How/Why does the Mach principle define what is a 'direction'?

[mark_gg]

I now have a general understanding of relativity but it threw up a few issues.

I understand that there are no 'fixed' points of reference in the universe, which of course begs the question as to why inertia exists. The way I imagine it is if I am the only matter in the universe, then why should up be up, down be down, if I turn left or right, or rotate, why should there be inertia? If I stand in my living room and spin, why should my arms fly out.. It seems that, of course, there shouldn't be inertia if the universe is truly relative.

I know that Einstein grappled with this and he referred to Mach's principle to vaguely explain this problem in that matter over there (far away) has an unexplainable effect on matter here, so in a way, we can say there are reference points in the universe... sort of.

But then I got thinking more about it, and then it also threw up another 'observation'. I understand the universe lacks any real geometry.. as in, it's not like space is a room and I can pin point my location X,Y,Z in relation to the walls... Its better to imagine it as a void with 'stuff' inside it.

But do you notice that the Mach principle applies exactly to light too? In that, if I fly in a 'straight line' (or a particular direction), then light waves also follow the same 'straight' line that matter does.. What I mean is that if I 'veer' from the course that light follows with a left or right turn, I feel inertia. (could it be that inertia is caused by us 'crossing' the path of light)

I guess my question is WHY is 'straight' is straight for matter, as well as for light?

Also, I wander what would happen if all the matter in the universe disappeared, except for me in my small rocket ship. I guess if we extrapolate the Mach principle to this situation, my rocket ship dictates the geometry of all of space, and if I 'spin' I won't feel anything at all (as I am not really spinning). I wander if there is zero inertia in this situation? But I also wander, if I shine a light beam in front of me, and I rotate.. will I perceive the light fly away from rotating around me? If I use a 'left thruster' to spin to the right, would the light follow the same path as me? Would I perceive it spinning around in a outward spiral, as I should be dictating the geometry of all of space no? but then this created a new problem which goes to the heart of this issue for me.. Why should my rotation or lack of dictate the 'geometry' of space. If we apply that to the universe as a whole, WHY has matter dictated what is a 'straight line'. I just cannot see any explanation or plausible reason why it would... Light and matter should be going in crazy random directions if the universe is truly relative and inertia should either not exist, or be a completely random force that isn't consistent... Is gravity and inertia the same thing?

Wait a minute... is gravity defining space, and the 'pull' I would feel near a massive object is really just 'inertia'?

This is all bugging me so any explanation or thoughts are welcome please. Anything!

 

[Bill_K]

I understand that there are no 'fixed' points of reference in the universe, which of course begs the question as to why inertia exists. The way I imagine it is if I am the only matter in the universe, then why should up be up, down be down, if I turn left or right, or rotate, why should there be inertia? If I stand in my living room and spin, why should my arms fly out.. It seems that, of course, there shouldn't be inertia if the universe is truly relative.

Forget Mach's Principle, mark_gg, it was a vague pre-relativistic nineteenth-century philosophy that turned out to be false.

Not everything in physics is relative. Acceleration is absolute, and rotation is absolute. These are locally determined properties - they do not depend on the existence or motion or observation of the "distant stars". An inertial reference frame is one that is nonaccelerating and nonrotating. Inertial forces will appear in any other frame.

 

[WannabeNewton]

Why should my rotation or lack of dictate the 'geometry' of space.

Because rotation is absolute and a rotating body has angular momentum that generates a gravitational field i.e. a rotating curved space-time, according to the Einstein field equations.

If we apply that to the universe as a whole, WHY has matter dictated what is a 'straight line'.

This is a philosophy question, not one of physics; we don't know why, we just know how.

 

[mark_gg]

'rotation is absolute'... in relation to what?

With respect, but I don't think it's a philosophical question at all. Inertia is a real force that needs explaining. The feeling of pull when someone moves left or right has to have a cause if the universe is truly relative, as well as the fact considering light follows the same arbitrary lines that matter does.

Newton dealt with this problem using an absolute space to explain why the water in the glass bulged towards the outside of the glass, but how relativity deal with this considering the idea of absolute space has been debunked?

I guess nobody really knows at this point?

 

[Matterwave]

Forget Mach's Principle, mark_gg, it was a vague pre-relativistic nineteenth-century philosophy that turned out to be false.

Not everything in physics is relative. Acceleration is absolute, and rotation is absolute. These are locally determined properties - they do not depend on the existence or motion or observation of the "distant stars". An inertial reference frame is one that is nonaccelerating and nonrotating. Inertial forces will appear in any other frame.

But how can this be said in such absolute words when we know that frame-dragging exists, and that rotating objects can, in fact, induce a rotation in objects around them from nothing but the geometrical effects of gravity?

 

[WannabeNewton]

But how can this be said in such absolute words when we know that frame-dragging exists, and that rotating objects can, in fact, induce a rotation in objects around them from nothing but the geometrical effects of gravity?

None of that has to do with Mach's principle as originally stated by Mach, which concerned the absolute nature of rotation (c.f. Newton's bucket). Over the years, people have basically come up with their own versions of Mach's principle, including those statements regarding the dichotomy between local and global rotation in general relativity in a rotating space-time.

'rotation is absolute'... in relation to what?

It's absolute, so it isn't relational. I can measure local rotation unambiguously with a set of gyroscopes. In GR one must be careful to distinguish local and global rotation, a distinction that does not arise in Newtonian gravity.

 

[mark_gg]

I guess another way I've considered this, is if we step back from the entire universe and imagine it's race car.. why should it be 'uniform' in that it's overall inertia is zero and space seems to be a resting car.. Why shouldn't we all be stuck to the floor, or the ceiling, or being pulled one way or another, perhaps changing over time. Why/how does it 'appear' to have absolute properties about it. Why does space appear to be a 'resting race car' and not a car going around the track. Why should light follow identifiable 'straight lines' when we shine it off into space.

If there is relative space, there should be no reason why the light shouldn't fly off, do a zig-zag, and fly back into our faces again (like a cup of water in a race car). There should also be no reason why when I set off in my car, I suddenly get thrown into the side, or my car flies off the street, or into space or whatever...

Space has some kind of absolute properties about it but how can GR reconcile this fact.

I'm interested in the science of it and this is not a philosophical question.

if there is no answer, then that's fine... Perhaps one day someone will find out.

Thank you.

 

[mark_gg]

"It's absolute, so it isn't relational"

I understand, but what is it absolute in relation to?

There seems only three possible explanations:

1) in relation to itself
2) in relation to space overall (some kind of absolute property)
3) in relation to all the other mass in space.

 

[Matterwave]

None of that has to do with Mach's principle as originally stated by Mach, which concerned the absolute nature of rotation (c.f. Newton's bucket). Over the years, people have basically come up with their own versions of Mach's principle, including those statements regarding the dichotomy between local and global rotation in general relativity in a rotating space-time.

Why does this not have to do with Mach's principle? Even in Wald, there is a homework problem (chapter 4 problem 3) showing that if you had a shell of material which is rotating, the definition of "rotating" inside this shell of material is different than if that shell of material were not rotating. Quoting Wald: "At the center of the shell the local standard of "non-rotating" defined by parallel propagation along a geodesic, is changed from what it would be without the shell, in a manner in accord with Mach's principle."

Perhaps this does not prove Mach's principle (in any case Mach's principle is pretty ambiguous physically speaking), but it seems that at least in some sense G.R. has at least incorporated a little bit of Mach's principle in it.

 

[WannabeNewton]

There have already been countless threads on this terminological issue and I have specifically commented on Wald's references to Mach's principle in two of the problems from his text (the one from chapter 4 you referenced and another from chapter 7). What he calls Mach's principle is simply not Mach's principle as originally formulated by Mach, as I have already stated. Both of the aforementioned problems from Wald illustrate the fact that in GR, rotation as measured locally, with respect to gyroscopes and for Born rigid systems codified by the twist 1-form, disagrees with rotation as measured globally, with respect to the distant stars, when the space-time possesses angular momentum. This may just be an argument over terminology but it needs to be said that Mach's original formulation never elucidated such a phenomenon-his issue rested in the absolute vs. relative nature of rotation and more generally of space.

 

[mark_gg]

Sure, but what is a thing rotating in relation to?

 

[mark_gg]

I guess no one can help?

:-(

 

[pervect]

Sure, but what is a thing rotating in relation to?

I guess no one can help?

Not unless something changes on your part.

"It's absolute, so it isn't relational"

I understand, but what is it absolute in relation to?

Apparently there is a language issue here, and you do not share the same definition of relative and absolute as the rest of us.

Because we don't share the same definitions you do (of relative and absolute), you don't understand our replies to your question.

If you asked some questions about the meaning of relative and absolute, such as "what is the difference between relative and absolute" or "what sort of instruments or procedures can measure absolute quantities" then we might get somewhere,

Until that time, I don't see a lot happening, you'll keep getting answers you don't understand and repeating the same question over and over again, expecting a different answer.

 

[mark_gg]

I took this from a forum to help try and explain what I am asking as maybe I haven't articulated it well enough based on the responses:

"So motion in physics is not all relative. There is a set of reference frames, called inertial frames, that the universe somehow picks out as being special. Ships that have no angular velocity in these inertial frames feel no artificial gravity. These frames are all related to each other via the Poincare group."

My question: Why/How does the universe 'somehow pick out [inertial frames] as being special'?

If there is no answer then that's fine. I was just wandering if there was or any accepted theories.

 

[mark_gg]

No answers... A shame.

 

[Matterwave]

I took this from a forum to help try and explain what I am asking as maybe I haven't articulated it well enough based on the responses:

"So motion in physics is not all relative. There is a set of reference frames, called inertial frames, that the universe somehow picks out as being special. Ships that have no angular velocity in these inertial frames feel no artificial gravity. These frames are all related to each other via the Poincare group."

My question: Why/How does the universe 'somehow pick out [inertial frames] as being special'?

If there is no answer then that's fine. I was just wandering if there was or any accepted theories.

That quote is specifically for special relativity (which is why they mention the Poincare group). You pick out the "special" frames as the frames (no gravity in SR) in which no fictitious forces arise. In other words, you sit there, and don't feel any inclination to move to the left, or to the right, or forwards or backwards etc. You just float. Once you establish that you are in an inertial frame, anyone moving with respect to you at a constant velocity, is also in an inertial frame. Their coordinate system is related to you by a Poincare transformation.

 

[pervect]

No answers... A shame.

There's been a lot of discussion of this, for instance in https://www.physicsforums.com/showthread.php?t=751543