[SOLVED] entangled states

Ilja Schmelzer

"Andreas Most" <Andreas.Most@nospam.de> schrieb
> Ilja Schmelzer wrote:
> > "Andreas Most" <Andreas.Most@nospam.de> schrieb
> >> Ben Rudiak-Gould wrote:
> >>> Not impossible, just unheard of. It's worth thinking about why
causality
> >>> violation is considered such a bad thing. There's no inherent problem
> >>> with an effect preceding a cause with respect to some frame. The
> >>> problems show up when there are closed causal loops, i.e. when A
causes
> >>> B causes ... causes Z causes A. Forbidding FTL communication is
> >>> sufficient but not necessary to prevent causal loops in special
> >>> relativity. A much weaker condition which suffices is that no effect
may
> >>> precede its cause with respect to some particular inertial frame S.
> >>> Effects may still precede causes with respect to other frames, but
> >>> that's not a paradox, just a somewhat surprising result.

> >> However, you lost me with your last statement.
> >> I agree that "forbidding FTL communication" is not the necessary
> >> condition to prevent causal loops. But, as of my understanding,
> >> the weaker condition, that no effect may precede its cause in some
> >> inertial frame, directly implies that information cannot be
communicated
> >> faster than light. Otherwise you could use tachyons to send some
> >> information into your own past.
> >
> > The weaker condition requires a fixed choice of a preferred frame
> > or preferred time t. Then, causal connection A->B is possible
> > if t(A)<t(B).
>
> I don't think this was Bens point.

The point is that there _is_ a condition weaker than "forbidding FTL
communication" which allows to prevent causal loops. (BTW, this
remains true even if you don't like this condition because it violates
a strong form of the relativity principle.)

> > That means that from point of view of other Lorentz frames t' it
> > may happen that t'(A)>t'(B), thus, information is send into the
> > "past" of "time" t'. But the "time" t' is in this interpretation only
> > some artificial local time-like coordinate with no fundamental
> > importance. Fundamental, and related with causality, is only
> > one time coordinate t.
>
> Apart from the fact, that you obviously reject the relativity principle,

I reject a strong form of the relativity principle. The weaker
form of the relativity principle, which is only about observables,
remains valid. (At least for distances large compared with the
critical length of unification of SM with gravity.)

> what exactly is the preferred frame and how can I identify it?

You can roughly identify it as the rest frame of CMBR.

> Is the preferred frame globally valid (in our universe) and static?

Yes. (You need a theory of gravity with preferred frame
for this purpose, see gr-qc/0205035.)

> > Note that the mechanism which describes the FTL information
> > transfer necessarily violates Lorentz covariance, depends on
> > the preferred time.
>
> FTL communication does not violate Lorentz covariance at all.
> Tachyons are described perfectly well in a covariant way.
> The problem is causality.

Ok, but if we include a reasonable notion of causality, without
causal loops, as an additional requirement for the mechanism,
my statement holds.

Ilja

Ilja Schmelzer

"Hendrik van Hees" <hees@comp.tamu.edu> schrieb
> Ilja Schmelzer wrote:
> > Ok. But, in this case, if you want to be consistent, you should be
> > careful not to use realistic terminology.
>
> I try to use consistent terminology. For me an experimental setup in the
> lab *is* realistic, and I use common language to describe it. Quantum
> theory tells us that we cannot know all observables of a system with
> certainty,

To know something with certainty is quite irrelevant for a realist if
the question is if something really exists.

If you reject realism, you not only give up some hope to know some
state of reality with certainty (or without certainty). In this case, you
nonetheless would be allowed to use realistic terminology.

> You may dream of a deterministic theory, where the outcome of all
> measurements is predetermined by the preparation of the state, but
> that's still a dream, and the success of quantum theory makes it very
> difficult to make that dream come true ;-). Here we discuss physics,
> not dreams!

I don't dream about a theory where everything may be predetermined
by some human preparation of the state. Realism is much weaker -
the hypothesis that there exists something out there which determines
the result of the measurement.

> > But what we observe in reality ;-) are single events. Only later we
> > combine all our single observations into a statistical picture, which
> > may be compared with QM predictions. In this sense, QM
> > is obviously incomplete.
>
> So far, no physical theory is complete. So what?

In this sense - that it describes what happens for single events -
Bohmian mechanics (and Nelsonian stochastics - determinism is
not the relevant point) are complete.

> Up to now QM describes
> all outcomes of experiments very well. Maybe further scientific
> progress comes up with a more satisfying explanation for the phenomeno.
> So far it's not!

Bohmian mechanics and Nelsonian stochastics are more satisfying
explanations, simply because they are realistic explanations, while
minimal QM refuses to explain anything.

> > (To say "there are single events, but it is impossible to make
> > predictions about them" already uses realistic language and
> > therefore presupposes some notion of realism.)
>
> As I said, for me an experimental setup in the lab is real. Your notion
> of "realism" is too narrow. One cannot talk about experiments without
> that minimal "realistic language".

Too narrow?

For an experiment, we measure expectation values E(f|c) for functions
f on measurement results M in dependence of control parameters c in C.
There exists some reality X with probability distribution rho(x)dx so
that E(f|c)= int f(m(x,c)) rho(x) dx.

> >> Let's take this most simple example of polarisation-entangled
> >> photons.
> >
> > There is no disagreement about the math.
>
> The math describes the outcome of experiments very well. So it's a
> successful physical theory. I don't know, what you disagree about,
> except a dream about a special philosophical conception about nature,
> but nature does not care about our philosophical prejudices, but
> behaves as she likes.

The hypothesis about the existence of some state of reality x in X so
that the preparation of the experiment defines some probability
distribution rho(x) on X with E(f|c)= int f(m(x,c)) rho(x) dx defines,
of course, a special philosophical conception of nature named realism.

But Nature does not seem to object against this philosophical
conception. We have realistic theories in agreement with
observation.

> > No necessity, because I have never questioned that to prove
> > Bell's inequality you need some notion of reality.
> > In the theory "Gods Will is unpredictable and unexplainable" I
> > cannot prove Bell's inequality too.
>
> Quantum theory is much more than such religious conceptions.

Of course. But the part which is useful remains valid in realistic
theories.

The rejection of the search for realistic explanation the minimal
interpretation shares with this religious conception.

> >> Then one finds a violation of Bell's inequality,
> >
> > It has also never been questioned that Bell's inequality is
> > violated in QM.
>
> It is violated in a way agreeing with QM, and thus it's very difficult
> to think of a deterministic theory agreeing with all the observations,
> QM describes successfully.

No, it is simple, and well-known how to do this. BM, NS.

> > Moreover, I don't think it makes much sense to talk about
> > causality in a theory where we cannot even talk about single events.
> > The notion named "causality" in QM literature is IMHO better called
> > statistical correlation.
>
> The state (statistical operator) evolves according to causal laws.
> That's why I call QM a causal theory. Without causality you'd really
> need not do science at all. In my language QM is an indeterministic but
> causal theory.

Again, I see no justification to talk about causality in a
nonrealistic theory. In statistics, as long as you don't care
about realistic explanation, you have to use, instead, the
notion of correlation.

QM is in this sense not causal, but a scheme which allows
to compute correlations.

> > I would insert "the minimal interpretation of" before "quantum
> > theory".
>
> Yes, and one should not interpret more into the theory than there is
> contained in it.

The minimal interpretation is, in some sense, not an interpretation
but a refusal to interprete.

> >> According to
> >> quantum theory, we cannot have more than that probabilistic
> >> knowledge.
> >
> > That's already beyond the minimal interpretation. The minimal
> > interpretation simply remains silent. (Else, it would not be minimal,
> > and I would define a more minimal interpretation.)
>
> This I do not understand. Minimal interpretation contains the
> probabilistic interpretation of the state

Yes.

> and takes this stochastic nature of the QM description serious.

No. The minimal interpretation is not in conflict with
other, non-minimal interpretations, but defines the common
part of various interpretations. In all questions where
different interpretations give different answers the minimal
interpretation remains silent.

(If not, I simply define another interpretation which
remains silent about this question. This new interpretation is
smaller than your "minimal" interpretation, therefore I can
claim that your choice of denotation of your interpretation
is incorrect, and my new interpretation is the minimal one.)

Ilja

Ilja Schmelzer

"Andreas Most" <Andreas.Most@nospam.de> schrieb
> Ilja Schmelzer wrote:
> > ...
> > I see, the phrase "a correlation existed" may be meaningful also from
> > a purely positivistic point of view, where only observables are
relevant.
> > But the full phrase was "existed the whole time from the preparation
> > of the particle pair", which already refers to something not observed,
> > thus, to some not purely positivistic idea of reality.
>
> The correlation existed, not the outcome of the measurement.

That's meaningless without a concept of realism beyond pure
positivism.

> If you start from an entangled state
>
> |Psi>=1/sqrt(2)[|HV>-|VH>]
>
> and you find photon 1 to be horizontally polarised you could have
> as well started off with a wave function
>
> |Psi>=|HV>
>
> for this single photon pair. I.e., you would have found a horizontal
> polarisation for photon 1, even if you had performed the measurement
> earlier.

A counterfactual statement. Such statements are meaningless outside
a concept of realism beyond positivism.

There is a meaningful notion of realism, there such claims make sense.
I like it, and I defend it. But if you reject it, without defining an
alternative
concept of realism which makes such claims meaningful, you are simply
inconsistent.

> > But a notion of _existence_ of something (the value or the correlation
> > observed later) at some moment of time t0 should not depend on
> > human decisions made at later time t>t0.
>
> Existence is a pretty philosophical term.

No, it is a well-defined notion, which allows you to prove theorems
if you accept it.

> The question would be
> what is the meaning of the existence of something that has no impact
> on our universe at all

Very simple. What is real has to be specified by a realistic physical
theory. Realism simply means that we search for scientific truth only
among realistic theories.

More specific: you have experiments which measure expectation values
E(f|c) of functions on measurement results f: M->R depending on
control parameters C. A realistic theory has to explain this using
a state of reality x in X which defines the measurement results
m=m(x,c) and a probability distribution rho(x) so that
E(f|c)= int f(m(x,c)) rho(x) dx.

The question "what is real" has the answer "if this explanation
is correct, x is real".

Once we also use Ockhams razor to choose among theories, things
which have no impact on our universe will not be part of the preferred
realistic theory.

> I could assume its existence as well as its nonexistence
> without any change to the description of our world.

You cannot assume the nonexistence of a preferred frame.
Because no realistic description of the world is possible
without some real effects happening FTL. That's because
realism is not a pretty philosophical theory but a well-defined
concept which allows to prove theorems.

Ilja

Ilja Schmelzer

"Oz" <Oz@farmeroz.port995.com> schrieb
> Is this what bell's inequality states?

Current state of a text explaining it:

Definition of statistical observation:

A statistical experiment gives a probality
distribution rho(m|c) of measurement results
m in M which depends on control parameters
c in C which may be defined by free decisions
of the experimenters. Expectation values for
functions f: M->R are defined by

E(f|c) =int f(m) rho(m|c) dm

Definition of statistical dependence:

A dependence of rho(m|c) or E(f|c) on c in C
or some subset c' in C', C = C'x C'', this is
called statistical dependence.

Definition of realistic explanation:

A realistic explanation consists of a probability
description rho(x) of "states of reality" x in X
and a function m(x,c) so that

E(f|c)= int f(m(x,c)) rho(x) dx.

Definition of causal dependence:

If m(x,c) depend on c in C or some subset
c' in C', C = C'x C'', this is called
causal dependence.

Definition of Einstein causality:

There are two possibilities to understand
Einstein causality. The weak (statistical)
notion of Einstein causality forbids only
statistical dependencies between spacelike
separated events.

Instead, realistic Einstein causality
predicts that for every observation exists
a realistic explanation which does not
contain causal dependencies between spacelike
separated event.

Proof of Bell's inequality:

Situation: We have two space-like separated
regions of spacetime A and B. We have
M = M_A x M_B, C = C_A x C_B,
M_A = M_B = {-1,1}, C_A = C_B = {1,2,3}

We denote the expectation value E(f|C) of the
product f(m_A,m_B) = m_A m_B with P(c_A,c_B) so that

P(c_A,c_B) = int m_A(x,c_A,c_B) m_B(x,c_A,c_B) rho(x) dx.

Now Einstein causality forbids m_A to depend on c_B
and reverse, so that

P(c_A,c_B) = int m_A(x,c_A) m_B(x,c_B) rho(x) dx.

Now, for c_A = c_B we observe m_A = m_B. This
is possible only if m_A(x,.) = m_B(x,.) are the same
function m(x,.). (This is the EPR argument.) Thus,

P(c_A,c_B) = int m(x,c_A) m(x,c_B) rho(x) dx.

For the three function values m(x,1),m(x,2),m(x,3)
at most two of the following statements may be true:

m(x,1)==m(x,2); m(x,2)==m(x,3); m(x,1)=/=m(x,3)

(Indeed, if two are true, the third must be false.)
Thus, m(x,1)m(x,2)+m(x,2)m(x,3)-m(x,1)m(x,3)<=1.
(Each part is 1 if one statement is true, else -1.)
It follows that

P(1,2) + P(2,3) - P(1,3) <= int rho(x)dx = 1.

which is Bell's inequality.

Consequences of the violation:

Once Bell's inequality is violated, every realistic
explanations contains:

or a causal dependence m_A(x,c_A,c_B) of m_A on c_B,
or a causal dependence m_B(x,c_A,c_B) of m_B on c_A.

In other words, we have some causal connection,
A->B or B->A, but don't know its direction. It is
easy to see that, indeed, realistic explanations
with causal connections of above types exist.

If A and B are spacelike separated, above causal
connections are forbidden by realistic Einstein
causality, thus, realistic Einstein causality is
falsified by violations of Bell's inequality.

On the other hand, the existence of two realistic
explanations with different causal connections
has consequences:

First, we can immediately prove that the violation
of Bell's inequality cannot be used for information
transfer. Indeed, an application for information
transfer A->B contradicts the explanation B->A,
and reverse. Thus, weak Einstein causality is
not falsified.

Second, classical causality based on a preferred
frame is not falsified too. For every choice of
absolute time t we have a realistic explanation
compatible with classical causality: If t(A)<t(B)
we choose the explanation A->B, and reverse.

Moreover, assume that for every pair of open
spacetime regions A, B we have violations
of Bell's inequality. Now, assume we have a
general realistic theory which allows to explain
all these violations. Assume that its notion
of causality does not contain closed causal loops.
Then the realistic theory contains a preferred
foliation of spacetime. The construction of this
foliation is quite straightforward: We decide
p1<p2 if there exists some environments U1, U2
of p1, p2 so that all causal explanations
of violations of Bell's inequality between
U1 and U2 are of type U1 -> U2. This order
defines the preferred foliation.

Of course, the preferred foliation depends on
the choice of explanation. Other explanations
lead to other preferred foliations. But each
realistic explanation contains a preferred
foliation.

Ilja

Hendrik van Hees

Ilja Schmelzer wrote:

> I don't dream about a theory where everything may be predetermined
> by some human preparation of the state. Realism is much weaker -
> the hypothesis that there exists something out there which determines
> the result of the measurement.

But that's determinism again. You may say that there are no really
closed systems, but everything interacts with everything else in the
universe and that the indeterminism of quantum mechanics is just lack
of knowledge about the "rest of the universe". I'm not sure whether
this possibility is or is not in contradiction to the violation of
Bell's unequality, because this seems to be a concept introducing
nonlocal interactions, which have to be strictly distinguished from the
nonlocal correlations which are encoded in entangled states (EPR
states).

> In this sense - that it describes what happens for single events -
> Bohmian mechanics (and Nelsonian stochastics - determinism is
> not the relevant point) are complete.

Ok, now we shall again enter our old battle about what are different
theories. For me Bohmian mechanics is, insofar it is formulated
successfully in non-relativistich quantum mechnaics, the same theory as
quantum mechanics with an ugly additional concept, because also Bohmian
mechanics cannot tell me which polarisation state I will measure for a
single photon in an entangled state. Bohm's "trajectories" are well
hidden from our observations, and they cannot tell us about the outcome
of measurements beyond what we can already know about the system within
the minimal interpretation. Thus, Bohmian Mechanics does not help to
make quantum mechanics more complete than it already is in the much
simpler minimal interpretation.

> Too narrow?
>
> For an experiment, we measure expectation values E(f|c) for functions
> f on measurement results M in dependence of control parameters c in C.

Let's get it a little cleaned up. We measure observables which (in the
sense of the minimal interpretation) are not determined by the state,
we have prepared before doing the measurement. Thus the outcome of
these measurements for an ensemble of identically prepared systems show
variations, and the only thing quantum mechanics tells me is the
probability distribution about the outcome of these measurements.

To say, we measure expectation values for observables also implies that
I have to repeat the experiments sufficiently often to obtain this
expectation value with a given accuracy. So you have the same trouble
as with minimally interpreted QT: You do not make any statement about
the outcome of a single measurement. You cannot tell with certainty
which value you will measure before you actually measure it.

> The hypothesis about the existence of some state of reality x in X so
> that the preparation of the experiment defines some probability
> distribution rho(x) on X with E(f|c)= int f(m(x,c)) rho(x) dx defines,
> of course, a special philosophical conception of nature named realism.

Could you remind me about your mathematical notation? What means X and x
in X etc.
>
> But Nature does not seem to object against this philosophical
> conception. We have realistic theories in agreement with
> observation.

Before I though I have understood, what you mean by "realistic theory".
Now again this notion slipped away. If it's not predeterminism of all
observables as in good old classical physics, I do not understand yet
what you mean.

> Of course. But the part which is useful remains valid in realistic
> theories.
>
> The rejection of the search for realistic explanation the minimal
> interpretation shares with this religious conception.

You are right in the sense, that we have not yet a proof that there does
not exist a deterministic theory, which is as successful as QT to
explain the phenomena.

>> It is violated in a way agreeing with QM, and thus it's very
>> difficult to think of a deterministic theory agreeing with all the
>> observations, QM describes successfully.
>
> No, it is simple, and well-known how to do this. BM, NS.

See my objection against BM above. I have to think about NS again, but I
thought that even Nelson himself doesn't believe anymore in his own
concept.

> Again, I see no justification to talk about causality in a
> nonrealistic theory. In statistics, as long as you don't care
> about realistic explanation, you have to use, instead, the
> notion of correlation.

Again, I need to understand, what is a "realistic explanation" if it is
not determinism.
>
> QM is in this sense not causal, but a scheme which allows
> to compute correlations.

The trouble is, that we use different language. The best essay about the
subject "determinism vs. causality" is in Schwinger's book "Quantum
Mechanics, symbolism for atomistic measurements".

> The minimal interpretation is, in some sense, not an interpretation
> but a refusal to interprete.

Not at all. It takes the probabilistic nature of QT seriously not more
and not less.

> No. The minimal interpretation is not in conflict with
> other, non-minimal interpretations, but defines the common
> part of various interpretations. In all questions where
> different interpretations give different answers the minimal
> interpretation remains silent.

Where give different interpretation different answers? Can I
experimentally decide about the success or failure of one or the other
interpretation? If so, then you have not only a new interpretation but
a new theory!
>
> (If not, I simply define another interpretation which
> remains silent about this question. This new interpretation is
> smaller than your "minimal" interpretation, therefore I can
> claim that your choice of denotation of your interpretation
> is incorrect, and my new interpretation is the minimal one.)

As I said, don't interpret more into QT than it contains!

--
Hendrik van Hees Texas A&M University
Phone: +1 979/845-1411 Cyclotron Institute, MS-3366
Fax: +1 979/845-1899 College Station, TX 77843-3366
http://theory.gsi.de/~vanhees/ mailto:hees@comp.tamu.edu

Andreas Most

Ilja Schmelzer wrote:
> "Andreas Most" <Andreas.Most@nospam.de> schrieb
>
>>Ilja Schmelzer wrote:
>>
>>>...
>>>I see, the phrase "a correlation existed" may be meaningful also from
>>>a purely positivistic point of view, where only observables are
>
> relevant.
>
>>>But the full phrase was "existed the whole time from the preparation
>>>of the particle pair", which already refers to something not observed,
>>>thus, to some not purely positivistic idea of reality.
>>
>>The correlation existed, not the outcome of the measurement.
>
>
> That's meaningless without a concept of realism beyond pure
> positivism.
>
>
>>If you start from an entangled state
>>
>>|Psi>=1/sqrt(2)[|HV>-|VH>]
>>
>>and you find photon 1 to be horizontally polarised you could have
>>as well started off with a wave function
>>
>>|Psi>=|HV>
>>
>>for this single photon pair. I.e., you would have found a horizontal
>>polarisation for photon 1, even if you had performed the measurement
>>earlier.
>
>
> A counterfactual statement. Such statements are meaningless outside
> a concept of realism beyond positivism.
>
> There is a meaningful notion of realism, there such claims make sense.
> I like it, and I defend it. But if you reject it, without defining an
> alternative
> concept of realism which makes such claims meaningful, you are simply
> inconsistent.

Things are perfectly consistent if you consider the wave function as a
mathematical object in which all information we have about a quantum
state is encoded. A measurement changes the knowledge about the quantum
state and thus the wave function.
Then it is also obvious that different obervers may have different
description (wave function) of a quantum state based on their specific
knowledge about a state (consider e.g. the thought experiment about
"Wigner's friend")
And actually, the correlation of observables of an entangled system is
to me as mysterious as is in Newtonian mechanics an object moving on
a straight line forever if no forces are present. ;-)

>
>
>>>But a notion of _existence_ of something (the value or the correlation
>>>observed later) at some moment of time t0 should not depend on
>>>human decisions made at later time t>t0.
>>
>>Existence is a pretty philosophical term.
>
>
> No, it is a well-defined notion, which allows you to prove theorems
> if you accept it.
>
>
>>The question would be
>>what is the meaning of the existence of something that has no impact
>>on our universe at all
>
>
> Very simple. What is real has to be specified by a realistic physical
> theory. Realism simply means that we search for scientific truth only
> among realistic theories.
>
> More specific: you have experiments which measure expectation values
> E(f|c) of functions on measurement results f: M->R depending on
> control parameters C. A realistic theory has to explain this using
> a state of reality x in X which defines the measurement results
> m=m(x,c) and a probability distribution rho(x) so that
> E(f|c)= int f(m(x,c)) rho(x) dx.
>
> The question "what is real" has the answer "if this explanation
> is correct, x is real".
>
> Once we also use Ockhams razor to choose among theories, things
> which have no impact on our universe will not be part of the preferred
> realistic theory.
>
>
>>I could assume its existence as well as its nonexistence
>>without any change to the description of our world.
>
>
> You cannot assume the nonexistence of a preferred frame.
> Because no realistic description of the world is possible
> without some real effects happening FTL. That's because
> realism is not a pretty philosophical theory but a well-defined
> concept which allows to prove theorems.

In order to not be in the urge of assuming such a preferred frame
I avoid using hidden variables. Apart from this I do not see that
Bohmian mechanics makes any testable (by experiment) prediction that
goes beyond the predictions of QM. (Also your paper makes no testable
predictions as far as I have read it).
I agree that the Bohmian interpretation does not contradict experiment.
But I think you give up to many well-established principles without
gaining anything new in terms of testable predictions.

Andreas.


>
> Ilja
>
>

Hendrik van Hees

Andreas Most wrote:

> Things are perfectly consistent if you consider the wave function as a
> mathematical object in which all information we have about a quantum
> state is encoded. A measurement changes the knowledge about the
> quantum state and thus the wave function.

So far I can agree.

> Then it is also obvious that different obervers may have different
> description (wave function) of a quantum state based on their specific
> knowledge about a state (consider e.g. the thought experiment about
> "Wigner's friend").

I think that's not what is meant when we say: "We assign the state [psi]
(let [psi] denote a ray in Hilbert space represented by a vector |psi>)
to a system." It's too subjectivistic a view.

I think, what is meant by this statement is that a system was prepared
by the experimenter in this state [psi]. Within the minimal
interpretation that's a little bit unprecise, because the information,
encoded in [psi] is only probabilistic. So what it really means is,
that the system under consideration belongs to a (really prepared or at
least in principle preparable) ensemble of independent systems which
shows the statistic features encoded in [psi]. Different observers all
assign this state [psi] and not any other to it, although one observer
may use another observer's states mapped by a unitary (or antiunitary)
operator. This covers also the case of observers in different frames of
reference or using different pictures of time evolution (Schroedinger,
Heisenberg, or Dirac).

Of course, one also has the more common case of an incomplete knowledge
about the system, and then different observers might assign different
impure states (statistical operators) to the system, based on their
knowledge of the system.

> And actually, the correlation of observables of an entangled system is
> to me as mysterious as is in Newtonian mechanics an object moving on
> a straight line forever if no forces are present. ;-)

In fact, physics does not give an "explanation" for this. It's just an
experimental fact about moving bodies which Galileo and Newton used to
base their further analysis on. The principle of inertia is a basic
observation, we cannot deduce from more basic observations (despite the
fact that general relativity refines the principle of inertia in a
subtle way).

> In order to not be in the urge of assuming such a preferred frame
> I avoid using hidden variables. Apart from this I do not see that
> Bohmian mechanics makes any testable (by experiment) prediction that
> goes beyond the predictions of QM. (Also your paper makes no testable
> predictions as far as I have read it).

I agree completely.

> I agree that the Bohmian interpretation does not contradict
> experiment. But I think you give up to many well-established
> principles without gaining anything new in terms of testable
> predictions.

You make an already complecated subject even more complicated by
introducing unobservable "elements of reality" and name them
trajectories to make QT sound a little bit more like classical
mechanics.

--
Hendrik van Hees Texas A&M University
Phone: +1 979/845-1411 Cyclotron Institute, MS-3366
Fax: +1 979/845-1899 College Station, TX 77843-3366
http://theory.gsi.de/~vanhees/ mailto:hees@comp.tamu.edu

Ralph Hartley

Ilja Schmelzer wrote:
> "Hendrik van Hees" <hees@comp.tamu.edu> schrieb
>>... one should not interpret more into the theory than there is
>>contained in it.
>
> The minimal interpretation is, in some sense, not an interpretation
> but a refusal to interprete.

A *justified* refusal to interpret. Because all other interpretations
interpret more into the theory than is contained in it.

> ... The minimal interpretation is not in conflict with
> other, non-minimal interpretations, but defines the common
> part of various interpretations. In all questions where
> different interpretations give different answers the minimal
> interpretation remains silent.

Just so. But that's only *one* of it's good properties.

Another it that it *is* complete, in the sense that it answers all
questions that are experimentally testable. (Ignoring the fact that
Quantum Mechanics is really a framework not a particular theory)

No one ever promised you answers to any other questions.

No one promised that any others even *have* answers.

Certainly there are questions that do not have answers, e.g. "What color
are electrons?"

Other interpretations are useful aids to thought, for example they make
the causal properties easier to see, but they all contain something
unneeded.

Suppose someone suggested a bet on what the "correct" interpretation is.
How would you *settle* such a bet? Even if there were a "correct"
interpretation, what would it be good for? It would not predict the
results of even one more experiment.

> The question "what is real" has the answer "if this explanation
> is correct, x is real".
>
> Once we also use Ockhams razor to choose among theories, things
> which have no impact on our universe will not be part of the preferred
> realistic theory.

The answer to the question "what is real" does not have any impact on
our observable universe. I would be willing to let that one slide,
except for:

> You cannot assume the nonexistence of a preferred frame.
> Because no realistic description of the world is possible
> without some real effects happening FTL.

Therefore *all* realistic (in your narrow sense) theories contain
something with no impact on our universe.

In a broader sense, "many worlds", if taken literally (which I do *not*
normally recommend), is completely realistic. If it is correct, all
those worlds are real (the ones with nonzero amplitude). There is an
absolutely real independent reality which really determines everything
that really is determined.

Individual outcomes are an illusion. They don't happen, so they don't
need to be determined by anything.

There is no preferred frame, and the universe is locally causal. In fact
it is even deterministic. We don't remember things happening that way,
but we wouldn't be expected to. In each world we remember only one
particular outcome, and wonder what determined it, or why our
"consciousness", whatever that is, ended up in that particular world.

Science consists of finding realistic (in the broad sense), local
deterministic, theories. Many worlds has those properties, and BM does
not, so BM should not even be considered.

Do I really think that? No. But if I did, I would be just as consistent
in using realistic language, and in calling myself a realist, as you are.

I don't actually prefer any interpretation, except as aids to intuition.
Questions that cannot be answered *should* not be answered.

Ralph Hartley

Andreas Most

Ilja Schmelzer wrote:
> "Andreas Most" <Andreas.Most@nospam.de> schrieb
>
>>Ilja Schmelzer wrote:
>>
>>>"Andreas Most" <Andreas.Most@nospam.de> schrieb
>>>
>>>>Ben Rudiak-Gould wrote:
>>>>
>>>>>Not impossible, just unheard of. It's worth thinking about why
>
> causality
>
>>>>>violation is considered such a bad thing. There's no inherent problem
>>>>>with an effect preceding a cause with respect to some frame. The
>>>>>problems show up when there are closed causal loops, i.e. when A
>
> causes
>
>>>>>B causes ... causes Z causes A. Forbidding FTL communication is
>>>>>sufficient but not necessary to prevent causal loops in special
>>>>>relativity. A much weaker condition which suffices is that no effect
>
> may
>
>>>>>precede its cause with respect to some particular inertial frame S.
>>>>>Effects may still precede causes with respect to other frames, but
>>>>>that's not a paradox, just a somewhat surprising result.
>
>
>>>>However, you lost me with your last statement.
>>>>I agree that "forbidding FTL communication" is not the necessary
>>>>condition to prevent causal loops. But, as of my understanding,
>>>>the weaker condition, that no effect may precede its cause in some
>>>>inertial frame, directly implies that information cannot be
>
> communicated
>
>>>>faster than light. Otherwise you could use tachyons to send some
>>>>information into your own past.
>>>
>>>The weaker condition requires a fixed choice of a preferred frame
>>>or preferred time t. Then, causal connection A->B is possible
>>>if t(A)<t(B).
>>
>>I don't think this was Bens point.
>
>
> The point is that there _is_ a condition weaker than "forbidding FTL
> communication" which allows to prevent causal loops. (BTW, this
> remains true even if you don't like this condition because it violates
> a strong form of the relativity principle.)

I didn't say I don't like it. I just wanted to understand Ben's
argument.

>>>That means that from point of view of other Lorentz frames t' it
>>>may happen that t'(A)>t'(B), thus, information is send into the
>>>"past" of "time" t'. But the "time" t' is in this interpretation only
>>>some artificial local time-like coordinate with no fundamental
>>>importance. Fundamental, and related with causality, is only
>>>one time coordinate t.
>>
>>Apart from the fact, that you obviously reject the relativity principle,
>
>
> I reject a strong form of the relativity principle. The weaker
> form of the relativity principle, which is only about observables,
> remains valid. (At least for distances large compared with the
> critical length of unification of SM with gravity.)
>
>
>>what exactly is the preferred frame and how can I identify it?
>
>
> You can roughly identify it as the rest frame of CMBR.
>
>
>>Is the preferred frame globally valid (in our universe) and static?
>
>
> Yes. (You need a theory of gravity with preferred frame
> for this purpose, see gr-qc/0205035.)

As of my understanding, if you have two observers being at different
locations and each being at rest relative to the CMBR at their position,
the two observers move relative to one another.
That is you cannot define a preferred frame globally.
(BTW: I read in your paper that you can prove a flat
universe in your GLET. How would you then explain the redshift of
objects being far away if not by an expanding universe?)

>>>Note that the mechanism which describes the FTL information
>>>transfer necessarily violates Lorentz covariance, depends on
>>>the preferred time.
>>
>>FTL communication does not violate Lorentz covariance at all.
>>Tachyons are described perfectly well in a covariant way.
>>The problem is causality.
>
>
> Ok, but if we include a reasonable notion of causality, without
> causal loops, as an additional requirement for the mechanism,
> my statement holds.

Again, causality has nothing to do with covariance.
Instead, causality considerations tell us which (covariant) solution
makes physically sense. For example, a spacelike line cannot be the
world line of anything that interacts with our observable world.
Excluding mathematical possible solutions to physics equations based on
such considerations is also done elsewhere (E.g. the broken cup that
does not recompile or using retarded solutions in electrodynamics and
rejecting advanced ones). But these exclusion schemes do not change the
properties of the physics equation (properties like e.g. covariance)

Ilja Schmelzer

"Hendrik van Hees" <hees@comp.tamu.edu> schrieb
> Ilja Schmelzer wrote:
> > I don't dream about a theory where everything may be predetermined
> > by some human preparation of the state. Realism is much weaker -
> > the hypothesis that there exists something out there which determines
> > the result of the measurement.
>
> But that's determinism again.

Determinism is not the point. Random number generators may
be involved.

> You may say that there are no really
> closed systems, but everything interacts with everything else in the
> universe and that the indeterminism of quantum mechanics is just lack
> of knowledge about the "rest of the universe". I'm not sure whether
> this possibility is or is not in contradiction to the violation of
> Bell's unequality,

This possibility is certainly inside the domain of common sense
realism and also within EPR-Bell realism. The main formula
is

E(f|c)= int f(m(x,c)) rho(x) dx.

for the expectation values E(f) of some function f M->R on
the results of the measurement. x in X describes reality outside,
our lack of knowledge about it, as well as, possibly, some
inherent indeterminism, is included in the probability distribution
rho(x).

> because this seems to be a concept introducing
> nonlocal interactions, which have to be strictly distinguished from the
> nonlocal correlations which are encoded in entangled states (EPR
> states).

The nonlocality is only about the dependence of the localized
macroscopic measurement results m from the localized
macroscopic preparation parameters c in the function m(x,c).

x in X may be nonlocal or whatever you like, it doesn't matter.
All we need is the _existence_ of some X, rho(x), m(x,c)
If the dependence of m on c is Einstein-local, Bell's inequality
may be proven.

> > In this sense - that it describes what happens for single events -
> > Bohmian mechanics (and Nelsonian stochastics - determinism is
> > not the relevant point) are complete.

> Ok, now we shall again enter our old battle about what are different
> theories. For me Bohmian mechanics is, insofar it is formulated
> successfully in non-relativistich quantum mechnaics, the same theory as
> quantum mechanics with an ugly additional concept, because also Bohmian
> mechanics cannot tell me which polarisation state I will measure for a
> single photon in an entangled state. Bohm's "trajectories" are well
> hidden from our observations, and they cannot tell us about the outcome
> of measurements beyond what we can already know about the system within
> the minimal interpretation.

No problem. I do not want to suggest you to compute Bohmian trajectories.
(Moreover, I tend to think that Nelsonian stochastics is closer to truth.)

> Thus, Bohmian Mechanics does not help to
> make quantum mechanics more complete than it already is in the much
> simpler minimal interpretation.

You have to distinguish a complete description of reality from a
complete description of our observable expectation values. Last not least,
expectation values we observe only indirectly, combining lots of particular
real observations.

> > Too narrow?
> >
> > For an experiment, we measure expectation values E(f|c) for functions
> > f on measurement results M in dependence of control parameters c in C.
>
> Let's get it a little cleaned up. We measure observables which (in the
> sense of the minimal interpretation) are not determined by the state,
> we have prepared before doing the measurement. Thus the outcome of
> these measurements for an ensemble of identically prepared systems show
> variations, and the only thing quantum mechanics tells me is the
> probability distribution about the outcome of these measurements.

Correct.

> To say, we measure expectation values for observables also implies that
> I have to repeat the experiments sufficiently often to obtain this
> expectation value with a given accuracy. So you have the same trouble
> as with minimally interpreted QT: You do not make any statement about
> the outcome of a single measurement. You cannot tell with certainty
> which value you will measure before you actually measure it.

Indeed. I'm unable to prepare pure states of reality x. Our preparation
procedures only allow to prepare some subset of probabilistic states
rho(x)dx.

> > The hypothesis about the existence of some state of reality x in X so
> > that the preparation of the experiment defines some probability
> > distribution rho(x) on X with E(f|c)= int f(m(x,c)) rho(x) dx defines,
> > of course, a special philosophical conception of nature named realism.
>
> Could you remind me about your mathematical notation? What means X and x
> in X etc.

X means the set of all states of reality. This set has to be defined by
a realistic theory/interpretation.

x means a particular state of reality which is realized in a particular
experiment.

c in C describes the control or input parameters of the experiment -
parameters
which may be set by a free will decision of the experimenter.

rho(x)dx is the probability distribution of the states of reality defined
by the preparation procedure. (Better, the part of preparation
procedure before the choice of the control parameters c.)

> > But Nature does not seem to object against this philosophical
> > conception. We have realistic theories in agreement with
> > observation.
>
> Before I though I have understood, what you mean by "realistic theory".
> Now again this notion slipped away. If it's not predeterminism of all
> observables as in good old classical physics, I do not understand yet
> what you mean.

If you like, you can intepret the function m(x,c) as some deterministic
rule which describes how the unknown state of reality x, together with
the control parameters, defines the measurement result. But, again, I
don't think determinism is the point. A classical stochastic process is
described in the same way.

> > Of course. But the part which is useful remains valid in realistic
> > theories.
> > The rejection of the search for realistic explanation the minimal
> > interpretation shares with this religious conception.

> You are right in the sense, that we have not yet a proof that there does
> not exist a deterministic theory, which is as successful as QT to
> explain the phenomena.

Here I disagree. BT is a general scheme, as general as QT, and
may be applied in field theory in a similar way. As usual I refer you
to Bell, beables for QFT.

> >> It is violated in a way agreeing with QM, and thus it's very
> >> difficult to think of a deterministic theory agreeing with all the
> >> observations, QM describes successfully.
> >
> > No, it is simple, and well-known how to do this. BM, NS.
>
> See my objection against BM above.

I see, but your objection about an "ugly additional concept" in BM
does not prevent BM from being a deterministic theory agreeing
with all the observations QM describes successfully.

But the "ugly additional concept" is what I want to have. I impose
the restriction "realistic theory" to QM and observe that to make them
compatible I have to introduce some additional concepts. Fine. Now,
we cannot observe these additional things in detail, not fine. And
there may be (are) different proposals for these additional concepts,
which cannot be distinguished by observation. Also not fine.
But considerations about simplicity and beauty of theories have
to be applied in science anyway, and they may be applied here too.
Thus, not that problematic.

But, even much better, we can _prove_, that all these different
"ugly additioal concepts" have something in _common_. Thus,
there is no necessity to care about the ugly details of the ugly
additional concept - we know for sure about this common property.

This common property is a preferred foliation.

> I have to think about NS again, but I
> thought that even Nelson himself doesn't believe anymore in his own
> concept.

AFAIK after he has recognized that the wave function lives
on configuration space instead of 3D space.

> > Again, I see no justification to talk about causality in a
> > nonrealistic theory. In statistics, as long as you don't care
> > about realistic explanation, you have to use, instead, the
> > notion of correlation.
>
> Again, I need to understand, what is a "realistic explanation" if it is
> not determinism.

Determinism or classical stochastics. (Classical stochastics
may be, in principle, interpreted as a combination of determinism
and lack of knowledge. But this question as well may be left open.
If there is some "inherent nondeterminism" in Nature, but as far as
this "inherent nondeterminism" - whatever this means - may be
described with the math of classical stochastics, it is covered too.)

Observation gives you E(f|c)= int f(m) rho(m|c)dm.

Realism requires to explain this in the form
E(f|c)= int f(m(x,c)) rho(x) dx
for some hypothetical X, rho(x)dx, m(x,c), which the realistic
theory has to construct from rho(m|c)dm on M.

> > The minimal interpretation is, in some sense, not an interpretation
> > but a refusal to interprete.
>
> Not at all. It takes the probabilistic nature of QT seriously not more
> and not less.

If it would, it would not be minimal. The minimal interpretation
clarifies that |psi|^2 is a probabity distribution and leaves anything
else unanswered.

> > No. The minimal interpretation is not in conflict with
> > other, non-minimal interpretations, but defines the common
> > part of various interpretations. In all questions where
> > different interpretations give different answers the minimal
> > interpretation remains silent.
>
> Where give different interpretation different answers?

For example, in BM we have determinism, in NS classical stochastics
(Wiener process).

> Can I
> experimentally decide about the success or failure of one or the other
> interpretation?

No.

> > (If not, I simply define another interpretation which
> > remains silent about this question. This new interpretation is
> > smaller than your "minimal" interpretation, therefore I can
> > claim that your choice of denotation of your interpretation
> > is incorrect, and my new interpretation is the minimal one.)

> As I said, don't interpret more into QT than it contains!

Do it yourself. QT doesn't tell that you have to take
the probabilistic nature of QT seriously (that means, it
doesn't tell that its probabilistic nature is more
complex/deep/serious than that of classical probabilistic
theories like thermodynamics.)

Ilja

Ilja Schmelzer

"Andreas Most" <Andreas.Most@t-online.de> schrieb
> Ilja Schmelzer wrote:
> > "Andreas Most" <Andreas.Most@nospam.de> schrieb
> >>Ilja Schmelzer wrote:
> >>>"Andreas Most" <Andreas.Most@nospam.de> schrieb
> >>>>Ben Rudiak-Gould wrote:
> > The point is that there _is_ a condition weaker than "forbidding FTL
> > communication" which allows to prevent causal loops. (BTW, this
> > remains true even if you don't like this condition because it violates
> > a strong form of the relativity principle.)
>
> I didn't say I don't like it. I just wanted to understand Ben's
> argument.
>
> >>>That means that from point of view of other Lorentz frames t' it
> >>>may happen that t'(A)>t'(B), thus, information is send into the
> >>>"past" of "time" t'. But the "time" t' is in this interpretation only
> >>>some artificial local time-like coordinate with no fundamental
> >>>importance. Fundamental, and related with causality, is only
> >>>one time coordinate t.
> >>
> >>Apart from the fact, that you obviously reject the relativity principle,
> >
> >
> > I reject a strong form of the relativity principle. The weaker
> > form of the relativity principle, which is only about observables,
> > remains valid. (At least for distances large compared with the
> > critical length of unification of SM with gravity.)
> >
> >
> >>what exactly is the preferred frame and how can I identify it?
> >
> > You can roughly identify it as the rest frame of CMBR.
> >
> >>Is the preferred frame globally valid (in our universe) and static?
> >
> > Yes. (You need a theory of gravity with preferred frame
> > for this purpose, see gr-qc/0205035.)
>
> As of my understanding, if you have two observers being at different
> locations and each being at rest relative to the CMBR at their position,
> the two observers move relative to one another.

Yes. But it may be interpreted as well as a shortage of our rulers.

> That is you cannot define a preferred frame globally.

> (BTW: I read in your paper that you can prove a flat
> universe in your GLET.

Flat only in the approximation of a homongeneous universe.
The other homongeneous solutions with constant curvature
are not homogeneous in GLET.

> How would you then explain the redshift of
> objects being far away if not by an expanding universe?)

By an interpretation of the _observed_ increase of distances
between far away points by shrinking rulers.

> > Ok, but if we include a reasonable notion of causality, without
> > causal loops, as an additional requirement for the mechanism,
> > my statement holds.

> Again, causality has nothing to do with covariance.
> Instead, causality considerations tell us which (covariant) solution
> makes physically sense. For example, a spacelike line cannot be the
> world line of anything that interacts with our observable world.
> Excluding mathematical possible solutions to physics equations based on
> such considerations is also done elsewhere (E.g. the broken cup that
> does not recompile or using retarded solutions in electrodynamics and
> rejecting advanced ones). But these exclusion schemes do not change the
> properties of the physics equation (properties like e.g. covariance)

Causality is a word with different meanings. Your concept of causality
is also useful, but not what I'm talking about.

What I name causality is simply a partial order among events: A->B
if some (human) decision at A can influence the outcome of a
(macroscopic) measurement at B. This relation should be transitive
and should not allow closed causal loops.

Now, we have x(t1)->x(t2) for t1<t2 along usual worldlines x(t).
But, according to my realistic interpretation of violations of Bell's
inequality, we have also "A->B or B->A" for space-like separated
events.

Despite the fact that all these observational facts are covariant,
there exists no covariant relation A->B with these properties.

Ilja

Andreas Most

Hendrik van Hees wrote:
> Andreas Most wrote:
>
>> Things are perfectly consistent if you consider the wave function as a
>> mathematical object in which all information we have about a quantum
>> state is encoded. A measurement changes the knowledge about the
>> quantum state and thus the wave function.
>
> So far I can agree.
>
>> Then it is also obvious that different obervers may have different
>> description (wave function) of a quantum state based on their specific
>> knowledge about a state (consider e.g. the thought experiment about
>> "Wigner's friend").
>
> I think that's not what is meant when we say: "We assign the state [psi]
> (let [psi] denote a ray in Hilbert space represented by a vector |psi>)
> to a system." It's too subjectivistic a view.
>
> I think, what is meant by this statement is that a system was prepared
> by the experimenter in this state [psi]. Within the minimal
> interpretation that's a little bit unprecise, because the information,
> encoded in [psi] is only probabilistic. So what it really means is,
> that the system under consideration belongs to a (really prepared or at
> least in principle preparable) ensemble of independent systems which
> shows the statistic features encoded in [psi]. Different observers all
> assign this state [psi] and not any other to it, although one observer
> may use another observer's states mapped by a unitary (or antiunitary)
> operator. This covers also the case of observers in different frames of
> reference or using different pictures of time evolution (Schroedinger,
> Heisenberg, or Dirac).
>
> Of course, one also has the more common case of an incomplete knowledge
> about the system, and then different observers might assign different
> impure states (statistical operators) to the system, based on their
> knowledge of the system.

I agree with you so far. But I was heading into a different direction.
Consider an EPR-like setup with an entangled photon pair ("diphoton"
as it was mentioned in d.s.physik ;-) ) with the previously mentioned
wave function |psi> = 1/sqrt(2) (|HV> - |VH>)

Let Alice and Bob each receive one of these photons (Maybe they are
doing some quantum cryptography). If Alice has performed a measurement
and has reduced the state to, say, |psi(Alice)> = |HV>, what wave
function would Bob use to describe the system?

If Bob is spacelike separated, he cannot
possibly know whether Alice has performed the measurement at all.
And as long as he leaves the system unchanged and does not get
information from Alice, he must describe the system as
|psi(bob)> = 1/sqrt(2) (|HV> - |VH>). Anything else without better
knowledge would lead to contradictions (I think GHZ like setups
would show contradictions.)

As soon as he gets to know about Alice measurement, he can use
(so to say with 20/20 hindsight) |psi> = |HV> to interpret his
previous observations (measurements).

I am simply trying to say that spacelike separated observers might have
different descriptions for a quantum mechanical system. It might be even
possible for timelike connected events, if you do not receive any
information about a measurement like in the "Wigner's friend" thought
experiment, though I think that decoherence effects play a bigger role here.

>> And actually, the correlation of observables of an entangled system is
>> to me as mysterious as is in Newtonian mechanics an object moving on
>> a straight line forever if no forces are present. ;-)
>
> In fact, physics does not give an "explanation" for this. It's just an
> experimental fact about moving bodies which Galileo and Newton used to
> base their further analysis on. The principle of inertia is a basic
> observation, we cannot deduce from more basic observations (despite the
> fact that general relativity refines the principle of inertia in a
> subtle way).

Yes, and I think that quantum mechanical behaviour is fundamental in a
similar manner. There is maybe no explanation for it.

However, just to add "my two cents": I have the impression that the
so-called collapse of the wave function being related to information
gain has to do with the arrow of time (because of entropy...).
Maybe, If we sometime solve the "arrow of time" puzzle,
we might be able to solve also the so-called "measurement problem".
(please don't flame me on this. It's just my personal opinion...)

>
>> In order to not be in the urge of assuming such a preferred frame
>> I avoid using hidden variables. Apart from this I do not see that
>> Bohmian mechanics makes any testable (by experiment) prediction that
>> goes beyond the predictions of QM. (Also your paper makes no testable
>> predictions as far as I have read it).
>
> I agree completely.
>
>> I agree that the Bohmian interpretation does not contradict
>> experiment. But I think you give up to many well-established
>> principles without gaining anything new in terms of testable
>> predictions.
>
> You make an already complecated subject even more complicated by
> introducing unobservable "elements of reality" and name them
> trajectories to make QT sound a little bit more like classical
> mechanics.

Yes!

Regards,
Andreas.

Ilja Schmelzer

"Andreas Most" <Andreas.Most@t-online.de> schrieb
> Ilja Schmelzer wrote:
> > "Andreas Most" <Andreas.Most@nospam.de> schrieb
> >> I.e., you would have found a horizontal
> >>polarisation for photon 1, even if you had performed the measurement
> >>earlier.

> > A counterfactual statement. Such statements are meaningless outside
> > a concept of realism beyond positivism.
> > There is a meaningful notion of realism, there such claims make sense.
> > I like it, and I defend it. But if you reject it, without defining an
> > alternative
> > concept of realism which makes such claims meaningful, you are simply
> > inconsistent.
>
> Things are perfectly consistent if you consider the wave function as a
> mathematical object in which all information we have about a quantum
> state is encoded.

I'm not talking about consistence. I accept that the minimal interpretation
is consistent and that there may be other, nonrealistic but consistent
interpretations.

> A measurement changes the knowledge about the quantum
> state and thus the wave function.

An interpretation which talks about human knowledge without
talking about states of reality is certainly not a realistic interpretation.

> And actually, the correlation of observables of an entangled system is
> to me as mysterious as is in Newtonian mechanics an object moving on
> a straight line forever if no forces are present. ;-)

As well, there is nothing mysterious in our world for somebody
who believes "Gods Will is unexplainable".

> > You cannot assume the nonexistence of a preferred frame.
> > Because no realistic description of the world is possible
> > without some real effects happening FTL. That's because
> > realism is not a pretty philosophical theory but a well-defined
> > concept which allows to prove theorems.
>
> In order to not be in the urge of assuming such a preferred frame
> I avoid using hidden variables.

A common but IMHO wrong decision - the rejection of reality
once reality does not behave according to your prejdices (against
the preferred frame).

> Apart from this I do not see that
> Bohmian mechanics makes any testable (by experiment) prediction that
> goes beyond the predictions of QM.

That's not the aim of BM. The aim is to provide a realistic
(even deterministic) interpretation of QM.

> (Also your paper makes no testable predictions as far as I have read it).

GLET includes additional terms, and makes different predictions
(inflation, some dark matter term, stable "frozen stars" slightly greater
than their BH horizons).

> I agree that the Bohmian interpretation does not contradict experiment.
> But I think you give up to many well-established principles without
> gaining anything new in terms of testable predictions.

The other choice is to give up an even much more fundamental
principle: realism.

On the other hand, the acceptance of a hidden preferred frame
is not dangerous at all. Instead, it allows to revive lots of
other principles which are incompatible with the underlying
philosophy of GR. (Local energy and momentum conservation,
the interpretation of the wave function as real, positive
definiteness in the "big" space of quantum gauge theories,
canonical quantization using a Hamiltonian formalism.)

Ilja

Andreas Most

Ilja Schmelzer wrote:
> "Andreas Most" <Andreas.Most@t-online.de> schrieb
> ...
>>>>what exactly is the preferred frame and how can I identify it?
>>>
>>>You can roughly identify it as the rest frame of CMBR.
>>>
>>>
>>>>Is the preferred frame globally valid (in our universe) and static?
>>>
>>>Yes. (You need a theory of gravity with preferred frame
>>>for this purpose, see gr-qc/0205035.)
>>
>>As of my understanding, if you have two observers being at different
>>locations and each being at rest relative to the CMBR at their position,
>>the two observers move relative to one another.
>
>
> Yes. But it may be interpreted as well as a shortage of our rulers.

That's about what GR says about the expanding universe. So where is the
difference?

>>That is you cannot define a preferred frame globally.
>>(BTW: I read in your paper that you can prove a flat
>>universe in your GLET.
>
>
> Flat only in the approximation of a homongeneous universe.
> The other homongeneous solutions with constant curvature
> are not homogeneous in GLET.
>
>
>>How would you then explain the redshift of
>>objects being far away if not by an expanding universe?)
>
>
> By an interpretation of the _observed_ increase of distances
> between far away points by shrinking rulers.

As I said, this is the interpretation of GR.

>>>Ok, but if we include a reasonable notion of causality, without
>>>causal loops, as an additional requirement for the mechanism,
>>>my statement holds.
>>Again, causality has nothing to do with covariance.
>>Instead, causality considerations tell us which (covariant) solution
>>makes physically sense. For example, a spacelike line cannot be the
>>world line of anything that interacts with our observable world.
>>Excluding mathematical possible solutions to physics equations based on
>>such considerations is also done elsewhere (E.g. the broken cup that
>>does not recompile or using retarded solutions in electrodynamics and
>>rejecting advanced ones). But these exclusion schemes do not change the
>>properties of the physics equation (properties like e.g. covariance)
>
> Causality is a word with different meanings. Your concept of causality
> is also useful, but not what I'm talking about.
>
> What I name causality is simply a partial order among events: A->B
> if some (human) decision at A can influence the outcome of a
> (macroscopic) measurement at B. This relation should be transitive
> and should not allow closed causal loops.
>
> Now, we have x(t1)->x(t2) for t1<t2 along usual worldlines x(t).
> But, according to my realistic interpretation of violations of Bell's
> inequality, we have also "A->B or B->A" for space-like separated
> events.

What about the closed causal loops?
( I assume it is your definition of "causal" as above )
If there are three space-like seperated events A,B,C you have:

A->B or B->A
A->C or C->A
B->C or C->B

So it might be possible to have A->B->C->A. You will always be left with
causal loops.

> Despite the fact that all these observational facts are covariant,
> there exists no covariant relation A->B with these properties.

Still, tachyons would do the job and they are perfectly covariant!

>
> Ilja
>

Hendrik van Hees

Andreas Most wrote:

> Let Alice and Bob each receive one of these photons (Maybe they are
> doing some quantum cryptography). If Alice has performed a measurement
> and has reduced the state to, say, |psi(Alice)> = |HV>, what wave
> function would Bob use to describe the system?

He should not use a wave function at all, but the reduced state, based
on his knowledge, i.e.,

Tr_A {|Psi><Psi|}=1/2 (|H><H|+|V><V|).

>
> If Bob is spacelike separated, he cannot
> possibly know whether Alice has performed the measurement at all.

Right, and as the above state tells us, whether or not Alice measures
the polarisation of her photon, he will find always the same outcome,
namely in 50% of all cases he'll get a horizontally or a vertically
polarised photon. That's why there is no contradiction to causality in
this setting: He cannot even know whether Alice has measured the
polarisation of her photon or not. He also can not check whether his
photon was entangled with Alice's or not.

This they only can do by comparing there measurement protocols (i.e.,
they also need to note precisely enough which photon was measured,
i.e., by taking the precise time of their measurements) and look
whether there is the correlation encoded in |Psi> or not.

That makes the whole thing also good for cryptography, because by
measuring a single photon of an entangled pair tells you nothing, but
if a spy measured one of the photons, Alice and Bob will know
immediately, because then the entanglement was destroyed before they
measured the state of their photons, and there will be no correlation.

> And as long as he leaves the system unchanged and does not get
> information from Alice, he must describe the system as
> |psi(bob)> = 1/sqrt(2) (|HV> - |VH>). Anything else without better
> knowledge would lead to contradictions (I think GHZ like setups
> would show contradictions.)

As I said, the single photons must be described by reduced states
(tracing over the part of the system, not accesible by Bob).

> Yes, and I think that quantum mechanical behaviour is fundamental in a
> similar manner. There is maybe no explanation for it.
>
> However, just to add "my two cents": I have the impression that the
> so-called collapse of the wave function being related to information
> gain has to do with the arrow of time (because of entropy...).
> Maybe, If we sometime solve the "arrow of time" puzzle,
> we might be able to solve also the so-called "measurement problem".
> (please don't flame me on this. It's just my personal opinion...)

Well that all may be true, but I have my doubts about the collapse
business. I don't think that the collapse is a physical process
happening to an individual system when we measure it.

--
Hendrik van Hees Texas A&M University
Phone: +1 979/845-1411 Cyclotron Institute, MS-3366
Fax: +1 979/845-1899 College Station, TX 77843-3366
http://theory.gsi.de/~vanhees/ mailto:hees@comp.tamu.edu

Andreas Most

Ilja Schmelzer wrote:
> "Andreas Most" <Andreas.Most@t-online.de> schrieb
>> Ilja Schmelzer wrote:
>>> "Andreas Most" <Andreas.Most@nospam.de> schrieb
>>>> I.e., you would have found a horizontal
>>>> polarisation for photon 1, even if you had performed the measurement
>>>> earlier.
>
>>> A counterfactual statement. Such statements are meaningless outside
>>> a concept of realism beyond positivism.
>>> There is a meaningful notion of realism, there such claims make sense.
>>> I like it, and I defend it. But if you reject it, without defining an
>>> alternative
>>> concept of realism which makes such claims meaningful, you are simply
>>> inconsistent.
>> Things are perfectly consistent if you consider the wave function as a
>> mathematical object in which all information we have about a quantum
>> state is encoded.
>
> I'm not talking about consistence. I accept that the minimal interpretation
> is consistent and that there may be other, nonrealistic but consistent
> interpretations.
>
>> A measurement changes the knowledge about the quantum
>> state and thus the wave function.
>
> An interpretation which talks about human knowledge without
> talking about states of reality is certainly not a realistic interpretation.

I didn't say human knowledge. This could imply that it is the human mind
which causes the collapse of the the wave function.
The wave function is the description of a quantum mechanical system.
(knowingly letting aside more complex situations where you would need
a statistical operator to describe a system)
It is thus just a mathematical object and not physical one.
The information about the outcome of a measurement changes this
description. This is different from classical physics where, e.g.
the observation of the moon does not change its orbit.
The physical entities in QM are things like position, energy, spin, etc.
There are however physical limits on having the knowledge about all of
them and I don't see a reason to assign them some sort of "existence" or
"realism" while I cannot possibly know them nor describe them.

>
>> And actually, the correlation of observables of an entangled system is
>> to me as mysterious as is in Newtonian mechanics an object moving on
>> a straight line forever if no forces are present. ;-)
>
> As well, there is nothing mysterious in our world for somebody
> who believes "Gods Will is unexplainable".

Well, using BM to fit QM into our classical educated picture of the
world and introducing an ether to make EM comply with Newtonian physics
while not questioning the classical conception, is to me pretty
narrow-minded.

>>> You cannot assume the nonexistence of a preferred frame.
>>> Because no realistic description of the world is possible
>>> without some real effects happening FTL. That's because
>>> realism is not a pretty philosophical theory but a well-defined
>>> concept which allows to prove theorems.
>> In order to not be in the urge of assuming such a preferred frame
>> I avoid using hidden variables.
>
> A common but IMHO wrong decision - the rejection of reality
> once reality does not behave according to your prejdices (against
> the preferred frame).
>
>> Apart from this I do not see that
>> Bohmian mechanics makes any testable (by experiment) prediction that
>> goes beyond the predictions of QM.
>
> That's not the aim of BM. The aim is to provide a realistic
> (even deterministic) interpretation of QM.

You mean "realistic" in terms of what we call "realistic" being biased
by classical physics.

>> (Also your paper makes no testable predictions as far as I have read it).
>
> GLET includes additional terms, and makes different predictions
> (inflation, some dark matter term, stable "frozen stars" slightly greater
> than their BH horizons).

That is so far not very convincing, even because there are still two
parameters in your GLET which have to be determined.
You could as well add higher order terms to GR to make such predictions.

>> I agree that the Bohmian interpretation does not contradict experiment.
>> But I think you give up to many well-established principles without
>> gaining anything new in terms of testable predictions.
>
> The other choice is to give up an even much more fundamental
> principle: realism.
>
> On the other hand, the acceptance of a hidden preferred frame
> is not dangerous at all. Instead, it allows to revive lots of
> other principles which are incompatible with the underlying
> philosophy of GR. (Local energy and momentum conservation,

Are you trying to claim that there is no (local) energy and momentum
conservation in GR ???

> the interpretation of the wave function as real, positive
> definiteness in the "big" space of quantum gauge theories,
> canonical quantization using a Hamiltonian formalism.)

Mathematical simplicity is nowadays not considered to be
a necessary criterion.

>
> Ilja
>
>

Andreas.

Ilja Schmelzer

"Andreas Most" <Andreas.Most@t-online.de> schrieb
> Ilja Schmelzer wrote:
> > "Andreas Most" <Andreas.Most@t-online.de> schrieb
> >>>>Is the preferred frame globally valid (in our universe) and static?
> >>>
> >>>Yes. (You need a theory of gravity with preferred frame
> >>>for this purpose, see gr-qc/0205035.)

> >>As of my understanding, if you have two observers being at different
> >>locations and each being at rest relative to the CMBR at their position,
> >>the two observers move relative to one another.

> > Yes. But it may be interpreted as well as a shortage of our rulers.

> That's about what GR says about the expanding universe. So where is the
> difference?

You can use the CMBR frame and consider it as globally valid and
static (relative to the preferred background or the ether).

> >>How would you then explain the redshift of
> >>objects being far away if not by an expanding universe?)

> > By an interpretation of the _observed_ increase of distances
> > between far away points by shrinking rulers.
>
> As I said, this is the interpretation of GR.

It is a common property of many metric theories of gravity.

>
> >>>Ok, but if we include a reasonable notion of causality, without
> >>>causal loops, as an additional requirement for the mechanism,
> >>>my statement holds.
> >>Again, causality has nothing to do with covariance.
> >>Instead, causality considerations tell us which (covariant) solution
> >>makes physically sense. For example, a spacelike line cannot be the
> >>world line of anything that interacts with our observable world.
> >>Excluding mathematical possible solutions to physics equations based on
> >>such considerations is also done elsewhere (E.g. the broken cup that
> >>does not recompile or using retarded solutions in electrodynamics and
> >>rejecting advanced ones). But these exclusion schemes do not change the
> >>properties of the physics equation (properties like e.g. covariance)
> >
> > Causality is a word with different meanings. Your concept of causality
> > is also useful, but not what I'm talking about.
> >
> > What I name causality is simply a partial order among events: A->B
> > if some (human) decision at A can influence the outcome of a
> > (macroscopic) measurement at B. This relation should be transitive
> > and should not allow closed causal loops.
> >
> > Now, we have x(t1)->x(t2) for t1<t2 along usual worldlines x(t).
> > But, according to my realistic interpretation of violations of Bell's
> > inequality, we have also "A->B or B->A" for space-like separated
> > events.
>
> What about the closed causal loops?
> ( I assume it is your definition of "causal" as above )
> If there are three space-like seperated events A,B,C you have:
>
> A->B or B->A
> A->C or C->A
> B->C or C->B
>
> So it might be possible to have A->B->C->A. You will always be left with
> causal loops.

The point is that a realistic interpretation has to define which of the
alternatives are correct. Some attempts for explanation may have
causal loops, in this case they have to be rejected as inconsistent
explanations. But other have no causal loops.
For example, the time order t(A) < t(B) < t(C) defines one consistent
explanation of all three observations without closed causal loops.
Thus, there exists a realistic explanation without closed causal loops,
contrary to your claim.

> > Despite the fact that all these observational facts are covariant,
> > there exists no covariant relation A->B with these properties.

> Still, tachyons would do the job and they are perfectly covariant!

Which job? To describe which of the alternatives holds in

> A->B or B->A
> A->C or C->A
> B->C or C->B

without closed causal loops? I don't think so.

Ilja