GODEL'S PARADOX

     Godel talking to Einstein said "It's fine for time to be relative,
but its not fine for existence to be relative." (My words).

     Take a standard Minkowsky space time diagram with two observers.

     Time is the vertical axis and X is the horizontal access.

     Positive time is up and postive space to the right.

     Observer A and B are both on the same spot of space time at each
other's respective Minkowsky Zero Point (MZP), namely 0,0 on the time
and X axes.

     Observer A is 'stationary' and observer B is moving to the right at
Gamma .866 or half the speed of light.

     Gamma .866 means A and B will measure each other's meters to be
.866 meters long, and each other's seconds to be 1/.866 or 1.15 seconds
long.

     The diagram is a snap shot is taken at the exact moment the two
observer's cross each other's path at their now coincident MZP for each
of them.

     For the stationary observer A, his now line is the X axis.

     For the moving observer B, his now line is slanted upwards and to
the right 26.56 degrees or the arctan of .5 (half the speed of light).

     By definition an observer's now line is the locus of all space time
points that happen at the same time, thus A and B have a different
concept of what is 'now' for them and who or what occupies that now at
the time the diagram is made.

     Notice that at the MZP, both observers are at 0,0 in their own
coordinate system and are also in fact on the same space time point in
the diagram.  B is however moving past A at .5 the speed of light to the
right.

     Further notice that if two different events happen at the same
space and time for one observer, they will happen at the same space and
time point for all observers, although each observer may label those
space and time points differently.  In other words they are on same
point on the diagram with two different assigned coordinates to them.

     Now consider that all that 'exists' is now and now is all that
exists.

     Existence is the locus of all space time points that exist for each
observer and from which cause may be issued.

     Things that are in the past no longer exist and can no longer
affect us or anything else.

     Things that are in our future do not exist yet, and also can not
affect us or anything until they come into the present.

     Only those things that exist NOW can cause anything.

     Yet both observer A and B have different concepts of the locus of
space time points which contain things in their respective but different
nows and which thus exist in such a way as to be able to cause something
to them or anyone down the road.

     Any point on the X axis to the right of observer A is in his now
and thus can issue a casual wave from that point of spacetime.

     But that same point is below the now line of B and thus is in B's
past, and thus can no longer issue a causal wave to affect anything.

     So each observer has two different concepts of what exists now and
is or can be causally active.

     Worse for an observer C moving to the left, his now line is slanted
to the right and DOWN, and thus that same point on A's now line, is
ABOVE C's now line and thus is in C's FUTURE and hasn't yet become
causally active for C.

     How then can there be multiple different collections of points in
space and time that all exist or do not exist according to the movement
of the observer?

     Worse, motion is relative, any observer can consider him self still
and the others moving.

     So if we remove A and C from the above diagram and leave B, his now
line does not change, it continues to slope to the right and up, and
clearly indicates to him the locus of existing things to the right an up
of his present location at his MZP.

     Likewise if we remove A and B from the diagram, C's now line does
not change either, it still points to the right and down, yet it points
to a completely different selection of what exsits now and is causally
active than either A or B.

     So how can existence be relative to different observers?

     What does it mean to exist at a location in space time where you
are not and how can that existence depend on whether or not you are
moving?

     Homer

------------------------------------------------------------------------
Homer Wilson Smith   Clean Air, Clear Water,    Art Matrix - Lightlink
(607) 277-0959       A Green Earth, and Peace,  Internet, Ithaca NY
homer@lightlink.com  Is that too much to ask?   http://www.lightlink.com
Mon Jul 11 22:06:17 EDT 2016