Understand Mach's Principle: What does it Mean?

[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?

 

[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.

 

[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.

 

[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.

 

[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?

 

[masudr]

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

 

[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.

 

[pervect]

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

However, among specialists in the foundations of mechanics, as opposed to popularizers, there is much less agreement as to what extent Einstein implemented Mach's ideas on space and time in his theory. An amusing indication of the variety of opinions about the 'Machian' quality of general relativity is provided by two opinion polls made at a conference on the Mach's principle (the proceedings are in the book Mach's Principle, edited by J. Barbour and H. Pfister, Birkhauser, 1995). In the entrance poll the question Is general relativity perfectly Machian? got 2 'yes' and 30 'no', while at the exit poll there were 3 'yes' against 21 'no'. Notice that one of the organizers, Julian Barbour, contributed a paper entitled General Relativity as a Perfect Machian Theory, so there is no mystery as to where he cast his vote!

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.

 

[Nacho]

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

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.

 

[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.

 

[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.

 

[Nacho]

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.

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"?

 

[masudr]

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

 

[Nacho]

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

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

 

[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.

 

[JUboy]

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.

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

 

[masudr]

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

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.

 

[yogi]

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

Don't tell Garth

 

[Nacho]

masudr,

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.

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".

 

[Garth]

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

Don't tell 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

 

[masudr]

In empty space: 1. "What is the physical significance of any coordinate system?"

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).

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

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

Now add particles with inertial mass to the system -

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

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.

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

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.

 

[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?

 

[Garth]

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).

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.

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.

But not in the presence of curvature, geodesic deviation and the relative acceleration of nearby inertial frames are the measure of that curvature.

// 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).

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.

//nature determines it (G) 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 $c$,

These are emphatic statements, are they taken 'by faith' or can you substantiate them?

or it (G) emerges from some "more fundamental" theory which I (or anyone else, it seems) haven't come across yet.

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 .

Garth

 

[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.

 

[masudr]

Assuming GR:

In empty space: "What is the physical significance of any coordinate system?"

Nothing, they are all equivalent.

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

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

(Now add matter) 3. "What is the source of their inertia?"

Innate particle property.

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

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.

 

[masudr]

...are we saying SR is 'unphysical' in this respect?

SR is not really a theory of the universe. It provides constraints on what theories can be, based on some wonderful symmetry principles.

I mean, you wouldn't call Galilean invariance a theory of the universe, but you would call Newton's scheme just that.

 

[Garth]

Thank you masdur for your thoughtful replies, if I may respond?

Assuming GR:

In empty space: "What is the physical significance of any coordinate system?"

Nothing, they are all equivalent.

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

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

I agree; however, what is it then that does define an inertial frame when space is not empty? The mass that has just been added perhaps? - But is that not Mach's Principle?

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

Innate particle property.

As I said above this is an emphatic statement, but how can you be sure? Can you substantiate this or is it simply 'taken on faith'?

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.

As it was Dicke's version of Mach's Principle that: "The gravitational constant should be a function of the mass distribution in the universe", whether this hypothesis or an ad hoc value of G is unnatural or not, is the discussion in hand! In the quest for a quantum gravity there are many papers that try to use the BD scalar field in one way or another.

The real question is, "Are these different formulations of gravitational theory concordant with experiment and observation?" BD itself is only concordant if the scalar field is only vanishingly weakly coupled to mass.

I believe BD has not gone far enough in modifying GR, which is why I have modified it in my http://en.wikipedia.org/wiki/Self_creation_cosmology and found a theory that does appear to be concordant with present experimental and observational constraints. The results of Gravity Probe B will resolve the degeneracy between GR and SCC.

Garth

 

[masudr]

Thank you masudr for your thoughtful replies, if I may respond?

Of course you may; thank you for your responses too.

I agree; however, what is it then that does define an inertial frame when space is not empty? The mass that has just been added perhaps? - But is that not Mach's Principle?

An inertial frame is defined by how things happen in them, not by things in them. In a 2 particle universe, if in some choice of co-ordinates, the particles don't accelerate w.r.t. each other (or travel on geodesics if you like) then it is an inertial frame. If God (whoever your God is) adds a 3rd particle then there should be no change (at least that's what I expect, obviously I could be entirely wrong).

As I said above this is an emphatic statement, but how can you be sure? Can you substantiate this or is it simply 'taken on faith'?

I ask kindly, do you have a problem with charge/spin being an innate particle property or do you believe that they should be derived from some theory?

As it was Dicke's version of Mach's Principle that: "The gravitational constant should be a function of the mass distribution in the universe", whether this hypothesis or an ad hoc value of G is unnatural or not, is the discussion in hand!

As far as I know, BD theory (and now I can add SCC theory to that list) agrees with experimental observation. You certainly know more about BD theory than I do, at least enough so that I don't think we can have a discussion on it.

But my disbelief in MP stems from what I said above. And all this aside, gravity probe B results will certainly be interesting.

Masud.

ps. your 0401136 arXiv.org paper makes interesting reading

 

[Garth]

I ask kindly, do you have a problem with charge/spin being an innate particle property or do you believe that they should be derived from some theory?

inertial mass, charge, spin - the question is how are they measured?

Measurements are simply comparisons with some defined standard. But how is that comparison to be made? Especially when the object is separated across the depths of space and time and the standard is in a laboratory in Paris.

In the measurement of force mass is both the standard and the definition.

I do not speak for charge or spin, but if in future it should be shown that they are derived from a basic property of a quantum gravity theory of everything I would not be surprised.

Mass on the other hand has a relationship with energy, therefore they might yet be shown to have a dependence on each other. (In SCC particle rest masses vary with gravitational potential energy.)

Garth

 

[yogi]

I would prefer the definition of an inertial frame as one in which inertia is isotropic - this then contains w/i it both free float orbiting frames as well as liinear and geodesic paths.

Physics is relational - at least on the level that it is presently probed. We do not have a theory of why the electron has a particular charge, why particles exhibit spin in quantified units, etc The real challenge is to look for the tie to the global properties to which these may be related. Mach fumbled for a cosmological reason that would relate inertia to the whole - Einstein, as near as I can see, rejected the notion of distant masses per se as being the cause of inertia - opining instead that local space is conditioned in some way that avoids action at a distance, specifically space and matter have an interactive relationship. While it could be argued that the distant masses are necessary for this conditioning of space, there are other reasons why the properties of the void are what they are - e.g., the expansion of space may create stress independent of any localized chunks of matter here or there.

 

[loopgrav]

Look at chapters 2 and 3 of "The Fabric of the Cosmos" by Brian Greene. It is an excellent discussion of Newton's bucket and Mach's Principle.

 

[yogi]

I don't have "Fabric of the Cosmos" handy. What does he say that is new and different?