THE PHYSICAL TRANSFORMATION EQUATIONS

I have argued before that the physical SR transformation equations
cannot be simply applied directly to all events in the physical
reality,
so here I shall attempt to show the manner in which I argue that they
can be applied to all events in the physical reality.

I will assume here that if, in the transformation equations, the
variable
t is identified as a physical time, the equations are dynamic in
nature
and, physically, MUST involve the transmission of light within both
inertial frames. I have argued this before, and assume I needn't
lengthen this post by repeating it again here. The necessary dynamic
circumstances can be illustrated as follows:

A rod AB lies along the x axis of a primed (moving) frame, and moves
at velocity v, parallel to the x axis of an unprimed (stationary)
frame.
A light pulse is emitted at A, forming event A, transmitted to B,
forming event B, and reflected back to A, forming a second event A.
I will therefore examine a first interval, A to B, which I will call
AB,
describing the transmission of light from A to event B, and a second
interval, BA, describing the transmission of light from B to the
second
event A. D represents a macroscopic interval, to distinguish it from
a differential, and I use capital T and X, so I can more easily write
subscripts Ta and Xa.

The transformation equations for the first interval, AB, are:

DX' = g(cDT -v DT)
DT' = g(DT - (v/c)DT)

here DX is written as cDT, because this represents the intrinsically
dynamic nature of the physical equations, in which light scans
coordinate values along the x axis, thus dynamically creating,
or measuring, spatial intervals over time.

The transformation equations for the second interval, BA, are:

-DX'a = g(-cDTa - vDTa)
DT'a = g(DTa + (v/c)DTa)

where DT'a = -DX'a/-c. DX'a, DXa (cDTa), and c, all have a negative
sign, to indicate their negative direction. We now have to get the
coordinate values of the second event A, which will be obtained by
adding the above interval transformations, which I will later refer to
as 'components' of a final equation:

x' = DX'-DX'a = 0
t' = DT' + DT'a

DX' - DX'a = 0 = g(c(DT-DTa) - v(DT+DTa))
or DT-DTa = (v/c)(DT+DTa)

then DT'+DT'a = g((DT+DTa)- (v/c)(DT-DTa))
= g(1 - (v/c)^2)(DT+DTa) = (1/g)(DT+DTa)

so we have, for event A

x' = 0
t' = (1/g)t, where t = DT+DTa

The generalised transformation equations, as physical equations,
which can be applied to all events, of both type A and type B,
therefore must have the form

x' = g(DX - vDT) - g(DXa + vDTa)
t' = g(DT - vDX/c^2) + g(DTa +vDXa/c^2)

where DX > vDT, and DXa > vDTa. Referring to events of the kind B,
the first components of the equations represent coordinates, and
the second components are zero. Referring to events of the kind A,
both components exist, and the stationary frame coordinates are
represented by the sums of the relevant parts of the components
(such as Dx + DXa, etc.).

One might ask: since the final equations, when converted to
coordinate equations, have the usual forms, such as x' = g(x-vt),
could we not incorporate all the above in the normal coordinate
equations, which simply refer directly to the final result, without
the need to refer to interval transformations?

But I ask: how can it be claimed that the physical reality is
explained, if it is described by, as it were, transcendent, static
equations, which make no mention of the necessary dynamics
intrinsic to the actual reality? I would say that such a claim
must lack credibility in the sense that, if such details are not
explained, the matter is merely declared, and is really not
explained at all. What is worse, such a deficiency can even
encourage misinterpretation.

The dynamical, physical reality does not manifest what kind
of static reality, if any, underlies it. The reality thus does not
allow it to be assumed that the transformation equations,
written from a static, spacetime viewpoint, are unmistakably
geometric in nature, in the sense of representing a spacetime
rotation. They are not manifestly a rotation, and could, therefore,
possibly not be.

In the case of any equation like x = ks, for example, where
k< or =1, people might say: oh - that represents the rotation
of s through an angle A, and the projection of s onto the x axis
as, x = sCosA. But there might, physically, be no rotation,
and k might just as well represent, for example, a scale change,
or even a mechanistic ratio. In the same way, the SR
transformation equations are geometric rotations only in the
chosen interpretation, which could, therefore, be incorrect.
And I have argued before that it can be shown to be incorrect.

Alen

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