**From:** Mitchell Porter (*mitchtemporarily@hotmail.com*)

**Date:** Mon May 05 2003 - 06:40:41 MDT

**Next message:**D. Goel: "Re: many worlds (was RE: Einstein)"**Previous message:**Marc Geddes: "Book ideas"**Next in thread:**D. Goel: "Re: many worlds (was RE: Einstein)"**Reply:**D. Goel: "Re: many worlds (was RE: Einstein)"**Maybe reply:**Mitchell Porter: "Re: many worlds (was RE: Einstein)"**Reply:**Lee Corbin: "RE: many worlds (was RE: Einstein)"**Maybe reply:**Mitchell Porter: "Re: many worlds (was RE: Einstein)"**Maybe reply:**Mitchell Porter: "Re: many worlds (was RE: Einstein)"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Lee Corbin said:

*>Also, I too think that Einstein would have felt relieved
*

*>if he'd lived to hear Everett's explanation. The whole
*

*>issue for him was determinism, I believe, and the famous
*

*>dice remark refers to the universe taking just one of the
*

*>possible random branches. MWI is, of course, completely
*

*>deterministic.
*

I think MWI is rather contrived, but you need to know a few

technicalities to appreciate why. Naively, it might sound

like this:

1) Quantum mechanics says that some things happen completely

at random: one out of a set of possibilities occurs, for no

reason.

2) The many-worlds interpretation says that every possibility

is realized: whenever such a choice-point is reached, the

universe 'splits', with one offspring for each possibility.

This is MWI according to DeWitt, and it has some problems

which are widely recognized:

a) Complementary observables. A quantum particle can't have

definite position and definite momentum at the same time.

When the split occurs, does the particle start out in each

branch with a definite position, or with a definite momentum,

or in some other state?

b) Relativity. Is the whole universe copied at each split?

If so, what reference frame are we using? Alternatively,

one could suppose that the split propagates outwards at

lightspeed, with the parent universe dynamically cleaving

in superspace, but no-one has expressed this mathematically.

c) Interference effects. Quantum effects such as the

interference fringes which show up in the double-slit

experiment require *recombination* of separated wavepackets

(in that example, the recombination of wavepackets that

have passed through the separate slits). If the universe

splits before recombination is to occur, recombination would

seem to be impossible, because the two wavepackets are now

in separate universes. So either universes can recombine,

or splits don't occur between measurements, both of which

pose further problems.

All this is well-known amongst MWI advocates, and so most

of them prefer MWI according to Everett, which is a more

subtle approach. Instead of splitting universes, Everett

talks about "relative states" of subsystems of the universe.

Formally, this involves taking the total wavefunction of

the universe, and expressing it as a superposition of

"product states" of parts of the universe:

z1|a1>|b1>|c1>... + z2|a2>|b2>|c2>... + ...

(Just to explain: a,b,c,... are physical systems.

|a1>,|a2>,... are distinct quantum states of system a.

|a1>|b1> means 'a is in state a1, b is in state b1', etc.

z1,z2,... are complex numbers, coefficients in the overall

superposition.)

The basic task of the MWI is to connect the particular

universe we see with the ensemble of universes implicit

in the supreme wavefunction. Everett does it through this

algebraic decomposition: you-in-this-world are one of

those physical systems, in one of those distinct quantum

states appearing in the sum above.

But here's the very first problem: there's more than

one way of decomposing a wavefunction. One instance of

this is illustrated by problem (a) for DeWitt's version

of MWI, mentioned above. In the quantum mechanics of a

single particle, exact position states are represented

by "delta functions", formal functions which are infinitely

peaked at a single coordinate and which are zero everywhere

else; and exact momentum states are represented by "plane

waves", the sort of functions which show up in Fourier

analysis on multidimensional spaces. A generic wavefunction

can be decomposed into a sum over delta functions, *or*

a sum over plane waves (or indeed, a sum over many many

other possible sets of functions). Which "basis set" is

the real one?

The same consideration applies to finite-dimensional

quantum states, such as the state of a qubit. Qubits are

normally thought of as existing in a superposition of

|0> states and |1> states, but they can equally well be

thought of as being in a superposition of |0>+|1> states

and |0>-|1> states.

In the many-worlds FAQ, which is the most popular

exposition of MWI available online, a particular basis

is singled out for attention, but it's also explicitly

stated that this basis is preferred only for purposes

of calculation, it's not ontologically special in any way.

There's a further step in the MWI according to Everett:

the construction of a probability measure. Again, I think

this involves the postulation of extra structure, rather

than being implicit in the wavefunction. I'm in the middle

of discussing these issues with the author of the FAQ,

and we haven't got to this step yet, so I won't say more.

But I just wanted to point out *why* the MWI is not as

natural as it might sound.

_________________________________________________________________

MSN Instant Messenger now available on Australian mobile phones. Go to

http://ninemsn.com.au/mobilecentral/hotmail_messenger.asp

**Next message:**D. Goel: "Re: many worlds (was RE: Einstein)"**Previous message:**Marc Geddes: "Book ideas"**Next in thread:**D. Goel: "Re: many worlds (was RE: Einstein)"**Reply:**D. Goel: "Re: many worlds (was RE: Einstein)"**Maybe reply:**Mitchell Porter: "Re: many worlds (was RE: Einstein)"**Reply:**Lee Corbin: "RE: many worlds (was RE: Einstein)"**Maybe reply:**Mitchell Porter: "Re: many worlds (was RE: Einstein)"**Maybe reply:**Mitchell Porter: "Re: many worlds (was RE: Einstein)"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

*
This archive was generated by hypermail 2.1.5
: Wed Jul 17 2013 - 04:00:42 MDT
*