🚀 go-pugleaf

On Jun 21, 5:18 am, jem <x...@xxx.xxx> wrote:
> John Kennaugh wrote:
> > GSS wrote:
> >> On Jun 12, 6:31 pm, jem <x...@xxx.xxx> wrote:
> >>> John Kennaugh wrote:
> >> .........
> >>>> How a mathematical abstraction (a FoR) can posses the same physical
> >>>> properties as the aether and force light to propagate every which
> >>>> way at
> >>>> c when it defines physical space which those same relativists are
> >>>> adamant contains nothing physical - no aether - is absurd.
>
> >>>> I have Tom Roberts in effect saying "never mind the physical, jump in
> >>>> the maths is luverly." The maths works provided you have complete
> >>>> freedom to redefine anything which prevents it from working and you
> >>>> accept the modern view that physical interpretation is not only
> >>>> unnecessary but a singularly bad idea.
>
> >>> The math of *every* physical theory has a direct link to measurement,
> >>> and that link /is/ the "physical interpretation".
>
> >> Do you consider GR to be a physical theory?
> >> If so then where is the direct link of *space curvature* to
> >> measurement?
>
> The link mentioned above is between real-world measurements (e.g.
> ruler and clock measurements) and the variables (e.g. x,y,z,t) of
> physical theories (e.g. GR).
>
> >> In reality you can neither physically measure the space curvature nor
> >> describe a technical procedure for measurement of space curvature even
> >> in principle. You cannot even define the space curvature in physical
> >> terms (other than the usual mathematical definition in GR).
>
> In reality, you don't know what you're talking about.
>
Well, let me then explain the physical significance of the popular
term 'space curvature'.  Strictly speaking, the term 'space curvature'
implies 'deformation of space' induced by a change in its metric
(other than through the admissible transformation of coordinate
system). Let us first start with a spacetime curvature.

1.     An important mathematical notion of spacetime curvature had
dominated the fundamental physics during the last century.
Mathematically however, the term 'spacetime curvature' implies a non-
zero value of the Riemann tensor computed from the metric coefficients
of the 4D spacetime manifold.  In any gravitation free region of
space, the metric of 4D spacetime manifold may be represented by
g_ij(x) such that the corresponding Riemann tensor is zero and an
infinitesimal separation distance  ds  between two neighborhood
points  P(x^i)  and  Q(x^i+dx^i)  is  given  by:
     (ds)^2 = g_ij dx^i dx^j               ..................... (1)
However, in the same region of space under the influence of a
gravitational field, the metric of 4D spacetime manifold will be
represented by h_ij(x) (as per EFE) such that the corresponding
Riemann tensor is non-zero and an infinitesimal separation distance
ds'  between the neighborhood points  P'  and  Q'  is  given  by:
    (ds')^2 = h_ij dx^i dx^j               ..................... (2)

2.     To distinguish between a rigid and a deformable continuum of
space points, let P be any point in this continuum and P1, P2,  ....
Pn  be n points in the neighborhood of P. Let ds_1 be the separation
distance between points P and P1, ds_2 be the separation distance
between points P and P2, ..., ds_n be the separation distance between
points P and Pn. If these separation distances ds_1, ds_2, .... ds_n
from point P to all of its neighborhood points, remain constant under
all circumstances, then the continuum under consideration can be
regarded as rigid. If under certain circumstances, these separation
distances change to say ds_1', ds_2', .... ds_n'  then the continuum
under consideration will be regarded as deformable. Since the
separation distance ds between two neighborhood points of the
spacetime continuum does change under the influence of gravitational
field (as per GR), the spacetime continuum is assumed to be deformable
in GR.  Considering only the spatial components of the metric tensor,
it can be shown that the separation distance ds between two
neighborhood points of the space continuum also changes under the
influence of gravitational field (as per GR). Therefore the space
continuum is also assumed to be deformable in GR.

3.      Obviously, whenever the separation distance between
neighboring points P and Q in the space continuum, changes from ds to
ds' it implies a relative shift in the original positions of P and Q
to the changed positions say P' and Q' such that arc element P'Q' =
ds'.  This relative shift in positions of P and Q to the changed
positions P' and Q' may be referred as the relative displacement of
these points. Specifically, the vector PP' may be defined as the
displacement vector U and the corresponding displacement of Q to Q'
will then be represented by the incremented displacement vector U
+dU .   Hence, whenever  the separation distance ds between two
neighboring points P and Q changes to ds' as given by equations (1)
and (2), the associated displacement vector field U will be defined at
all points P of the space continuum.
The deformation of the continuum can be said to be fully determined
when the displacement of every point P in the continuum is known or
uniquely determined.  The existence of displacement vector U at every
point P as a function of position coordinates of P will constitute a
displacement vector field U in the continuum.  The displacement vector
from point P(r) to P’(r') is given by the relation,
      U  =  r' – r
           =  u^i a_i        ………………….  (3)
where u^i are the components of vector U  and r, r' are the position
vectors of P and P'.

4.      In general the  displacement vector field U in the space
continuum will be a function of space coordinates and time.  As such
the time dependent deformations of physical space, that could be
represented through a time dependent displacement vector field U, may
be described as the space-time distortions.  The representation of
space-time distortions through displacement vector field U is far
superior than its current representation through spacetime curvature.
The space and time derivatives of U  will correspond to the strain
tensor field in the space continuum.  Since the above referred time
dependent deformations in the space continuum are reversible, the
physical space continuum can be assumed to be elastic in nature.
Hence logically the displacement vector and strain tensor fields will
also be accompanied by the corresponding stress tensor field in the
physical space continuum. The study of space-time distortions through
the detailed study of corresponding displacement vector, strain tensor
and stress tensor fields in the space continuum may be termed as space
dynamics.   I believe that a detailed analytical study of space
dynamics can provide us a valuable insight into the fundamental
structures of various elementary particles and their interactions.

GSS
http://www.geocities.com/gurcharn_sandhu/index.html