Regarding the discussion on the cause of gravitation:
>Davison: "... Everyone accepts gravitation and the equations associated with
>it, yet no one yet understands the cause of gravity. ..."
>
>DNAunion: Being a physics instructor, Bowman could surely shed more light on
>this than I can, and might even show that I am wrong, but I thought Einstein
>*did explain* the cause of gravity in his theory of general relativity.
I had planned on staying out of this, but since DNAunion has suggested
that I comment, I thought I would do so. In short, Einstein's theory of
general relativity (and some other similar metric theories of
gravitation) *do* explain gravitational effects in terms of the curvature
of spacetime locally produced due to the matter (more precisely, due to
the stress-energy-momentum tensor of the matter and radiation which
serves as the source of the curvature) present in that spacetime. But
the theory does not explain *why* the matter/radiation's stress-energy-
momentum tensor causes the spacetime to curve in the first place.
It is true that Newton's theory of gravitation explained the mathematical
relationships of how masses seemed to attract each other via
gravitational forces (within the limits of that theory). But that theory
did not explain *why* such forces should be so exerted (& Newton's
comtemporary critics considered this to be a defect in the theory).
Einstein's theory *did* solve this immediate 'why' question by answering
the related 'how' question. Einstein's theory shows how the mathematical
formalism of Newton's theory is the automatic consequence of the simple
requirement that gravitating matter follows (in the absense of other
force fields) timelike (or null, in the case of massless radiation)
geodesics (i.e. straightest possible paths) in curved spacetime (which
describe the equations of motion of the matter/radiation), and that the
spacetime's curvature is itself determined by the stress-energy-momentum
of the matter present (according to Einstein's field equations). Both of
these sets of equations (i.e. the equations of motion for both the matter
and for the spacetime the matter is in) are automatic consequences of
Hamilton's Principle of least action where the action to be minimized is
the so-called Hilbert action. What Einstein's theory does *not* explain
is *why* the Hilbert action ought to be the relevant action in the first
place for the interacting system of the matter/radiation and the
spacetime it is embedded in. Nor does it explain *why* Hamilton's
Principle ought to apply to it so that that action ought to, indeed, be
minimized in nature.
It is true that Feynmann (in his PhD work which developed the path
integral formulation of quantum mechanics) did show how, in general,
Hamilton's principle of least action for all forms of classical physics
(including even relativity theories) is itself an automatic consequence
of to the operation of quantum processes taken to the classical limit.
What was left unexplained was *why* the underlying rules of those quantum
processes ought to be what they are.
This is a general feature of the development of physical theory. At any
given level of development a given theory has some features which are
just *given* with no reason (other than that the logical consequences of
those features happens to describe behaviors that agree with experimental
observations). The theory is developed by working out the detailed
consequences of the axiomatic features, and is tested by making those
predictions/worked out results confront experiment & observation. When
that theory is superseded by a deeper more general theory, the axiomatic
features of the former theory are found to be logical *consequences* of
the deeper more general theory when it is restricted to the parameter
domain under which the original theory was found to be valid (or
asymptotically valid) as a special case of the more general theory. But
the new deeper more general theory has its *own* set of axiomatic
features that it doesn't have any explanation for as to why they ought to
be the case. Its just that the new set of axioms occur at a deeper level
of abstraction (than the corresponding axioms for the former theory), and
they involve (hopefully) fewer total a priori unmotivated assumptions
which are also more globally valid and which describe a much larger and
more general domain of phenomena than was described by the former theory.
The important point here is that the unanswered 'why' questions of a
given theory are answered as automatic 'how' consequences of the
processes of a subsequent deeper more general theory. Once the new
theory is adopted the unanswered 'why' questions become shifted to a
deeper level of abstraction and generality, but they *don't* disappear.
Even if a fully successful "Theory of Everything" is developed it will
still have some very profound unanswered 'why' questions.
DNAunion:
>In his generalizing of his theory of special relativity (which deals only
>with reference frames in uniform motion) to accelerated motion, Einstein
>stated that matter and energy warp four-dimensional spacetime, and that
>matter follows the straightest possible line through spacetime (which may not
>be a Euclidean straight line, because of the curvature of the 4 dimensions),
>that is, as has been said, "matter gets its marching orders locally". The
>more matter or energy concentrated in a particular area, the more the
>surrounding spacetime is curved/warped, correlating to what Newton would call
>a greater gravitational attraction in that area (Einstein does not consider
>gravity to be a true force because it can be transformed away: the affects of
>gravity are indistinguishable from the affects of acceleration, according to
>his equivalence principle, as Einstein explained in several thought
>experiments involving free-falling and intergalactic elevators).
Although a couple pedantic quibbles could be made with some of this, I
won't do so because, overall, it is a very nice layman-level overview.
DNAunion:
>So while Newton would have simply stated that two massive objects attracted
>each other more strongly than two less massive objects - but without giving a
>reason - Einstein would have *explained* that the greater attraction was due
>to the greater curvature of spacetime by the more massive objects.
True.
DNAunion:
>So isn't the *cause* of gravity the curvature of spacetime generated by
>matter and energy?
The curvature of spacetime is the immediate reason for how gravitation
affects the behavior of matter/energy. The theory of general relativity
doesn't give any reason for why the spacetime ought to curve the way it
does in the presence of the matter/energy that is embedded in it, other
than "that's just how it is" (and that that curvature pattern happens to
minimize the Hilbert action). Note that different metric theories
of gravitation differ with each other because they each have a different
action functional to be minimized (via Hamilton's principle) and each
different action functional generates different field equations that are
supposed to describe how spacetime curves in the presence of the matter/
radiation in it.
David Bowman
David_Bowman@georgetowncollege.edu
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