On Sat, 5 Nov 2011 06:40:00 -0700 (PDT), Daryl McCullough <
stevend...@yahoo.com> wrote:
>For the various thought-experiments involving rockets and clocks and
>measuring rods and poles and light signals, Special Relativity can be
>developed with a small number of assumptions about the way that clocks
>and rods behave. The rest is all pure mathematics, deriving consequences
>from assumptions. If someone thinks that SR is contradictory, (and that
>this can be shown using thought experiments of various types), then they
>should be able to derive a contradiction from the following assumptions:
>
>We will make use of the following concepts:(A) ideal clocks,
>(B) ideal measuring rods, (C) light signals, (D) an inertial
>path of an object, (E) a "standard inertial coordinate system".
>These concepts are related through the following axioms:
>
>Definition: A coordinate system, is a way of associating four
>numbers, x,y,z,t, with every point in space at every time.
>
>Assumption: there exists a coordinate system and a real number c
>making the following true:
>
>1. An inertial path is defined by three functions x(t), y(t),
>z(t) satisfying dx/dt = constant, dy/dt = constant, dz/dt = constant.
>2. A light signal follows a path that is an inertial path such that
>(dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2 = c^2.
>3. An ideal clock in motion shows an elapsed time T satisfying
>dT/dt = square-root(1-(v/c)^2), where v is the current speed of
>the clock.
>4. An ideal measuring rod that has length L when at rest in the
>coordinate system, will have length L' when traveling at speed
>v in the direction of the orientation of the rod, where L' is
>given by: L' = L square-root(1-(v/c)^2)
>5. An ideal measuring rod that has length L when at rest in the
>coordinate system, will still have length L when traveling at speed
>v in a direction perpendicular to the orientation of the rod,
>
>A coordinate system satisfying 1-5 will be called a "standard
>inertial coordinate system". So the assumption is that there
>exists at least one standard inertial coordinate system.
>
>Here's the challenge for anti-relativists: can you show that
>assumptions 1-5 are contradictory? Note what's missing from
>these assumptions: there is NO mention of "relativity" at all.
>There is no mention of equivalence of different observers.
>There is no mention of observers at all.
>There is no mention of laws of physics having the same form
>in every inertial frame. All the claims 1-5 are only claimed
>to be true in one, specific coordinate system.
>
>So, does anyone believe that 1-5 are contradictory? If so, show
>it: derive a contradiction from 1-5.
>
>If not, then you have agreed that SR is consistent, at least as
>far as thought experiments involving clocks, rods, light signals,
>rockets, etc. The "relativity" part of SR is actually *PROVABLE*
>from 1-5, without making any additional assumptions.
>
>Theorem, if (x,y,z,t) is a coordinate system satisfying 1-5, then
>so is any other coordinate system (x',y',z',t') related to the
>first through one of the following transformations:
I think you could significantly clarify this by saying the following:
At any given instant, in any local frame, one can accurately describe
what will be S-E-E-N in any other arbitrarily defined frame moving wrt
it by computing the coordinates using the above methodology. However
no one can claim that what is seen in this fashion is the actually
situation at those location at that instant. This is as far as you
can 'scientifically' get with this.
Since this is ALL that can be said, such things as observed pole
lengths, light flashes, ... etc. measured at remote locations by
use of light signals which are limited to traveling at light speed
have inherrent signal delays. Couple that with a directiomal physical
length contraction with speed and such remote observations can and
DO result in a distorted perspective. Thus may not reflect the actual
physical situation of objects at the very same instant. This is the
crux of the issue, what you see may not reflect actual reality. Just
like watching the Magician's trick from the perspective of the audience.
>* Rotations.
>* Translations.
>* Lorentz transformations.
>
>So if 1-5 hold in *any* coordinate system, whatsoever, then they hold
>in *every* standard inertial coordinate system.