Re: Postulates for quantum mechanics (was; Is State Vector Reduction


Arnold Neumaier wrote:
> Seratend wrote:

> I do care. For I want to be able to represent ultimately _everything_
> physicists do in their work on the formal level, so that it can be
> discussed with the same rigor as formal logic discusses what
> mathematicians do. Thus every concept used by physicists must
> ultimately get a formal version.

Flanagan
Notice that, if we assign the primary and secondary properties to the
elements of such a formal system (T), then T cannot define these
properties: If it could define these elements then they would not be
elements. Just so, perhaps, are we unable to define these elements of
perception.

Thus, e.g., Maxwell, Wittgenstein and Russell & Whitehead:

"When a beam of light falls on the human eye, certain sensations are
produced, from which the possessor of that organ judges of the color
and luminance of the light. Now, though everyone experiences these
sensations and though they are the foundation of all the phenomena of
sight, yet, on account of their absolute simplicity, they are incapable
of analysis, and can never become in themselves objects of thought. If
we attempt to discover them, we must do so by artificial means and our
reasonings on them must be guided by some theory." (Maxwell)

"When we're asked "What do 'red', 'blue', 'black', 'white' mean?" we
can, of course, immediately point to things which have these
colours,--but that's all we can do: our ability to explain their
meaning goes no further." (Wittgenstein, Tractatus)

"Thus 'this is red,' 'this is earlier than that,' are atomic
propositions." (Russell & Whitehead, PM)


> Interpretational axioms necessarily have this form, since they must
> assume some unexplained common cultural background for perceiving
> reality.


Flanagan
Kuhn remains relevant on this point ('Structure of Scientific
Revolutions'), but also apposite are Schrödinger and Wittgenstein:

"The aspects of things that are most important for us are hidden
because of their simplicity and familiarity." (Wittgenstein)

"Thus, the task is, not so much to see what no one has yet seen; but to
think what nobody has yet thought, about that which everybody sees."
(Schrödinger)


> There is no formal connection, however, between X (whether random
> vector or observable) and the corresponding object in reality.
> Formal connections can exist only between formal objects.

Flanagan
Of course, if the recent revival of the "hidden variables" approach
bears fruit, we may look forward to doing without all these random
considerations.

Hartle: arXiv:quant-ph/0209104 v5

Holland: http://users.ox.ac.uk/~gree0579/index_files/spinor.pdf

't Hooft: arXiv:quant-ph/0212095 v1

Smolin: arXiv:hep-th/0201031 v1

Peres: arXiv:quant-ph/9707026 v1


> >> In order to decrease the risk of confusion, I propose to use the word
> > "physical result" when we want to attach to a real object a given
> > property:
> >
> > e.g. a ball: we have a ball as a physical result (ball)
> > e.g. the speed of a ball is x m/s: we have a physical result x m/s
> > e.g. the colour of a ball is red: we have a physical result red
> > e.g. the ball is moving ~ we have a physical result path(t)

Notice that all the above depend on the observer's/object's state of
motion. In the case of color vectors, those vectors vary mechanically
in Doppler motion and remain invariant or symmetric under translations,
rotations, reflections and changes of scale. Assigning RGB to the axes
of a unit sphere (ball), we "generate" all other visible colors by
vector addition. We also map changes in those (projective) color
vectors by a matrix (tensor) mechanics (which ought to be suggestive),
rotating and scaling those vectors by a determinate number of degrees
and magnitudes. In this connection it is interesting to consider the
intimate relations between projective relativity, Kaluza-Klein theory
and string/M-theory.

Also, see Isham's discussion of properties in his 'Lectures on Quantum
Theory.'

> I call these 'objective properties' - they are there in reality
> independent of observers (i.e., different observers are able to
> reach consensus about their properties) and hence are to be explained.

Flanagan
A tricky issue, given that these properties all depend on observers in
order to agree upon them.

> In complete foundations, there would also be formal objects in the
> mathematical theory such that talking about the formal objects
> and talking about the real objects is essentially isomorphic.
> We are currently far from such complete foundations.

Flanagan
I am also interested in an EPR-complete formalism. In this wise it is
crucial to remember that the secondary properties are not, at present,
incorporated within the body of standard physical theory. although
these variables are only "hidden" in plain sight, their physical status
has been obscured by 300 years of dogma, going back to Galileo and
Newton, who, following the Greek atomists, banished these properties to
the mysterious realm of the mind.

"If you ask a physicist what is his idea of yellow light, he will tell
you that it is transversal electro- magnetic waves of wavelength in the
neighborhood of 590 millimicrons. If you ask him: But where does yellow
come in? he will say: In my picture not at all, but these kinds of
vibrations, when they hit the retina of a healthy eye, give the person
whose eye it is the sensation of yellow." (Schrödinger)


.

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