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Re: Parallel Universe



Referring to
<http://www.allsci.com/parallel.html>

Robert Cohen wrote:
On the website, it says that two holes produce five "shadows" whereas
four holes produce three "shadows". The first question I have is:
does that actually happen?

It's not the general result, nor even the most common result.

The second is: can the effect be explained simply by wave
interference?

The effects that _really_ occur can be described quite nicely
by wave interference.

The pseudo-effects that Sam Sachdev describes depend on
wave mechanics plus various accidents due to imperfections
in his setup.

Can someone reproduce the "five shadows" to "three shadows" effect
and describe it for me so I know what it is we are supposed to be
explaining (and so must rely on the parallel universe explanation)?

It doesn't deserve an explanation.

What you actually see depends on things like how big are
your pinholes, how evenly matched are the pinholes, how
long is the "throw" (i.e. leverage) of the interferometer,
how big of a dip in intensity you choose to call a "shadow",
how spectrally pure and coherent is your light source,
et cetera.....

Under ideal conditions, the two-slit interference pattern
has an infinite number of minima. See Feynman volume III
chapter 1, especially equation 1.4.

=============================================

Hugh Logan wrote:

I have read that Maxwell literally tried to explain his
electromagnetic theory in terms of "gears and machinery," well at
least gears (like differential gears), but I never heard that he
> got it right.
. ^^
. ^^

Upon reflection, I assume that "it" refers back to "machinery".

(The first time I read that msg, I thought the antecedent of
"it" was electromagnetic theory. Maxwell got that right,
pretty much!)

As for "machinery", Maxwell for years favored the idea that
lines of force were like vortices in a fluid. But eventually
he wised up and took the "hypotheses non fingo" approach. That
is, the equations are primary and fundamental. The field is
what the equations say it is, whether we can visualize the
"machinery" or not.

The vortex-machinery approach wasn't silly; keep in mind
that the equations of magnetostatics look a whole lot like
the equations of inviscid fluid flow. "The same equations
have the same solutions." See the Feynman chapter on "The
Flow of Dry Water".



Tangential notes:

1) Maxwell did this work many decades before relativity was
discovered. So it is quite remarkable that the equations
have the fully correct relativistic invariance. They
work not just for v<<c but for all v.

2) Maxwell did this work without using vector calculus.
So he had to write things out component by component. That
increased his workload, taking away a lot of the elegance
and making the symmetries harder to see.

3) Combining points (1) and (2), if you want machinery you
might try the Clifford-algebra approach: the field is a
bivector. Bivectors are reasonably easy to visualize, and
they stand up to scrutiny better, including being
relativistically invariant (in contrast to vector-like
_lines_ of force, which are definitely not invariant).

4) I suspect Maxwell would have been quite amused by parts
of modern string theory, which has some quantum numbers that
are "topological" in essentially the way that a vortex is
a topological defect in a fluid.