Mach's Principle: Inertia, Newton, Einstein & Gedanken Experiments

[Garth]

There is no "No preferred frames" principle in SR. .

I disagree

Garth

 

[Ich]

SR subsumes Galiei´s relativity principle from Newtonian mechanics and extends it to electrodynamics. It states that physics is the same in all inertial systems. Neither Newton nor Maxwell nor Einstein said that rotation had no physical effects.
From my limited knowledge of GR i can´t tell how it handles rotating frames. Maybe as some kind of acceleration effects, but still rotation is absolute. What´s new in GR is that rotation of spacetime is partly influenced (and not defined) by rotating masses.

 

[Garth]

But the question is: "What defines an inertial (either non-accelerating or non-rotating) frame of reference?" Non-accelerating or non-rotating with respect to what?

As you have gathered, I am Machian in that I believe that inertial frames have to be defined with respect to the distribution of the rest of the matter in motion in the universe.

However, one can further ask: "What was it that decided that frame of reference (probably identified now by the globally isotropic CMB frame) in the first place?"

Garth

 

[Ich]

Non-accelerating with respect to spacetime. As I pointed out, I have no problems with spacetime being an entity in itself.
And for CMB, it is just light with some special energy distribution. Maybe it really shows us how the universe expanded, but I don´t expect physics to be bifferent in this frame.

 

[Stingray]

But the question is: "What defines an inertial (either non-accelerating or non-rotating) frame of reference?" Non-accelerating or non-rotating with respect to what?

As I stated before, you can define it with respect to local geodesics. If you overinterpret the principle of relativity, you'll be left with nothing resembling reality...

 

[Garth]

As I stated before, you can define it with respect to local geodesics. If you overinterpret the principle of relativity, you'll be left with nothing resembling reality...

To be precise the point I was making was that SR is built on the principle of "no preferred inertial frames of reference".

However Einstein himself asked the same question as Bishop Berkeley and Ernst Mach about what was it that decided which frames were to be inertial or not? The situation is particularly acute in the gedanken of a test particle in an otherwise empty universe.

Einstein was somewhat satisfied that his GR theory partially included Mach's Principle, but it is generally understood by him and most other researchers in the field that GR does not fully include it. Hence the point of such work as that of Brans Dicke and others including myself.

Merely erecting a coordinate system, and a metric to go with it, is only doing mathematics and not physics. You have to physically define how the mathematical symbols relate to physical realities. This means basically repeatedly asking the question, when writing a mathematical representation of a physical quantity, "How do you measure it?"

Rather that "over interpreting PR and being left with nothing resembling reality", the opposite seems to be the case.

Garth

 

[Stingray]

To be precise the point I was making was that SR is built on the principle of "no preferred inertial frames of reference".

Definitions of "inertial" can be found in better textbooks. It is not mysterious, especially when thinking in terms of Minkowski's formulation of SR. There, you can measure the metric, and all coordinate systems which diagonalize it are called inertial.

Merely erecting a coordinate system, and a metric to go with it, is only doing mathematics and not physics. You have to physically define how the mathematical symbols relate to physical realities. This means basically repeatedly asking the question, when writing a mathematical representation of a physical quantity, "How do you measure it?"

The physical relevance of the metric is well-known. It is not conceptually difficult to measure it in a small region around some worldline (e.g. the lone particle). Again, look in textbooks.

Lastly, Ich said

It [SR] states that physics is the same in all inertial systems.

It is actually the same in all frames. Although SR wasn't originally formulated this way, it usually is now. The problem is that the physics is the "same" only for a properly defined sense of "same" . It is IMO more a requirement for mathematical statements than of physical principle.

For example, you can write down Newtonian gravity so that it looks the same in all frames as well. It's unfortunate that this formulation is rarely discussed in a standard physics education. It is really very elegant, and shows a surprising amount of similarity between Einstein's and Newton's theories.

 

[Ich]

It is actually the same in all frames. Although SR wasn't originally formulated this way, it usually is now. The problem is that the physics is the "same" only for a properly defined sense of "same" . It is IMO more a requirement for mathematical statements than of physical principle.

For example, you can write down Newtonian gravity so that it looks the same in all frames as well. It's unfortunate that this formulation is rarely discussed in a standard physics education. It is really very elegant, and shows a surprising amount of similarity between Einstein's and Newton's theories.

That´s beyond my scope; I guess what you mean has something to do with covariance and this sort of stuff.
What I meant is that there is no way to tell whether you are inertially moving or not, but there are thousands of experiments to tell whether your apparatus is rotating or not.

 

[moving finger]

To be precise the point I was making was that SR is built on the principle of "no preferred inertial frames of reference".

However Einstein himself asked the same question as Bishop Berkeley and Ernst Mach about what was it that decided which frames were to be inertial or not? The situation is particularly acute in the gedanken of a test particle in an otherwise empty universe.

Einstein was somewhat satisfied that his GR theory partially included Mach's Principle, but it is generally understood by him and most other researchers in the field that GR does not fully include it. Hence the point of such work as that of Brans Dicke and others including myself.

Merely erecting a coordinate system, and a metric to go with it, is only doing mathematics and not physics. You have to physically define how the mathematical symbols relate to physical realities. This means basically repeatedly asking the question, when writing a mathematical representation of a physical quantity, "How do you measure it?"

Rather that "over interpreting PR and being left with nothing resembling reality", the opposite seems to be the case.

Garth

Garth - I agree 100%

MF

 

[moving finger]

What I meant is that there is no way to tell whether you are inertially moving or not, but there are thousands of experiments to tell whether your apparatus is rotating or not.

But the real question is whether that "rotation" you measure is an absolute rotation (with respect to some mystical absolute non-rotating reference frame), or whether it is a relative rotation (with respect to, perhaps, the rest of mass-energy in the universe). The former is perhaps assumed in GR, the latter is Machian. These two are very different concepts.

MF

 

[Ich]

But the real question is whether that "rotation" you measure is an absolute rotation (with respect to some mystical absolute non-rotating reference frame), or whether it is a relative rotation (with respect to, perhaps, the rest of mass-energy in the universe).
MF

Let me rephrase that: the real question is whether that "rotation" you measure is a rotation with respect to local spacetime, or whether it is a rotation with respect to the rest of mass-energy in the universe, of which your probe knows via some mystical distance effect.
I´m not the one to decide which is true, but: Einstein, himself a "Machian", came up ith a working theory which passed every experimental test so far. And this theory works strictly local via the mediation of a spacetime with some physical properties in itself.
Even if you like more the strictly machian view, be sure you would need a whole bunch of "New Physics" to implement it. Einstein tried, but failed.
Maybe Garth has the solution, but until there is some evidence for his theory, i stick to GR.

 

[Garth]

Let me rephrase that: the real question is whether that "rotation" you measure is a rotation with respect to local spacetime, or whether it is a rotation with respect to the rest of mass-energy in the universe, of which your probe knows via some mystical distance effect.
I´m not the one to decide which is true, but: Einstein, himself a "Machian", came up ith a working theory which passed every experimental test so far. And this theory works strictly local via the mediation of a spacetime with some physical properties in itself.
Even if you like more the strictly machian view, be sure you would need a whole bunch of "New Physics" to implement it. Einstein tried, but failed.
Maybe Garth has the solution, but until there is some evidence for his theory, i stick to GR.

Although Einstein was a Machian at heart he worried that GR did not fully include that Principle.

I would argue that Mach's Principle is actually inconsistent with the principles of GR as it can identify a preferred inertial frame of reference, that is the one co-moving with the centre of mass/momentum of the entire universe. At any event in space-time I would identify that with the globally isotropic CMB frame at that event.

SCC does have 'evidence' to support it: viz: It is concordant with cosmological constraints without the need to invoke Inflation, non-baryonic Dark Matter or Dark Energy. It predicts the Pioneer anomaly as a clock drift between atomic and ephemeris time, and it predicts a secular speeding up of the Earth's rotation at a rate equal to Hubble’s constant that is indeed observed. These are described in the preprint Self Creation Cosmology - An Alternative Gravitational Theory .

Garth

 

[Ich]

I downloaded your paper and will read it when I have time. But don´t expect too much of enlightenment for me, I even did not understand GR.

 

[moving finger]

Let me rephrase that: the real question is whether that "rotation" you measure is a rotation with respect to local spacetime,

To me, THIS is the mystical concept. What meaning does "local spacetime" have in the absence of mass/energy?

or whether it is a rotation with respect to the rest of mass-energy in the universe, of which your probe knows via some mystical distance effect.

why mystical? gravitational fields propagate (as far as we know) without any distance limit, and all mass/energy produces a gravitational field - therefore every atom in your body is experiencing right now the combined gravitational fields of all of the rest of the mass/energy in the universe. What is mystical about that?

I´m not the one to decide which is true, but: Einstein, himself a "Machian", came up ith a working theory which passed every experimental test so far. And this theory works strictly local via the mediation of a spacetime with some physical properties in itself.

Simply because nobody so far has been able to carry out a test which distinguishes between rotation with respect to absolute space, or with respect to local spacetime (whatever that means) or with respect to the rest of the cosmos.

Even if you like more the strictly machian view, be sure you would need a whole bunch of "New Physics" to implement it.

That is the whole point of this thread

MF

 

[Ich]

Simply because nobody so far has been able to carry out a test which distinguishes between rotation with respect to absolute space, or with respect to local spacetime (whatever that means) or with respect to the rest of the cosmos.

AFAIK they will do next year. Should we bet whether GR will win again?

 

[moving finger]

AFAIK they will do next year. Should we bet whether GR will win again?

what do you think the results will prove? That there is an absolute rotational rest-frame that is NOT the same as the Machian rest-frame?

MF

 

[Ich]

They will not prove anything, but they may show evidence that frame-dragging is as predicted by GR. Any alternative theory then would have to reproduce this result. Or better, predict this result before.
Or even better, predict a different result and be shown to be more exact than GR. I think Garth´s predicts 5/6 ? (Sorry still had no time to read the paper)

 

[moving finger]

They will not prove anything, but they may show evidence that frame-dragging is as predicted by GR. Any alternative theory then would have to reproduce this result. Or better, predict this result before.
Or even better, predict a different result and be shown to be more exact than GR. I think Garth´s predicts 5/6 ? (Sorry still had no time to read the paper)

I don't think the expectation is as clear-cut as you suggest. Yes, Garth suggests that his SCC theory can be distinguished from GR by Gravity Probe B, but SCC is not the only Machian theory in town. Frame dragging is apparently a direct consequence of the equations of GR, but it is also a Machian effect.

I'm not an expert on GR, so it is not clear to me how one can distinguish in this way between the alleged GR assumption of an "absolute rotational reference frame", and a Machian "relative rotational reference frame" (relative to the background stars)? Can anyone enlighten me?

Thanks

MF

 

[Garth]

The difference is to be found in the gedanken experiment of a spinning spherical mass in an otherwise empty universe. In GR the frame dragging, Lense-Thirring effect, will rotate space-time at a small fraction of the rate of rotation of the mass. In a fully Machian theory space-time will be dragged completely with the mass, so that relative to the space-time metric the mass will not be rotating, for there is nothing to compare its rotation to, and inertial centrifugal and coriolis forces will disappear.

B.T.W. In SCC the geodetic precession is 5/6 GR whereas the Lense-Thirring effect is the same as GR. The universe not being otherwise empty! In SCC inertial mass is also determined by the distribution of mass in motion in the rest of the universe.

Garth

 

[moving finger]

The difference is to be found in the gedanken experiment of a spinning spherical mass in an otherwise empty universe. In GR the frame dragging, Lense-Thirring effect, will rotate space-time at a small fraction of the rate of rotation of the mass. In a fully Machian theory space-time will be dragged completely with the mass, so that relative to the space-time metric the mass will not be rotating, for there is nothing to compare its rotation to, and inertial centrifugal and coriolis forces will disappear.

Thanks, Garth!

Is it expected that Gravity Probe B will be able to distinguish between the two above, given that the Earth is NOT spinning in an empty universe? In other words, the frame dragging caused by the Earth should rotate space-time at a fraction of the rotation rate of the Earth both in GR and in a Machian view, because in the latter the background stars will have an effect?

Are there any straightforward publications you are aware of which compare and contrast the expected magnitude of the frame dragging that Gravity Probe B will measure (a) assuming GR is corrrect and (b) assuming the universe is Machian?

(I know you like to promote the SCC theory, but I'm looking for a generic "Machian" prediction rather than the SCC prediction, if that's possible )

Cheers

MF

 

[Garth]

Yes, the standard approach is to remain within a fully metric theory, i.e. one that has a metric and obeys the equivalence principle. The only Machian theory that does this is the Brans Dicke theory. The frame dragging gravitomagnetic precession in an E-W direction of the GPB gyros will measure the difference between BD and GR, as well as SCC.
As I posted above
BD prediction: Geodetic effect {(3w+4)/3w+6)}6.6144 arcseconds/yr
Gravitomagnetic effect {(2w+3)/(2w+4)}40.9 millarcseconds/yr
where w is the BD coupling constant such that in the limit as w -> infinity BD -> GR.
Other tests of BD constrain w to be 'quite large', w ~ 100 or so, and so there is not much difference between the two theories. See Weinberg 'Gravitation and Cosmology' pages 244-248.

For information: SCC is a 'semi-metric' theory in which a scalar field force exists that naturally exactly compensates for the presence of the 'BD type' scalar field affect on space-time in all experiments to date.

Garth

 

[moving finger]

As I posted above
BD prediction: Geodetic effect {(3w+4)/3w+6)}6.6144 arcseconds/yr
Gravitomagnetic effect {(2w+3)/(2w+4)}40.9 millarcseconds/yr
where w is the BD coupling constant such that in the limit as w -> infinity BD -> GR.
Other tests of BD constrain w to be 'quite large', w ~ 100 or so

Garth

Hmmm. I read on the Stanford Uni website that Gravity Probe B expects to measure the gravitomagnetic frame dragging effect to within 1%. Actually they estimate the predicted GR effect to be 42 milliarcseconds/yr.
If this can be measured to within 1%, then that would only distinguish between GR and BD (based on the info you give above) for values of w less than 48 (ie it could put a lower bound of 48 on w).

If, as you say, other tests have already put a lower bound of w ~ 100, then I do not see how Gravity Probe B, if it measures frame dragging to just 1%, can improve on this?

We would need a precision better than 0.5% to put a lower bound on w in excess of 100.

Edited : I also see that Gravity Probe B is supposed to measure the geodetic effect to one part in 10,000. This translates to a lower bound on w of ~ 6,600. OK, I agree this would be interesting!

But no matter what the result of Gravity Probe B, as far as I can see it can never distinguish between GR and BD - the most it can do is to put a lower limit on w?

MF

 

[Ich]

But no matter what the result of Gravity Probe B, as far as I can see it can never distinguish between GR and BD - the most it can do is to put a lower limit on w?

MF

As I understand it, BD is a modification of GR. And it is considered quite unattractive, because it does not predict any differences. It merely states that GR could also be somewhat different. So you can never falsify it - and that is not what one would expect from a solid theory.

 

[Garth]

As I understand it, BD is a modification of GR. And it is considered quite unattractive, because it does not predict any differences. It merely states that GR could also be somewhat different. So you can never falsify it - and that is not what one would expect from a solid theory.

On the contrary BD does predict differences to GR that converge on the GR predictions as w -> infinity. The presence of the BD scalar field that endows particles with inertial mass perturbs the GR space-time and that affects the freeling falling paths - geodesics - of photons and test particles, i.e. 'planets'.

The theory has fallen out of favour because the observed values of these solar system tests have always been so close to the GR values that w would have to be large and the BD scalar field insignificant. However interest has been re-awakened in the theory by the need to explain Dark Energy required by cosmological constraints.

Garth

 

[Ich]

What I wanted to say is that it does not predict an actual value of w. If I remember correctly, it´s more like a loophole in the maths - w could be <inf but there is no reason why it should.
Anyway, as w->inf, relevance->0. And w>100 is IMO already a long way down that road.

 

[Garth]

Anyway, as w->inf, relevance->0. And w>100 is IMO already a long way down that road.

I agree, which is why my approach has been to seek modifications of BD.

Garth

 

[Kamataat]

I've not read the whole thread, but this is my view on rotation in empty space:

Let's say we a particle A. There is no way to determine whether this particle is in motion or not. To determine this, we can bring in another particle B. Now by looking at whether the distance between A and B changes, we can determine if one of them is in movement or not. However, what if we set both of them, A and B, into motion on paths parallel to each other with the same speed? Then there is no way to determine their state of motion without bringing in another particle C from which to observe A and B. So, if the distance from A to B is constant, then we can't say whether they both are stationary or in motion. If the distance is not constant, then at least one of them is in motion.

Now, about rotation. Let's say we have a body that rotates about an axis X. Let this body be composed of a number of particles. Can this body know whether it is rotating or not (w/o an external body to compare to)? If the body is rotating, then all particles making up the body are moving around the axis of rotation X. The distance between any two (or more) particles A and B remains constant as they both rotate around X. So there is no way to determine whether A and B are in motion or not and thus there is now way to determine whether the body is rotating or not.

To speak of rotation, one must consider a body that is made of smaller bodies (particles). To measure the state of rotation of a body (which is perfectly spherical), one must lock onto a particle/point of that body and see whether the distance from oneself to that particle changes with time. If it changes with time and if this change follows some rules, then we can say that the body is rotating wrt to X (I say some rules, because the particle of the body could be in movement wrt to ourselves and yet not rotate about X, i.e. the body is moving away from us in a straight line etc.). That is why one can't consider a completely solid body (or a point particle) when talking about rotation of that body, because such a body doesn't have any particles/points onto which to "lock on" for observation.

Now, back to the body in paragraph #2. I said that one couldn't determine the rotational state of that body because one can't determine whether particles A and B are in motion or not. One solution would be to place one particle D (which is part of the body) so that X passes right through it. This would mean that D is not rotating along with the rest of the body. Then one could measure rotation by looking from D at some other particle, say in A's direction. Now, if A disappears from D's field of view, then either A or D (or both) is in motion. If A reappears after some time and does this again with some period T, then we can say that maybe A is rotating around X (D). However, there is no way to be sure, because A could just as well move out of D's FOV in a random direction for a time T and then return.

So, I think that there is no way to determine with 100% certainty whether a body is rotating in empty space or not.

This is of course assuming that there is no absolute space (and that one can measure distances, directions and speeds w/o such a space) and that the body in question is perfectly spherical.

Now, I have a question: how is it meaningful to speak of more than one point particle if there is no absolute space? If there is no space between them, then how can one talk about their interactions and distances and so on? A possible way would be to image a line connecting the two points. Then, if we measure the length (time a signal takes from point A to point B along the line) of the line, we can determine whether the points are in relative motion.

When speaking about non-absolute space, one can picture it in this way: the space is simply moving along with the particle, so from the POV of the particle, there is no absolute background space (doesn't matter what the space is moving in relation to; we only consider a closed system of a particle and it's attached space). Now, if there are two particles, and the space is non-absolute, then this means that neither of the two particles are allowed to look at space and say: "Hey, it's in motion!" So what happens when one particle starts to move wrt to the other one? We have the requirement that the space, when looked upon from either particle, remains stationary. To remain stationary, the space must follow the moving particle. But then the space must become distorted because around particle A it can't move and around B it can't move either, but particle B is in motion (B drags the space surrounding it along) wrt A (A is stationary). So now this creates a problem: if the space becomes distorted, then it (or parts of it) must change position and then particles A and B can see that space is moving and is thus absolute. Thus it is not possible to have two particles and put one into motion wrt the other in non-absolute space.

Anyway, this is my $0.02, but I have no formal education in math so it all may be wrong, wrong, wrong!

- Kamataat

 

[moving finger]

One solution would be to place one particle D (which is part of the body) so that X passes right through it. This would mean that D is not rotating along with the rest of the body.

This does not necessarily follow. If D is precisely on the axis of rotation X then D could be simply spinning along with the rotation of the entire body - so that all points/particles are "rotating" the same amount wrt absolute space, but are "at rest" wrt each other.

MF

 

[Kamataat]

This does not necessarily follow. If D is precisely on the axis of rotation X then D could be simply spinning along with the rotation of the entire body - so that all points/particles are "rotating" the same amount wrt absolute space, but are "at rest" wrt each other.

Yes, of course, but what if D is a point particle? Does it make physical sense to say that a point particle is spinning (I'm aware of the spin property of elementary particles, but I look at this spin more like a mathematical approximation of nature)?

P.S.: Anyone care to confirm/refute what I said in my last paragraph in post #77?

- Kamataat

 

[moving finger]

but what if D is a point particle? Does it make physical sense to say that a point particle is spinning?

Does it make any physical sense to talk of a "point particle" (whereby I assume you mean a particle with infinitesimal dimensions)?

MF

 

[Kamataat]

Does it make any physical sense to talk of a "point particle" (whereby I assume you mean a particle with infinitesimal dimensions)?

From a naturalistic scientific point of view of course not, but we can model a physical system by assuming it consists of point particles. Such a model couldn't possibly tell anything useful about rotation.

Anyway, I stand by what I said before: A body w/o external absolute space can't know whether it's spinning or not.

P.S.: Sorry for my poor English.

- Kamataat

 

[yogi]

As a matter of historical interest, it was apparently Bishop Berkeley that first formalized the notion of space as contrary to Newton's idea of absolute space - In 1721 Berkeley published a book asserting that space only existed by virtue of its association with matter, and that unclothed space had no physical properties of its own..it was a sideless box and its only characteristic was extension. Berkeley insisted there was no space of independent existence and invoked a sky of fixed stars which became the reference points of all motion. Leibniz also weighed in on the side of Berkeley asserting "There is no space where there is no matter." Mach was apparently not aware of Berkely's earlier work - and did not refer to it in his publications - he of course added the additional element that the background stars determined the inertia of local matter. Einstein, apparently also unaware of Berkeley's philosophy, attributed these ideas entirely to Mach, and coined the term "Mach's Principle."