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Wheeler's delayed choice experiment is actually several
thought experiments in
quantum physics, proposed by
John Archibald Wheeler, with the most prominent among them appearing in 1978 and 1984.
[1] These experiments are attempts to decide whether light somehow "senses" the experimental apparatus in the
double-slit experiment
it will travel through and adjusts its behavior to fit by assuming the
appropriate determinate state for it, or whether light remains in an
indeterminate state, neither wave nor particle until measured.
[2]
The common intention of these several types of experiments is to
first do something that, some interpretations of theory say, would make
each photon "decide" whether it was going to behave as a particle or
behave as a wave, and then, before the photon had time to reach the
detection device, create another change in the system that would make it
seem that the photon had "chosen" to behave in the opposite way. Some
interpreters of these experiments contend that a photon either is a wave
or is a particle, and that it cannot be both at the same time.
Wheeler's intent was to investigate the time-related conditions under
which a photon makes this transition between alleged states of being.
His work has been productive of many revealing experiments. He may not
have anticipated the possibility that other researchers would tend
toward the conclusion that a photon retains both its "wave nature" and
"particle nature" until the time it ends its life, e.g., by being
absorbed by an electron which acquires its energy and therefore rises to
a higher-energy
orbital in its atom. However, he himself seems to be very clear on this point. He says:
"The thing that causes people to argue about when and how the photon
learns that the experimental apparatus is in a certain configuration and
then changes from wave to particle to fit the demands of the
experiment's configuration is the assumption that a photon had some
physical form before the astronomers observed it. Either it was a wave
or a particle; either it went both ways around the galaxy or only one
way. Actually, quantum phenomena are neither waves nor particles but are
intrinsically undefined until the moment they are measured."[3]
This line of experimentation proved very difficult to carry out when
it was first conceived. Nevertheless, it has proven very valuable over
the years since it has led researchers to provide "increasingly
sophisticated demonstrations of the wave–particle duality of single
quanta."
[4] [5] As one experimenter explains, "Wave and particle behavior can coexist simultaneously."
[6]
Introduction
"
Wheeler's delayed choice experiment" refers to a series of
thought experiments in
quantum physics,
the first being proposed by him in 1978. Another prominent version was
proposed in 1983. All of these experiments try to get at the same
fundamental issues in
quantum physics.
Many of them are discussed in Wheeler's 1978 article, "The 'Past' and
the 'Delayed-Choice' Double-Slit Experiment", which has been reproduced
in A. R. Marlow's
Mathematical Foundations of Quantum Theory, pp. 9–48.
According to the
complementarity principle, a photon can manifest properties of a particle or of a wave,
but not both at the same time.
What characteristic is manifested depends on whether experimenters use a
device intended to observe particles or to observe waves.
[7]
When this statement is applied very strictly, one could argue that by
determining the detector type one could force the photon to become
manifest only as a particle or only as a wave. Detection of a photon is a
destructive process because a photon can never be seen in flight. When a
photon is detected it "appears" in the consequences of its demise,
e.g., by being absorbed by an electron in a
photomultiplier
that accepts its energy which is then used to trigger the cascade of
events that produces a "click" from that device. A photon always appears
at some highly localized point in space and time. In the apparatuses
that detect photons, the locations on its detection screen that indicate
reception of the photon give an indication of whether or not it was
manifesting its wave nature during its flight from photon source to the
detection device. Therefore, it is commonly said that in a
double-slit experiment
a photon exhibits its wave nature when it passes through both of the
slits and appears as a dim wash of illumination across the detection
screen, and manifests its particle nature when it passes through only
one slit and appears on the screen as a highly localized scintillation.
Given the interpretation of quantum physics that says a photon is
either in its guise as a wave or in its guise as a particle, the
question arises: When does the photon decide whether it is going to
travel as a wave or as a particle? Suppose that a traditional
double-slit experiment is prepared so that either of the slits can be
blocked. If both slits are open and a series of photons are emitted by
the laser then an interference pattern will quickly emerge on the
detection screen. The interference pattern can only be explained as a
consequence of wave phenomena, so experimenters can conclude that each
photon "decides" to travel as a wave as soon as it is emitted. If only
one slit is available then there will be no interference pattern, so
experimenters may conclude that each photon "decides" to travel as a
particle as soon as it is emitted.
Simple interferometer
One
way to investigate the question of when a photon decides whether to act
as a wave or a particle in an experiment is to use the interferometer
method. Here is a simple schematic diagram of an interferometer in two
configurations:
If a single photon is emitted into the entry port of the apparatus at
the lower-left corner, it immediately encounters a beam-splitter.
Because of the equal probabilities for transmission or reflection the
photon will either continue straight ahead, be reflected by the mirror
at the lower-right corner, and be detected by the detector at the top of
the apparatus, or it will be reflected by the beam-splitter, strike the
mirror in the upper-left corner, and emerge into the detector at the
right edge of the apparatus. Observing that photons show up in equal
numbers at the two detectors, experimenters generally say that each
photon has behaved as a particle from the time of its emission to the
time of its detection, has traveled by either one path or the other, and
further affirm that its wave nature has not been exhibited.
If the apparatus is changed so that a second beam splitter is placed
in the upper-right corner, then the two detectors will exhibit
interference effects. Experimenters must explain these phenomena as
consequences of the wave nature of light. They may affirm that each
photon must have traveled by both paths as a wave; if not so, that
photon could not have interfered with itself.
Since nothing else has changed from experimental configuration to
experimental configuration, and since in the first case the photon is
said to "decide" to travel as a particle and in the second case it is
said to "decide" to travel as a wave, Wheeler wanted to know whether,
experimentally, a time could be determined at which the photon made its
"decision." Would it be possible to let a photon pass through the region
of the first beam-splitter while there was no beam-splitter in the
second position, thus causing it to "decide" to travel, and then quickly
let the second beam-splitter pop up into its path? Having presumably
traveled as a particle up to that moment, would the beam splitter let it
pass through and manifest itself as would a particle were that second
beam splitter not to be there? Or, would it behave as though the second
beam-splitter had always been there? Would it manifest interference
effects? And if it did manifest interference effects then to have done
so it must have gone back in time and changed its decision about
traveling as a particle to traveling as a wave. Note that Wheeler wanted
to investigate several hypothetical statements by obtaining objective
data.
Albert Einstein did not like these possible consequences of quantum mechanics.
[8]
However, when experiments were finally devised that permitted both the
double-slit version and the interferometer version of the experiment, it
was conclusively shown that a photon could begin its life in an
experimental configuration that would call for it to demonstrate its
particle nature, end up in an experimental configuration that would call
for it to demonstrate its wave nature, and that in these experiments it
would always show its wave characteristics by interfering with itself.
Furthermore, if the experiment was begun with the second beam-splitter
in place but it was removed while the photon was in flight, then the
photon would inevitably show up in a detector and not show any sign of
interference effects. So the presence or absence of the second
beam-splitter would always determine "wave or particle" manifestation.
Many experimenters
[who?] reached an interpretation of the experimental results that said that the change in final conditions would
retroactively
determine what the photon had "decided" to be as it was entering the
first beam-splitter. As mentioned above, Wheeler rejected this
interpretation.
Cosmic interferometer
Double quasar known as QSO 0957+561, also known as the "Twin Quasar", which lies just under 9 billion light-years from Earth.
[9]
In an attempt to avoid destroying normal ideas of cause and effect, some theoreticians
suggested that information about whether there was or was not a second
beam-splitter installed could somehow be transmitted from the end point
of the experimental device back to the photon as it was just entering
that experimental device, thus permitting it to make the proper
"decision." So Wheeler proposed a cosmic version of his experiment. In
that thought experiment he asks what would happen if a
quasar
or other galaxy millions or billions of light years away from Earth
passes its light around an intervening galaxy or cluster of galaxies
that would act as a gravitational lens. A photon heading exactly towards
Earth would encounter the distortion of space in the vicinity of the
intervening massive galaxy. At that point it would have to "decide"
whether to go by one way around the lensing galaxy, traveling as a
particle, or go both ways around by traveling as a wave. When the photon
arrived at an astronomical observatory at Earth, what would happen? Due
to the gravitational lensing, telescopes in the observatory see two
images of the same quasar, one to the left of the lensing galaxy and one
to the right of it. If the photon has traveled as a particle and comes
into the barrel of a telescope aimed at the left quasar image it must
have decided to travel as a particle all those millions of years, or so
say some experimenters. That telescope is pointing the wrong way to pick
up anything from the other quasar image. If the photon traveled as a
particle and went the other way around, then it will only be picked up
by the telescope pointing at the right "quasar." So millions of years
ago the photon decided to travel in its guise of particle and randomly
chose the other path. But the experimenters now decide to try something
else. They direct the output of the two telescopes into a beam-splitter,
as diagrammed, and discover that one output is very bright (indicating
positive interference) and that the other output is essentially zero,
indicating that the incoming wavefunction pairs have self-cancelled.
Paths separated and paths converged via beam-splitter
Wheeler then plays the devil's advocate and suggests that perhaps for
those experimental results to be obtained would mean that at the
instant astronomers inserted their beam-splitter, photons that had left
the quasar some millions of years ago retroactively decided to travel as
waves, and that when the astronomers decided to pull their beam
splitter out again that decision was telegraphed back through time to
photons that were leaving some millions of years plus some minutes in
the past, so that photons retroactively decided to travel as particles.
Several ways of implementing Wheeler's basic idea have been made into
real experiments and they support the conclusion that Wheeler
anticipated — that what is done at the exit port of the experimental
device before the photon is detected will determine whether it displays
interference phenomena or not. Retrocausality is a mirage.
Double-slit version
Wheeler's double-slit apparatus.
[10]
A second kind of experiment resembles the ordinary double-slit
experiment. The schematic diagram of this experiment shows that a lens
on the far side of the double slits makes the path from each slit
diverge slightly from the other after they cross each other fairly near
to that lens. The result is that at the two wavefunctions for each
photon will be in superposition within a fairly short distance from the
double slits, and if a detection screen is provided within the region
wherein the wavefunctions are in superposition then interference
patterns will be seen. There is no way by which any given photon could
have been determined to have arrived from one or the other of the double
slits. However, if the detection screen is removed the wavefunctions on
each path will superimpose on regions of lower and lower amplitudes,
and their combined probability values will be much less than the
unreinforced probability values at the center of each path. When
telescopes are aimed to intercept the center of the two paths, there
will be equal probabilities of nearly 50% that a photon will show up in
one of them. When a photon is detected by telescope 1, researchers may
associate that photon with the wavefunction that emerged from the lower
slit. When one is detected in telescope 2, researchers may associate
that photon with the wavefunction that emerged from the upper slit. The
explanation that supports this interpretation of experimental results is
that a photon has emerged from one of the slits, and that is the end of
the matter. A photon must have started at the laser, passed through one
of the slits, and arrived by a single straight-line path at the
corresponding telescope.
The retrocausal explanation, which Wheeler does not accept, says that
with the detection screen in place, interference must be manifested.
For interference to be manifested, a light wave must have emerged from
each of the two slits. Therefore, a single photon upon coming into the
double-slit diaphragm must have "decided" that it needs to go through
both slits to be able to interfere with itself on the detection screen.
For no interference to be manifested, a single photon coming into the
double-slit diaphragm must have "decided" to go by only one slit because
that would make it show up at the camera in the appropriate single
telescope.
In this thought experiment the telescopes are always present, but the
experiment can start with the detection screen being present but then
being removed just after the photon leaves the double-slit diaphragm, or
the experiment can start with the detection screen being absent and
then being inserted just after the photon leaves the diaphragm. Some
theorists aver that inserting or removing the screen in the midst of the
experiment can force a photon to retroactively decide to go through the
double-slits as a particle when it had previously transited it as a
wave, or vice versa. Wheeler does not accept this interpretation.
The double slit experiment, like the other six idealized experiments
(microscope, split beam, tilt-teeth, radiation pattern, one-photon
polarization, and polarization of paired photons), imposes a choice
between complementary modes of observation. In each experiment we have
found a way to delay that choice of type of phenomenon to be looked for
up to the very final stage of development of the phenomenon, and it
depends on whichever type of detection device we then fix upon. That
delay makes no difference in the experimental predictions. On this score
everything we find was foreshadowed in that solitary and pregnant
sentence of Bohr, "...it...can make no difference, as regards observable
effects obtainable by a definite experimental arrangement, whether our
plans for constructing or handling the instruments are fixed beforehand
or whether we prefer to postpone the completion of our planning until a
later moment when the particle is already on its way from one instrument
to another."[11]
Bohmian Interpretation
One of the easiest ways of "making sense" of the delayed-choice paradox is to examine it using
Bohmian mechanics.
The surprising implications of the original delayed-choice experiment
led Wheeler to the conclusion that "no phenomenon is a phenomenon until
it is an observed phenomenon", which is a very radical position. Wheeler
famously said that the "past has no existence except as recorded in the
present", and that the Universe does not "exist, out there independent
of all acts of observation".
However Bohm et al. (1985, Nature vol. 315, pp294–97) have shown that
the Bohmian interpretation gives a straightforward account of the
behaviour of the particle under the delayed-choice set up, without
resorting to such a radical explanation. A detailed discussion is
available in the open-source article by Basil Hiley and Callaghan,
[12] while many of the quantum paradoxes including delayed choice are conveniently and compactly discussed in Chapter 7 of the Book
A Physicist's View of Matter and Mind (PVMM)
[13] using both Bohmian and standard interpretations.
In Bohm's quantum mechanics, the particle obeys classical mechanics
except that its movement takes place under the additional influence of
its
quantum potential.
A photon or an electron has a definite trajectory and passes through
one or the other of the two slits and not both, just as it is in the
case of a classical particle. The past is determined and stays what it
was up to the moment T
1 when the experimental configuration for detecting it as a
wave was changed to that of detecting a
particle at the arrival time T
2. At T
1,
when the experimental set up was changed, Bohm's quantum potential
changes as needed, and the particle moves classically under the new
quantum potential till T
2 when it is detected as a particle.
Thus Bohmian mechanics restores the conventional view of the world and
its past. The past is out there as an objective history unalterable
retroactively by delayed choice, contrary to the radical view of
Wheeler.
The "quantum potential" Q(r,T) is often taken to act instantly. But in fact, the change of the experimental set up at T
1 takes a finite time dT. The initial potential. Q(r,T
1
) changes slowly over the time interval dT to become the new quantum potential Q(r,T>T
1).
The book PVMM referred to above makes the important observation (sec.
6.7.1) that the quantum potential contains information about the
boundary conditions defining the system, and hence any change of the
experimental set up is immediately recognized by the quantum potential,
and determines the dynamics of the Bohmian particle.
Experimental details
John
Wheeler's original discussion of the possibility of a delayed choice
quantum appeared in an essay entitled "Law Without Law," which was
published in a book he and Wojciech Hubert Zurek edited called
Quantum Theory and Measurement,
pp 182–213. He introduced his remarks by reprising the argument between
Albert Einstein, who wanted a comprehensible reality, and Niels Bohr,
who thought that Einstein's concept of reality was too restricted.
Wheeler indicates that Einstein and Bohr explored the consequences of
the laboratory experiment that will be discussed below, one in which
light can find its way from one corner of a rectangular array of
semi-silvered and fully silvered mirrors to the other corner, and then
can be made to reveal itself not only as having gone halfway around the
perimeter by a single path and then exited, but also as having gone both
ways around the perimeter and then to have "made a choice" as to
whether to exit by one port or the other. Not only does this result hold
for beams of light, but also for single photons of light. Wheeler
remarked:
The experiment in the form an interferometer,
discussed by Einstein and Bohr, could theoretically be used to
investigate whether a photon sometimes sets off along a single path,
always follows two paths but sometimes only makes use of one, or whether
something else would turn up. However, it was easier to say, "We will,
during random runs of the experiment, insert the second half-silvered
mirror just before the photon is timed to get there," than it was to
figure out a way to make such a rapid substitution. The speed of light
is just too fast to permit a mechanical device to do this job, at least
within the confines of a laboratory. Much ingenuity was needed to get
around this problem.
After several supporting experiments were published, Jacques et al.
claimed that an experiment of theirs follows fully the original scheme
proposed by Wheeler.
[14][15] Their complicated experiment is based on the
Mach-Zender interferometer,
involving a triggered diamond N-V colour centre photon generator,
polarization, and an electro-optical modulator acting as a switchable
beam splitter. Measuring in a closed configuration showed interference,
while measuring in an open configuration allowed the path of the
particle to be determined, which made interference impossible.
In such experiments, Einstein originally argued, it is unreasonable
for a single photon to travel simultaneously two routes. Remove the
half-silvered mirror at the [upper right], and one will find that the
one counter goes off, or the other. Thus the photon has traveled only one
route. It travels only one route. but it travels both routes: it
travels both routes, but it travels only one route. What nonsense! How
obvious it is that quantum theory is inconsistent!
Interferometer in the lab
The
Wheeler version of the interferometer experiment could not be performed
in a laboratory until recently because of the practical difficulty of
inserting or removing the second beam-splitter in the brief time
interval between the photon's entering the first beam-splitter and its
arrival at the location provided for the second beam-splitter. This
realization of the experiment is done by extending the lengths of both
paths by inserting long lengths of fiber optic cable. So doing makes the
time interval involved with transits through the apparatus much longer.
A high-speed switchable device on one path, composed of a high-voltage
switch, a
Pockels cell, and a
Glan–Thompson prism,
makes it possible to divert that path away from its ordinary
destination so that path effectively comes to a dead end. With the
detour in operation, nothing can reach either detector by way of that
path, so there can be no interference. With it switched off the path
resumes its ordinary mode of action and passes through the second
beam-splitter, making interference reappear. This arrangement does not
actually insert and remove the second beam-splitter, but it does make it
possible to switch from a state in which interference appears to a
state in which interference cannot appear, and do so in the interval
between light entering the first beam-splitter and light exiting the
second beam-splitter. If photons had "decided" to enter the first
beam-splitter as either waves or a particles, they must have been
directed to undo that decision and to go through the system in their
other guise, and they must have done so without any physical process
being relayed to the entering photons or the first beam-splitter because
that kind of transmission would be too slow even at the speed of light.
Wheeler's interpretation of the physical results would be that in one
configuration of the two experiments a single copy of the wavefunction
of an entering photon is received, with 50% probability, at one or the
other detectors, and that under the other configuration two copies of
the wave function, traveling over different paths, arrive at both
detectors, are out of phase with each other, and therefore exhibit
interference. In one detector the wave functions will be in phase with
each other, and the result will be that the photon has 100% probability
of showing up in that detector. In the other detector the wave functions
will be 180° out of phase, will cancel each other exactly, and there
will be a 0% probability of their related photons showing up in that
detector.
[16]
Interferometer in the cosmos
The
cosmic experiment envisioned by Wheeler could be described either as
analogous to the interferometer experiment or as analogous to a
double-slit experiment. The important thing is that by a third kind of
device, a massive stellar object acting as a gravitational lens, photons
from a source can arrive by two pathways. Depending on how phase
differences between wavefunction pairs are arranged, correspondingly
different kinds of interference phenomena can be observed. Whether to
merge the incoming wavefunctions or not, and how to merge the incoming
wavefunctions can be controlled by experimenters. There are none of the
phase differences introduced into the wavefunctions by the experimental
apparatus as there are in the laboratory interferometer experiments, so
despite there being no double-slit device near the light source, the
cosmic experiment is closer to the double-slit experiment. However,
Wheeler planned for the experiment to merge the incoming wavefunctions
by use of a beam splitter.
[17]
The main difficulty in performing this experiment is that the
experimenter has no control over or knowledge of when each photon began
its trip toward earth, and the experimenter does not know the lengths of
each of the two paths between the distant quasar. Therefore, it is
possible that the two copies of one wavefunction might well arrive at
different times. Matching them in time so that they could interact would
require using some kind of delay device on the first to arrive. Before
that task could be done, it would be necessary to find a way to
calculate the time delay.
One suggestion for synchronizing inputs from the two ends of this cosmic experimental apparatus lies in the characteristics of
quasars
and the possibility of identifying identical events of some signal
characteristic. Information from the Twin Quasars that Wheeler used as
the basis of his speculation reach earth approximately 14 months apart.
[18] Finding a way to keep a quantum of light in some kind of loop for over a year would not be easy.
Double-slits in lab and cosmos
Replace beam splitter by registering projected telescope images on a common detection screen.
Wheeler's version of the double-slit experiment is arranged so that
the same photon that emerges from two slits can be detected in two ways.
The first way lets the two paths come together, lets the two copies of
the wavefunction overlap, and shows interference. The second way moves
farther away from the photon source to a position where the distance
between the two copies of the wavefunction is too great to show
interference effects. The technical problem in the laboratory is how to
insert a detector screen at a point appropriate to observe interference
effects or to remove that screen to reveal the photon detectors that can
be restricted to receiving photons from the narrow regions of space
where the slits are found. One way to accomplish that task would be to
use the recently developed electrically switchable mirrors and simply
change directions of the two paths from the slits by switching a mirror
on or off. As of early 2014 no such experiment has been announced.
The cosmic experiment described by Wheeler has other problems, but
directing wavefunction copies to one place or another long after the
photon involved has presumably "decided" whether to be a wave or a
particle requires no great speed at all. One has about a billion years
to get the job done.
The cosmic version of the interferometer experiment could easily be
adapted to function as a cosmic double-slit device as indicated in the
illustration. Wheeler appears not to have considered this possibility.
It has, however, been discussed by other writers.
[19]
Current experiments of interest
The
first real experiment to follow Wheeler's intention for a double-slit
apparatus to be subjected to end-game determination of detection method
is the one by Walborn et al.
[20]
An experiment by Ma et al., "Quantum erasure with causally
disconnected choice," concludes: "Our results demonstrate that the
viewpoint that the system photon behaves either definitely as a wave or
definitely as a particle would require faster-than-light communication.
Because this would be in strong tension with the special theory of
relativity, we believe that such a viewpoint should be given up
entirely.
[21]
Researchers with access to radio telescopes originally designed for
SETI research have explicated the practical difficulties of conducting the interstellar Wheeler experiment.
[22]
A recent experiment by Manning,
et al. confirms the standard predictions of standard quantum mechanics with an atom of Helium.
[23]
Conclusions
Ma,
Zeilinger, et al. have summarized what can be known as a result of
experiments that have arisen from Wheeler's proposals. They say:
Any explanation of what goes on in a specific individual observation
of one photon has to take into account the whole experimental apparatus
of the complete quantum state consisting of both photons, and it can
only make sense after all information concerning complementary variables
has been recorded. Our results demonstrate that the viewpoint that the
system photon behaves either definitely as a wave or definitely as a
particle would require faster-than-light communication. Because this
would be in strong tension with the special theory of relativity, we
believe that such a viewpoint should be given up entirely.[24]