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This question was prompted by another question about a paper by Woodward (not mine). IMO Mach's principle is very problematic (?wrong) thinking. Mach was obviously influenced by Leibniz. Empty space solutions in GR would result in a Minkowski metric and would suggest no inertia. Mach's principle seems incompatible with GR. Gravitational waves could also be a problem. I had thought that papers like one by Wolfgang Rindler had more or less marginalised the Mach Principle, but I see lots of Internet discussion of it. Is it correct? Wrong? Is there evidence? (frame dragging experiments)?

Let's use this definition from ScienceWorld.Wolfram.com:

In his book The Science of Mechanics (1893), Ernst Mach put forth the idea that it did not make sense to speak of the acceleration of a mass relative to absolute space. Rather, one would do better to speak of acceleration relative to the distant stars. What this implies is that the inertia of a body here is influenced by matter far distant.

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10 Answers 10

Mach's principle has influenced Einstein but the final formulation of general relativity as of 1916 clearly invalidates Mach's conjecture. According to Mach's principle, motion - including accelerating and rotating one - may only be defined relatively to other objects. That would imply that there can't exist any gravitational waves.

However, general relativity predicts and experiments confirm that gravitational waves do exist: the relevant observations were awarded by the 1993 physics Nobel prize, too. The waves are vibrations of the space itself. It means that the metric tensor remembers the information about the geometry - and curvature at each point, even in the empty space, something that Mach's principle specifically wanted to prohibit.

Moreover, the perceptions and other effects of acceleration were supposed to be determined by comparisons with distant objects. This simple fact itself violates locality that has become important already in special relativity, and was simply inherited by general relativity.

If you care about history, the new cold relationship is mutual: much like general relativity rejected Mach's principle, Mach rejected general relativity - and already special relativity, in fact. ;-) If you care about sociology, there's been a poll among physicists active in relativity, and a vast majority of them would also say that Mach's principle is invalidated by general relativity.

Some people sometimes say that some effects predicted by general relativity, such as frame-dragging, are "Machian" in character. I think it is very misleading because it tries to make the listeners think that Mach's principle may be made compatible with the observations. It's very questionable what Mach's principle would predict about frame-dragging because Mach's principle has never become any viable candidate for a physical theory. But the idea that frame-dragging is Machian is more ideology and hype than a valid observation. Despite the vagueness about such very detailed effects, Mach's principle has said enough for us to be sure that it's incorrect in all of its forms.

Well, there's a lot of discussion on the Internet about long-dead ideas in physics - and maybe mostly about them. However, the Internet has nothing to do with the current state of physics.

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Using Mach's 1893 definition of Mach's principle condemns the discussion to irrelevance. It's like posting on physics.SE with a question titled "How is the emission spectrum of hydrogen determined?," but then saying in the body of the question that we want an answer written in terms of the aether and Newtonian mechanics.

In the 1960's and 70's, there was a golden age of tests of GR, and one of the most active topics was testing GR against alternative theories such as Brans-Dicke gravity. B-D gravity is physically a very well motivated theory. The original paper is available online http://loyno.edu/~brans/ST-history/ and is very readable even if you're not a specialist. The idea of B-D gravity is to couple matter to a scalar field $\phi$, which provides a physical mechanism for Mach's idea that an object's inertia comes from the other matter in the universe. B-D gravity is more Machian than GR. Neither GR nor B-D gravity is completely Machian or completely non-Machian. B-D gravity has a dimensionless parameter $\omega$. In the limit $\omega\rightarrow\infty$, B-D gravity reduces to GR. Brans and Dicke committed themselves to the idea that "[...]in any sensible theory $\omega$ must be of the general order of magnitude of unity." This makes the theory falsifiable.

Experiments show that $\omega$ must in fact be quite high. The best current limit comes from the Cassini probe, which requires $\omega \ge 40,000$. Therefore, B-D gravity should be considered as falsified. So the modern, sensible answer to the OP's question is: Mach's principle is false, in the sense that experiments determine the universe to be no more Machian than GR -- which is not very Machian.

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Mach's principle is simply a philosophical ancestor of the equivalence principle: matter tells geometry how to curve, geometry tells matter how to move. So, yes, you can have Minkowski as a solution for the vacuum Einstein equations, but the minute you introduce even the tiniest mass your solution is no longer Minkowski. You might point out that asymptotically the spacetime will still be flat and Minkowski. However, in GR (and in QFT) it is not only the local geometry that matters. Point is that there is no interesting geometry which does not also contain some matter.

Mach's principle has been interpreted in many different ways. I find the following Wikipedia definition to be one I'm most comfortable with:

A very general statement of Mach's principle is "Local physical laws are determined by the large-scale structure of the universe."

Depending on what day of the week it is and whatever interpretation is your favorite for that day, Mach's principle could be "right", "wrong" or "obsolete". But if stated in the simple manner above, then it is nothing more than a restatement of the equivalence principle and the question of its "correctness" is no longer an issue.

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In psychology there is a special effect called the "verbal overshadowing effect". It concerns the phenomenon that describing a previously seen face impairs recognition of this face.

Mach's principle is essentially target of this psychological effect. It is theoretically overshadowed in such a way that most physicists do not relate to the underlying empirical core but to the theoretical context under discussion.

Hermann Bondi and Joseph Samuel have tried to fix this observational core of Machs Principle. (The Lense–Thirring Effect and Mach’s Principle, Physics Letters A 228, 1997, S. 121–126) They called it "Mach0": "The universe, as represented by the average motion of distant galaxies, does not appear to rotate relative to local inertial frames."

This "coincidence" is measured to a very high accuracy: 0.25 milliarcsec/year. (J. Kovalevsky, et. al. "The Hipparcos catalogue as a realisation of the extragalactic reference frame", Astron. Astrophysics. 323, 620 - 633 (1997)

It is just this coincidence that has theoretically to be explained. General Relativity is only a preferred theoretical tool of explaining this coincidence, but all attempts failed. Hence, from a historical point of view this empirical coincidence appears as an ANOMALY - as a fact that cannot be explained in any way by the running paradigm. The Answers given in this website do reflect this epistemological feature in an almost idealized way. MOSHE f.e. has compared it with a hotel shower that changes abruptly from being too hot or too cold, but is never quite comfortable.

As this empirical coincidence refers obviously to the ultimate boundaries of our universe, its solution resp.explanation can possibly not be found within the world, but outside from it.

HELMUT

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Mach's principle, if interpreted charitably, requires that one include horizons as matter, along with gravitational waves, and light, and all particles. This is required to include black holes, and for consistency requires cosmological horizons too. Once you understand that "matter" means "horizon", the statement that all rotation is relative to distant horizons is just a stunted classical version of the holographic principle, and is sort of vacuously true.

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It is not really a case of Mach principle being wrong. It is something related to general relativity, and frame dragging or Lense-Thirring effect are similar to Mach’s principle. However, these are local laws of physics and Mach’s principle is a global hypothesis. Gravity does tell us that spacetime curvature induces motion of masses, and if these masses are large enough that can in turn change curvature. So gravity or spacetime curvature acts on a mass locally and the same experiences acceleration as seen from another frame. This is a geodesic deviation which is defined by the Riemann curvature. So this tells us the mass which is observed to accelerate is the same mass which responds to the curvature --- the equivalence principle. This also sounds similar to Mach’s principle: Inertia there determines inertia here.

Mach stated the centripetal force on a local rotating frame is equivalent to what happens if the frame is nonrotating and the entire universe rotates around the frame. Kurt Godel worked out a model of a rotating universe and found a very strange time-looping spacetime. If the universe rotates it has a structure which is radically different from Mach’s original conjecture. Further, this universe violates energy conditions. It is not a physical spacetime, even if it comes from the Einstein field equations. This does at least suggests there are some radical departures from Mach’s principle and general relativity. Mach’s principle does not appear to be a consequence of general relativity.

Mach’s principle is rather vague in some respects. The inertia of a body is said to be determined by the inertia (or masses) of all other bodies. Again this sounds like GR, but this extends across the universe. The actual gravitational interaction a particle here has with a galaxy at z = 8 around12.5 billion light years out is miniscule. So the interaction picture appears funny. It might be tempting to say the entire universe is some sort of single quantum wave function, and single masses we observe are entangled subsets. This might sound global and gets away from the $q/r^2$ drop off of gravity. From there one might be tempted to say inertial is inherited this way. However, entanglements do not involve forces, and inertia as an entanglement not defined.

I will also say that I suspect Mach had ideas of an ether in space when he suggested this. So he probably had some picture of a rotating frame moving through this medium, and this is somehow equivalent to the whole medium rotating around the frame. So the ether vortex in the case of a rotating world is what generated the centrifugal force on the rotating frame.

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The Mach's principle in short is that inertia is not absolute, determined by the matter configuration, and there is no other source.

This can be summed up in two statements:

  1. Massive bodies can affect inertia of other objects (inertia is determined by the matter configuration)

  2. The Universe does not rotate and linearly accelerate as a whole (there is no other source of inertia)

The first statement is included in GR and has been proven with the experimental measurement of frame-dragging. In fact inertia even can be screened so people in a rotating (against distant stars) spaceship could not detect the rotation.

The second statement is still not proven (in the rotational part) although verified to a high precision. The linear part simply follows from the conservation of momentum.

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The honest answer should be no body knows for sure. Einstein was inspired initially by this principle when he was formulating GR. However it gradually became clear that there are solutions to GR field equations which does not confirm to Mach's principle. Einstein was thoroughly disillusioned in his latter years. As a matter of fact GR has some features which are definitely "Machian" but other features which are "non Machian". Whether this principle is right or wrong has been always subject of controversy. The present opinion of most experts seem to be totally negative about the Mach principle.

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If you consider that rotation is relative then an observer on a rotating body may regard herself as stationary with the universe rotating about her. In such a view, to avoid exceeding the speed of light, distant objects must have orbits less than c/omega so space must be extremely distorted. Most of the mass in the universe will have a relative velocity close to that of light and will thus have hugely increased mass and therefore enormous gravitational fields. It seems quite possible to me that the resulting net force on the observer will increase linearly with distance from the centre of the frame as do centrifugal forces.

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Many researchs has been carried out in last dacade on the machs principle. Researchers are trying to develop the theory based on mach's principle which can explain the universe properly. There are some recent papers where it is shown that the mach principle can explain quantum mechanics and also the cosmology without dark matter and dark energy. Therefor is not correct to say that the mach principle is wrong. You can go through these following research papers. They are ofcourse extremely mathematical, but most probably anybody can understand the logic. http://arxiv.org/abs/1206.6755 machian agravity and giant galactic forces. http://arxiv.org/abs/1206.0923 on the wavy mechanics of particles.

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protected by Qmechanic Jul 26 '13 at 2:55

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