🚀 go-pugleaf

On Jun 22, 6:48 am, GSS <gurcharn_san...@yahoo.com> wrote:
> 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.
>
> GSShttp://www.geocities.com/gurcharn_sandhu/index.html- Hide quoted text -
>
> - Show quoted text -

Gravity is round curvature.

Mitch Raemsch