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

[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."