[ExI] QT and SR

[Lee Corbin]

Stuart writes

> Lee wrote:
>
>> If you believe SR, then how can you believe
>> "instantaneous" wave-function collapse?
>> (Even if somehow that bizarre idea becomes
> coherent, which almost no one claims it is.)
>
> Because SR is a theory about physics, Lee, and a
> wave function has no physical existence. It is a
> mathematical abstraction

yes

> and a mathematical abstraction can undergo a
> mathematical operation at any speed it needs to.

All right---so long as you remain in the abstract
realm. After all, it's timeless in there.

> For example, imagine an incredibly large finite
> integer as a binary string that is 10^46 bits long.
> Now imagine I add 1 to that integer, what happens?
> That huge binary string grows by a single bit which
> becomes a 1, while the other 10^46 bits become zeroes:
>
> {11111 . . . 10^46 . . . 11111} + {1} = {10000 . . . 10^46+1 . . .00000}
>
> How long did that take?

Unless you are performing it in Virtual Reality,
or performing this operation on a real machine,
then asking how long it took doesn't make any
sense to me. It doesn't "take" because in
Platonia there is no becoming, no actions at all.

> If arithmetic addition can carry faster than light, then a
> wave function can collapse faster than light. And I don't
> mind the instantaneous collapse of a wavefunction any
> more than than I do of getting hit over the head with a
> probability density.

But what does "instantaneous" mean? Are you sure
that you are not simply consulting your intuition about
that? For, when one has internalized the reference-frame
dependence of everything in SR, then "instantaneously"
doesn't even mean anything. If event A and event B
are outside each other's light cone, then as you very
well know, neither can be said to happen before the
other, and it's equally nonsensical to say that they
"happened at the same time".

Your arithmetic example of addition going faster
than light arises from your projection of the abstract
process (which is timeless) onto the radius of the
Earth's orbit, or onto some other length (once
again reference-frame dependent!) in 4D spacetime.

>> But when the Mississippi splits into two separate streams,
>> is any conservation law broken? Likewise, at the delta
>> where it splits into innumerable streams, no conservation
>> laws are broken because the entire flow of water is still
>> the same, merely broken into discrete channels.
>
> Yes, but the amount of water flowing in each channel is
> diminished. What gets diminished in the separated universes?

Measure.

One really does not need to have studied measure theory
to understand this, however (although it does perfectly
conform to the principle of countable additivity). One
merely thinks of a stream having half the content, or
a light shining half as brightly, or a wave with half the
amplitude, and so on.

This is a *theory* in the sense that you were using the term,
and people like David Deutsch believe that this theory
applies as well to our existences and our universe as,
say, Keplerian ellipses apply to solar system orbits.

>> But it's the same on MWI branching. The "measure"
>> of two separate streams, when added, equals the
>> measure of the single undistinguished branch before
>> splitting.
>
> What is the "measure"? What SI unit is it in?

Measure could be thought of in terms of ratio (i.e.
unitlessly), I think. For example, say that you are
about to throw a fair die. Then I for one will claim
that the measure of the universes in which you get
a 3 or higher is twice the measure of the universes
in which you throw a 1 or a 2.

>> (It's this last "merging" process
>> that I myself find so weird. It
>> doesn't work unless the two
>> beams are nearly perfectly set
>> up so that the two beams are
>> in exactly the same phase, and
>> even then, the probability of
>> merging is quantum-mechanical,
>> and falls off if the beams
>> are ever so little out of phase.)
>
> I find it weird too. And if I have
> mechanistic problems with the split,
> then I have even more problems
> about the "merge". Do the Langoliers
> eat the extra universe?

Only if the universe has been a bad
little boy or bad little girl.

> How do the proper two universes
> find each other to merge? What
> happens if a Swiss physicist on the
> other side of the planet splits his
> own beam before the presumably
> American physicist in your example
> gets his split beams back in phase
> enough to merge them back together?

"Before"?  Ahem. You risk me
foaming at the mouth yet one
more time on the nature of
relativistic reference frames!

If you mean, suppose that S
(the Swiss event) and A (the
American event) are outside
each other's light cones, then
these two things have no
effect on each other. Four
universes result. (It's only
two if we have some reason
to expect correlation.)

> Which alternate universe does the
> American physicist merge with?

Since these merges were of such
short duration (i.e. the spacetime
interval between the photons
hitting the first half-silvered mirror
and hitting the last one where they
merge) is so small that they don't
include the two physicists.

But let's suppose that we make
the experiment large enough so
that although each physicist is
affected and does split, and each
one sees that he or she is in just
*one* universe (and is not aware
of the other), he or she does not
remember *which*---this is
necessary for them to be able to
merge again. See David Deutsch's
remarkable story of the conscious
computer that can feel the universes
split in his remarkable essay in
Davies' "The Ghost in The Atom".

> I was just saying that if we owe
> the stability of our universe to
> "interference" between the parallel
> universes *and* the diligent split
> occurring in a timely fashion, then
> it's a precarious existence we lead.

Not if you identify with all your copies
in all the universes who are similar
enough to you.

> How does MWI time the disappearance
> of all the extra matter-energy when two
> universe "merge" again?

No matter disappears, any more than
water disappears if a river splits at
one place and then recombines
downstream.

> Admittedly, I have never read Deutsch.
> "Shadow photons"? That sounds an
> awful lot like an antiparticle of light.
> Bosons are supposed to be their own
> antiparticle. Besides, Lee, you have
> explained MWI to me far better than
> anyone has explained it to me before.

Thanks. But think of it as payback for
(most recently) the material analysis
of Bell's two spaceships.  :-)

> I doubt Deutsch could do it better.

Ha!

>> On the other hand, on p. 211
>> of "The Fabric of Reality", Deutsch
>> is completely definite about the
>> number of universes (i.e. branches)
>> being on the order of the continuum.
>> So that's not merely a *countable*
>> infinity at all. We're already at
>> aleph-one. So any more splitting
>> isn't conceptually problematical
>> at that point, (when things are already
>> about as "worse" as they can get).
>
> But this is my point exactly. Infinity
> is a mathematical treasure-trove and
> MWI treats it like a waste dump for
> unnecessary universes.

Great quote! At least in one way,
methinks your immortality now
insured, even if you don't get frozen.

> Yes, until one starts to wonder
> what could be keeping track of
> the transfinite aleph-1 universes
> out there so that only the right
> ones get merged. If it's not a
> Turing machine, what is it?

Oh, one could have asked Newton
the same question:  "Just explain to
us, Isaac, please, how can the
universe compute the answers to
your gravitation formula so damn
fast?"

My guess is that we may be looking
at the universe in a parochial sense,
based upon the computer or calculating
paradigm. First, things happen. Second,
humans evolve. Third, they get theories
going that describe how things happen.
It's probably anthropomorphic (or
"sentientmorphic" to look at what the
universe does as calculation).

Lee

> Furthermore, if the universe really is aleph-1
> infinite, then it never really splits and instead
> of calling it the "Many Worlds Interpretation"
> they should call it the "Single Hairy World
> Interpretation".
> ...
>
> Stuart LaForge
>
> "See them clamber, these nimble apes!  They clamber over one another, and thus scuffle into the mud and the abyss."- Friedrich 
> Nietzsche