Re: Quantum Interference and the Plentitude

From: Mirek Dobsicek <m.dobsicek.domain.name.hidden>
Date: Mon, 21 Jan 2008 15:31:20 +0100

Russell Standish wrote:
> On Mon, Jan 07, 2008 at 02:48:35PM +0100, Mirek Dobsicek wrote:
>>
>>> If quantum mechanics was done using a real-valued Hilbert space, you
>>> simply don't get wavelike interference patterns.
>> To my knowledge, you don't get interference patterns for *positive*
>> real-valued Hilbert space, but for real-valued Hilbert space you do.
>>
>>
>> Check http://mina4-49.mc2.chalmers.se/~dobsicek/PhDThesis.pdf on page 39
>> for a quick review and references.
>>
>> Sincerely,
>> Mirek
>>
>
> Thanks for the info - I will take a look, when I'm on top of a few
> things. However, I'm not sure what you mean by positive real Hilbert
> space, as the positive real numbers do not form a field. I can only
> guess you mean some kind of non-Hilbert space generalisation, a bit
> like my non-Hilbert space non-commutative division ring gadgets I've
> alluded to in the past.

Hi Russel,

you are right, a "*positive* real Hilbert space" is a wrong term.
However, the point of my comment was to express a belief that your sentence

>>> If quantum mechanics was done using a real-valued Hilbert space, you
>>> simply don't get wavelike interference patterns.

is not correct. But of course, QM as physical framework and as derived
from experiments goes with complex numbers.

Best,
 Mirek

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Received on Mon Jan 21 2008 - 09:41:21 PST

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