Feynman Gate
Ed Fredkin
The Billiard Ball Model (BBM) is a Newtonian model of computation
where hypothetically perfect and identical billiard balls (diameter=1)
interact synchronously with each other in order to do the same kind of
logic as computer circuits. Collision points have integer coordinates
(on a Cartesian Lattice) and the velocity of every ball is x dot= + or
- 1, y dot= + or - 1. The x and y coordinates of every ball are
integers when time is an integer. The basic circuit is a place where
2 billiard balls might collide. If we call the incoming paths A and
B, then there are 4 output paths. If 2 balls collide then the 2 balls
exiting the collision are each called "A.B" (A and B).
A B
\ /
\ / The BBM Gate
\ /
\ XX / "XX" marks a possible collision point
/ \ / \
/ \/ \
/ /\ \
/ / \ \
/ / \ \
A.B ~A.B A.~B A.B
If only one Ball enters the gate, it continues in a straight line. If
both balls enter, both leave on different paths. The BBM gate has an
abstract property reminiscent of QM. The only way we can "measure"
whether or not a ball is present on path B is to run it through a BBM
Gate along with a test ball (A) and see if the path of A is deflected
by the potential ball B. Of course, it is obvious that you cannot
measure B without deflecting it, since it must be involved in a
collision in order to make the measurement.
It is easy to show that any kind of digital computer can be
constructed within the BBM. A few days after the invention of the
BBM, Feynman came up with a simple circuit made up out of 2 BBM gates,
it has since been called the "Feynman Gate." This gate has an unusual
property.
A B
\ /
\ /
\ /
\ XX /
/ \ / \ |
/ \/ \ |Reflector
| / /\ / |
| / / \ /
| \ / \
\ / / \
XX / \
/ \ \
/ \ \
B A.B A.~B
In the Feynman Gate, A detects the presence of B without affecting the
path of B! The reason is that when A and B are both present, there
are 2 collisions. If a ball enters at B (at the top) a ball exits at
B (at the bottom) whether or not A is present. However when A is
present, a ball exits at A.B (meaning B was there) or at A.~B (meaning
B was not there). If a ball enters at B (top) a ball always exits at
B (bottom). Thus the signal B can be measured without being affected
by the measurement.
One question is: "Are there analogies to this kind of phenomenon in
QM?"
Ed F
akha...@yahoo.com
In QM a wave nature will always limit the ability of such experiment.
The lighter the balls, the less they are localized and less certain
output of measurement.
Alex
karl robold
"Ed Fredkin" <edfr...@yahoo.com> schrieb im Newsbeitrag
news:c91c8a19.04040...@posting.google.com...
I searched the arXiv for 'Feynman /\ Gate' in the Quantum-section and didn't
find
any reference. So it seems, a Feynman Gate is not yet available in the
quantum mechanical sense.
maybe is an QM-analogy for that phenomenon called 'quantum nondemolition
measurement', but I don't know, (if any) how far the analogy goes.