Poll: Where does unitary evolution happen?

[selfAdjoint]

This is for those who believe QM includes a phase of unitary evolution. In ordinary QM the state is given by a complex vector (actually a ray) in Hilbert space and it evolves by unitary operators transforming it. Does this complex thing and its behavior exist in out spacetime? If not, then where? Or how?

Below I give some choices and the opportunity to specify other answers. Please participate, as this is intended more to spark discussion that to pin down final answers.

{Added in edit) I really don't want to get into a discussion here on whether spacetime itself is "physical". If you have some other view of spacetime, adjust the meaning of the choices to conform to that in your mind and vote accordingly. Then if you will, explain how your view interacts with your choice.

 

[vanesch]

I voted "something different than spacetime" because I have to say I didn't really understand the question
If we take spacetime to be a fixed background (minkowski) then this is a structure that will play a crucial role, but of course it is not big enough to contain the wave function description... mmm, maybe I should have voted for the "bundle", but then a bundle where each point is mapped onto a set of Heisenberg operators ! Ouch...

cheers,
Patrick.

 

[selfAdjoint]

I voted for the bundle as a physical extension of spacetime. This goes back to when I first read Hlavaty's book on Einstein's unified field theory (EUFT). Hlavaty developed spinors that weren't introduced into spacetime ad hoc, but represented relationships between the metric and torsion, point by point in the unified spacetime. Of course EUFT has never been quantized, AFAIK, but I like to think that whenever we get to a "final" field theory it will be somehow or other incorporated.

 

[Kea]

I voted for informational because this is the way to look at it in the category theoretic description of quantum computation. The term not physical is difficult to interpret! In some sense, by definition, of course its physical, but I guess you just meant to differentiate things like concrete background internal spaces from more abstract stuff.

Regards
Kea

 

[pervect]

Taking standard quantum theory, my view is that the space in which a multi-particle wavefunction evolves isn't physical, but is a mathematical abstraction. I'm not sure which of the choices in the poll best reflects this viewpoint, so I didn't actually vote.

For instance, it would take six spatial dimensions to describe a two particle wave-function - it's the tensor product of two three-dimensional spaces. Because it's not a 3-d space, I would say that it's not "physical" as I think of physical.

The number of dimensions depends on the number of particles. This is fine when the number of particles is conserved, but things get even more complicated when particles are being created and destroyed. Basically one winds up with an infinite number of dimensions.

To try and visualize this, I think of dividing space up into an array of boxes and thinking of each box as a being a separate dimension. There are probably some mathematical difficulties with this simple picture, a slightly better one has the boxes being gaussian shaped pulses, which all overlap to form a 3-d function, and the coefficient of each pulse's amplitude is a separate dimension.