Extrapolated Light Frame (3)

If we consider time as the rate at which events progress at some point,
then what is the shortest duration in which separate events can occur?
If we look close enough, will we see the fastest possible clock in a
state between two events?

In other words, if we were to observe an object in motion, is there some
point at which the object could be observed to be occupying two
positions (between one point and another).

This concept was first raised by Zeno. There are various hypothetical
solutions. One can calculate to any precision where an object should be
at any point in time. But that does not explain how an object can
arrive at another point after some infinitesimal interval.

One solution is to consider a minimum interval, such as Planck's time.
At each of these tiny intervals the object can be found to have moved an
infinitesimal distance.

There seems to be no reason to pursue this further. However, it is not
an infinitesimal interval recorded on the E.L.F clocks, it is no time.
The instant of the transit, that takes not Planck's time but no time at
all, may last for seconds, minutes, or billions of years according to
any non-E.L.F. frame.

Thus the "instant" when things actually happen, when change actually
occurs, can be longer than Planck's time. Put another way, the
"present" is an instant (absolute minimum duration possible) at any
given *point*, but for any two points that are spatially separated, the
instant of "now" or the "present" has temporal extension.

= = = = = = = = = = = = = = = = = = = = = = =

The passage of time at any point can be trivially accounted for by the
passage of time on a clock at that point. We ask whether the passage of
time on any two points in the same inertial frame is equally as trivial?

Consider the two points, A and B, in the same inertial frame and
separated by one light second.

In the Extrapolated Light Frame, B's clock is at +1s when A's clock is
at zero (E.L.F. object C travelling from A to B).

Whilst the observer at A can count B's clock at 0 when C leaves, and
that events can occur at B whilst C is in transit, A can not causally
effect B in any way whatsoever during the transit of C. The two points
are causally connected in the E.L.F. frame.

This is just Minkowski's light cone approached from a different
direction.

But we also observe that whilst the passage of time, showing the
evolution of events at, say, A, can be trivially calculated simply by
placing a clock at A, events that occur at A+B are not so trivial. It
takes time for the instant of the present moment to expand to the entire
set of points A and B.

To calculate the passage of time for two spatially separated points we
can apply a simple formula:-
dT(AB)=dTa-[A-B]/c^2
that is, the change in time, or the progression of time, for frame AB is
the passage of time (delta T) at any point (eg A or B) minus the
temporal extension of the frame. That is, the time it takes for a
photon to transit the distance between A and B.

Lets say 10s passes on the clock at A. How much time passes for the
entire frame AB ie how many one second events can occur?

dT(AB)=10-1=9s

If the event is a photon being reflected from A to B, then in A's
measure, 9 events can occur in 10s by local time.

Where this math becomes more interesting is where we consider the very
large scale. If the universe is as old as the expansion is wide, then
if the oldest proton is 13 billion years old and the universe has
expanded by 13 billion light years then
dt=13billion-13billion=0

Whilst time may have passed at some point in the universe, time for the
entire universe remains at zero ie this *is* the instant of the big bang
by the measure of the entire universe.

= = = = = = = = = = = = = = = = = = = = = = =

We note also that (returning to A and B separated by 1Ls in the same
inertial frame), that if the E.L.F. object C leaves A at 0s, object B
must exist at 1s ie no change can occur while the object C is in
transit. This only reflects the light cone in that there is no way that
A can be causally involved in the evolution of events at B.

That the two points exist at the same time in the E.L.F. frame is
logical and easily shown to be true. But for very distant objects, say
1 billion light years away, we can show that when the E.L.F. object
brings information of the distant object as it is now according to the
E.L.F. frame, by our measure the distant object has another 1 billion
years on their clock.

But the fact remains that if a common event occurred that effects both
the distant and local object, say 1 billion years in the common past,
that:-
dT(AB)=dTa-[A-B]/c^2 therefore
dTa=[A-B]/c^2+dT therefore
dTa=1 billion+1 billion=2billion years
That is, if an event occurs in the common past of two objects spatially
separated, then you must add the common interval to the interval of
separation to find the total amount of time that must pass at either
object.

That assumes that they retain their common separation distance. If the
event was a collision between A and B, then that event occurred when
there was no spatial separation.

--
Kind Regards,
Robert Karl Stonjek.