🚀 go-pugleaf

On Jan 30, 5:30 am, Pentcho Valev <pva...@yahoo.com> wrote:
> http://hem.bredband.net/b153434/Works/Einstein.htm
> Divine Albert: "In a space which is free of gravitational fields we
> introduce a Galilean system of reference K (x, y, z, t), and also a
> system of co-ordinates K' (x', y', z', t') in uniform rotation
> relatively to K. Let the origins of both systems, as well as their
> axes of Z, permanently coincide. We shall show that for a space-time
> measurement in the system K' the above definition of the physical
> meaning of lengths and times cannot be maintained. For reasons of
> symmetry it is clear that a circle around the origin in the X, Y plane
> of K may at the same time be regarded as a circle in the X', Y' plane
> of K'. We suppose that the circumference and diameter of this circle
> have been measured with a unit measure infinitely small compared with
> the radius, and that we have the quotient of the two results. If this
> experiment were performed with a measuring-rod at rest relatively to
> the Galilean system K, the quotient would be [pi]. With a measuring-
> rod at rest relatively to K', the quotient would be greater than [pi].
> This is readily understood if we envisage the whole process of
> measuring from the "stationary" system K, and take into consideration
> that the measuring-rod applied to the periphery undergoes a Lorentzian
> contraction, while the one applied along the radius does not. Hence
> Euclidean geometry does not apply to K'."
>
> Why does Divine Albert believe that, "with a measuring-rod at rest
> relatively to K', the quotient would be greater than [pi]"? Obviously
> because "the measuring-rod applied to the periphery undergoes a
> Lorentzian contraction". Then why does the segment of the periphery,
> to which the measuring-rod is applied and which moves together with
> the measuring-rod, fail to undergo a Lorentzian contraction?
>
> In 1902, in "La Science et l'hypothese", Henri Poincare, in order to
> justify non-Euclidean geometries, presented a parabole. Bidimensional
> creatures live on a disc. The disc is heated under its center so that
> the temperature is high at the center and decreases towards the
> periphery. The creatures use rigid measuring rods in order to
> determine the geometry of their world. They know nothing about the
> heater and accordingly discover that the ratio of the circumference
> and the diameter is greater than [pi]. The creatures conclude that
> Euclidean geometry cannot be true on their disc.
>
> Pentcho Valev
> pva...@yahoo.com

xxein:  We are K' to any other observer (gravity or not).  For your
question (sans gravity) who would not be K'?  How do WE get pi?

Perhaps the answer is that we measure the circumference in segments
with the ruler.  Likewise, we measure a radius in the same way.  As
you might realise, any rotation wrt the direction of motion will cause
both measurements to vary in exactly the same way.  But even without a
rotation, there is a necessary rotation of the ruler and you can still
see the mapping of the ruler and and the circumference/radius as being
a co-temporary measurement regardless of the actual shape (< circular)
to K (zero v in a simplified and flat ether system).

Bell is both right and wrong.  K' is not a circle/sphere, but pi still
remains the differential measure for those of K'.

We ARE K'.  We cannot rationalize any differently.  A logic prevails.
There is no paradox.