Re: Is spacetime curvature the source of inertia?
- From: Tom Roberts <tjroberts137@xxxxxxxxxxxxx>
- Date: Thu, 31 May 2007 03:43:55 GMT
Todd wrote:
[...]
Good question, well phrased, but as I am not going to reply directly to your text I have omitted it. I will get to the question in the Subject.
The first problem to be faced is: what exactly is inertia? In modern physics there is no definitive answer to this simple question. For instance, there is no equation in which inertia is unambiguously represented by a specific symbol. One can get close, and find "inertial mass" (the m in F=ma), and also "moment of inertia" (which is really a moment of the mass distribution), but there is no symbol or equation for inertia itself.
Since Galileo, inertia has meant the property of an object that opposes changes in its motion. And about the closest symbol we have for this property is m, the mass of the object. But mass is different from inertia, as commonly conceived.
Mach thought that the inertia (and mass) of each object was related to the object's gravitational interactions with all the matter in the universe, primarily the very distant but very massive "fixed stars" (they are not really "fixed", but ignore that here). But Mach wrote in a mystical manner that is difficult to interpret, and left numerous different statements of his Principle; in any case he presented no equation to compute the inertia of an object.
Einstein thought a lot about Mach's ideas when starting on the path to GR, and he initially expected Mach's Principle to be a cornerstone of the theory. But this was not to be, and GR has only a distant echo of Mach's principle: in GR the mass of an object is intrinsic (i.e. unrelated to anything else in the universe), but the class of inertial frames at any given point is related to the mass-energy distribution throughout the universe by the field equation. In particular, even an empty universe (e.g. the Minkowski spacetime of SR) has "inertia" in the sense that each and every point in the manifold has a class of locally inertial frames, and test particles have mass (and follow straight-line paths relative to those locally inertial frames).
So let's look at your question in the context of GR: Is spacetime curvature the source of inertia? Interpreting "inertia" as mass: no. Interpreting "inertia" as the class of locally inertial frames at a given point: not really -- spacetime curvature in some sense _describes_ how the classes of locally inertial frames at different points are related, but this is not really any sort of "source" (in the sense of "generator" or "cause"); the closest one can come to a "source" is the total distribution of mass-energy throughout the universe, but that is not completely accurate as the empty universe shows.
But from the abstract you quoted there is an alternative interpretation that is only mildly strained: consider "source" not as the usual "generator" or "origin" (as in the previous paragraph) but rather as "implementation" or "realization" -- then it makes sense to consider spacetime curvature to be the realization of the various classes of locally inertial frames at different points in the manifold as it relates them to each other.
IMHO either the author of that abstract was using poetic
license in an inappropriate context, or was downright wrong;
I have never seen "source" used in this manner. But I have
not read the paper.
It is rather remarkable, however, that inertia remains obscure after so many centuries. Or maybe not: after all, phlogiston, caloric, and aether remain obscure, too -- perhaps this is an indication that they are not good models of the world we inhabit....
Tom Roberts
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