----- Forwarded message from Russell Standish <hpcoder.domain.name.hidden> -----
Date: Tue, 22 May 2007 08:43:28 +1000
From: Russell Standish <hpcoder.domain.name.hidden>
To: Ricardo Aler <aler.domain.name.hidden>
Subject: Re: Theory of Nothing
In-Reply-To: <43ed4f2b0705211023q2ac918c4jbb83a73072cb0319.domain.name.hidden>
User-Agent: Mutt/1.4.2.1i
On Mon, May 21, 2007 at 07:23:47PM +0200, Ricardo Aler wrote:
> Hello,
>
> I just read your book and I was specially interested on the Quantum
> Mechanics part. I found that a bit abstract in the sense that (at
> least for me, not being a physicist), it is a bit difficult to go from
> the QM postulates, to more well-known properties of QM, like
> interference (two slits) and entanglement (EPR).
>
Fair enough, but there are some excellent expositions of how the
axioms give rise to the well-known properties of QM. For instance, I
can highly recommend Shankar's book. However it is an undergraduate
text book, so may be a little mathematical for your taste.
> As for interference, I tried to see in your book wether it was a
> direct consequence from your theory of observation or from something
> else. But from what I understand, it seems that Interference has more
> to do with using complex numbers than with observation. I mean, you
> could have used a positive real measure, instead of a complex one, and
> you would have obtained a different physics (I wonder which one,
> classical physics?). So it seems that interference (at least) is
> independent of your theory of observation.
>
You are indeed correct, that it depends on the measure being
complex. As I describe in a couple of places in the book, a complex
measure is a more general situation to a real measure, and so is more
probable according to the Occam's razor theorem. In other words, to
have a real measure, there has to be a good reason for it. Since we
obviously observe a complex valued measure (QM experiments), there is
no need to look for a reason for the measure to be real. The cannot be
any such reason.
The only fly in the ointment is that complex measures are not the most
general measure. One can have quaternion measures, octonion measures -
in general a spectral measure. I do not have a good answer as to why
the measure should be complex. Perhaps there is some good
reason. Perhaps the measure may be more general, but makes no
difference to physical outcomes. Perhaps. Its an open research
question, which I only became aware of in writing the book :). Its
also very difficult to work with these more general measures, as the
state space will no longer be a vector space.
> Also, I don't understand when you say that "a" observers partition the
> state this way, and "b" observers in some other way (like measuring
> the spin along the y axis or the x axis). But, wouldn that be
> impossible to do simultaneously?.
>
Don't forget that we have already made the "many minds" move
earlier. All possibilities exist. Therefore two different observers
can observe different incompatible observations, but clearly in that
case they are inhabiting different realities (or "worlds" in the MWI
terminology).
> Finally, do you think that entanglement is a direct consequence of
> your theory of observation?
Yes, in that entanglement is a direct consequence of the mathematical
formulation of QM, which follows (at least if I'm correct :) ) from my
assumptions. However, trying to see how this might be so intuitively
without going through the maths route is tough.
>
> Best regards,
>
> Ricardo Aler.
>
> --
> Ricardo.
> -------------
> mailto: "Ricardo Aler Mur" <ricardo.aler.domain.name.hidden>
> http://www.uc3m.es/uc3m/dpto/INF/aler
Good questions Ricardo. I've taken the liberty of posting this
response to the everything-list and to avoid-L, as the points you
raise are of general interest.
--
----------------------------------------------------------------------------
A/Prof Russell Standish Phone 0425 253119 (mobile)
Mathematics
UNSW SYDNEY 2052 hpcoder.domain.name.hidden
Australia http://www.hpcoders.com.au
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----- End forwarded message -----
--
----------------------------------------------------------------------------
A/Prof Russell Standish Phone 0425 253119 (mobile)
Mathematics
UNSW SYDNEY 2052 hpcoder.domain.name.hidden
Australia http://www.hpcoders.com.au
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Received on Mon May 21 2007 - 18:44:59 PDT