Mach’s principle

A)    “When we look at the stars, the stars look back at us.”

1.      This argument has its roots in Newton’s thought about inertia and absolute rotation. It is often called Newton’s bucket argument, and it is described in his Principia as follows: 

“If a vessel, hung by a long cord, is so often turned about that the cord is strongly twisted, then filled with water, and held at rest together with the water; after, by the sudden action of another force, it is whirled about in the contrary way, and while the cord is untwisting itself, the vessel continues for some time this motion; the surface of the water will at first be plain, as before the vessel began to move; but the vessel by gradually communicating its motion to the water, will make it begin sensibly to revolve, and recede by little and little, and ascend to the sides of the vessel, forming itself into a concave figure...This ascent of the water shows its endeavor to recede from the axis of its motion; and the true and absolute circular motion of the water, which is here directly contrary to the relative, discovers itself, and may be measured by this endeavor. ... And therefore, this endeavor does not depend upon any translation of the water in respect to ambient bodies, nor can true circular motion be defined by such translation. ...; but relative motions...are altogether destitute of any real effect. ...It is indeed a matter of great difficulty to discover, and effectually to distinguish, the true motions of particular bodies from the apparent; because the parts of that immovable space in which these motions are performed, do by no means come under the observations of our senses.” [1]

2.      The argument that motion is absolute, not relative, has been challenged since the time of Newton. One of the challengers was Mach, arguing that only relative motion can be established:

“Newton’s experiment with the rotating vessel of water simply informs us, that the relative rotation of the water with respect to the sides of the vessel produces no noticeable centrifugal forces, but that such forces are produced by its relative motion with respect to the mass of the Earth and the other celestial bodies…” [2]

3.      Mach’s view that the water in the bucket (together with the bucket) is pulling towards the opposite side (away from the person who turns the bucket around) because it is somehow attracted by its environment (the rest of the universe) is known as Mach’s principle. This is the name given by Einstein to the idea that the existence of absolute rotation (the distinction of local inertial reference frames vs. rotating reference frames) is determined by the large-scale distribution of matter, as exemplified by this anecdote:

“You are standing in a field looking at the stars. Your arms are resting freely at your side, and you see that the distant stars are not moving. Now start spinning. The stars are whirling around you and your arms are pulled away from your body. Why should your arms be pulled away when the stars are whirling? Why should they be dangling freely when the stars don’t move?”

Mach’s principle says that this is not a coincidence- that there is a physical law that relates the motion of the distant stars to the local inertial frame. If you see all the stars whirling around you, Mach suggests that there is some physical law which would make it so you would feel a centrifugal force. There are a number of rival formulations of the principle. It is often stated in vague ways, like ‘mass out there influences inertia here.’ [3]

4.      A very general statement of Mach’s principle is that local physical laws are determined by the large-scale structure of the universe. This concept was a guiding factor in Einstein’s development of the general theory of relativity. He found an effect which he interpreted as being evidence of Mach’s principle:

We assume a fixed background for conceptual simplicity, construct a large spherical shell of mass, and set it spinning in that background. The reference frame in the interior of this shell will precess with respect to the fixed background. This effect is known as the Lense- Thirring effect. Einstein was so satisfied with this manifestation of Mach’s principle that he wrote a letter to Mach expressing this:

“It... turns out that inertia originates in a kind of interaction between bodies, quite in the sense of your considerations on Newton’s pail experiment... If one rotates [a heavy shell of matter] relative to the fixed stars about an axis going through its center, a Coriolis force arises in the interior of the shell; that is, the plane of a pendulum is dragged around…” [4]

5.      The Lense-Thirring effect certainly satisfies the very basic and broad notion that ‘matter there influences inertia here.’ However there is a fundamental problem with Mach’s hypothesis. If the whole universe (the ‘fixed stars’) participates in the rotation of the bucket (or if it rotates at the opposite direction if we are spinning around) then how come the centrifugal force which is produced on the bucket (or on ourselves) is transmitted instantaneously, if, according to relativity, nothing (no signal or force field) can travel faster than light?

6.      A way to explain this is Gödel’s rotating universe. This is an exact solution of the Einstein field equations. Among many unusual properties of this solution is the existence of closed time-like curves that would allow time travel. [5]

7.      Up till now nobody has taken seriously Gödel’s rotating universe. After Newton’s time of absolute space, in the modern times ‘everything is relative’ (without anyone challenging ‘relative to what?’). The problem with the hypothesis of a rotating universe is that nobody knows where its center could be. I believe that sooner or later such a center will be found, and that the universe is just another one among a vast distribution of universes. At that time particles propagating faster than light (e.g. gravitons?) will  have also been discovered. 

8.      The hypothesis of a rotating universe is perhaps the best explanation of both Newton’s bucket and Mach’s principle. Even in an empty shell a Coriolis force can be produced and measured (Lense- Thirring effect), if the shell is spinning, as a reaction to the rotation of the universe, in the same sense that gravity is manifested at free fall (when something is not falling we cannot see or measure the acceleration of gravity).

9.      But the latter remark has in fact a deeper aspect. If we cannot feel the effects of gravity (either its acceleration or its tidal effects) before we do something to feel or measure the effects, is there any gravity (or any other force) before we observe it? If we could find an empty place in the universe (devoid of any stars) and begin to rotate, would there be any centrifugal force acted upon us? Since the Coriolis force can be produced even in an empty shell, is there such a force if there isn’t any observer to observe it?

10.  What is the role of the observer’s mind in the process? Does the mind have inertia? Can one literarily be dragged along by one’s own thought?

B)    And to finish where we started:

“When we look at the stars, the stars look back at us.”

“When we reflect on our thought, our thought reflects on us.”

[1]: [https://en.wikipedia.org/wiki/Bucket_argument]

[2]: [http://www.peterallport.com/newbuc.htm]

[3]: [https://en.wikipedia.org/wiki/Mach%27s_principle]

[4]: [https://www.researchgate.net/post/Has_this_interpretation_of_the_Machs_principle_already_been_explored]

[5]: [https://en.wikipedia.org/wiki/G%C3%B6del_metric]

8/30/2018

Picture: [https://machprinciple.wordpress.com/the-definition-of-machs-principle/]