> Now, consider the set of all integers. Some of these will represent
> Universe State Strings (USS's). By the rules of QM, each USS can be
> converted to another USS.
Ok, another USS...
> If we confine ourselves to one Feynman interaction per conversion,
> then each USS can convert to a finite number of other USS's,
Now we've gone from "another" to "a finite number." Are you sure
there will be more than one?
> One way to visualise this is to imagine a line or grid of dots
> representing the integers... The integers which represent
> possible USS's are marked in some way (say red dots).
> Each red dot has lines running to other USS's, each line representing
> an allowed QM interaction.
Ok, so there are lines, plural; and...
> Note that each red dot also has INCOMING lines,
> representing the set of possible ancestor USS's.
Again there are lines, plural. But is this necessary?
Imagine a grid of dots, some red, some "off". The red ones represent
possible states of the universe, the others represent impossible states.
What if you take a point in the latter group, one of the "off" points:
Does the concept "Feynman interaction" still apply to it?
Does it too have lines leading to other points?
If so, do all its lines lead to other "off" points, or could some of them
lead to red points?
In other words, could you have a situation where each red point
has more than one line leading into it, but only one of those
incoming lines comes from another red point?
Suppose each red point does have more than one line leading out,
toward other points. Does it follow that each red point has more than
one line leading into it? No! Consider:
Let the integers be represented by points on a line. Suppose numbers
divisible by three are red: 3, 6, 9, 12, etc. All other numbers are "off."
Suppose each point n has two lines leading out, one going to 3n + 1,
the other going to 3n + 2.
Each point has two outgoing lines.
Each point has at most one incoming line.
Red points have no incoming lines.
Of course this universe would die out quickly; I'm just using it as an
example to show that it is possible to have more than one line leading
out of each point, without having more than one (or any!) leading into
the red points.
So, your conclusion,
> One point to notice here is that every state of the Universe
> comes from a large and finite number of possible past states,
> that there is NO single past.
is far from obvious, at least to me. Maybe I'm missing something.
I hope so, because
> MIracles require absolute forgetfulness.
is too beautiful not to be true.
[PS Nadia, are you with us on this thread? Imagining grids of points,
and having them light up in various patterns and colors, is the
connection between art and mathematics. Mathematics, when you learn
to see it as it is, is like a laser show in a cathedral full of mirrors.]
Lyle