From Osher Doctorow

COPYRIGHT NOTICE
Observing The Double-Slit Experiment Can Change It Via PI
Copyright By Owner Osher Doctorow Ph.D.
First Published 2005

Let A be a light wave-particle (wave-photon) or even particle-field in
"modern" terminology very soon after it issues from a source of light,
let B be the double slit screen, let C be a plate behind B on which the
diffraction pattern forms under the proper conditions, and let D be an
observer who when he/she is involved observes B say by turning on a
light bulb near B. We'll also let A1 be whatever part of A goes
through one slit and A2 be the part of A that goes through the second
slit.

If A goes through B with splitting into A1 and A2 and then reunites by
the time it reaches C, then in Rare Events the set description is:

1) A--(A1 U A2)--A

where I have omitted reference to B for simplicity. We could claim
that A1 U A2 = A where U is "and/or" (set union), so that expression
(1) looks trivial, but watch this. Recall that the expression:

2) (V--W) = (definition) V' U W

for any V, W (sets/events). Also, although A = A1 U A2 in space, A1
and A2 constitute a separation of A at a different (later) time, so (1)
isn't trivial. The definition of (1) can comes from:

3) E--F--G = (E--F)(F--G) = (E' U F)(F' U G)

where adjacent parentheses represent interesting sets and (E--F) is
defined as E' U F, for any sets E, F.

Therefore, A--(A1 U A2) --A is the intersection of the set A' U (A1 U
A2) with the set (A1 U A2)' U A. The former is
A' U A1 U A2, the latter is A1'A2' U A. The intersection by the laws of
set theory is:

4) (A--(A1 U A2)--A) = (AA1A2) U (A'A1'A2')

I'll try to continue this shortly.

Osher Doctorow

From Osher Doctorow

I made a slight typo error in (4) which should be:

4' ) A--(A1 U A2)--A) = (A U A1 U A2) U
A1'A2'A'

and readers may recognize the right hand side as A--A1--A2. Taking
the probabilities of both sides then yields:

5) P(A--(A1 U A2)--A) = P(A--A1--A2)

which is the probable correlation among A, A1, and A2.

So we're dealing with entangled objects by the definition of
entanglement.

Osher Doctorow

From Osher Doctorow

By the way, in practice I'm going to drop the time condition on A
because I'm going to identify A as the same object at the different
times in the experiment. Notice that otherwise A--(A1 U A2)--A
wouldn't describe the experiment.

Let me explain that if A--B--C reduces to A--B--C for any
sets/events A, B, C, then these sets/events have to be "entangled" in a
causal sense or a mutual influence sense. P(A--B--C) is their
probable mutual influence, which is entirely the probability of the
original set P(A--B--C), so there's no "spurious" correlation
reflected in these expressions but only probable correlation. Recall
that causation is non-spurious correlation, that is to say that
correlated events can either be causally related or spuriously
("coincidentally", "non-causally") related.

Next, if observer D observes A1 U A2 at B, what does that do in terms
of probable influence?

Let's consider more generally D observing any event E or let's say
event E influencing D via light waves or D influencing E via light
waves. Consider this:

1) P(E--D) = what with regard to P(D--E)?

Well, we have:

2) P(E--D) = 1 + P(ED) - P(E)
3) P(D--E) = 1 + P(ED) - P(D)

So we get:

4) P(D--E) - P(E--D) = P(E) - P(D)

and therefo

5) P(D--E) = P(E--D) + P(E) - P(D)

In Rare Events, one-way observation D--E (light wave from some object
impinges on the object/event E) has an "equal and opposite reaction"
E--D probabilistically provided that the probabilities of the events
E, D are equal. The closer the probabilities of E and D are to each
other, the more does the equal and opposite observation reaction
scenario hold. You can see this by setting P(E) = P(D) in equation
(5), and by making P(E) very close to P(D) in equation (5), so that it
follows that P(D--E) equals or is close to P(E--D) in the respective
cases.

This has nothing to do with consciousness, although I'm a believer in
consciousness. There was no mention of consciousness in the above.

Osher Doctorow

From Osher Doctorow

Now we're in a position to see why quantum events and not so much
classical/macroscopic events have entanglement.

What happens when P(E) and P(D) in the equation (5) of last time are
both small, i.e., for Rare Events? Then P(E--D) = approximately
P(D--E) but also both are very large because:

1) P(E--D) = 1 + P(ED) - P(E)

and for very small P(E), close to 0, P(ED) is close to 0 by
monotonicity of probability and so P(E--D) is close to 1 and hence
P(D--E) is close to 1 ("total probable causation"). Also, we have:

2) P(E--D) = P(E--D) + P(D--E) - 1

as is easy to verify from the definitions, and hence we have:

3) P(E--D) is very close to 1 when P(E), P(D) are very close to 0

But isn't everything in the quantum realm a Rare Event? Not
necessarily. Light and electron-waves arguably are Rare Events. Other
quantum massive objects may not be. The gravitational, strong and
weak nuclear forces behave very differently from the electromagnetic
force.

But on a macroscopic scale, "macroscopic entanglement" would
theoretically be possible if P(E) = approximately P(D). Macroscopic
events can have very low probabilities just as much as quantum events,
there's a definite tenency for high probability events to be very much
observable on Earth especially if probability is high for high masses
(planets, the Sun, and even large mountains and buildings and oceans
and rivers).

Osher Doctorow

From Osher Doctorow

Was dropping the time condition on A justified? Yes, because time is
implicitly involved in Birkhoff causation and hence in PI. In fact:

1) P(A--A) = P(A' U A) = 1 for all events A

The -- operation and causation itself involves an implicit time,
although it can be "infinitesimal".

What about the fact that:

2) P(A--A) = P{(A--A)(A--A)} = 1

Which version of A, the earlier or later time version, is involved?
In (2), both. But even in (1), whenever an object/event/process
returns to approximately its original spatial (or other non-time)
state, there is some "reaction" in the opposite time direction
involved. This also relates to quantum erasure. In scenarios not of
this type, the role of time is often irrelevant even in PI, though it
is good to keep an eye on macroscopic scenarios where time is important
rather than just independent or nearly independent (often markov)
processes.

Osher Doctorow

From Osher Doctorow

What about space? What does PI have to say about space?

Well, pick a question, as they said in Hitchhiker's Guide to the
Galaxy. Any question. How about Stokes' theorem? How about more
generally boundaries?

OK, let's find a property of PI that tells about boundaries, and also
answers something else. The movie already talked about the meaning of
life and the universe, so let's try a new one. How about, the meaning
of probability?

So let's see: a want a property of PI that tells us about boundaries
and the meaning of probability. Here's the property:

1) P(A) = P(A' -- A), P(A' ) = P(A -- A' )

This says that the probability of A is the probable influence of its
outside or complement on A, and the probability of A' ("outside of A)
is the influence of A on its outside.

Why the difference between P(A) and P(A' )? ( By the way, from
elementary probability P(A' ) = 1 - P(A) .) According to (1), the
probability of any set/event is its probability as an effect, i.e., as
an object of probable influence by its outside. That's common to both
equations in (1), although since a Rare Event A is in a sense
distinguished (by P(A) = 0 or = epsilon close to 0 and positive), we
see that the probability of a Rare Event increases the more its outside
exert(s) probable influence on it. Actually, this also holds for any
event, but it's especially interesting for Rare Events because their
outside is Non-Rare Events, and the smaller the probability of a Rare
Event, the more Rare it becomes, and at the same time the less
influence do Non-Rare (Fairly Frequent, Very Frequent) events have on
it probabilistically.

Aren't we defining probability in terms of probability here? First of
all, it's not a definition. It's more like the category of "the
meaning of life". If we take probable influence or probable causation
as a primitive notion, then we get probability in the opposite
direction. In more roughly deterministic language, probability is
something like "influenceability", and 1 - probability is something
like non-influence-ability.

Next time, I'll try to comment on how (1) relates importantly to the
boundary.

Osher Doctorow

From Osher Doctorow

We have:

1) P(A) = P(A' -- A)
2) P(A' ) = 1 - P(A) = P(A -- A' )

So the probability of A is the probability of its outside (A' )
influencing it, which from the local viewpoint occurs through the
boundary of A or near its boundary. We could regard either
probability or probable influence as primitive terms, in which case
probability is defined via the boundary and outside.

From (1), the smaller the probability of A, the less its probable
influence by its outside.

From (2), the bigger 1 - P(A), which is equivalent to P(A) being
smaller, the more A probably influences its outside.

So Rare Events, i.e., events of small probability (usually less than
..05), are least influenced by their outsides and most influence their
outsides in the probability sense.

Boundaries can also be regarded as having fundamental properties from
(1) and (2), not only for sets/events in spacetime but for any spaces
in which inside or interior, outside, and boundary are defined.

Osher Doctorow

"OsherD" wrote in message
oups.com...
From Osher Doctorow

COPYRIGHT NOTICE

Whenever you explicitly copyright something, you also need to state under
what conditions it is permissible to use copied material. For example, if
someone replies to your post and copies your entire message to reply to it,
they can go to jail. Perhaps this is why you get so few replies...

Greysky

If A goes through B with splitting into A1 and A2 and then reunites by
the time it reaches C, then in Rare Events the set description is:


Your beginning here has destroyed all that follows. A photon can never
be split in two and is never represented as such in QM. The photon is a
exchange of energy from one atom to another. It may move as wave and
self interfere through slits but can only be one exchange from one atom
to one atom, no matter where the wave goes or what it does in between.