21 Interpretations of Mach’s Principle
We start by stating a few facts about Mach’s Principle, without going into details. These will be explored later, in future posts.
Mach’s Principle as an initial guide to General Relativity
The initial inputs that guided Einstein to conceive his General Theory of Relativity (GR) were, basically:
Although the last two principles of the above list are relatively well understood, the first one is not.
The blurred Mach’s Principle
Mach’s Principle is on people’s mind as basically a general statement on the origin of inertia. This is often understood by many as a problem that has been solved by Einstein’s GR, although Einstein himself disregarded Mach’s Principle later on.
From time to time, you may find obscure papers by obscure people on Mach’s Principle, but also authoritative works written by well-known experts of various areas of physics. This curious phenomenon serves as a testimony to the enthusiasm and reverence to a subtle and deep matter, even if stated so imprecisely.
But what exactly is Mach’s Principle?
The problem is the term “exactly”. There is no consensus on what Ernst Mach really meant by the principle which carries his name. In fact, the term “Mach’s Principle” was coined by Einstein. But, there is no clear statement of the principle in Mach’s book, “The Science of Mechanics” [Mach10], as cited by Einstein as one of the books which impressed him mostly while constructing his ideas towards GR.
If you want to know all there is to know about Mach’s Principle, you should start by reading a collection of contributions to the Tübingen meeting (1993) entirely dedicated to Mach’s Principle, edited by Barbour and Pfister [Barb95]. This collection is extremely interesting and includes transcriptions of the discussion sections as well.
The various interpretations of Mach’s Principle
Here I merely list the various interpretations identified on that meeting. Hopefully, we will be able to go into each of them (or some of them) in more detail in future posts.
- As the problem of defining velocity (motion).
- As mere redescription of Newtonian Mechanics.
- As determination of inertial frames from relative motions of masses.
- As mechanical interaction of masses, in particular through an interactive Machian ‘kinetic energy’.
- As generation of inertial forces in any body accelerated with respect to distant masses.
- As induction of inertial forces by accelerated masses by analogy with electromagnetic induction.
- As requirement that the metric tensor be completely determined by matter.
- The same, but by matter and gravitation (geometrical) degrees of freedom.
- As prediction of the future given relational initial data (initial-value approach).
- As cosmic derivation of inertial mass.
- As generalization of the special principle of relativity to nonuniform motions.
- As requirement of general covariance of the laws of nature.
- As need for generally covariant boundary conditions.
- As need for nonexistence of boundary conditions.
- There should be no matter-free, singularity-free solutions of GR.
- As an appeal to the principle of sufficient reason (observable facts must have observable causes).
- As expectation there will be dragging effects.
- As explanation of nonrotation of compass of inertia relative to distant masses.
- As proposition that the universe at large influences local physics (Dicke-type approach).
- As selection principle of solutions of GR that are intuitively ‘Machian’.
- As requirement that dynamics should not contain absolute elements.
Hi Christine,
Thanks to Steven Coyler I’ve become aware that you have started up this new blog with a very interesting focus. However I’m not surprised by all the confusion about Mach’s principle, even as it being this concept which had Einstein to reconsider physics in terms of the relative position and action of things as opposed to Newton’s conception of the same within absolute space. What I consider one of the best reviews in respect to all this confusion is a book by Harvey R. Brown entitled “Physical Relativity; Space-time structure from a dynamical perspective”. Harvey R. Brown is a professor of philosophy at Oxford who recently completed a sabbatical out at Perimeter Institute and was fortunate enough to attend his public lecture there.
Now as you know I’m not a physicist yet simply someone who has had the physical sciences as a general interest for much of his life. In so being I would highly recommend Harvey Brown’s PI Lecture to those that consider themselves novices as in my opinion it gives one some sense of what the current controversy is about including the implications. You might be also interested to discover that Prof. Brown began his career as an Assistant Professor in Department of Philosophy, São Paulo State University in Brazil from 1978-1984. Also you might find it interesting that while there he wrote a book called “ Albert Einstein: A simple man of vision” which is only available in Portuguese which has always had me intrigued as to what it was about.
Steven and some of your reader might also like to know that much of the book “Mach’s Principle” by Barbour & Prister is open for reading at Google book’s. With that said I find it interesting that Harvey Brown makes several references to Barbour in his book “Physical Relativity”. A quote of Barbour’s that Brown makes note of in his book you migh find relative (no pun intended) which I find emphasises what to lie at the very heart of much of the confusion and is as follows:
“Minkowski, Einstein, and Weyl invite us to take a microscopic look, as it were, for little featureless grains of sand, which closely packed, make up space time. But Leibnitz and Mach suggest that if we want to get a true idea of what a point of space-time is like we should look outward at the universe , not inward into some supposed amorphous treacle called the space-time manifold. The complete notion of a point of space-time in fact consists of the appearance of the universe as seen from that point. Copernicus did not convince people that the earth was moving by getting them to examine the earth but rather the heavens. Similarly, different points of space-time rests ultimately on the existence of different (coherently related) viewpoints of the universe as a whole. Modern theoretical physicists will have us believe that the points of space are uniform and featureless; in reality they are incredibly varied, as varied as the universe itself.”
-Harvey Brown quoting Barbour, “Physical Relativity; Space-time structure from a dynamical perspective”, page 14.
Best,
Phil
P.S. I will be following this blog regularly to see where you might be taking all of this.
P.S. Christine you will find I reposted my comment as I found some errors in the first and now also have a Word Press account. Please feel free to erase the first or any of course
Phil Warnell
December 30, 2010 at 10:05 AM
Hi Phil!
It’s very nice to “see” you here, and thanks for your interest. As usual, a very informative comment that certainly enriches us. Brown’s book is now on my reading list and I’ll watch his lecture opportunely.
Kind regards,
Chistine
PS: I removed your first post and kept the second, corrected one. Sorry for not having for now a preview tool.
ccdantas
December 30, 2010 at 10:20 AM
[...] I had to give a long break in our tensor course. More on that sometime. Now I have to get back a little to what I had promised in one of my first posts, concerning Mach’s Principle. [...]
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