On 05-07-2021 12:18, Bruce Kellett wrote:
On Mon, Jul 5, 2021 at 7:39 PM smitra <[email protected]> wrote:
On 05-07-2021 09:00, Bruce Kellett wrote:
On Mon, Jul 5, 2021 at 2:23 PM smitra <[email protected]> wrote:
I don't think this is actually done in the experiment. What is
observed is the presence or absence of the interference pattern on
the
screen where the balls hit. The photons are not detected. But if,
in
principle, they are of suitable wavelength to resolve the slit
difference, then the interference pattern vanishes. The experiment
is
convincing in that they start wil cold buckyballs which show a
clear
interference pattern. They then gradually heat the balls so that
the
typical wavelength of the photons decreases. This gradually washes
out
the interference pattern. (Because at lower temperatures, the
wavelength distribution of the IR photons is such that a few of
them
have shorter wavelengths.) As the temperature is increased so that
most IR photons have short enough wavelengths, the interference
pattern disappears completely. The paper by Hornberger et al. is
at
arXiv:quant-ph/0412003v2
This is then what I said previously, what you denied, i.e. that you
are
only considering part of the system which is defined by the reduced
density matrix. The complete system of buckyball plus photons will
show
interference, even if the wavelength is small enough to resolve the
slits provided you perform the right sort of measurement on the
balls
and photons.
That is false.
This is easy to see. Denote the buckyball state of a buckball moving
through the left slit by |L> and moving through the right slit by |R>.
Suppose that a photon is emitted by the by the buckyballs such that the
ball moving through the left slit emits a photon in a state |PL> that
will be orthogonal to the state |PR> of the photon emitted by the ball
moving through the right slit . The state of the system after the ball
passes the slits is then:
|psi> = 1/sqrt(2) [|L>|PL> + |R>|PR>]
This state then evolves under unitary time evolution, we can write the
state just before the ball hits the screen as:
|psi_s> = 1/sqrt(2) [|L_s>|PL_s> + |R_s>|PR_s>]
There is then no interference patter on the screen for the buckyballs
because |PL_s> and |PR_s> are orthogonal, the unitary time evolution
preserves the orthogonality of the initial states. The probability to
observe a buckyball on position x on the screen is:
P(x) = ||<x|psi_s>||^2 = 1/2 [|<x|L_s>|^2 + |<x|R_s>|^2] + Re[<x|L_s>
<x|R_s>* <PR_s|PL_s>]
And the last interference term is zero because <PR_s|PL_s> = 0
But if we also observe the photon on another screen and keep the joint
count for buckyballs landing on spot x on the buckyball screen and for
photons landing on spot y on the photon screen as a function of x and y,
then we do have an interference pattern as a function of x for fixed y.
If we de note by U the unitary time evolution for the photons until they
hit their screen, and put |PL_t> =U|PL_s> and |PR_t> = U|PR_s>, then the
probability distribution is:
P(x,y) = |<x,y|U|psi_s>|^2 = 1/2 [|<x|L_s>|^2|<y|PL_t>|^2 +
|<x|R_s>|^2|<y|PR_t>|^2] +Re[<x|L_s> <x|R_s>* <y|PL_t><y|PR_t>*]
The interference term Re[<x|L_s> <x|R_s>* <y|PL_t><y|PR_t>*] does not
vanish as it involves evaluating the components of the buckyball and
photon states in the position basis and so there is no inner product
involved anymore. For fixed y the quantity <y|PL_t><y|PR_t>* will have
some value that will be nonzero in general, so if we keep y fixed then
there will be an interference term.
So, we can conclude that invoking escaping IR photons does not male any
sense in this discussion because all it does is it scrambles the
interference pattern to make it invisible in a way that allows it to be
recovered in principle using measurements on those IR photons. You can,
of course, erase the interference patter by measuring the observable for
the photons that has |PR> and |PL> as its eigenstates. But even in that
case the information will still be there in the state of all the atoms
of the measurement apparatus for the photons. But if you don't perform
any measurement then the information will simply continue to exists in
the escaping photons.
So, in general we can conclude by generalizing this to any large number
of particles that even with what we consider to be permanent records,
you don't get rid of the theoretical possibility of interference between
the sectors where those records are different. So, the existence of
parallel worlds cannot be made fully 100% irrelevant if QM is rigorously
correct, and we cannot therefore argue that QM is exactly equivalent to
an alternative theory that leaves out parallel worlds. Even though the
difference may be almost 100% insignificant FAPP, it's not exactly 100%
even in the macroscopic realm.
The argument against the existence of parallel worlds by invoking
decoherence that makes superposition hard to detect for complex systems
is thus analogous to the defense of creationists when they invoke a God
of ever smaller gaps of things that have not yet been fully explained.
Saibal
This is not what happens. Read the paper referenced above.
It's not what happens in that experiment, but you can in principle
demostrate an interference pattern also when photons are emitted by
the
balls.
Provided the wavelength of the IR photons is too large to resolve the
inter-slit distance. When you heat the balls further, the interference
disappears.
This is all totally irrelevant to the actual experiment in
question.
And that experiment is in turn irrelevant to the question of whether
or
not a real superposition actually exist. You can always perform a
measurement involving more particles where an interference has
vanished,
that only demonstrates that the reduced density matrix described a
mixed
state, the entire system is still in a pure state.
Of course real superpositions exist. The experiment shows that
decoherence need not involve large numbers of degrees of freedom.
These considerations do apply to each and every case. I mentioned
the
buckyball experiment because it makes things obvious. But the
general
principle is always true. Experiments that produced recorded
results
are not reversible. Because, for example, they are not thermally
isolated, and IR photons can always escape to infinity and be
irretrievable.
Even if IR photons always escape to infinity, the complete quantum
state
of the entire system is still a pure state. There is still a
superposition between the balls going through one and the other
slit.
Maybe that is not what is observed. That superpostion has decohered.
For example, one may object by invoking that the universe is
filled with a plasma and that the IR photons travel at a speed
slightly below the true vacuum speed of light.
What difference would that make. The IR photons are still faster
than
any material object sent after them to capture them. They will
always
escape. And because the universe is expanding, they will
eventually
pass over the Hubble horizon and be forever lost from sight!
But the observations on the balls will be completed long before
that, so
how is this relevant for the existence of parallel worlds?
I think it is relevant to the question of reversibility.
Whether this means that the off-diagonal terms of the density
matrix
(in the appropriate basis) do actually vanish, or if this is
achieved
by some other means, your theory has to adapt to the reality of
irreversibility or your theory does not describe the real world.
It is
clear that for many reasons, pure Everettian QM, based solely on
the
Schrodinger equation, fails to explain many important features of
the
world we observe.
Which would mean that QM cannot be correct as a fundamental theory.
It is very probable the QM, in its current form, is not the correct
fundamental theory. In the history of science it is never the case
that the dominant theory at one time survives unaltered into the
future. The negative induction against scientific realism is that all
scientific theories are ultimately shown to be false.
Bruce
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