[extropy-chat] Many worlds and Hugh Everett

Thu Jan 1 01:10:36 UTC 2004

From: "Dirk Bruere"

> The point is though, that there are no (currently) testable QM theories
> that both make different predictions from standard QM and are not already
> falsified by experiment.

It seems (to me) a bit difficult to define what is "standard QM", sometimes
called "orthodox" QM. Perhaps there are many "standard QM". There are many
"schools" and many "standard" interpretations: Cambridge, Copenhagen,
Gottingen, Princeton, Zurich, etc. If you read Dirac's book you cannot even
find the term "wavefunction". But you can find that the photon only
interferes with itself (which is not in line with Born's postulate) and
never interferes with other photons (which was proved wrong, experimentally,
in the '60s). If you read von Neumann's book you find that
hidden variables are not allowed, in QM, in principle, something that was
falsified later by John Bell, whose philosophy (realism, Einstein's locality
principle) was then falsified by those experiments performed by A. Aspect.

But von Neumann wrote, perhaps for the first time, a detailed "theory of
quantum measurement", while Dirac avoided as much as he could the issue.
There are other problems with von Neumann's book, since some theorist found
that the definition of "tensor product", given in the book, might be
arbitrary, or worse, and his definition is crucial if one wishes to keep the
"peaceful coexistence" between QM and SR. If you read Bohr's papers you
find, few times, the expression "reduction of wave packets" or "reduction of
probability packets" but he did not speak of a "real" or, better, "physical"
collapse. The "collapse" is un-physical, according to Bohr, which means
"epistemological". Actually the "Copenhagen Interpretation" (so called after
Heisenberg, 1955) is essentially "epistemological".

What about the physical collapse, then? Well, you must read the papers by
Heisenberg and, maybe, the book of von Neumann, if you want to find
something like that. But then came the paper by EPR (1935, but Popper,
von Weizsaecker, and Einstein himself had, independently, the same idea
many years before). And this paper seems to have much to do with a "physical
collapse" which produces "spooky actions" at a distance. Only Bohr found
a consistent way out, based on his "complementarity principle" and his idea
of a non-physical (only epistemological) collapse. But Bohr's words were so
obscure, so deep, and a bit inaccurate, and then people did not realized who
really won that debate, if EPR + Schroedinger, or Bohr, or nobody. (You can
find below something that maybe represents in a more formal way what Bohr
had in mind. For clarity it is discussed the EPR in the Bohm version, that
is to say the EPR-B).

What does it mean all the above? That there is no "standard QM"? No, it just
means that there was no "standard interpretation of QM", since the
beginning. There is of course a general agreement on the fundamental
equations, and rules, and principles.

> The point is though, that there are no (currently) testable QM theories
> that both make different predictions from standard QM and are not already
> falsified by experiment.

There are theories that make different prediction (from standard
QM, and have been falsified by experiments. In example the de Broglie
double solution, in the Selleri-Croca version, which has been falsified
by experiments performed by Mandel, Wang, etc. Also Bohmian mechanics is
tested now and it seems to be wrong.

But if you ask if "standard QM" has been falsified, I would respond:
yes, more or less as Newtonian description has been falsified by SR.
There are theories ("weak measurement", i.e.) which predict what QM,
in the present formalism, cannot predict, and they have been positively
tested. They are radical "extensions" of QM, more than new theories.

We can also say that QM many times falsified itself, in a certain sense.
There was, around 1926-1927, the famous Bohr-Heisenberg debate about the
meaning of UP (uncertainty pr.) and the meaning of CP (complementarity).
Heisenberg was saying that UP has its roots in disturbances, during
measurements. Bohr was saying that UP is a part of CP, and no disturbance
was much involved, the essence of uncertainty was deeper, already present
in the formalism of the QM. Modern experiments ("quantum erasure",
"welcher weg" and distinguishability, etc.) have shown that Bohr was right.
Heisenberg's gamma ray microscope gedanken experiment is obsolete now.

(Btw, it was also shown that in the Bohr-Einstein
debate, Bohr himself introduced many times arguments,
which are completely wrong).

What about the uncertainty relation DE Dt > h which
Aharonov and Bohm proved to be completely false
(meaningless) in 1961? Also Dirac's uncertainty
relation D phase D N = 1 has been proved to be wrong.
And also the famous relation Dposition Dmomentum > h
has been proved to be meaningless in many specific
cases (when one observable is bounded and the other
non commuting observable is stationary, so to speak).

Even the general Robertson's uncertainty relation
for two observables A, B, has some problem since
it depends on the same wavefunction on both sides!
DA(psi) DB(psi) = 1/2 |<psi|[A,B]|psi>|

What about the "correspondence principle", one of the
basic points of the standard QM and the Copenhagen interpretation,
which is even difficult to find, in modern books,
and was proved to be wrong (by A.Leggett et al.)?

> Given the physical equivalence of the various interpretations does
> that mean quantum suicide experiments will have the same outcome?

I do not agree about that "physical equivalence", because theories
are different, and formalisms are, often, different too.

Imo, it is not easy to perform a *quantum* suicide, but, in case of
necessity ..., I would suggest a "weak" quantum suicide. In such a
strategy, the suicide is accomplished in several rounds. One sacrifices
knowledge of the system, on any given round, to avoid the
entanglement with the "device" and the ensuing "split" (or "collapse",
depending on the interpretation) of the wavefunction. This makes it
possible to contemplate (or self-contemplate) the behavior of the "system"
defined by preparation and by a later (hopefully lucky) post-selection,
without significant disturbance of the "system" in the intervening period.
Due to the many rounds strategy, and the weakness of the suicide
procedure, you could stop it as soon as you realize that the post-selection
state is not satisfactory. Or something like this :-)

s.

"What is much more likely is that the new way of seeing things will
involve an imaginative leap that will astonish us. In any case it seems
that the quantum mechanical description will be superseded. In this it
is like all theories made by man. But to an unusual extent its ultimate
fate is apparent in its internal structure. It carries in itself the
seeds of its own destruction."
- John Bell
"The Moral Aspect of Quantum Mechanics" in Speakable and Unspeakable in
Quantum Mechanics,Cambridge University Press (1987).

---------------------------

EPR-B 'a la Bohr'

Look that rho(1) = trace(2) rho(1,2) and
rho(2) = trace(1) rho(1,2) where
rho(1,2) = density matrix of the composite EPR-B system =
=(|1.up>|2.down>-|1.down>|2.up>)(<1.up|<2.down|-<1.down|<2.up|)

Look also that for rho(1,2) the total angular momentum
operator has values = 0 for all spatial components,
since the two spins are (pre)correlated, and thay point to
opposite directions. Note also that this is not the case
of rho(1) and rho(2) because they are mixed states,
with no definite values for angular momentum components.

Suppose now that an appatratus.2 measures sub-system.2
(an observable of this sub-system.2). From the universality
of QM, also apparatus.2 will be a mixed state, with no
definite value, for the measured abservable. But since
sub-system.2 is correlated with sub-system.1, apparatus.2
will be also correlated with sub-system.1.

Thus when we read, on apparatus.2, that the observable
of sub-system.2 is "spin up" we know that the observable
of sub-system.1 is "spin down". But since we assumed that
sub-system.1 and sub-system.2 are space-like separated, no
physical interaction is possible. Hence when we read,
on apparatus.2, the value of the observable of sub-system.2,
we do not have any interaction with sub-system.1, which
rests in its mixed state. We can infer, though, the
value of the observable of sub-system.1, without interacting
with it. The above is a conditional inference, or a
conditional probability = 1.

The only possible effect is on "relationships" between sub-system.
Not between the physical states of sub-systems (rectius, between
apparata measuring sub-systems).

Look also that the relationship between sub-systems
(correlation) is pre-existent, it is not due to any
measurement.

If you want to check the (defined above) conditional inferences,
or conditional probabilities, you must measure
with apparatus.2 the sub-system.2 (say spin up) and
with apparatus.1 the sub.system.1 (say spin down) and
see if the measurements agree.

Since sub-system.1 and sub-system.2 (apparatus.1, apparatus.2)
are represented by mixed states there is no need to assume
any physical collapse between them. No collapse -> no interaction ->
no energy transfer -> no FTL 'informations' -> no FTL 'influences' ->
no spooky actions.