In barely one-month-old [1],  Rovelli argues that 'EPR-type
correlations do not entail any form of "non-locality", when viewed
in the context of a relational interpretation of quantum mechanics.'

This sounds somewhat familiar (cf. [2]).

IV

[1] http://arxiv.org/abs/quant-ph/0604064
[2] in
http://groups.google.com/group/sci.physics.research/msg/9bebf67819f08315
I wrote "Entanglement will then appear as a property of the
interaction/information-exchange between superposed D1 and D2 , when
measurement  outcomes are matched/compared. In this setting nonlocality
disappears, together with the hidden assumptions that spawned it."

Thus spake tttito <vec...@weirdtech.com>

In so far as I can see, all this is saying is what we already know, that
there is nothing we can say within the formal structure of quantum
theory which yields a contradiction.

I think that is a slightly different, and somewhat weaker, statement
than the one which I, and I think also rof, would like to see, namely an
answer to the question "what is really going on?".

The program outlined by Rovelli (1996, Relational Quantum Mechanics,
Int. J. Th. Phys., 35 1637) is this:

"The program outlined is thus to do for the formalism of quantum
mechanics what Einstein did for the Lorentz transformations: i. Find a
set of simple assertions about the world, with clear physical meaning,
that we know are experimentally true (postulates); ii. Analyze these
postulates, and show that from their conjunction it follows that certain
common assumptions about the world are incorrect; iii. Derive the full
formalism of quantum mechanics from these postulates. I expect that if
this program could be completed, we would at long last begin to agree
that we have understood quantum mechanics".

I believe that that is what I have done in gr-qc/0508077. But it only
answers the question "what is quantum mechanics saying", and I am not
convinced that it is really a huge step forward from what Von Neumann
was saying when he identified Hilbert space with a formal language, vis
quantum logic. In the context of EPR I don't think it answers the
question, "what is really going on?".

To answer that question I think we have to go much deeper. I think we
have to first use the formalism of quantum mechanics to construct
quantum electrodynamics - itself regarded as an unsolved question which
I tackle in Discrete Quantum Electrodynamics (physics/0101062). Then we
have to introduce a physical metric by reworking Einstein's development
of special relativity in terms of photon interactions as defined in qed.
This will show us that the metric is a product of particle interactions,
and not a prior physical property of space. A satisfactory treatment
will produce gtr, rather than sr, which I seek to show in gr-qc/0508077.

Such a treatment shows that spin is not a property of a particle in
isolation, but a part of a relationship between a particle and space-
time. At the time when the entangled pair is produced, as it seems to
me, the relationship which they have with spacetime is not fully
defined, and in particular their spin properties are not defined. Their
spin properties only become defined when they interact with A's or B's
measurement apparatus. Spin is conserved, so that the spin property does
become defined, it becomes defined for the past as well as the present.
Thus A's measurement determines the spin relationship between the
particles and space-time at the time of the original production of the
particles, and hence it also determines it in B's measurement.

As an explanation that does not violate locality. It does violate a
traditional notion of causality, which is one of the possibilities
mentioned by Bell. I don't have much of a problem with that. If space-
time only exists as a consequence of particle interactions, then
traditional causality is out of the window anyway. Also it ties in with
time reversibility and the Feynman-Stuckelberg interpretation that an
antiparticle is a time reversed particle. As has been discussed
elsewhere, the "arrow of time" which we perceive is a result of entropy,
a statistical effect based on many particle interactions. I see no
reason to think that the arrow of time should exist within the quantum
domain.

Regards

--
Charles Francis
substitute charles for NotI to email

I believe this program was successfully completed a while ago:

G. Birkhoff and J. von Neumann,
The logic of quantum mechanics, Ann. Math. 37 (1936), 823.

G. W. Mackey, The mathematical foundations of
quantum mechanics  (W. A. Benjamin, New York, 1963), see
esp. Section 2-2.

C. Piron, Foundations of Quantum Physics,
(W. A. Benjamin,  Reading,  1976)

Eugene Stefanovich.

"tttito" <vec...@weirdtech.com> a écrit dans le message de news:
1147284408.875812.183...@y43g2000cwc.googlegroups.com

I would rather say: "when not looked at"  As soon as you compare each side,
locality doesn't intervene since it can only be made at a same point.  The
relational interpretation entails some kind of globality, which when set
aside as belonging to the theory and not to the system, leave
nothing non-local. Indeed, this interpretation only considers relations
between systems at a given point, similarly as a circle is seen locally as a
line.

The relational interpretation isn't necessary to see that, the Copenhagen
interpretation suffices if used appropriately, that is, if the collapse
occurs only at the time of the comparison.  Quantum mechanics give exactly
the same result whenever is introduced the projection onto the eigenstate,
be it at the time of the polarization measurement or even just before
conscious perception.

Of course, the advertisement of the relational interpretation is quite
another stuff.

--
~~~~ clmasse on free F-country
Liberty, Equality, Profitability.

Thus spake Eugene Stefanovich <euge...@synopsys.com>

I have not read Mackey or Piron, though I have read a number of books on
foundations which are not nearly so sure. Neither are in print. I am not
convinced that Birkhoff and Von Neumann gave a set of simple assertions
about the world with clear physical meaning. They simply said that qm
has the structure of a formal language which tells us everything we can
find out from experiment, and that, pretty much is what is said of the
orthodox interpretation. To carry out the program the language must also
be shown to make sense in translation into English, imv. And it should
not simply enable us to predict the results of experiments, it should
work from precepts which, like Einstein's, are obviously true.

If you think the programme has been completed, perhaps you could tell
me, for example, why the Schrodinger equation is obeyed.

Regards

--
Charles Francis
substitute charles for NotI to email

...

The "novelty" in Smerlak-Rovelli ([1]) is that they introduce the
notion of local information exchange between superposed observers as
the key to EPR locality. Here are a few pointers.

"What changes instantaneously at time t 0, for A , is not the objective
state of ß , but only its (subjective) relative state, that codes the
information that A has about ß .... if I see an elephant and I ask you
what you see, I expect you to tell me that you too you see an elephant.
If not, something is wrong. ... everybody hears everybody else stating
that they see the same elephant he sees. This, after all, is the best
definition of objectivity.

[i.e. in RQM regards "objective" reality as a  locus of intersubjective
agreement and ...]

"any such conversation about elephants is ultimately an interaction
between quantum systems"

[i.e. between superposed observers, see below]

"This fact may be irrelevant in everyday life, but disregarding it may
give rises to subtle confusions, such as the one leading to the
conclusion of nonlocal EPR influences. ... .In the EPR situation, A and
B can be considered two distinct observers, both making measurements on
á and â. The comparison [!!!] of the results of their measurements,
we have argued, cannot be instantaneous, that is, it requires A and B
to be in causal contact."

[i.e. since information exchange is a local process, EPR is local]

"More importantly, with respect to A, B is to be considered as a normal
quantum system (and, of course, with respect to B, A is a normal
quantum system)"

[i.e A is superposed in B's perspective and viceversa]

As far as superpositions can be detected, all the above is testable.

Cheers,

IV

PS Smerlak and Rovelli also realise that "From this perspective,
probability needs clearly to be interpreted subjectively", i.e.
according to the DeFinetti interpretation which I have been ranting
about ([2]).

[1] http://arxiv.org/abs/quant-ph/0604064
[2]
http://groups.google.com/group/sci.physics.research/msg/fc81d7a091622078

My understanding of Smerlak and Rovelli's preprint was that one can
replace non-locality by the axiom  that "reality is local" to the
extent that a distant measurement event does not become "real" for an
observer until it enters that observer's past light cone.

So e.g., there is no "element of reality" (for observer Alice) to be
associated with the (for her as yet unmeasured) spin state of the
distant space-like separated member of a pair of spin anti-correlated
particles, at the time of her selection of the earlier (for her)
orientation of  the  axis of the measurement of the near particle's
spin.  Such an "element of reality" need only arise for her when the
distant (Bob's) measurement enters into her past.   Symmetrically
similar for Bob, or any other observer.

There is (to me) an oblique reference to this loophole in the original
EPR paper and other writings of Einstein, but this localization of
"elements of reality" was apparently distasteful to him.

So the question becomes, what, if anything to we actually give up by
localizing "reality" in this way?

Briefly, what these people did is the following:
1) they recognized that classical Boolean logic has its realization
in terms of unions and intersections of subsets of a given set. In
classical physics this set can be identified with the phase space of
the physical system.
2) they noticed that the distributive law of classical logic is far
from obvious, and they substituted it with a weaker postulate
(orthomodularity). This gives rise to the so-called "quantum logic".
This logic has a mathematical realization in terms of intersections and
spans of closed subspaces in the Hilbert space. So, the phase space
of classical mechanics should be generalized to the Hilbert space
of quantum mechanics.

I think, this is a powerful result as it shows that classical theories
form a subset of quantum theories: classical distributivity is a
particular case of quantum othomodularity.

The interpretation of quantum mechanics that is most consistent with
the Bikhoff-von Neumann logical approach is the "ensemble" or
"statistical" interpretation presented in

L.E. Ballentine Quantum Mechanics: A Modern
Development (World Scientific, Singapore, 1998)

I highly recommend this book.

Yes, quantum logic says nothing about dynamics. In order to get the
Schrodinger equation you need to add the principle of relativity to
your postulates. As demonstrated by

E. P. Wigner, On unitary representations of
the inhomogeneous Lorentz group, Ann. Math. 40 (1939), 149.

and

P. A. M. Dirac, Forms of relativistic
dynamics, Rev. Mod. Phys. 21
(1949), 392.

this requires a definition of the unitary representation of the
Poincare group in the Hilbert space of the system. The Hamiltonian
is a representative of the generator of time translations of the
Poincare group, and the Schrodinger equation

-ih d/dt |Psi(t)> = H |Psi(t)>

is just a compact form of writing how the state vector changes
under time translations.

Eugene.

On page 71, Mackey introduces "Axiom VII", which says:
        The partially ordered set of all questions in quantum mechanics is
        isomorphic to the partially ordered set of all closed subspaces
        of a separable, infinite dimensional Hilbert space.

That this is an axiom, and not a theorem, is the sense in which
we do not know why quantum mechanics works. Mackey is refreshingly
honest about this point:

        This axiom has rather a different character from Axioms I through
        VI. These all had some degree of physical naturalness and
        plausibility. Axiom VII seems entirely ad hoc. Why do we make it?
        Can we justify making it? What else might we assume? We shall
        discuss these questions in turn. The first is the easiest to
        answer. We make it beacuse it "works," that is, it leads to
        a theory which explains physical phenomena and successfully
        predicts the results of experiments. It is conceivable that a
        quite different assumption would do likewise but this is a
        possibility that no one seems to have explored. Indeed, one
        would like to have a list of physically plausible assumptions
        from which one could deduce Axiom VII. Short of this one
        would like a list from which one could deduce a set of
        possibilities for the structure of Q, all but one of which
        could be shown to be inconsistent with suitably planned
        experiments. At the moment such lists are not available
        and we are far from being forced to accept axiom VII as
        logically inevitable. ...

Mackey's description of the situation is fairly accurate, and he
thankfully does not attempt (as, for example, Gottfried does,
with his "algebra of filters") to dupe the reader into thinking
that we know why the probabilities assigned by quantum mechanics
coincide with experimentally observed frequencies of individual
experimental results. Birkhoff and Von Neumann's argument, which
Mackey refers to, is the closest that anybody has come, as far
as I can determine, to providing some justification for the
use of quantum mechanics, although at best they have shown
that quantum mechanics is one of a number of procedures which
could conceivably be used to assign probabilities.

Charles has presented a paper which he claims provides the
explanation required. I have examined this paper but cannot
find a satisfactory explanation of why quantum mechanics,
rather than some other procedure, is the correct procedure
to use for assigning probabilities to the results of
measurements. There are some things in the paper with which
I agree, but two of the principal foundations, namely
relationalism and quantum logic, seem to me to be unlikely
to be fruitful.

I have explained before why I find relationalism to be incoherent.
Either it is a founding principle on which his argument is based,
which I hope it is not, because it would be difficult to base
a coherent argument on an incoherent principle, or the argument
can be presented without any appeal to relationalism (or any
other "ism"), which would greatly improve its clarity.

The use of quantum logic also seems to me to present no improvement
in understanding, since it merely replaces one unexplained procedure
with another. To say that the procedures used in quantum mechanics
consitute logic is at best a poetical metaphor, because quantum
mechanics is literally not logic. When somebody says that statements
have "truth values" which can be complex, I do not know what they
mean.  I can consider maps from statements to sets other than
{true,false}, but if somebody wants to say that these are "truth
values", then there are two possible cases.

One possibility is that this is just the introduction of a new term,
"truth value", and that any other term could have been used just
as well, for example "fribble". In that case, one would have to
conclude that quantum logic is not a more appropriate name than
quantum fribbology, and that those who opt to study quantum logic
should be warned that it is not a system used to model inference,
as actual logic is, but that it is a particular mathematical system
to which actual normal true-and-false logic applies, and that calling
it logic is just poetry.

(In mathematics, we often speak of a distance between numbers, and
this is an example of perhaps similar poetry, because numbers do
not have locations in space, and the map from (say) R times R to R
could have been given any other name apart from distance. It could
have been called the alpha function, for example, and mathematics
would be just the same. The usage of terms like "distance" is
whimsical and metaphorical.)

The other possible position that an advocate of quantum logic
could adopt is that the choice of the term "truth value" does
indeed carry an important message of some kind, and then
they have the obligation to tell us what that message is. Is
the message that normal logic has to be abandoned and replaced
by this new system? Why, and how could anybody possibly ever
know such a thing?

In Charles' paper, and in my correspondence with him, he has
been keen to insist that his introduction of the entire Hilbert
space formalism, along with the identification of kets as
propositions about measurement results in a formal language,
is little more than a choice of notation. However, the set
of things which can be proven about the results of measurements
if one merely accepts the Hilbert space formalism and the
rules of quantum mechanics for assigning probabilities to
the results of measurements is non-trivial.

For example, if there are 10 mutually exclusive complete
measurements than I can perform on a system, each
of which can give 10 possible results, then a complete
specification of the probabilities of obtaining each
of the 100 results requires 90 parameters to specify.
That's 100 possible results, grouped into sets of 10.
In each set of 10, I assign 9 probabilities, and the
10th is fixed by the fact that the probabilities must
sum to one.

If I suppose that measuring the same thing twice always
gives the same result, then I can prepare a system by
making a measurement. Then 10 probabilities are fixed
(one probability is 1 - if I measure the same thing
again, I will get the same result, nine are zero - if
I measure the same thing again, the chance of me getting
any of the other nine results is zero). That leaves 81
parameters which I need in order to specify the probabilities
of obtaining the various results of the different measurements
I could perform.

Quantum mechanics, however, tells us that we can
specify all of the probabilities with only 18 parameters.
All that we need to do is specify a ray in a ten-dimensional
Hilbert space, so that's 9 complex numbers or 18 parameters.

So if we have accepted the Hilbert space formalism, and if
we have accepted that the square of the inner product
gives us probabilities of finding particular measurement
results given particular preparations, then we have
already agreed to some very non-trivial statements
about the results of experiments and how many parameters
are needed to describe them. A mere choice of notation
can't change an 81-dimensional space into an 18-dimensional
space. It is noteworthy that this is all before any mention
has been made of time evolution, the Hamiltonian, or any dynamics.

The question is: "Why are there 18 and not 81 parameters needed to
specify the probabilities of obtaining the various possible measurement
results?" Right now, the only answer we have is that the symbols
tell us so, and I do not believe that Charles, Mackey, Rovelli,
Birkhoff & Von Neumann, or anybody else has come even remotely
close to addressing this question.

R.

Thus spake tttito <vec...@weirdtech.com>

If so, then I do not accept this part of it. What we can say about
reality is subjective. That does not mean there is no objective reality.
I do not think Rovelli thinks there is no objective reality either.

As for the rest of what you say, it does not alter what I said. In
discussions here on spr a few years back Matt McIrvin proved very good
at expressing this point of view. Nonetheless it does not alter the
fundamental position of the realist, that reality exists whether or not
it is outside the light cone.

Certainly, in the sense that probability depends on the information
available to an observer.

Regards

--
Charles Francis
substitute charles for NotI to email

 Thus spake sigoldbe...@gmail.com

Also to me.
Yes, I think there is. We have to give up realism, that some sort of
material reality exists independent of observation, and adopt some sort
of sophisticated form of idealism in which reality only exists for
observers inside a light cone. If we are doing that then I don't think
we have really solved the question of interpretation at all.

Regards

--
Charles Francis
substitute charles for NotI to email

What Rovelli is asking for can be done more simply still. I show this
in the suggestively titled "On The Quantum Dynamics of Moving Bodies",
which can be found under

                          http://federation.g3z.com/Physics/Index.htm

I'll summarize, here, what's done there.

In effect, the postulates are
(1) A system is described by a set (q1,q2,...,qN) of configuration
space coordinates that satisfy a 2nd order law of motion, q''(t) =
A(q(t),q'(t))
(2) At each time [q(t),q(t)] = 0
(3) At each time [q(t),[q(t),q'(t)]] = 0.

A stronger version of (3) is taken: particularly, that the [q,q']
commutators are c-numbers. There is a brief mention of weakening this
condition to only requiring that [q,q'] be a function of q's only,
independent of q'.

For the following, define the "quantum" Poisson brackets by
                       {A,B} = [A,B]/(i h-bar).

What Hojman and Shepley showed in 1990 is that if one assumes that the
classical limit of the {q,q'} commutators forms a non-singular matrix,
W, then W will be the inverse mass matrix of a non-singular Lagrangian
system. Thus, the quantum theory must have a classical Hamiltonian
theory as its classical limit, and must therefore be the quantization
of a classical Hamiltonian theory.

As I point out initially, this generalizes. If one starts out with
general phase space coordinates {s1,s2,...,sp} without making any
assumptions about the commutators; and one assumes they satisfy a first
order law s'(t) = V(s(t)), then in the classical limit one gets what is
known as a Poisson manifold.

Locally, this layers into what are known as "symplectic leaves". This
layering defines what eventually becomes the superselection structure
of the quantum theory. On each layer, the Poisson tensor Omega = {s,s'}
is invertible, with Omega^{-1} = omega, which yields the symplectic
form
                                           omega_{ij} ds^i ^ ds^j.

The requirement that the commutators cohabit with the equations of
motion is a very strong restriction and, here, implies that the system
comes from a Lagrangian that is the first order in ds/dt -- as
expected.

Locally, the coordinates can be divided into coordinates and velocities
s = (q, v = dq/dt) such that the symplectic form takes on the form
                                              m_{ij} dq^i dv^j,
which yields the mass matrix m = d^L/dv^2 of a Lagrangian. The inverse
W = m^{-1} gives you the [q,v] commutator matrix (in the classical
limit),
                                        {q, dq/dt} -> W, as h-bar -> 0.

The rest of the writeup focuses on the special case where the total
system has a decomposition into (q, v), with a 1st order law (dq/dt =
v, dv/dt = A(q,v)), such that the (q) part is a classical algebra,
[q,q] = 0, and [q,v] is restricted to c-number.

There is, at this point, no restriction on the number N of degrees of
freedom (N may be infinite). This case, therefore, covers much of field
theory and the quantum mechanics. What's not included in here is a
prospective quantum mechanics of a test particle in a gravitational
field, since then the [q,v] commutators will yield -- up to proportion
-- the dual spacetime metric, which is dependent on q.

Again, here, the requirement of having both the commutators and the
equations of motion is a severe restriction. It shows up by
differentiating the [q,q] = 0 equation and by taking various Jacobi
identities (the same strategy Hojman and Shepley used).

Definining W = {q,v}, and S = {v,v}, the constraints amout to the
following:
         d/dt {q,q} = 0 -> W^{ab} = W^{ba}
         dW/dt = d/dt {q,v} -> dW^{ab}/dt = 1/2 ({q^a, A^b} + {q^b,
A^a})
Also one gets from this equation
           S^{ab} = 1/2 ({q^b,A^a} - {q^a,A^b}).
Finally
         dS/dt = d/dt {v,v} -> dS^{ab}/dt = 1/2 ({v^a,A^b} -
{v^b,A^a}).

The Jacobi identities yield
         On (q,q,q) -> nothing
         On (q,q,v) -> {q^a,W^{bc}} = {q^b,W^{ac}}
         On (q,v,v) -> {q^a,S^{bc}} = {v^b,W^{ac}} - {v^c,W^{ab}}
         On (v,v,v) -> {v^a,S^{bc}} + {v^b,S^{ca}} + {v^c,S^{ab}} = 0.

It's at this point that the punchline is dropped. Since the commutators
are already c-numbers, there's no need to take any classical limit, as
Hojman and Shepley did. The adjoint action of the q coordinates on
functions F(q,v) is that of a derivative operator
                      {q^a,F(q,v)} = W^{ab} dF/dv^b
and the adjoint action of the velocities v on functions F(q) alone is
                      {v^a,F(q)} = -W^{ab} dF/dq^b.
This is the case, when the functions are restricted to polynomials. One
has to make technical assumptions (that are not yet spelled out clearly
in the writeup) on the underlying topology of the algebra in order to
pass over to a limit and incorporate a larger class of operators within
this.

I assume this can be taken care of appropriately (e.g. one method may
be to restrict one's focus to C*-algebras and use the method of induced
representations to arrive at operator forms for the respective adjoint
actions -- this is where the number N of degrees of freedom may be
required to be finite).

The result of this is that one arrives at what are in essence the
Helmholtz conditions. The Helmholtz conditions determine when a 2nd
order system has a Lagrangian.

More precisely, one has to factor out the 0-subspace of the W matrix.
This is the primary reason I required the W matrix to be c-numbers. The
0-subspace gives you the coordinates (q_C, v_C) which form a classical
subsystem. The remainder of the system (q_Q, v_Q) is the quantum part
of the system.

The classical subsystem evolves independently of the quantum
coordinates, and must therefore be regarded as external.

So, in the following I'll let (q,v) refer to just the quantum
coordinates (q_Q,v_Q).

In the quantum subsystem, the W matrix is invertible, giving you the
mass matrix m. Defining the KINETIC MOMENTUM P = m v, one arrives at
commutators
                      {q,q} = 0, {q,P} = I, {P,P} = s,
which almost gets you there. The 2nd order system takes on the form
                         m dq/dt = P; dP/dt = F(q,p).

The Jacobi relations on (q,p,p) establish that s is a function of q
only. The relations on (p,p,p) show that the 2-form s = s_{ij} dq^i ^
dq^j is exact and that, locally, s = dA, with A a function of q only.
This allows one to define the CANONICAL MOMEMTNUM, p = mv + A,
resulting in commutators
                       {q,q} = 0, {q,p} = I, {p,p} = 0.

The equations of motion now become
                              m dq/dt + A = p; dp/dt = f.
Differentiating the commutator relations and applying these equations
yields
                            df^j/dp_i = W^{ik} dA_k/dq^j; df_i/dq^j =
df_j/dq^i,
from which one arrives at (locally):
                     f_i = -dU/dq^i, A_i = -m_{ij} dU/dp_j.

But A is a function of q only, therefore U is linear in the momenta.
The result is that the equations of motion become
                    dp_i/dt = -dU/dq^i = -d/dq^i (U + 1/2 W^{ij} p_i
p_j)
                    dq^i/dt = d/dp_i (U + 1/2 W^{ij} p_i p_j)

showing that the quantum part of the system is canonically quantized
with a Hamiltonian that is quadratic in the momenta.

Competing the square, one arrives at the final form for the
Hamiltonian,
                           H = 1/2 W^{ij} (p_i - A_i(q)) (p_j - A_j(q))
+ phi(q).

The final result is that the system in question is proven to be -- in
the most general case -- a hybrid classico-quantum system, in which the
quantum subsystem is canonically quantized with respect to a
Hamiltonian quadratic in the momenta evolving in superselection sectors
parametrized by the (external) classical subsystem.

A good example of how this works -- and an illustration of how the
constraint of having both equal-time commutators and equations of
motion -- is to consider the case of a 2-body system in ordinary
3-space, with
                    {q,v} = I/m; {Q,V} = I/M; {q,q} = {v,v} = {Q,Q} =
{V,V} = 0
and with (q,v)'s commuting with (Q,V)'s. If one assumes a force law of
the form
                    dq/dt = v; m dv/dt = F(q,v,Q,V); dQ/dt = V; M dV/dt
= -F(q,v,Q,V),
then the requirement of consistency severely restricts the form the
interaction force F may have.

Differentiating the {q,v} relation, one gets {q,F} = 0. Similarly,
{Q,F} = 0. Therefore F is independent of v and V. Differentiating the
{v,v} relation, one gets -- in component form --
                      {v^a, F^b/m} - {F^a/m, v^b} = 0 -> dF^a/dq^b =
dF^b/dq^a.
Similarly for the Q coordinates
                                           dF^a/dQ^b = dF^b/dQ^a.
Differentiating the {v,V} relations yields
                                 (1/M) dF^a/dq^b + (1/m) dF^b/dq^a = 0.
This shows that the force is independent of the center of mass
coordinates (mq + MQ) and depends only on the relative coordinates
(q-Q) with the other two relations showing that the dependency is given
by
                                        F = -dU(q-Q)/dq =
...

leggi tutto

Thus spake Eugene Stefanovich <euge...@synopsys.com>

This is true. But I think that to complete Rovelli's program one should
do more, that is to translate the fundamental statements of quantum
logic into simple, and preferably obvious, statements about measurement
in the English language.
Good answer. I wasn't aware of the references you gave, but this is what
I also do.

Regards

--
Charles Francis
substitute charles for NotI to email

 Thus spake r...@maths.tcd.ie

The fundamental principle is that we can only say where something is if
we say where it is relative to other matter. That does not strike me as
being incoherent. In fact I find it simple, and even empirically
obvious. What is perhaps a lot less simple is building it into a
mathematical structure. Doing so certainly defeated Descartes and
Leibniz, but then we know a lot more now than they did then.

I would be happy enough with that. Actually as a result of the
correspondence we have had I have altered my terminology, so that "truth
value" now refers to the modulus |<f|g>|, so that it is real. This also
remains consistent with the formal definition of a many valued logic. I
have also demoted the notion of a truth value in the account, and it now
only serves to complete that formal definition, and is not used in any
other way. In practice quantum logic gives a formal structure for the
calculation of probabilities (which may also be regarded as truth
values, as they are in Bayesian reasoning).

In general one should not treat truth values as carrying much in the way
of an important message. They are really just a measure of how much we
think we ought to believe in a proposition, which is itself a pretty
woolly, and frequently subjective concept (as in fuzzy logic) unless one
can find objective reasons which may, for example, relate truth values
to probabilities. In my paper I start with the idea of probabilistic
results to experiments, and the structure of Hilbert space as a logic is
determined from that, and not the other way around.

Yes. But quantum logic is not the whole of quantum mechanics. It only
applies to experimental results at a given time. We cannot usefully
determine anything much from that unless we also have a time evolution
equation. As Eugene has just remarked time evolution comes from adding
the principle of relativity. The principle of relativity is contained
within the fundamental principle of relationism, so introducing it is
not a problem.

You can lose some of those. There are only nine parameters; so long as
we stick strictly within a Hilbert space defined at given time, phase is
meaningless. It becomes important when dynamics are introduced.

In practice your fundamental assumption appears to be wrong, that you
can have 10 independent mutually exclusive complete measurements of a
system, each giving 10 possible results. All the measurements described
in quantum theory are represented as operators, and as such are linear
combinations of each other. I think you are overlooking a fundamental
point which I make in my paper, that all measurements can be reduced to
measurements of position.

If we stick to measurement at one particular time, which is the way
Hilbert space is formulated, then strictly we can only measure position,
and your other nine possible measurements are a fiction. If you want to
measure something else, momentum say, then you have to take measurements
over a period of time, and therefore you do have to invoke dynamics.
That means a determination of changes in position, so it is not
unreasonable to expect the momentum operator to be a linear combination
of position operators.

To make your case stick you would have to find a genuinely independent
measurement. That's not impossible. Spin, for example. But if there is
such a genuinely independent measurement, then you were wrong in your
original claim that your first measurement was complete, and in that
case you can't describe the system with a 10 dimensional Hilbert space.

Regards

--
Charles Francis
substitute charles for NotI to email