Re: Is spacetime curvature the source of inertia?

On May 30, 10:43 pm, Tom Roberts <tjroberts...@xxxxxxxxxxxxx> wrote:
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

Very concise reply, as always. As indicated by my previous post I'm
in general agreement with you. "Inertia" is not a property at all,
just a sentiment. An incorrect one at that. A mass doesn't have
inertia, it has mass. A mass doesn't exhibit inertia, it exhibits
conservation of energy and momentum wrt other masses. Just one of many
meaningless concepts still present in modern texts.


.

Relevant Pages

  • Re: Could Machs Principle be a real force?
    ... inertia recuperated the 18/02/2009) ... M a distant mass ... due to acceleration and is  what is responsible for inertia. ... and opposite  force due to all the forces in the whole universe. ...
    (sci.physics.relativity)
  • Could Machs Principle be a real force?
    ... inertia recuperated the 18/02/2009) ... M a distant mass ... due to acceleration and is what is responsible for inertia. ... and opposite force due to all the forces in the whole universe. ...
    (sci.physics.relativity)
  • Re: The Relativity of Motion in Space
    ... define motion relative to the inertia phenomena. ... space" If we imagine the universe in a perpetual ... Let us assume that inertial mass and gravitational mass ...
    (sci.physics.relativity)
  • Re: The Barnes & Noble Effect
    ... and we increase the mass of the universe, at that point he answers, ... How about an operational definition of inertia? ... wall of the bucket when the bucket rotates? ...
    (sci.physics.relativity)
  • Re: Uh Oh, Discrepancy Alert
    ... And that says nothing at all about pecks of "inertia". ... Newton's first law is the definition of the principle of inertia, ... You said before that "inertia is the measure of mass", ...
    (alt.machines.cnc)