Mach's Principle

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When you spin around, you look out and you see the stars twirling and your hands sort of are propelled outward (by a thing we call a centrifugal force). Mach's principle supposes that these two things are not a coincidence, that rotation and centrifugal force is defined in relation to all other mass in the universe. In other words, your hands spin because you are rotating in relation to all those distant stars.

However this leads to many questions. Like how does this law operate? Is it based upon the relative ratio's of mass? Does distance between two bodies have an effect?

You may imagine that you have some godlike power to rearrange the universe in a particular way - and for the purpose of this demonstration you choose a configuration of a donut and a small ball directly in the center.

In the donut resides the vast majority of mass (say 99.99999% of all mass in the universe). In the ball only a negligible amount of mass.

The implication of mach's principle is that if you spin the donut around with your godlike powers, you notice a centrifugal bulging effect on the ball as if it's the one being rotated!

The other supposition would be that the donut bulges out, because at rest motion is defined by some arbitrary "resting" state.

The allure of this way of thinking is in a large part influenced by the case of linear motion. There is no true "at rest" state in relation to linear motion, so why should it be any different in relation to rotational motion? Intuition would have us believe that it should be no different. But this isn't anything different than speculation - which is pointless - so the real question is, What are the observable consequences?

In order to be able to get even some kid of indication of what to look for. Lets suppose that there are some determining factors. Intuition would tell me that it has something to do with the ratio of mass of the rotating system and the non rotating one, and distance away from the rotating and non rotating systems should also play a part.

Implications would be that it is harder for an object to fall into a spinning black hole (or neutron star) than it is for it to fall into one which is not rotating. This is because from the perspective of the black hole, it is the object that is rotating around it in the opposite direction, and the object behaves as if it is revolving around it and has to overcome centrifugal forces - even though it's not revolving around the heavy bodies from the perspective of the distant universe.

Mach's principle goes both ways, if a rotating body bulges because it is spinning then it must impart a bit of its perspective on the surrounding mass bodies, that is there is a small component of imparted force on the perpective as if the universe really is rotating around this object.

If Mach's principle does operate in this way, the body falling into a spinning black hole would experience an imparted centrifugal force, because to the perspective of the spinning mass of the black hole, it sees the mass as revolving around and plays into account of reality.

How do we define inertia? Is it momentum, Mass x Velocity? Is inertia defined by the force you feel when on an object of changing velocity with time?

How do I know that when I drop something, the thing is falling towards the ground, and not the ground accelerating upwards to meet it?

If we accepted this latter definition of inertia, we may be lead to believe some silly things about how the universe operates. When a skydiver falls towards earth, he doesn't experience a force accelerating him towards the ground - if anything this may be the first moment in his entire life in which he doesn't experience any force at all. He is weightless, so why do we suppose he's falling, and its not just the ground accelerating up to meet him?

Perhaps all gravity is is the phenomenon of solid objects expanding - and every body of mass unit expands at the same rate proportionally so we are unable to detect it- absent the force (or lack there of) which implies it.

This seems like a good idea and everything, but the problem is it doesn't conform with experiment. Besides the point that multiple orbit systems don't work with this, there are phenomenon which disprove this idea - at least in the respect it's presented hear.

Take shoemaker-Levy-9 a comet which passed by Jupiter, and as the result of something we can only describe as a force, it disintegrated into many parts. Now if the comets attraction to Jupiter were merely an illusion of the two bodies expanding towards one another, there is no explination for how this occurs. However this doesn't completely disprove the expansion idea, because if you were attached enough to this idea, you could always attach greater levels of complexity in order to conform the idea more readily with experiment, you could always introduce something extra to explain it. However this isn't very scientific because with science we aren't looking for the most complex way of describing the universe we are looking for the simplist.

And so the answer to the question "How do I know when I drop something, that the thing is falling and it's not the ground coming up to meet it."
The reason science chooses to see it this way is because it's the simpliest (or most elegant) way of describing this phenomenon on a consistent basis.

In order to have a theory be accepted it has to be more simple than the current understanding or if it is more complex it has to have some observable consequence which contradicts current understanding.