach's Principle v. Mach Principle

Mach's principle is a particular statement—the content of which is, unfortunately, very vague. On the other hand, a Mach principle is any statement (hopefully less vague) which either is, or pursues the spirit of the original Mach's principle.

"A Mach principle" is syntactically and semantically distinct from "Mach's principle". The class of principles qualifying as Mach principles deserves its own page, as does the historically important and distinct Mach's principle. Thus, I have killed the redirect on Mach principle and put some distinct and (hopefully) useful information on that page. I think it is very useful to have one page dedicated to the history of this notion, and one to the jungle of statements which have actual scientific value. MOBle 01:11, 24 August 2006 (UTC)

As I am not a native English speaker I do not understand in full what "Mach principle" in fact means in this context. I wrote both articles for sl WP from English versions and named second term as "Machian principle" (Slovene machovsko načelo) in similarity to Euclidean space (evklidski prostor) (in contrast to Euclid's lemma (Evklidova lema) or Euclid number (Evklidovo število)) and such - but I am not sure if this naming is correct. Are terms "Mach" and "Machian" in this case equivalent? --xJaM 14:19, 12 October 2006 (UTC)
The difference in meaning is only very subtle, so it's mostly just an issue of style. I think I might actually prefer "Machian principle" slightly, but others had already used "a Mach principle", so I figured we should stick with that, here. I'm not committed one way or the other for the English, and I guess you should use whatever sounds best in Slovene. My only concern was to clarify the distinction between history and science/philosophy. --MOBle 17:49, 12 October 2006 (UTC)
I see. I understand your concern for the distinction. Here I also see one difference between English and Slovene in one another example: a term Galilean transformation is in Slovene in fact named Galilei('s) transformation (Galilejeva transformacija and not galilejevska ~). Further on Lorentz transformation in English is not called Lorentzian. Perhaps I didn't choose the best example, because "Galilean" here might in fact mean "Galilei('s)", but also it can be one speciality in English. --xJaM 11:15, 13 October 2006 (UTC)


[edit] Removed paragraph

Archelon removed the following paragraph:

It is very easy to understand that we need some metrical system which consist of mutually related parameters (or observables) and to pin somehow one end of such proportions to some datum-point. This process is very well visualised in crystalization process when we have some initial place in the space where crystalization starts (this place can be called as a datum-point of crystalization). And the rest of the system is affected and obeys some rules created at that initial datum-point.

(It had apparently persisted for about a week). The paragraph is not claimed to be nonsensical, though it is worded a bit obscurely; but it makes no sense in the context where it was inserted. Archelon 00:23, 18 February 2007 (UTC)


[edit] 'Disputed Science'

Is there general agreement that this 'Pseudoscience Infobox' is appropriate here? Certainly at least some Mach principles do not fall under the heading of pseudoscience, disputed though all of them may be. Archelon 00:27, 18 February 2007 (UTC)

[edit] 'Mach's Holographic Principle"

There is a great preprint on the arxiv "Mach's Holographic Principle" by Khoury and Parikh (http://arxiv.org/abs/hep-th/0612117). There Mach's principle is taken to mean the idea that inertia is determined entirely by the matter content in the universe.

The common objections general relativity being Machian, it is argued within, essentially boil down to the fact that one, in solving GR's field equations, is allowed to select initia data for the induced metric and extrinsic curvature completely independently of the matter on the initial surface/boundary. Therefore, the geometry (given by the metric) defines inertia (acceleration is defined with respect to the geodesics of the spacetime). However, in GR this geometry is determined not just by the matter (via the Einstein field equations) but also by arbitrarily chosen initial conditions. A process of replacing the initial conditions by boundary matter so that inertia is determined entirely by matter content, is described. HaludzaHaludza 10:44, 20 April 2007 (UTC)


[edit] 'Disputed Science???'

I see no reason to describe this subject as pseudoscience. What justification is proposed for the pseudoscience box.

Martin Hogbin (talk) 20:25, 17 January 2008 (UTC)

[edit] 'Disputed Science???'

I propose to delete the pseudoscience box.

Martin Hogbin (talk) 09:18, 18 January 2008 (UTC)