# Mach's principle

1. Jan 8, 2010

### SW VandeCarr

Is Mach's principle still the best explanation for the force we feel when changing velocity? If the universe were infinite with infinite homogeneously distributed matter, would Mach's principle still apply?

EDIT: If it's not, how is the force associated with acceleration explained?

Last edited: Jan 8, 2010
2. Jan 8, 2010

### turbo

In his essays on relativity, 1920 and onward, Einstein rejected Mach's principle, calling it "spooky action at a distance". He claimed that inertial effects arose from matter's interaction with the local space in which it embedded. He called space it the "ether" of GR, which none of his contemporaries seemed to like, much.

3. Jan 8, 2010

### Al68

It seems you have it backward. The force we feel is the force applied. A change in velocity is the result of the force, not the other way around.

So the real question is what causes an object's resistance to acceleration (inertial mass), and there is no consensus on this. Mach's principle relates an object's inertial mass to distant masses because the acceleration being resisted is the object's change in velocity relative to those distant masses.

But Mach's principle offers no mechanism or reason for this relationship, so, like gravity, the cause is completely unknown.

4. Jan 9, 2010

### SW VandeCarr

Thanks Al68. Since we don't have any good hypotheses regarding this resistance to acceleration, is it safe to say there's no way to make an informed speculation as to whether an infinite universe would be any different than a finite one in this respect?

5. Jan 9, 2010

### turbo

In the 1920's, the universe was very poorly understood, but Einstein reasoned that since nothing could propagate faster than the speed of light, inertial effects could not be the result of the interaction of an accelerating or spinning body with ALL the massive bodies in the universe. As he rejected Mach's notion of inertia, he replaced it with the idea that inertial effects arise from matter's interaction with the local space in which it is embedded. In such a case, it matters little whether the universe is finite or infinite in extent.
The essay from which this paragraph was excerpted is Chapter One of "The Philosophy of Vacuum" by Saunders and Brown - highly recommended reading.

Last edited: Jan 9, 2010
6. Jan 9, 2010

### SW VandeCarr

Thanks for the recommendation turbo-1. Is there any current theory on this proposed local interaction with the vacuum? I haven't found any in my searches. I've read some discussion on an absolute vacuum in the setting of a rotating finite universe.

7. Jan 9, 2010

### edpell

I highly recommend "Gravitation and Inertia" by Ciufolini and Wheeler. To quote from page 4

"A letter of warm thanks he [Einstein] did, however, write to Mach. In it he explained how mass there does indeed influence inertia here, through its influence in the enveloping spacetime geometry. Einstein's geometrodynamics had transmuted Mach's bit of philosophy into a bit of physics, susceptible to calculation, prediction, and test.

Let us bring out the main idea in what we may call poor man's language. Inertia here, in the sense of local inertial frames, that is the grip of spacetime here on mass here, is fully defined by geometry, the curvature, the structure of spacetime here. The geometry here, however, has to fit smoothly to the geometry of the immediate surroundings; those domains, onto their surroundings; and so on, all the way around the great curve of space. Moreover, the geometry in each local region responds in its curvature to the mass in the region. Therefore every bit of momentum-energy, wherever located, makes its influence felt on the geometry of space throughout the whole universe--and felt, thus, on inertia here."

8. Jan 9, 2010

### turbo

Hal Puthoff, Haisch, Rueda et al have explored the nature of the vacuum, most notably with respect to the field of virtual particle pairs of the quantum vacuum. Their work is not mainstream, but was funded in part by NASA's breakthrough propulsion program.

9. Jan 9, 2010

### Jonathan Scott

A key paper on this topic is Dennis Sciama's 1953 paper "On the Origin of Inertia":

This paper illustrates beautifully how a simplified analogy between gravity and electromagnetism leads directly to inertia.

If gravity does in fact obey a similar scheme, at some level, then one consequence is that the gravitational "constant" G would actually be slightly variable, determined by the distribution of mass in the universe. (This would of course conflict with one of the assumptions of GR, but I find Sciama's basic idea so compelling that I feel that it cannot simply be dismissed on that basis).

Last edited by a moderator: Apr 24, 2017
10. Jan 9, 2010

### Al68

I'd say that's safe to say. As turbo pointed out, inertia can't depend on all the masses in an infinite universe anyway, only those close enough to have an effect, even if we assume such a relationship exists.

11. Jan 13, 2010

### yuiop

http://www.lightandmatter.com/html_books/genrel/ch03/figs/machian-planets.png [Broken]

The above image is from section 3.5.2 of fellow member bcrowell's web presentation http://www.lightandmatter.com/html_books/genrel/ch03/ch03.html#Section3.5 [Broken] which nicely describes how our universe is not fully "Machian". One of the two planets is rotating and has an equatorial hydrostatic bulge and General Relativity predicts this bulging of one planet, when both planets appear to be rotating from each other's perspective, will happen even if there are no distant stars, directly contradicting the Machian idea.

Last edited by a moderator: May 4, 2017
12. Jan 13, 2010

### heldervelez

The light and gravitational interactions propagate at 'c' speed.
We are receiving both influences here and now.
Isotropy caracterizes those effects.
If we move in relation to the present background we will introduce a dipole (same as with the CMB).
Inertia is the resultant of this motion induced dipole.
It is irrelevant if the universe is finite or not and it does not envolve action at a distance.

13. Jan 13, 2010

### Dmitry67

Yes, but this example is artificial.
You are assuming flat boundary conditions at infinity, while there are no such solutions for the whole universe.

Last edited by a moderator: May 4, 2017
14. Jan 13, 2010

### bcrowell

Staff Emeritus
He used this phrase to refer to quantum correlations between distant, entangled particles. If he also used it to refer to Mach's principle, this is the first I've heard of it.

I'm not sure here whether you're describing the Machian or anti-Machian view. The Machian view describes inertia as a relationship between matter and *distant* matter.

I don't think this statement is correct.

This doesn't sound quite right to me. First off, I don't think Einstein made an abrupt turn away from Machian ideas at any point in his career. When he initially tried to formulate a relativistic theory of gravity, he was loosely guided by Mach's principle. When he succeeded with GR, it had some Machian properties and some non-Machian properties (describing the vacuum as having dynamics of its own). When Schwarzschild found the Schwarzschild less than a year later, Einstein was disturbed because it was non-Machian, in the sense that there was a gravitational field that wasn't a relationship between two objects. Einstein's popularization of GR, published in 1920, is full of Machian arguments. There was a period of decades after that when various solutions to the field equations were inspected to see whether they had a Machian or anti-Machian character.

I also don't think it's right to associate Mach's principle with superluminal effects. I think Einstein believed GR to be highly Machian when he first published it in 1915, and the theory clearly didn't include superluminal effects. Brans-Dicke gravity is considered by many theorists to be more Machian than GR, and it doesn't include superluminal effects. There is no logical reason why the relationship between distant objects described by Mach's principle has to be an instantaneous relationship; in the Brans-Dicke theory, it isn't.

15. Jan 13, 2010

### turbo

bcrowell, please read Chapter One of The Philosophy of Vacuum. It is Einstein's essay "On the Ether" (1924), which expands upon his 1920 Leiden address regarding the role of space (ether) in relativity. By 1924, Einstein had come to believe that space has properties which are conditioned by local matter, and that gravity and inertial effects are emergent, arising from matter's interaction with the local space in which it is embedded. The essay should clarify the difference between what Einstein himself believed and what others believed about his theories. There is a disconnect.

The book is very expensive for such a small volume, but you should be able to find it in any decent college library.

16. Jan 13, 2010

### bcrowell

Staff Emeritus
The essay is accessible, except for 2 of the pages, via books.google.com. Your statement that 'He called space it the "ether" of GR' is a complete misrepresentation of the contents of the paper. First, "He called [...] it" implies that this was his general way of referring to it throughout his career, rather than just in this essay. Second, the essay is just setting up a loose analogy between various systems, such as Newtonian gravity and GR, and using "aether" in a general way to talk about those theories' attitudes toward space, and whether space has locally observable properties of its own.

This essay has been a magnet for cranks for a long time. John Baez has the following comments:

This has been discussed before on PF: https://www.physicsforums.com/archive/index.php/t-4021.html A PF member provided a translation of the opening of the essay in that thread.

I'm glad that you were more up front here about disclosing the crank character of what you were referring to. Puthoff is known for his research in parapsychology, http://www.parapsych.org/members/h_puthoff.html [Broken] , and for example was a participant in Ingo Swann's demonstration of his ability to psychically visit the planet Jupiter: http://en.wikipedia.org/wiki/Ingo_Swann

Last edited by a moderator: May 4, 2017
17. Jan 13, 2010

### turbo

I am so gratified to have such guidance in determining whether or not Einstein's words should be taken at face value. Surely Baez has a place in the Pantheon of eminent physicists.

If I had known about the "crank" designation earlier, I could have dismissed Dennis Sciama's paper out-of-hand. (Chapter 6. The Physical Significance of the Vacuum State of a Quantum Field) You know, the one in which he equates vacuum fluctuations with a Lorentz-invariant ether. Especially "cranky" is section 9 - Do Zero-Point Fluctuations Produce a Gravitational Field?

I should have known Sciama was a crank. After all, he earned his PhD under Dirac with a dissertation on Mach's Principle and the origin of inertia. And Sciama himself supervised a whole raft of cranks as they earned their PhDs, including Hawking, Ellis, Rees, and Carter.

/sarcasm

There is still plenty of work to be done in fundamental physics, and we do not know all there is to know about inertia or gravitation or how they arise. We have mathematical representations of these effects that are quite predictive, at least on some scales, but we should not confuse them with reality. The map is not the territory.

Last edited: Jan 13, 2010
18. Jan 13, 2010

### Dmitry67

BTW I am really surprised that nobody had mentioned the Goedels solution, as it had been designed as a contre-example to Mach principle:

http://en.wikipedia.org/wiki/Gödel_metric

19. Jan 13, 2010

### bcrowell

Staff Emeritus
Baez did not criticize Sciama as a crank. I did not criticize Sciama as a crank. Baez criticized crank interpretations of the Einstein essay. I agree with his criticism. I also criticized Puthoff as a crank.

20. Jan 13, 2010

### bcrowell

Staff Emeritus
Interesting! There's a clear similarity with Einstein's example of the two planets. I don't fully understand the discussion of Machian issues in the WP article, and it doesn't seem to reach a clear conclusion. In general, I would say that GR has lots of problematic solutions, such as solutions with CTCs or naked singularities, and if any of these solutions could be shown to be potential occurrences within our own universe, then GR would be in big trouble as a classical field theory that's supposed to be able to make predictions. However, the indications so far are that chronology protection and cosmic censorship do hold (in some form), and therefore I'm not sure how much attention to pay to solutions that violate them when I'm trying to interpret the physical meaning of GR.

21. Jan 14, 2010

### Al68

In the absence of any distant masses, which planet does GR predict will bulge?

Last edited by a moderator: May 4, 2017
22. Jan 15, 2010

### yuiop

GR predicts that the planet that is really spinning (B) will bulge.

What Mach predicts is more difficult to specify, because Mach never put his ideas in a mathematical form. However, it is probably safe to say Mach's ideas are more fully relativistic than GR. From that point view, an observer on planet B could consider planet B as stationary and to him it will look like it is planet A that is spinning and in the fully relativistic Machian interpretation planet A should bulge too. In other words in the Machian interpretation it should be impossible to tell which planet is really spinning, just as it is impossible to tell which observer is really moving in Special Relativity. Of course, your little smile tels me that you may have set up a trap for me (or I am just paranoid :tongue2:), but I do not mind. I am prepared to discuss the possibilities and I might learn something

Last edited: Jan 15, 2010
23. Jan 15, 2010

### D H

Staff Emeritus
What planet is "really" spinning? Without any remote stars, how do you even go about defining an inertial frame?

I am not convinced by these toy universe arguments. They are not scientific in the sense that they are not testable. There is no way to construct a universe that comprises only two planets, one spinning and the other not.

Discarding the fact that Mach's principle is not particularly well-specified, is there any test that would falsify Mach's principle in our real universe?

24. Jan 15, 2010

### yuiop

You could define an inertial frame as one in which you do not feel any forces acting upon you. Such a definition does not care about the distant stars and can be measured by accelerometers. In the two planets example, an observer on B feels forces acting upon him, so hs claim that he is a stationary inertial frame is not valid. There are clear differences between what observers on A and B would feel and measure. As for falsifying Mach, that would be very difficult, as with no clear definition of his ideas it is difficult to know what to falsify.

25. Jan 15, 2010

### Jonathan Scott

I'd say that the most obvious Machian interpretation would be that in the two-planet universe both planets would be spinning in opposite directions relative to the frame in which their average spin (in some sense) is zero.

Even in the Machian interpretation, there is a local concept of a local inertial frame of reference (non-rotating non-accelerating space), but it is effectively a field defined by the distribution and motion of all of the mass in the universe.