Extrapolated Light Frame

The Extrapolated Light Frame is frame that does not exist as such, but
the conditions of that frame can be calculated anyway by extrapolating
the properties and observations made in frames slower than light.

A second form of Light frame is one considered as "near light frame
rounded", that is, we consider a frame at a speed of
0.99999999999999999c but calculate using a two decimal place precision.
To two decimal places, the speed is 1.00c

We now consider observations made using the Extrapolated Light Frame.

Consider two points A and B at rest relative to each other and separated
by 1Ls in flat space.

Let clocks at A and B be synchronised (by using a laser light beam).

1) We ask if objects passing over A (object A') and B ( object B') at
1.0000c at '0' by clocks at A and B cross.

Object A' sees the clock at A showing '0' and the clock at B showing 1s.
Object B' sees the clock at B showing '0' and the clock at A showing 1s.
A clock half way between A and B, say point C (also synchronised) will
show 0.5 according to A' and 0.5 according to B'.

Thus the two objects cross. The time taken for A' or B' to reach C is
zero seconds and the distance to C is also zero. Thus the objects A'
and B' cover a zero distance in zero time.

2) We ask if events can occur at point A while A' is in transit from A
to B.

As no time passes for object A', it would seem that events can not occur
at point A while A' is in transit. This is because from the E.L.F.
frame, no time passes. But this also means that no events occur at A at
time zero. As time is required for events to occur, this is consistent
and logical.

When object A' arrives at B, observers at B will claim that events have
occurred at A during the transit of A'. But these events would have
occurred between time zero and time 1s. From the A' E.L.F., the clock
at A never progressed past zero during the transit.

3) We ask if events can occur at point B while A' is in transit from A
to B.

From the A' frame, the point B is already at +1s at the time of the
transit. It remains at +1s for the entire transit thus no events can
possibly occur during the transit of A'.

According to observers at A or B, however, the clock at B was not at +1
but at 0 when the object A' passed point A. Thus during the transit of
1s, events can occur at B.

The mind bending conclusion, however, is that in the ELF frame, the
clock at B is already at +1s and frozen during the entire transit.

4) What if the E.L.F. object is reflected at B?

As object A' passes A, the time at A is zero, the time at B is +1s.
After zero seconds, and after travelling zero distance in the E.L.F.
frame, the object arrives at B. For the return journey (assuming a
180deg change in velocity with no change in speed) the time at B is +1s,
the time at A is now +2s.

Despite there being no time on the A' clock, being still at zero, the
clock at A has progressed to +2s. When and how did this occur?

From the A frame, we note that light from the A clock could never catch
up to A'. This partially explains why A' never "sees" any change in the
A clock. But the same account does not follow for the time on the B
clock. The simultaneity calculation puts the clock at B at +1s at the
time that A' passes A.

Clearly the two events ie the transit from A to B and the transit back
from B to A, are completely separate and are not cumulative in any
simple way (for the Extrapolate Light Frame).

I'll consider the broader implications in a subsequent post.

--
Kind Regards,
Robert Karl Stonjek.