Re: Delayed choice experiment and interstellar signalling

On Mar 21, 4:51 pm, Sylvia Else <syl...@xxxxxxxxxxxxxxxxxxx> wrote:
Willie.Moo...@xxxxxxxxx wrote:
The interference is between the two entangled photons, which may have
been emitted from the proximity of one slit, or the proximity of the other.

I'm confused about what you're saying. It doesn't make sense to me.

My understanding is that one entangled photon goes through the double
slit apparatus, and one photon goes to a remote observer who decides
to observe the remote photon in a certain way that allows him to
figure something out about which way the entangled photon went through
the double slit apparatus.

No - that's not the way the delayed choice experiment was done. One
photon goes throw the double slit apparatus. The creation of the
entangled photons occurs afterwards.

Look at figure 2 inhttp://arxiv.org/PS_cache/quant-ph/pdf/9903/9903047.pdf

At the left there is the laser pump - then the double slit - then the
crystal that produces the entangled photons.

If you create the entangled photons first, and only one goes through the
slit, there's no measurement on the other photon that can tell you which
slit its companion went through.

Sylvia.

That URL won't load. Like I said I find your comments confusing and
your URL is unreadable. So, lets go back to something we can both
agree on.

We're talking about Young's double slit experiment. First performed
in 1801 by Thomas Young to determine whether light was corpuscular or
wavelike. Two slits, a projetion screen, an interference pattern
appears.

This interference pattern appears no matter if you're using photons,
electrons, or atoms. It also appears if you send one particle through
the apparatus at a time - so each particle need not interfere with
another particle in order to have the interference effect.

Sylvia,

Unfortunately, you're talking nonsense. We're always dealing with one
photon at a time throughout quantum mechanics. Otherwise the energy
doesn't add up right. So, when we talk about probabilities we're
talking about the probabilities of individual photons or particles.
The which way information is extracted by putting a quarter wave plate
in front of the slits and firing polarized photons through them.
Let's go back step by step and look at what is going on in detail in
the double slit experiment.

Two slits are separated by a distance d. Place a screen a distance L
from the slits. The distance from slit 1 to a point x on the screen is

r1 = SQRT(L^2 + x^2)

and the distance from slit 2 to the point x on the screen is

r2 = SQRT(L^2 + (x - d)^2)

For large L and small x compared with L, the difference between the
two distances is approximately

delta r ~ x*d/r1 ~ x*d/L

The electric field at a point x is given by the superposition of the
states of the waves from each of the slits and is proportional to the
real part of

| phi.1> + |phi.2> = |xi> {exp[i(kr1 - omega t)] + exp[i(kr2 - omega
t)]}
= |phi.1> exp[i(k delta r - omega t)]

The total electromagnetic energy striking the screen at point x is
proportional to the square of the electric field and is therefore
proportional to

cos(k*delta r)^2 ~ cos(2*pi*x*d/lambda)^2

where lambda is the wavelength of the light. The fields from the two
slits constructively interfere at the antinodes when the phase is
equal to mulittples of pi.

2*pi*x*d/lambda = n * pi, where n = 0,1,2,...

alternatively

xn = n*lambda / (2*d), where n=0,1,2,...

The waves interfere destructively and form nodes halfway between the
antinodes.
So this is the classical treatment. Lets reinterpret the classical
quantities so that we can get the quantum treatment. So the classical
state vectors | phi > now become quantum state vectors in the
description of photons.

First electromagnetic radiation is assumed to be composed of
irreducible packets of energy, known as photons. The energy of each
packet is related to the angular frequency of the wave by the
relation

epsilon = h_bar * omega

where h_bar is an experimentally determined quantity known as Planck's
constant.
N photons in a box of volume V has an electromagnetic field energy
of;

N*h_bar*omega

and the energy density is

N*h_bar*omega/V

The correspondence principle relates energy of a photon to classical
field energy. For a large number of photons, the quantum and
classical treatments must agree. So, for very large N, the quantum
energy density must be the same as the classical energy density

N*h_bar*omega/V = epsilon_c = |E|^2 / (8*pi)

The number of photons in the box is then

N = |E|^2 * V/(8*pi*h_bar*omega)

The correspondence principle determines the momentum of the photon
too.
The momentum density is

P_c = N*h_bar*omega/(c*V) = N*h_bar*k / V

which says that the momentum of an individual photon is

h_bar * k

Probability can calculate the probable number of photons in a
particular state.
Probability can calculate the likelihood of a single photon to be in a
particular state.
When you try to count photons energy conservation is violated. So,
you're only left with calculating the likelihood of a single photon
being in a particular state.
This is not an intuitive interpretation and leads to weirdness. Dirac
says of this interpretation in the Double-Slit experiment:

"Some time before the discovery of quantum mechanics people realized
that the connexion between light waves and photons must be of a
statistical character. What they did not clearly realize, however, was
that the wave function gives information about the probability of one
photon being in a particular place and not the probable number of
photons in that place. The importance of the distinction can be made
clear in the following way. Suppose we have a beam of light consisting
of a large number of photons split up into two components of equal
intensity. On the assumption that the beam is connected with the
probable number of photons in it, we should have half the total number
going into each component. If the two components are now made to
interfere, we should require a photon in one component to be able to
interfere with one in the other. Sometimes these two photons would
have to annihilate one another and other times they would have to
produce four photons. This would contradict the conservation of
energy. The new theory, which connects the wave function with
probabilities for one photon gets over the difficulty by making each
photon go partly into each of the two components. Each photon then
interferes only with itself. Interference between two different
photons never occurs" -Paul Dirac, The Principles of Quantum
Mechanics, Fourth Edition, Chapter 1

This is true for polarization states as well.

The probability itself is quadratic in the fields and consequently is
also quadratic in the quantum state of the photon. In quantum
mechanics, therefore, the state or probability amplitude contains the
basic probability information. In general, the rules for combining
probability amplitudes look very much like the classical rules for
composition of probabilities:

1. The probability amplitude for two successive probabilities is
the product of amplitudes for the individual possibilities. ...

2. The amplitude for a process that can take place in place in one
of several indistinguishable ways is the sum of amplitudes for each of
the individual ways. ...

3.The total probability for the process to occur is the absolute
value squared of the total amplitude calculated by 1 and 2.

The quantum eraser experiment is a double-slit experiment where
particle entanglement and selective polarization is used to determine
which slit a particle goes through by measuring the particle's
entangled partner. Only one particle at a time is being discussed -
though through the correspondence principle we can compute classical
versions of what's going on for lots of particles.

This entangled partner never enters the double slit experiment. The
measurement of "which way" destroys the interference pattern in the
"double-slit" portion of the experiment.

The quantum eraser can restore the interference pattern without
changing anything in the double-slit experiment by simply destroying
the "which way" information in the entangled particle that was
previously used to determine the "which way" path before the "which
way" information is available for observation.

The quantum eraser effectively erases the "which way" information (and
restores interference) without altering the double-slit experiment,
and thereby restores the readily visible interference pattern that
manifests itself through the constructive and destructive wave
interference.

A variation of this experiment, delayed choice quantum eraser allows
the decision whether to measure or destroy the 'which way' information
to be delayed until after the entangled particle partner (the one
going through the slits) has either interfered with itself or not.

This has the bizarre effect of determining the outcome of an event
after it has already occurred.

By taking a pair of double slit apparatus and delaying this
destruction of which way information until the which way photons are
separated from the original source by long distances, this bizarre
effect can be extended and used by a remote observer to signal to the
person who set up the experiment in the first place.

The classical quantum eraser experiment uses a photon which is shot
through a specialized nonlinear beta-barium borate (BBO) crystal. This
process, known as spontaneous parametric down conversion (SPDC),
converts the single photon into two entangled photons of lower
frequency.

These entangled photons then follow separate paths. One photon goes
directly to a detector, which sends information of the received photon
to a coincidence chamber.

The coincidence chamber then waits for news of the other, second
photon.

Meanwhile, the second photon is faced with the double-slit, whereafter
it proceeds to its own detector, which sends information of a received
photon to the original coincidence chamber.

At this point, the coincidence chamber has been told that both photons
of the original pair have been detected, it has been registered as
such, and more photons are repeatedly put through this process.

This setup yields the familiar interference pattern according to basic
QM, as we have no 'which way' information regarding either photon and
it is allowed to continue in an unobserved state.

Now, to gain the desired 'which way' information, a quarter wave plate
(QWP) is placed in front of each of the double-slits that the second
photon must choose. These crystals will change the polarization of the
light. In turn, the now repolarized photon will be measured at the
detector, and it can be determined which slit the photon passed
through. This 'which way' information about the photon will indeed
kill the interference pattern.

The next progression in the setup will attempt to bring back the
interference pattern.
This is done by placing a polarizer before the detector of the first
photon. This will cause the polarization information obtained by that
detector to be of no consequence in determining which photon is
actually being examined, and thus no conclusions may be drawn and the
'which way' information will be destroyed before it is able to be
analyzed and observed (this is the actual 'quantum erasure'). That
being done, the interference pattern does, in fact, return.

To use this setup for interstellar signaling, all we do is collimate
the which way beam and send it interstellar distances to a receiver
far away. The person receiving the beam can erase the information
which restores the interference pattern recorded in the double slit
apparatus.



.

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