[ExI] Branching vs. Interference (was Many Worlds)

[Lee Corbin]

Damien writes

> A basic premise of quantum theory, as I understand it (in a 
> rudimentary way), is that what we see always comprises a 
> superposition of all possible states of the relevant phenomenon. The 
> reason a light beam travels on the least action pathway is that this 
> is what happens when all conceivable pathways are taken 
> simultaneously, interfering with each other as they do so in such a 
> way that the observed straight line, or geodesic, comes out in the wash.
> 
> Uh-huh.

There is a complex number associated with each of those paths,
and indeed the theory---which does correspond so well to prediction
---calls for adding together those complex numbers.

I say this mantra over and over to myself:  "At the bottom of things are
amplitudes that add", and it seems to help.

> I have read Deutsch's book with its peculiar talk of shadow photons, 
> which appear to subsist in numerous orthogonal universes that 
> mysteriously influence each other. And yet most discussions of MWI as 
> applied to decisive choices, for example, appear to suppose that any 
> observed state branches into a multitude of alternative experiences.

Well, that does seem to explain everything.

> You turn right, and you turn left, and you go home, and very very 
> rarely you fly into the sky.

One confusion that may be present here is that these alternate
paths---you go home, you fly---are not interfering with each
other. They have attained an independence, and each goes
accordingly into its own separate universe. (There is a grand
superpositon of all these paths that constitutes the multiverse,
but that's not quite the same issue.)

Whereas before you were mentioning interference, which perhaps
can be best understood as incipient branching that undergoes
convergence "before it makes a difference", while here you are
speaking of instances of separate branches.  And "makes a difference"
requires, as some kind person on this list informed me a few months
back, at least one kT (a quantum) of energy. Branching doesn't
happen until an "irreversible" change has occurred. I.e., the
subsequent amplitudes of the separate branches to recombine is
miniscule.

> Presumably, therefore, we must imagine that in one universe
> a given light beam will jig along a random dog's leg path,
> and it's only a sort of "God's eye view" that might perceive
> the kind of hyperreality where all those dogs' legs congeal 
> into a straight line.
> 
> But actually there is no "God's eye view" unless it is the one we 
> experience routinely.
> 
> Does anyone see the problem here?

Yes, maybe.

> It's so basic that I must be making an elementary mistake [no!],
> but I have never been able to see what it is.

Perhaps the distinction I made above between cases in which
branching occurs and cases in which it does not will be helpful?
E.g., a light beam exhibits interference, and we don't speak of
the beam as going in different directions (one direction is singled
out as the path actually taken, because, again, of interference).
Whereas real branching has occurred if even so much as a
photon splits and does not recombine.

Actually, there *is* a God's Eye View:  it is Deutsch's multiverse.
I contend it's best to nurture the picture from an external perspective,
much as one should visualize the orbit of the Earth from a location
far away in space, not from the viewpoint of the Earth's surface.
The addition of observers to the multiverse picture can come later.

Lee