No Boundary Proposal --- Many Worlds?
michael
Is there any connection between Hugh Everett's "Many Worlds," and
Hartle and Hawking's "No Boundary Proposal"? I am writing an article
for a major English publication. I need citations if possible.
What is the relationship of Quantum Cosmology to Hawking's NBP, and to
Everret's MWs?
Also, does Feynman's sum-over-histories, path-integral approach have
any special connection to Hugh Everett's Many Worlds?
Thank you in advance for your answers.
Cheers,
CF
carlip...@physics.ucdavis.edu
> Is there any connection between Hugh Everett's "Many Worlds," and
> Hartle and Hawking's "No Boundary Proposal"? I am writing an article
> for a major English publication. I need citations if possible.
> What is the relationship of Quantum Cosmology to Hawking's NBP, and to
> Everret's MWs?
> Also, does Feynman's sum-over-histories, path-integral approach have
> any special connection to Hugh Everett's Many Worlds?
First, a little background. Quantum cosmology is the attempt to find
a fully quantum mechanical description of the large-scale Universe.
Gravity plays a key role in such a description, and since we don't
yet have a complete, consistent quantum theory of gravity, quantum
cosmology is necessarily very incomplete.
A quantum description of any system, though, has the same general
ingredients. We need
1. The observables (the quantities we can actually measure)
2. The initial state of the system, which determines probabilities
for various values of the observables. (This is roughly the
same as the "wave function," but more general -- one can have
a "mixed state," essentially a collection of wave functions
with various probabilities for each.)
3. A way to compute the evolution of the state, that is, its
development in time
A fourth "meta-ingredient" is an interpretation of the state. This
can help us think about what's going on, but typically many different
interpretations lead to exactly the same predictions for the outcomes
of measurements. It's worth noting that the "many worlds" idea is
actually all that well-defined, in the sense that there are many
rather different interpretations of quantum mechanics that can vaguely
be thought of as "many worlds" but that differ hugely in detail.
The three items you ask about address three different ingredients.
The Hartle-Hawking no boundary proposal is a proposal for the initial
state. The path integral approach is a method of computing the time
evolution of the state. The many worlds idea is an interpretation
of the meaning of the state.
In principle, these are almost completely independent. I can use
tunneling boundary conditions (an alternative to the "no boundary
proposal"), evolve with the path integral, and describe the results
in the consistent histories interpretation; I can use "no boundary"
initial conditions, evolve with the Wheeler-DeWitt equation, and
use a de Broglie-Bohm pilot wave interpretation. No piece uniquely
requires any other.
If you're looking for relationships, there are a few, but they're
rather weak.
1. The no-boundary proposal was initially formulated in terms
of a particular path integral approach (the "Euclidean path
integral"), and is probably most easily expressed in terms of
a condition on path integrals. But while this is convenient,
and arguably the "most natural" description of the proposal,
it is not necessary.
2. In practice, many of the people who work on quantum cosmology
lean towards some form of many worlds interpretation (though
as I said, this is a large umbrella, including interpretations
that certainly don't have "many" "worlds"). The simplest form
of the traditional Copenhagen interpretation requires an observer
who is outside the system being observed, and this doesn't make
a lot of sense if the system is the whole Universe. But, again.
while many worlds interpretations are one set of alternatives,
there are others.
(Note also that this is a statement about quantum cosmology in
general -- there's nothing special about the no boundary proposal
that makes it more many-worlds-like than any other proposed
initial condition.)
As for references, it depends what you are looking for. If you really
want to try to understand the issues (and aren't just looking for some
useful quotes for your article), get Bell's _Speakable and Unspeakable
in Quantum Mechanics_ and look at essays 15 and 20. Then look at a
couple of electronically available papers (these are somewhat technical,
but less than most, and you should be able to pull out the general ideas):
http://arxiv.org/abs/gr-qc/9906100 and http://arxiv.org/abs/gr-qc/9701022.
I'm sure others can recommend other references.
Steve Carlip
Oh No
>Hi,
>
>Is there any connection between Hugh Everett's "Many Worlds," and
>Hartle and Hawking's "No Boundary Proposal"? I am writing an article
>for a major English publication. I need citations if possible.
Start with the references given by Wikipedia:
http://en.wikipedia.org/wiki/Everett_many-worlds_interpretation
>
>What is the relationship of Quantum Cosmology to Hawking's NBP, and to
>Everret's MWs?
Not a lot of people pay much heed of this, but if I was Everett I might
feel pretty upset about the many world's tag. His relative state
formulation was actually quite subtle. Many worlds as commonly
understood, I believe started as a joke, due I think to his DeWitt.
>
>Also, does Feynman's sum-over-histories, path-integral approach have
>any special connection to Hugh Everett's Many Worlds?
Not really. The path integral is a mathematical formulation equivalent
to ordinary quantum theory. I think Feynman initially hoped it might
give some insight into interpretation, and that it might be easier to
learn than the standard approach. Actually it doesn't do either, but the
first chapter of the path integral book is a particularly clear account
of the issues in quantum theory, as I recall (many years since I read
it)
>Thank you in advance for your answers.
>
>Cheers,
>CF
>
Regards
--
Charles Francis
substitute charles for NotI to email