Can spacetime collapse a wavefunction?

[Ben]

Hi,
I beleive that the effect of general diffeomorphisms of a spacetime
over which a quantum field is defined is strictly unitary on the
quantum field. You can't use spacetime to collapse a wave function.
Below is a little explanation of why. Does anyone know exactly how to
identify transforamtions of a quantum system or field with
diffeomorphisms of the spacetime over which it is defined?
I have been wondering about how diffeomorphisms affect quantum fields
and quantum systems without departing into quantum gravity. I imagine
a flat minkowski background in which is embedded some quantum process,
perhaps mapped out by feynman diagram, or perhaps just a quantum system
evolving according to some hamiltonian. Now imagine a diffeomorphism
applied to the background. This diffeomorphism should affect the
quantum field, interaction or system. One might imagine a conformal
expansion of the spacetime that is faster than the speed of light,
separating two entangled particles in such a way that they cannot
communicate and are essentially isolated from one another. It is
standard practice that one traces out one of the systems. This assumes
that the diffeomorphism is having a non unitary effect. It is this
point that I think is ad hoc and false. In other words, I believe that
all diffeomorphisms will induce only unitary transformations. The
reason is that the set of observables is diffeomorphism invariant. If
you know about superoperators, you know that in order to perform a non
unitary transformation one essentially increases the size of the
hilbert space, entangles and then traces out the extra stuff, sort of.
However, if the observables are diffeomorphism invariant, where did
this extra bit come from?

[jambaugh]

The collapse of the wave function is a conceptual event not a physical
event.

Remember that the wave function is a probability amplitude density. When
you suddently change assumptions, like you suddenly assume a given
observable has been measured with a certain value. You then suddenly
must revise your description of the probabilities of what might occur.

By the same token, entangled pairs of particles are not communicating
instantaneously. The locality issues in Bell's inequality are not the
key issues. We use locality as an example of two systems which by
assumption cannot communicate. You need only assume there exists two
systems which you can prevent from communicating and you get Bell's
inequality derived from treating them classically and a quantum
measurement which will violate that inequality.

Note that the inequality is not violated for single measurements. You
must do enough repeated experiments in order to calculate relative
frequencies and hence determine probabilities.

The issue is not one of mysterious interactions we cannot see acting FTL
and backward in time. The issue is how we describe physical systems.
We grow up thinking in classical terms and we must be very very careful
to make those big world assumptions explicit and question their validity
when we consider quantum theory.

Most especially we must abandon the concept of physical system as an
independent object with and objective state of reality.

Regards,
James Baugh

[Ilja Schmelzer]

"jambaugh" <me@jamesbaugh.info> schrieb
> The collapse of the wave function is a conceptual event not a physical
> event.
>
> Remember that the wave function is a probability amplitude density. When
> you suddently change assumptions, like you suddenly assume a given
> observable has been measured with a certain value. You then suddenly
> must revise your description of the probabilities of what might occur.
>
> By the same token, entangled pairs of particles are not communicating
> instantaneously. The locality issues in Bell's inequality are not the
> key issues. We use locality as an example of two systems which by
> assumption cannot communicate. You need only assume there exists two
> systems which you can prevent from communicating and you get Bell's
> inequality derived from treating them classically and a quantum
> measurement which will violate that inequality.

"Treating them classically" is uncertain. What we need to prove Bell's
inequality (together with locality) is a very weak notion of realism. In
this weak sense, Bohmian mechanics is a realistic theory, but it is
certainly not a "classical" theory in the usual meaning of "classical".

> Note that the inequality is not violated for single measurements. You
> must do enough repeated experiments in order to calculate relative
> frequencies and hence determine probabilities.

Not an argument. The same holds for every communication channel with
noise.

> The issue is not one of mysterious interactions we cannot see acting FTL
> and backward in time. The issue is how we describe physical systems.

Yep. Realism (in the sense of EPR/Bell) is a reasonable scheme for the
description of physical systems.

> We grow up thinking in classical terms and we must be very very careful
> to make those big world assumptions explicit and question their validity
> when we consider quantum theory.

But "question their validity" does not mean "reject".

> Most especially we must abandon the concept of physical system as an
> independent object with and objective state of reality.

There is absolutely no reason to do this.

We have theories which allow to describe all quantum effects using an
objective state of reality, like Bohmian mechanics and Nelsonian
stochastics.

Bell's theorem shows that such theories need some FTL effects. So what?
Classical theories (like Newtonian gravity) have also FTL effects.

Ilja