# Mach's Principle

1. Apr 4, 2006

### gulsen

I'm sorry if I sound too dopey, I simply don't know much about the title.

I've seen various texts (such as this) and none were satisfactory to me. What I've understood from what Mach says, it's way too ridiculous.
An accelerating charge radiates, for instance. We can tell this without looking at any other charge, but observing the radiated photons.

How could it be that Einstein paid attention to it?

Last edited: Apr 4, 2006
2. Apr 4, 2006

### yogi

The various attempts to explain inertia based upon the collective influence of other bodies in the universe always involve some new physics (postuates) that as yet are not observed. Sciama developed a theory based upon matter radiation - if interested you can find it at p 131 in "Unity of the Universe" Einstein attempted to incorporate Mach's principle in developing GR, but eventually rejected it because it seemed to require instantaneous action at a distance.

3. Apr 6, 2006

### krab

Try this thought experiment. Empty the universe of all mass except yourself. Say you have a method like rockets or something to make yourself spin. How would you know you are spinning? If you are not spinning against anything else, could you be said to be spinning? Mach concluded not only that you couldn't tell, but that with no way to define spin, there would be no centrifugal force. He concluded that centrifugal force is created by all the other mass in the universe.

4. Apr 6, 2006

### masudr

krab

If there was nothing in the universe but a single particle, it couldn't spin. If there was more than one particle, then I would notice measurable non-inertial motion during spinning.

5. Apr 8, 2006

### gulsen

I'd answer like this: a spinning object should radiate. If I'm massive enough, sooner or later, the light will bend towards me and I'll understand that I'm spinning. Anything wrong with that?

6. Apr 8, 2006

### masudr

It assumes electromagnetism? Inertia should be a more fundamental property than EM. That's my opinion at least.

7. Apr 8, 2006

### Galileo

Mach's principle is very confusing. I don't understand what he was saying either, although from what I have read it is somewhat similar to what krab said.
Almost all websites are vague about it, claim that the description on other websites is not in the same spirit as Mach intended, but themselves fail to convey the essence of the principle in a clear way.

The term was first coined by Einstein, but people argue that Einstein's view differed from Mach's.

Last edited: Apr 8, 2006
8. Apr 8, 2006

### pervect

Staff Emeritus
The following might be interesting in that it shows a bit about what physicists think of Mach's principle on a general basis (the poll results).

http://www.david-roscoe.staff.shef.ac.uk/Home_page_files/Research/Overview/node1a.html [Broken]

So, after the conference, a fair number of people changed "no" to undecided, and one changed no to yes, but the vast majority of the peole polled don't believe that GR is Machian.

A lot of the debate is over just exactly what it means for the theory to "be Machian", of course.

Last edited by a moderator: May 2, 2017
9. Apr 8, 2006

### Nacho

From what I've read .. just popular accounts of it .. Einstein was enamored of Mach's ideas, tried to encorporate them in GR, but couldn't fully do it. And those accounts say that if the Universe is finite and unbounded, GR could fully encorporate Mach's Principle.

From what I get out of MP, it seems to try to say that not only are gravitational and inertial forces equivalent, but the exact same thing. But heh, I don't see how it can be considered as anything other than speculation, especially when it comes to GR. GR assumes there is mass (I'm not stating that as fact; only my very limited understanding of GR) and builds upon that .. a fundamental principle. So, proving MP should be like trying to prove an assumption.

If the essense of MP can be reduced to just the question: "What does a spinning body spin with respect to", and you consider Mach's answer just speculation, then other speculation could be considered, like: Inertial (and gravitational) forces arise by spinning/moving with respect to a point in a higher spatial dimension.

10. Apr 8, 2006

### Ich

Mach´s principle is something like the "absolute relativity principle" - even acceleration is relative. This may be appealing, but it doesn´t work unless you accept that spacetime is something rather than nothing. GR claims that spacetime has properties, eg it gives you the "rest frame" for everything concerning acceleration. If I recall correctly what Sexl said about it, even an empty spacetime (where you could place your test mass) would be enough to determine rotation.

11. Apr 8, 2006

### masudr

Well a single particle without extension just cannot rotate. And as I have said, if there were 2 particles, the non-inertial motion would be directly observable.

12. Apr 8, 2006

### Nacho

But, that is something that can't be achieved, and leads to the question: If there was only 1 particle in the Universe, would it still have mass? If you believe in Mach's Principle, that gravitational and inertial forces are the same, how could you answer anything but "No"?

13. Apr 8, 2006

### masudr

It could have any mass you wanted, to be honest. But without human minds to define these quantities...

14. Apr 8, 2006

### Nacho

Then how would you reconcile that mass and inertia are supposed to be the same? In your scenerio there would be no inertia.

15. Apr 8, 2006

### Ich

To express myself more clearly:
If you have a single particle in an empty space, you have a single particle and spacetime. The latter also exists. And it defines acceleration and rotation.

16. Apr 14, 2006

### JUboy

in a single particle universe how can it be experimentally ascertained that spacetime exists?

17. Apr 14, 2006

### masudr

Mass and inertia are the same up to some constant anyway (which we have chosen to be 1). So in my scenario, I'd just redefine that constant.

My point is, single particle universes are just silly. We could discuss them ad infinitum (in fact probably not, but certainly ad nauseam) and not get very far. The universe is NOT single particle. That's empirical fact.

I don't really believe in Mach's principle.

18. Apr 14, 2006

### yogi

Don't tell Garth

19. Apr 14, 2006

### Nacho

masudr,

My mistake. I thought you were making a point for MP. I don't believe it either. But, sometimes I think I'm looking at it wrong. Some of the accounts say that the origin of inertia is the "combined mass of the Universe". It might make more sense to term it as "the distribution of mass in the Universe".

20. Apr 15, 2006

### Garth

The questions are:

In empty space -

1. "What is the physical significance of any coordinate system?"

2. "What determines whether that system is inertial or not? - What do you 'hang' an inertial coordinate system on?"

Now add particles with inertial mass to the system -

3. "What is the source of their inertia?"

4. "What determines the ratio of their gravitational and inertial mass, i.e. the value of G?"

If you are happy to say that there are no answers to these questions, 'they just are', then there is no need for Mach's Principle.

Garth

21. Apr 15, 2006

### masudr

In (completely) empty space, there's nothing physical about a co-ordinate system, since completely empty space is unphysical (I assume you mean not even a vacuum).
Inertial frames are what they always have been to me: an inertial frame is one which moves at a constant linear velocity with respect to every other inertial frame. This is not a circular definition since there will be one single unique class of frames which are inertial (though it may take infinite time to work out what they are without any particles).

Ultimately, in a completely empty space, there is no physics, so this discussion is rather contrived
Not everything has a source in physics. Inertia is a property of the particle(s), at least in currently accepted theories. I have no qualms about insisting that inertia is a property of particles without having to invoke a principle involving all the stars in the universe; in fact I'm happier that way.
We determine it by experiment, nature determines it either one of three ways: either "God" chose it, the universe was born with that in the same way it was born with $\hbar$ or $c$, or it emerges from some "more fundamental" theory which I (or anyone else, it seems) haven't come across yet.

22. Apr 15, 2006

### hellfire

At least mathematically empty space-time is a solution as valid as any other solution to the Einstein field equations. However, it is a very strange solution, since, as shown by Einstein with his "hole argument", positions have no physical meaning in empty space-time due to diffeomorphism invariance. But, is this actually a reason to regard this solution as unphysical?

23. Apr 15, 2006

### Garth

In SR a vacuum is empty space. I agree it is an unphysical situation as the universe is not empty, and a more comprehensive gravitational theory would have to include the quantum vacuum, however the 'empty universe' is the scenario in which SR is valid - are we saying SR is 'unphysical' in this respect?

The problem arises when matter is introduced with its associated gravitational field and SR goes over to GR. The principle of no preferred inertial frames carries over into the equivalence principle, yet once matter is introduced there is the possibility of a preferred frame - that of the centre of momentum of the system - which is excluded in GR by the extrapolation of that 'unphysical' SR scenario. Whether this exclusion is justified or not is a matter of contention.
But not in the presence of curvature, geodesic deviation and the relative acceleration of nearby inertial frames are the measure of that curvature.
These are emphatic statements, are they taken 'by faith' or can you substantiate them?
As a matter of fact there are theories that determine the value of G - such as the Brans Dicke theory or the theory of http://en.wikipedia.org/wiki/Self_creation_cosmology [Broken].

Garth

Last edited by a moderator: May 2, 2017
24. Apr 15, 2006

### masudr

Are we talking about SR or GR here?

OK, we must first agree on which model of reality we are having this discussion under, otherwise we will be making different assumptions.

25. Apr 15, 2006

### masudr

Assuming GR:

Nothing, they are all equivalent.
I wouldn't bother defining inertial frame in empty space, it has nothing that a non-inertial frame would have.

Innate particle property.
As you say, Brans-Dicke theory does determine G, but I think it goes out of its way to do so. It doesn't fall naturally from the theory; it's put in by hand (Dicke's hand, if I remember correctly). And assuming we are discussing under the auspices of GR, then all I can say is that G is a constant -- it is one of the few things put in by hand.

We could discuss the relative merits of BD theory and Einstein theory (e.g. BD theory appears unnatural to me, but you could argue putting G in by hand in GR is unnatural &c.), but that's a different discussion.

Last edited: Apr 15, 2006