# Mach's Principle: Right or Wrong?

1. May 20, 2010

### sanman

Mach's Principle is regarded as a forerunner of Einstein's Theory of Relativity, but is it a legitimate principle in its own right?

http://en.wikipedia.org/wiki/Mach's_principle

Does Mach's Principle imply an origin of inertia? - ie. does it mean that a body can only experience inertia if there are other bodies in the universe to pull on it or interact with it?

What happens if a body is just sitting alone in the universe, and it starts rotating? Will it feel any rotational inertia in the absence of other bodies in the universe?

So does inertia originate from a body's interaction with other masses in our universe, or does it originate from a body's interaction with space itself?

2. May 20, 2010

### Jonathan Scott

Mach's Principle as normally interpreted does indeed imply a simple explanation for inertia (see Dennis Sciama's 1953 paper "On the Origin of Inertia", easily found on Google), and conceptually means that if the only body in the universe were rotating, the rotation could not be detected.

(However, I must point out that the shape of a single-body universe is not easy to define and might not look at all like one expects; for example, if you define a single small spherical particle at the origin, then you may well find that from the point of view of a test object in the surrounding space, the "particle" surrounds it as a distant spherical shell in all directions).

General Relativity shows signs of Mach's Principle in both linear and rotational frame-dragging effects, but cannot exactly satisfy the principle because the gravitational constant does not depend on the distribution of masses in the universe.

This means that either Mach's Principle is only loosely true for the actual whole universe (which to me seems odd, given that it is accurate for small local effects) or that GR is inaccurate on the scale of the whole universe.

3. May 20, 2010

Check out the Newton's Bucket thread for a comprehensive discussion about Mach's Principle. I for one think it's a great principle worthy of deeper thought. An empty universe is a strange place indeed, especially with regard to motion, acceleration, and inertia.

4. May 20, 2010

### starthaus

Yes, it will , this is what the Michelson-Gale class of experiments detect. This is what the Sagnac effect is all about: detection of rotation from within a closed lab.

5. May 20, 2010

I disagree. Unless I'm missing something here, this experiment simply measures angular velocity of an object within our universe. It cannot be isolated from the mass of the universe (the stars) so it cannot be used to prove the effects of rotation of an object in an otherwise empty universe.

6. May 20, 2010

### Staff: Mentor

Personally, that is why I really dislike Mach's principle. It always seems to come down to completely useless and unverifiable speculation about the behavior of "otherwise empty" universes. Physics is about describing the behavior of this universe, not fantasy universes.

7. May 20, 2010

### starthaus

The Sagnac effect is a purely kinematic effect, it has nothing to do with any "mass of the universe". So, it will happen exactly the same way whether the universe is empty or not. The result of the Michelson-Gale experiment has nothing to do with any gravitational effects.

8. May 20, 2010

### starthaus

Seconded.

9. May 20, 2010

How can you know what a forest is unless you step outside it? Speculating about an empty universe is a path to seeing what our universe actually is and can most definitely lead to experiments in our universe that can lead to expanded understandings of the fabric of space.

10. May 20, 2010

I agree it has nothing to do with gravitational effects, but this is not the question. The question is whether or not the reading in the Michelson-Gale experiment would change if the apparatus were to rotate relative to the stars and then the stars disappeared. This is a very fundemental question with very deep implications. An alternate way to state this is whether or not this apparatus is reading null if it is not rotating relative to the sum of the velocities of all the mass in the universe and if not, what is it not rotating with respect to when it IS null.

11. May 20, 2010

### Staff: Mentor

There is lots that you can learn about a forest without stepping outside of it, and if it is impossible for the forest dwellers to step outside of the forest then none of the "outside perspective" is of any value to the forest dwellers.

12. May 20, 2010

### Jonathan Scott

I agree that it's pointless to talk about "otherwise empty" universes, but that's what Einstein came up with himself when he first pointed out that GR is not completely compatible with Mach's Principle.

I became interested in Machian theories through thinking about the gravitational effect of the whole universe at the current location, which GR doesn't seem to handle very well, not even as an approximation. As Sciama demonstrated in his "Origin of Inertia" paper, if Newtonian gravity is extrapolated in a semi-relativistic way to the whole universe, it gives rise to inertia and rotational effects from relative motion. In contrast, we don't know how to extend GR to a whole universe (except for unrealistically hypothetical universes with special properties such as uniform density).

GR tells us precisely what the frame-dragging effect is due to the motion of a single object, and provided that speeds are non-relativistic and fields are weak, this can be extrapolated reasonably accurately up to almost any scale, if we define an "effective value" of m/r for a distant mass in terms of its contribution to the local potential. The more we do this, the more we see that a test object effectively feels acceleration and rotation caused by frame dragging of other bodies, and it would be logical that if we extend that scheme to all masses, the test object would perceive the overall frame of all the masses to be the rest frame.

With the known values for G and the distribution of the mass in the universe, the result could be (very roughly) around the right order of magnitude to support an exact match, giving the generalized form of the Whitrow-Randall relation:

sum(Gm/rc2) = n

where the sum is for all masses in the universe as seen from any point and n is a simple constant which depends on the specific theory. For the simplest model of linear frame-dragging, n=1. Note that we can't really define the mass and distances for very distant objects, but we can however assume that the effective ratio for a given mass is a constant value (apart from perhaps systematic changes with time).

This expression obviously cannot be true when G is a constant as in GR, because even the variation due to location with respect to a local mass could apparently cause a detectable variation in G.

However, it is possible instead that the local variation in G due to a central mass is part of what we consider to be the gravitational potential, and the effective value of G is given by the above relation for all other masses, in which case it would effectively be "locally constant".

In fact, the Schwarzschild solution to the Einstein Equations can be expressed in terms of this form of "locally constant" G by a coordinate substitution, but the resulting expression can then be simplified so that it only contains the full "variable G" instead, so the solution treats all masses in the universe identically. (The resulting solution only remains a valid solution to the Einstein Field Equations when the "locally constant" G term due to all other masses is really constant).

Even if Machian theory doesn't require the effective value of G to vary in the central mass case, if the Whitrow-Randall relation holds then G would be expected to vary with time and location on a larger scale (although some of the effects might cancel one another out). At present, there are strong experimental constraints from solar system experiments, in particular Lunar Laser Ranging (LLR), which make it unlikely that G could be varying at the moment even as 1/T where T is the age of the universe.

13. May 20, 2010

There is plenty to learn without stepping outside, but there may also be mistakes made in basic assuptions. For example, if there were no trees would the earth fall apart and the world explode? By speculating about areas of the planet that might have no trees this question can be addressed. I could give a billion analogies along these lines, but my point is that by imagining what something would be like if something didn't exist is a good way to find out what that somethings purpose in life is. By speculating on whether or not Einsteins principle of equivalence holds in an empty universe we may be able to say something about why it exists at all.

14. May 20, 2010

### Staff: Mentor

So you are of the opinion that mistaken assumptions can be corrected through imagining completely non-physical and unverifiable situations? What is to say that your speculation is not also mistaken? At least the assumptions can be experimentally challenged and tested, whereas speculation is unfalsifiable (and therefore unscientific).

Last edited: May 20, 2010
15. May 20, 2010

### starthaus

that was precisely the question, you need to re-read the OP.

You are trying to change the goal-posts, the presence (or absence) of the stars is totally irrelevant, the M-G experiment would detect the same exact effect in either case.

16. May 20, 2010

This is particularly interesting to me as I was thinking several months ago about how light from a flashlight would behave in an empty universe with only an observer and a flashlight off in the distance. I suspected that the light beam would not "know" what a straight line was and therefore could propagate in any number of directions. The light could therefore be seen by the observer even if the flashlight was pointing away from the observer. Indeed it might be that the light would "seek out" the single observer and this would define a straight line. A point of light on the other hand could propagate in any number of directions and the result might be this enveloping glope of light you describe. In your opinion, is my reasoning in line with your understanding about why the point of light might show itself as an encapsulation globe?

Just as an aside the reason I felt that light would not know what direction it should propagate is based on my reasoning that centrifugal force depends on a straight line in order to exist (the desired path of the atoms on a rotating wheel for example) and centrifugal force couldn't exist in an empty universe if and only if a straight line could not be defined, or the atoms had no mass (inertia).

If inertia did not exist in an empty universe, and if the equivalency principle holds in an empty universe, wouldn't this imply that gravity would not exist either, or that the constant could vary (along with mass) depending on the overall density of the universe?

17. May 20, 2010

"So does inertia originate from a body's interaction with other masses in our universe, or does it originate from a body's interaction with space itself? "

It is not asking if inertia depends on gravity, but rather if it depends on the total mass of the universe or on space itself. The outcome of the M-G experiment depends entirely on the answer to this question.

18. May 20, 2010

Speculation is not a theory or an assumption. Speculation is a tool that can be used to imagine how something might behave under different or even untestable circumstances. All I can tell you is that I use it and it has helped me in visualizing difficult concepts or in conceptualizing relationships. Even Einstein imagined what it would be like to ride along side of a light beam. This led to SR. So can you really say it's not a useful tool?

19. May 20, 2010

### Staff: Mentor

Not unless it leads to something that is testable from within this universe. Einstein certainly understood that.

20. May 20, 2010