Feynman checkerboard as a model of discrete space-time

Ed Hanna

Final paper and computer simulation on arXiv at
http://arxiv.org/abs/cs.CE/0607018

Questions, comments?

Peter S.

Dear Ed,

Interesting paper and simulations. The cause of the simulated
interference effect is still a bit mysterious to me. In a real slit
experiment the interference wavelength should depend on the wavelength
of the particle which becomes smaller at higher speeds (in your model
higher speed is higher probabitility of movement). However you have
also introduced a 'lookback' parameter by which the probability of
movement seems to depend on the history of the particle. Have you
investigated the effects of the 'speed' and the lookback parameter on
the observed interference fringes?

Best regards,

Peter

Ed Hanna schreef:

> Final paper and computer simulation on arXiv at
> http://arxiv.org/abs/cs.CE/0607018
>
> Questions, comments?

Ed Hanna

Dear Peter,

The cause of the simulated interference effect is a mystery to me as
well. Logically, the sum of the two single slits *ought* to be the
same as the double slit. The only thing I can figure is that since the
motion of all 5 million simulated particles are random / probabilistic,
there is some sort of "probability map" of where the random motion of
the simulated particle is most likely to go. When one slit is closed,
the probability map has only the one component. When both slits are
open, the probability map has a component from both slits at the same
time. Since the simulated random particle could go through either
slit, it's as if the probability map itself goes through both slits,
even though the simulated particle itself can obviously go through only
one slit or the other.

The original purpose of the lookback parameter is to allow the
experiment / simulation wavelength to be a variable. A *completely*
random particle motion would be more jittery like Brownian motion, and
there would be no way to change it. A rational for allowing the
lookback parameter in the simulation (other than the empirical one of
wanting to vary the wavelength) would be if the line representing the
simulated particle's path over time (its world line) were an object
unto itself, rather than a collection of unrelated particle positions
in time. In that case, as you pointed out, "the probability of
movement seems to depend on the history of the particle". It may be
similar to pushing on a piece of rope (an object unto itself) vs.
pushing on a chain (a collection of attached pieces) - the rope would
form a random curve, while the chain would form a more jittery pattern
of links.

I have not yet investigated the effects of the 'speed' or the lookback
parameter for two reasons.
First, this is being done in my spare time, and I haven't been able to
spend as much time on it as I would like (5 million trials takes a
while).
Second, calculating from the observed interference fringes spacing, the
wavelength seems to be about 0.23 units, which makes no sense to me.
The reason I set the lookback parameter=10, with a double slit spacing
of 10 cells was to try for an average wavelength of about 20. The
random simulated particle paths, as seen in figure 13 of the paper,
seem to have much more of a wavelength than either 0.23 or even 20. I
have been hesitant to make any changes until I understand what is going
on.

Regards,
Ed