Can Mach's Principle Be Tested with a Gyroscope in the Void of Space?

[Nacho]

Say you have a gyroscope, rotating in the ole' proverbial Star Trek "dead of space", far enough away from any single/multiple point of mass, to where the gravitational attraction of the Universe as a whole would be expressed. Or at least at a point to where the local bodies gravitational attraction would cancel out enough for this experiment.

If Mach's Principle is true, wouldn't you expect the axis of rotation of the gyroscope to precess, and if it didn't precess then Mach's Principle couldn't be true? That is because the distribution of matter in the Universe is not isotropic .. there is stucture and clumps of matter however far we look. (at least it is that way out to our gravitational horizon that we can currently see).

Then looking at the practibility of doing such an experiment. Do you have any idea of where that point in space would be, and how far from Earth it would be? Have any idea of the amount of precession that would be measured?


I've got more questions about Mach's Principle .. this is just a starter!

 

[turin]

... far enough away from any single/multiple point of mass, to where the gravitational attraction of the Universe as a whole would be expressed. Or at least at a point to where the local bodies gravitational attraction would cancel out enough for this experiment.

I'm afraid I would need a little clarification on this.

 

[Janitor]

As far as getting away from it all, maybe midway between superclusters of galaxies is as good as it gets.

 

[Nacho]

I'm afraid I would need a little clarification on this.

As far as getting away from it all, maybe midway between superclusters of galaxies is as good as it gets.

"Where" was really my secondary question .. the main question, assuming there could be a place, was: Would you expect precession or not if Mach's Principle is true?

As far as where it could be, let me answer this way without having to get too specific (I know it matters precisely where it could be, but I mean in general terms of feasibility):

My McGraw-Hill Encyclopedia of Astronomy says that stars typically move around galaxies with velocities of up to a few hundred MPS (miles per second). It also says galaxies typically move within clusters of galaxies from about 100 to several thousand MPS. I seem to remember the Milky Way was streaming towards the Great Attractor at around 600 MPS.

So, if the gyroscope could lose the motion of the Earth, and be in a similar orbit around the Milky Way as the Sun, I would think that would suffice. There would be at least a net motion towards the Great Attractor, and that (hopefully) would express the uneven distribution of matter in the Universe as a whole. By doing this, you really get to the "superclusters" level as Janitor suggested was needed. There would be more than 1 "signal" expressed on the precession found, but they could be separated by means of Fourier analysis, and the greatest magnitude would be because of Mach's Principle (if it would cause precession).

So, I would think that getting a gyroscope away from the Sun, in interstellar space, say a couple 2-3 light years from it and towards another star, would be sufficient.

So, would either one of you expect any precession to be caused by Mach's Principle being true?

-----------------------

And a second question about Mach's Principle that ties in with the "placement" question:

Does Mach's Principle cause effects that are purportional to how fast an object is spinning? Take a bucket of spinning water near the surface of the Earth, the axis of rotation pointing to the center of the Earth. The faster it spins the more convex the surface of the water gets. The explanations of this that I have read attributes all of this to Mach's Principle, and none of it to the gravitational attraction of the Earth. If that is the case, then I would expect 2 things:

1) In the above experiment I suggested, couldn't you get better/faster results by getting the gyroscope to spin as fast as possible?

2) Any effect the gravitational attraction Earth would have seems easily overcome in showing effects of Mach's Principle. Why couldn't my experiment be performed right here on Earth?

Heh, this is my proposal for "Gravity Probe C" ;). I know I'm missing something .. otherwise the scientists would not be able expect to measure the effects of frame dragging on Gravity Probe B.

Even another question. Say a sphere was rotating on the Earth, again the axis of rotation pointing to the center of the Earth, and that it could spin as fast as needed without flying apart. Could it spin fast enough to achieve escape velocity?

 

[turin]

I seem to remember the Milky Way was streaming towards the Great Attractor at around 600 MPS.

What is "the Great Attractor?"

There would be more than 1 "signal" expressed on the precession found, ...

This seems quite arbitrary. What do you mean?

So, would either one of you expect any precession to be caused by Mach's Principle being true?

Yes.

Does Mach's Principle cause effects that are purportional to how fast an object is spinning?

Yes.

... couldn't you get better/faster results by getting the gyroscope to spin as fast as possible?

Probably.

Say a sphere was rotating on the Earth, again the axis of rotation pointing to the center of the Earth, and that it could spin as fast as needed without flying apart. Could it spin fast enough to achieve escape velocity?

This is an interesting question. I don't know an answer. Certainly, points on the equator can be given a tangential velocity that exceeds the escape velocity of the earth, but I think what you're asking is whether or not the spinning motion in itself would cause the sphere to lift away from the earth.

 

[Nacho]

What is "the Great Attractor?"

The last I remember reading about "The Great Attractor" was a few years ago. It was purported to be a great accumulation of mass in the Universe .. a point in the Universe, that our galaxy, local group, and local supercluster (I believe) was streaming/moving towards. Though, on photographs no illuminated mass was ever identified as it. I'll add that it wasn't/isn't ever thought to be dark matter.

I brought it into the discussion because the scale of the movement towards it far outweighed the scale of movement the Sun has in the Milky Way, the Milky Way in the Local Group, etc. If you wanted to go to a higher order of structure in the Universe, I'd think the movement towards it would be of an even higher value. If Mach's Principle is supposed to be espressed by the gravitational attraction of the Universe, and the local gravitational fields are so easily overcome in espressing Mach's Principle, I think this might go to show that the placement of the gyroscope shouldn't make so much a difference .. that is, our local gravitational fields are not of consequence in talking about the gravitational influence of the Universe as a whole. And Mach's Principle is about the gravitational influence of the Universe as a whole.

Though, all of that has to be considered within the core question: Should an accumulation of matter effect a gyroscope if Mach's Principle is true?

This seems quite arbitrary. What do you mean?

It's not arbitary. There are quite a few different "movements towards", or relative movements the Earth has. It moves relative to the Sun, the Sun and Earth move relative to the Milky Way, the Milky Way move relative to the Local group, the Local Group ... etc. All of these different motions can be adding to or opposing the previous/lower order motion. What I was trying to say, was that if there was a movement of the gyroscope, all of those motions have to be taken into account. Mostly they will be different, and will make different "peaks" in the data analysis. Compare it to the analysis they do on extrasolar planets. After more data aquisition, and Fourier analysis, they are able to make out the a planet of lower mass than the original planet they found, exists. Same thing there .. the higher, or first, mass found out should be the highest accumulation of mass in the Universe .. again, given that Mach's Principle is true, and a gyroscope will precess to an accumulation of mass.

Yes.

Thanks for your answer. I think that Mach's Principle should cause precession also, but only because the Universe is bigger than the gravitational horizon, and because the Universe has structure greater than the gravitational horizon. If we are to believe that the gravitation of the Universe as a whole (our horizon) leads to a Mach's Principle, and that same structure is not isotropic, then it has to cause precession.

Yes.

This is in response to my question if Mach's Principle shows itself in purportion to the speed of a body revolving. I'm going to delay answering this .. because that brings up another line of questioning .. (sorry I have so many questions! ;) )

I also think a body that is spinning fast enough should attain escape velocity. A spinning body shows rigidness in "absolute space", though no one is [equipped|wants] to talk about absolute space outside what can be discarded through Einsteins Relativity. It can't so well be shoved/discussed away if you consider rotation of a body.

 

[Nacho]

I've brought up the consequences of and questions of Mach's Principle before on these boards, to be discussed. Not too many people respond. I think it might be because:

1) It's a boring subject (maybe), but I make it more boring (more probable than maybe);

2) It's taught as a given, to be accepted without question, with very little supporting evidence for and no observable evidence for, and no one really understands the implications of it, and they are glad when the professor gets past it and onto something else, and they swear that if they get through it and get a passing grade, that they will never revisit what they were forced to temporarily learn but don't give a hoot about it or it's implications.

 

[turin]

If Mach's Principle is supposed to be espressed by the gravitational attraction of the Universe, and the local gravitational fields are so easily overcome in espressing Mach's Principle, I think this might go to show that the placement of the gyroscope shouldn't make so much a difference .. that is, our local gravitational fields are not of consequence in talking about the gravitational influence of the Universe as a whole. And Mach's Principle is about the gravitational influence of the Universe as a whole.

Well, I suppose you can say "gravitational influence." It is a little confusing to hear you call it that, but I think that is probably the appropriate term. It is the gravitational influence due to a moving gravitational source that induces the effects of acceleration. That is how I understand Mach's principle. But, it is a little tenuous to combine a modern view of gravity (GR) with Mach's principle.

Though, all of that has to be considered within the core question: Should an accumulation of matter effect a gyroscope if Mach's Principle is true?

Absolutely. This was made very clear by, I believe it was, Mach himself. Have you heard the bucket discussion? He says that the water in a rotating bucket that is made to rotate by the shearing of the sides of the bucket obviously gets flung outward. This is understood as the centrifugal effect induced by rotation. He goes on to say, however, that, given a sufficiently massive, dense, and thickwalled bucket (I suppose this was his idea of gravitational shielding, he proposes a wall thickness of several kilometers if I remember correctly), he believed that the water should not suffer any centrifugal effect, because the "gravity" of the bucket would be the strongest influence.

All of these different motions can be adding to or opposing the previous/lower order motion. What I was trying to say, was that if there was a movement of the gyroscope, all of those motions have to be taken into account.

I see what your saying now. The Fourier analysis threw me. It seems more like a Taylor series.

Mostly they will be different, and will make different "peaks" in the data analysis. Compare it to the analysis they do on extrasolar planets. After more data aquisition, and Fourier analysis, they are able to make out the a planet of lower mass than the original planet they found, exists.

I don't know anything about that.

.. the higher, or first, mass found out should be the highest accumulation of mass in the Universe .. again, given that Mach's Principle is true, and a gyroscope will precess to an accumulation of mass.

I don't believe that this is in strict accord with Mach's principle. I think that there is also a locality issue. Not in the sense that Mach had any notion of modern relativistic considerations or the application of differential geometry to physics, but in the vague, intuitive notion that, the further away something is, the less of an effect is should have. I'm not sure about that though.

What do you mean by "... precess to an accumulation of mass?"

... the Universe is bigger than the gravitational horizon, and because the Universe has structure greater than the gravitational horizon. If we are to believe that the gravitation of the Universe as a whole (our horizon) leads to a Mach's Principle, and that same structure is not isotropic, then it has to cause precession.

What is "gravitational horizon?"

A spinning body shows rigidness in "absolute space", though no one is [equipped|wants] to talk about absolute space outside what can be discarded through Einsteins Relativity. It can't so well be shoved/discussed away if you consider rotation of a body.

I am in close agreement with you on this one. There was a philosopher named Berkley that also had Mach-like ideas. He posed a thought that so well demonstrates my personal misgivings concerning the marriage of what I have seen of GR and rotation, and Einstein's eventual abandonment of Mach's principle. I can't remember exactly how the quote goes, but basically, if you can imagine that there are only two spheres that exist in the universe, then the notion that they should revolve around some center of mass doesn't even make sense (and I would insert the stipulation, "in the absence of an absolute orientation, which is not much shy of an absolute space."). Let's see, I think I have a reference for that quote:

Quote by Bishop Berkley found in the source:
J. L. Anderson, Principles of Relativity Physics, pp. 330-4.

Sorry, I didn't write down the full citation.

 

[turin]

2) It's taught as a given, ... and they are glad when the professor gets past it and onto something else, ...

Are you saying that you actually learned about this in a lecture?! I'm so envious. What class was this?