Wheeler–Feynman absorber theory

From Wikipedia, the free encyclopedia

The Wheeler–Feynman absorber theory (also called the Wheeler–Feynman time-symmetric theory), named after its originators, the physicists Richard Feynman and John Archibald Wheeler, is an interpretation of electrodynamics derived from the assumption that the solutions of the electromagnetic field equations must be invariant under time-reversal transformation, as are the field equations themselves. Indeed, there is no apparent reason for the time-reversal symmetry breaking, which singles out a preferential time direction and thus makes a distinction between past and future. A time-reversal invariant theory is more logical and elegant. Another key principle, resulting from this interpretation and reminiscent of Mach's principle due to Tetrode, is that elementary particles are not self-interacting. This immediately removes the problem of self-energies.

T-symmetry and causality

The requirement of time-reversal symmetry, in general, is difficult to conjugate with the principle of causality. Maxwell's equations and the equations for electromagnetic waves have, in general, two possible solutions: a retarded (delayed) solution and an advanced one. Accordingly, any charged particle generates waves, say at time ${\displaystyle t_{0}=0}$ and point ${\displaystyle x_{0}=0}$, which will arrive at point ${\displaystyle x_{1}}$ at the instant ${\displaystyle t_{1}=x_{1}/c}$ (here ${\displaystyle c}$ is the speed of light), after the emission (retarded solution), and other waves, which will arrive at the same place at the instant ${\displaystyle t_{2}=-x_{1}/c}$, before the emission (advanced solution). The latter, however, violates the causality principle: advanced waves could be detected before their emission. Thus the advanced solutions are usually discarded in the interpretation of electromagnetic waves. In the absorber theory, instead charged particles are considered as both emitters and absorbers, and the emission process is connected with the absorption process as follows: Both the retarded waves from emitter to absorber and the advanced waves from absorber to emitter are considered. The sum of the two, however, results in causal waves, although the anti-causal (advanced) solutions are not discarded a priori.

Feynman and Wheeler obtained this result in a very simple and elegant way. They considered all the charged particles (emitters) present in our universe and assumed all of them to generate time-reversal symmetric waves. The resulting field is

${\displaystyle E_{\text{tot}}(\mathbf {x} ,t)=\sum _{n}{\frac {E_{n}^{\text{ret}}(\mathbf {x} ,t)+E_{n}^{\text{adv}}(\mathbf {x} ,t)}{2}}.}$

Then they observed that if the relation

${\displaystyle E_{\text{free}}(\mathbf {x} ,t)=\sum _{n}{\frac {E_{n}^{\text{ret}}(\mathbf {x} ,t)-E_{n}^{\text{adv}}(\mathbf {x} ,t)}{2}}=0}$

holds, then ${\displaystyle E_{\text{free}}}$, being a solution of the homogeneous Maxwell equation, can be used to obtain the total field

${\displaystyle E_{\text{tot}}(\mathbf {x} ,t)=\sum _{n}{\frac {E_{n}^{\text{ret}}(\mathbf {x} ,t)+E_{n}^{\text{adv}}(\mathbf {x} ,t)}{2}}+\sum _{n}{\frac {E_{n}^{\text{ret}}(\mathbf {x} ,t)-E_{n}^{\text{adv}}(\mathbf {x} ,t)}{2}}=\sum _{n}E_{n}^{\text{ret}}(\mathbf {x} ,t).}$

The total field is retarded, and causality is not violated.

The assumption that the free field is identically zero is the core of the absorber idea. It means that the radiation emitted by each particle is completely absorbed by all other particles present in the universe. To better understand this point, it may be useful to consider how the absorption mechanism works in common materials. At the microscopic scale, it results from the sum of the incoming electromagnetic wave and the waves generated from the electrons of the material, which react to the external perturbation. If the incoming wave is absorbed, the result is a zero outgoing field. In the absorber theory the same concept is used, however, in presence of both retarded and advanced waves.

The resulting wave appears to have a preferred time direction, because it respects causality. However, this is only an illusion. Indeed, it is always possible to reverse the time direction by simply exchanging the labels emitter and absorber. Thus, the apparently preferred time direction results from the arbitrary labelling.

T-symmetry and self-interaction

One of the major results of the absorber theory is the elegant and clear interpretation of the electromagnetic radiation process. A charged particle that experiences acceleration is known to emit electromagnetic waves, i.e., to lose energy. Thus, the Newtonian equation for the particle (${\displaystyle F=ma}$) must contain a dissipative force (damping term), which takes into account this energy loss. In the causal interpretation of electromagnetism, Lorentz and Abraham proposed that such a force, later called Abraham–Lorentz force, is due to the retarded self-interaction of the particle with its own field. This first interpretation, however, is not completely satisfactory, as it leads to divergences in the theory and needs some assumptions on the structure of charge distribution of the particle. Dirac generalized the formula to make it relativistically invariant. While doing so, he also suggested a different interpretation. He showed that the damping term can be expressed in terms of a free field acting on the particle at its own position:

${\displaystyle E^{\text{damping}}(\mathbf {x} _{j},t)={\frac {E_{j}^{\text{ret}}(\mathbf {x} _{j},t)-E_{j}^{\text{adv}}(\mathbf {x} _{j},t)}{2}}.}$

However, Dirac did not propose any physical explanation of this interpretation.

A clear and simple explanation can instead be obtained in the framework of absorber theory, starting from the simple idea that each particle does not interact with itself. This is actually the opposite of the first Abraham–Lorentz proposal. The field acting on the particle ${\displaystyle j}$ at its own position (the point ${\displaystyle x_{j}}$) is then

${\displaystyle E^{\text{tot}}(\mathbf {x} _{j},t)=\sum _{n\neq j}{\frac {E_{n}^{\text{ret}}(\mathbf {x} _{j},t)+E_{n}^{\text{adv}}(\mathbf {x} _{j},t)}{2}}.}$

If we sum the free-field term of this expression, we obtain

${\displaystyle E^{\text{tot}}(\mathbf {x} _{j},t)=\sum _{n\neq j}{\frac {E_{n}^{\text{ret}}(\mathbf {x} _{j},t)+E_{n}^{\text{adv}}(\mathbf {x} _{j},t)}{2}}+\sum _{n}{\frac {E_{n}^{\text{ret}}(\mathbf {x} _{j},t)-E_{n}^{\text{adv}}(\mathbf {x} _{j},t)}{2}}}$

and, thanks to Dirac's result,

${\displaystyle E^{\text{tot}}(\mathbf {x} _{j},t)=\sum _{n\neq j}E_{n}^{\text{ret}}(\mathbf {x} _{j},t)+E^{\text{damping}}(\mathbf {x} _{j},t).}$

Thus, the damping force is obtained without the need for self-interaction, which is known to lead to divergences, and also giving a physical justification to the expression derived by Dirac.

Criticism

The Abraham–Lorentz force is, however, not free of problems. Written in the non-relativistic limit, it gives

${\displaystyle E^{\text{damping}}(\mathbf {x} _{j},t)={\frac {e}{6\pi c^{3}}}{\frac {\mathrm {d} ^{3}}{\mathrm {d} t^{3}}}x.}$

Since the third derivative with respect to the time (also called the "jerk" or "jolt") enters in the equation of motion, to derive a solution one needs not only the initial position and velocity of the particle, but also its initial acceleration. This apparent problem, however, can be solved in the absorber theory by observing that the equation of motion for the particle has to be solved together with the Maxwell equations for the field. In this case, instead of the initial acceleration, one only needs to specify the initial field and the boundary condition. This interpretation restores the coherence of the physical interpretation of the theory.

Other difficulties may arise trying to solve the equation of motion for a charged particle in the presence of this damping force. It is commonly stated that the Maxwell equations are classical and cannot correctly account for microscopic phenomena, such as the behavior of a point-like particle, where quantum-mechanical effects should appear. Nevertheless, with absorber theory, Wheeler and Feynman were able to create a coherent classical approach to the problem (see also the "paradoxes" section in the Abraham–Lorentz force).

Also, the time-symmetric interpretation of the electromagnetic waves appears to be in contrast with the experimental evidence that time flows in a given direction and, thus, that the T-symmetry is broken in our world. It is commonly believed, however, that this symmetry breaking appears only in the thermodynamical limit (see, for example, the arrow of time). Wheeler himself accepted that the expansion of the universe is not time-symmetric in the thermodynamic limit. This, however, does not imply that the T-symmetry must be broken also at the microscopic level.

Finally, the main drawback of the theory turned out to be the result that particles are not self-interacting. Indeed, as demonstrated by Hans Bethe, the Lamb shift necessitated a self-energy term to be explained. Feynman and Bethe had an intense discussion over that issue, and eventually Feynman himself stated that self-interaction is needed to correctly account for this effect^[1].

Developments since original formulation

Gravity theory

Inspired by the Machian nature of the Wheeler–Feynman absorber theory for electrodynamics, Fred Hoyle and Jayant Narlikar proposed their own theory of gravity^[2][3][4] in the context of general relativity. This model still exists in spite of recent astronomical observations that have challenged the theory.^[5] Stephen Hawking had criticized the original Hoyle-Narlikar theory believing that the advanced waves going off to infinity would lead to a divergence, as indeed they would, if the universe were only expanding. However, as emphasized in the revised version of the Hoyle-Narlikar theory devoid of the "Creation Field" (generating matter out of empty space) known as the Gravitational absorber theory, the universe is also accelerating in that expansion. The acceleration leads to a horizon type cutoff and hence no divergence^[6]. Gravitational absorber theory has been used to explain the mass fluctuations in the Woodward effect (see section on Woodward effect below).

Transactional interpretation of quantum mechanics

Again inspired by the Wheeler–Feynman absorber theory, the transactional interpretation of quantum mechanics (TIQM) first proposed in 1986 by John G. Cramer,^[7][8] describes quantum interactions in terms of a standing wave formed by retarded (forward-in-time) and advanced (backward-in-time) waves. Cramer claims it avoids the philosophical problems with the Copenhagen interpretation and the role of the observer, and resolves various quantum paradoxes, such as quantum nonlocality, quantum entanglement and retrocausality.^[9][10]

Shu-Yuan Chu's quantum theory in the presence of gravity

In 1993, Chu developed a model of how to do quantum mechanics in the presence of gravity, which combines some of the latest ideas in particle physics, superstrings, and a time-symmetric Wheeler–Feynman description of gravity and inertia.^[11][12] In 1998 he extended this work to derive Einstein's equation for the "adjunct gravitational field" using concepts from statistics and maximizing the entropy.^[13]

Attempted resolution of causality

T. C. Scott and R. A. Moore demonstrated that the apparent acausality suggested by the presence of advanced Liénard–Wiechert potentials could be removed by recasting the theory in terms of retarded potentials only, without the complications of the absorber idea.^[14][15] The Lagrangian describing a particle (${\displaystyle p_{1}}$) under the influence of the time-symmetric potential generated by another particle (${\displaystyle p_{2}}$) is

${\displaystyle L_{1}=T_{1}-{\frac {1}{2}}\left((V_{R})_{1}^{2}+(V_{A})_{1}^{2}\right),}$

where ${\displaystyle T_{i}}$ is the relativistic kinetic energy functional of particle ${\displaystyle p_{i}}$, and ${\displaystyle (V_{R})_{i}^{j}}$ and ${\displaystyle (V_{A})_{i}^{j}}$ are respectively the retarded and advanced Liénard–Wiechert potentials acting on particle ${\displaystyle p_{i}}$ and generated by particle ${\displaystyle p_{j}}$. The corresponding Lagrangian for particle ${\displaystyle p_{2}}$ is

${\displaystyle L_{2}=T_{2}-{\frac {1}{2}}\left((V_{R})_{2}^{1}+(V_{A})_{2}^{1}\right).}$

It was originally demonstrated with computer algebra^[16] and then proven analytically^[17] that

${\displaystyle (V_{R})_{j}^{i}-(V_{A})_{i}^{j}}$

is a total time derivative, i.e. a divergence in the calculus of variations, and thus it gives no contribution to the Euler–Lagrange equations. Thanks to this result the advanced potentials can be eliminated; here the total derivative plays the same role as the free field. The Lagrangian for the N-body system is therefore

${\displaystyle L=\sum _{i=1}^{N}T_{i}-{\frac {1}{2}}\sum _{i\neq j}^{N}(V_{R})_{j}^{i}.}$

The resulting Lagrangian is symmetric under the exchange of ${\displaystyle p_{i}}$ with ${\displaystyle p_{j}}$. For ${\displaystyle N=2}$ this Lagrangian will generate exactly the same equations of motion of ${\displaystyle L_{1}}$ and ${\displaystyle L_{2}}$. Therefore, from the point of view of an outside observer, everything is causal. This formulation reflects particle-particle symmetry with the variational principle applied to the N-particle system as a whole, and thus Tetrode's Machian principle^[17]. Only if we isolate the forces acting on a particular body do the advanced potentials make their appearance. This recasting of the problem comes at a price: the N-body Lagrangian depends on all the time derivatives of the curves traced by all particles, i.e. the Lagrangian is infinite-order. However, much progress was made in examining the unresolved issue of quantizing the theory.^[18][19][20] Also, this formulation recovers the Darwin Lagrangian, from which the Breit equation was originally derived, but without the dissipative terms.^[17] This ensures agreement with theory and experiment, up to but not including the Lamb shift. Numerical solutions for the classical problem were also found.^[21] Furthermore, Moore showed that a model by Feynman and Hibbs is amenable to the methods of higher than first-order Lagrangians and revealed chaoticlike solutions.^[22] Moore and Scott^[14] showed that the radiation reaction can be alternatively derived using the notion that, on average, the net dipole moment is zero for a collection of charged particles, thereby avoiding the complications of the absorber theory. An important bonus from their approach is the formulation of a total preserved canonical generalized momentum, as presented in a comprehensive review article in the light of quantum nonlocality.^[23]

This apparent acausality may be viewed as merely apparent, and this entire problem goes away. An opposing view was held by Einstein.^[24]

Alternative Lamb shift calculation

As mentioned previously, a serious criticism against the absorber theory is that its Machian assumption that point particles do not act on themselves does not allow (infinite) self-energies and consequently an explanation for the Lamb shift according to quantum electrodynamics (QED). Ed Jaynes proposed an alternate model where the Lamb-like shift is due instead to the interaction with other particles very much along the same notions of the Wheeler–Feynman absorber theory itself. One simple model is to calculate the motion of an oscillator coupled directly with many other oscillators. Jaynes has shown that it is easy to get both spontaneous emission and Lamb shift behavior in classical mechanics.^[25] Furthermore, Jayne's alternatives provides a solution to the process of "addition and subtraction of infinities" associated with renormalization.^[23][26]

This model leads to essentially the same type of Bethe logarithm an essential part of the Lamb shift calculation vindicating Jaynes' claim that two different physical models can be mathematically isomorphic to each other and therefore yield the same results, a point also apparently made by Scott and Moore on the issue of causality.

Woodward effect

The Woodward effect^[27] is a physical hypothesis about the possibility for a body to see its mass change when the energy density varies in time. Proposed in 1990 by James Woodward, the effect is based on a formulation of Mach's principle proposed in 1953 by Dennis Sciama.^[28]
If confirmed experimentally (see timeline of results in the main article), the Woodward effect would open pathways in astronautics research, as it could be used to propel a spacecraft by propellantless propulsion meaning that it would not have to expel matter to accelerate. As previously formulated by Sciama, Woodward suggests that the Wheeler–Feynman absorber theory would be the correct way to understand the action of instantaneous inertial forces in Machian terms.^[29]

Conclusions

This universal absorber theory is mentioned in the chapter titled "Monster Minds" in Feynman's autobiographical work Surely You're Joking, Mr. Feynman! and in Vol. II of the Feynman Lectures on Physics. It led to the formulation of a framework of quantum mechanics using a Lagrangian and action as starting points, rather than a Hamiltonian, namely the formulation using Feynman path integrals, which proved useful in Feynman's earliest calculations in quantum electrodynamics and quantum field theory in general. Both retarded and advanced fields appear respectively as retarded and advanced propagators and also in the Feynman propagator and the Dyson propagator. In hindsight, the relationship between retarded and advanced potentials shown here is not so surprising in view of the fact that, in field theory, the advanced propagator can be obtained from the retarded propagator by exchanging the roles of field source and test particle (usually within the kernel of a Green's function formalism). In field theory, advanced and retarded fields are simply viewed as mathematical solutions of Maxwell's equations whose combinations are decided by the boundary conditions.

Wheeler's delayed choice experiment

From Wikipedia, the free encyclopedia

 

John Wheeler, 1985

 

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:

Open and Closed

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]

 

Wheeler's plan

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 T₁ when the experimental configuration for detecting it as a wave was changed to that of detecting a particle at the arrival time T₂. At T₁, 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 T₂ 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 T₁ takes a finite time dT. The initial potential. Q(r,T1
) changes slowly over the time interval dT to become the new quantum potential Q(r,T>T₁). 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]

Delayed choice quantum eraser

From Wikipedia, the free encyclopedia

 

A delayed choice quantum eraser experiment, first performed by Yoon-Ho Kim, R. Yu, S. P. Kulik, Y. H. Shih and Marlan O. Scully,^[1] and reported in early 1999, is an elaboration on the quantum eraser experiment that incorporates concepts considered in Wheeler's delayed choice experiment. The experiment was designed to investigate peculiar consequences of the well-known double-slit experiment in quantum mechanics, as well as the consequences of quantum entanglement.

The delayed choice quantum eraser experiment investigates a paradox. If a photon manifests itself as though it had come by a single path to the detector, then "common sense" (which Wheeler and others challenge) says it must have entered the double-slit device as a particle. If a photon manifests itself as though it had come by two indistinguishable paths, then it must have entered the double-slit device as a wave. If the experimental apparatus is changed while the photon is in mid‑flight, then the photon should reverse its original "decision" as to whether to be a wave or a particle. Wheeler pointed out that when these assumptions are applied to a device of interstellar dimensions, a last-minute decision made on Earth on how to observe a photon could alter a decision made millions or even billions of years ago.

While delayed choice experiments have confirmed the seeming ability of measurements made on photons in the present to alter events occurring in the past, this requires a non-standard view of quantum mechanics. If a photon in flight is interpreted as being in a so-called "superposition of states", i.e. if it is interpreted as something that has the potentiality to manifest as a particle or wave, but during its time in flight is neither, then there is no time paradox. This is the standard view, and recent experiments have supported it.^{[clarification needed][2][3]}

Introduction

In the basic double slit experiment, a beam of light (usually from a laser) is directed perpendicularly towards a wall pierced by two parallel slit apertures. If a detection screen (anything from a sheet of white paper to a CCD) is put on the other side of the double slit wall, a pattern of light and dark fringes will be observed, a pattern that is called an interference pattern. Other atomic-scale entities such as electrons are found to exhibit the same behavior when fired toward a double slit.^[4] By decreasing the brightness of the source sufficiently, individual particles that form the interference pattern are detectable.^[5] The emergence of an interference pattern suggests that each particle passing through the slits interferes with itself, and that therefore in some sense the particles are going through both slits at once.^[6]:110 This is an idea that contradicts our everyday experience of discrete objects.

A well-known thought experiment, which played a vital role in the history of quantum mechanics (for example, see the discussion on Einstein's version of this experiment), demonstrated that if particle detectors are positioned at the slits, showing through which slit a photon goes, the interference pattern will disappear.^[4] This which-way experiment illustrates the complementarity principle that photons can behave as either particles or waves, but not both at the same time.^[7][8][9] However, technically feasible realizations of this experiment were not proposed until the 1970s.^[10]

Which-path information and the visibility of interference fringes are hence complementary quantities. In the double-slit experiment, conventional wisdom held that observing the particles inevitably disturbed them enough to destroy the interference pattern as a result of the Heisenberg uncertainty principle.

However, in 1982, Scully and Drühl found a loophole around this interpretation.^[11] They proposed a "quantum eraser" to obtain which-path information without scattering the particles or otherwise introducing uncontrolled phase factors to them. Rather than attempting to observe which photon was entering each slit (thus disturbing them), they proposed to "mark" them with information that, in principle at least, would allow the photons to be distinguished after passing through the slits. Lest there be any misunderstanding, the interference pattern does disappear when the photons are so marked. However, the interference pattern reappears if the which-path information is further manipulated after the marked photons have passed through the double slits to obscure the which-path markings. Since 1982, multiple experiments have demonstrated the validity of the so-called quantum "eraser."^[12][13][14]

A simple quantum eraser experiment

A simple version of the quantum eraser can be described as follows: Rather than splitting one photon or its probability wave between two slits, the photon is subjected to a beam splitter. If one thinks in terms of a stream of photons being randomly directed by such a beam splitter to go down two paths that are kept from interaction, it would seem that no photon can then interfere with any other or with itself.

However, if the rate of photon production is reduced so that only one photon is entering the apparatus at any one time, it becomes impossible to understand the photon as only moving through one path, because when the path outputs are redirected so that they coincide on a common detector or detectors, interference phenomena appear.

Figure 1. Experiment that shows delayed determination of photon path

In the two diagrams in Fig. 1, photons are emitted one at a time from a laser symbolized by a yellow star. They pass through a 50% beam splitter (green block) that reflects or transmits 1/2 of the photons. The reflected or transmitted photons travel along two possible paths depicted by the red or blue lines.

In the top diagram, the trajectories of the photons are clearly known: If a photon emerges from the top of the apparatus, it had to have come by way of the blue path, and if it emerges from the side of the apparatus, it had to have come by way of the red path.

In the bottom diagram, a second beam splitter is introduced at the top right. It can direct either beam toward either exit port. Thus, photons emerging from each exit port may have come by way of either path. By introducing the second beam splitter, the path information has been "erased". Erasing the path information results in interference phenomena at detection screens positioned just beyond each exit port. What issues to the right side displays reinforcement, and what issues toward the top displays cancellation.^[15]

Delayed choice

Elementary precursors to current quantum eraser experiments such as the "simple quantum eraser" described above have straightforward classical-wave explanations. Indeed, it could be argued that there is nothing particularly quantum about this experiment.^[16] Nevertheless, Jordan has argued on the basis of the correspondence principle, that despite the existence of classical explanations, first-order interference experiments such as the above can be interpreted as true quantum erasers.^[17]

These precursors use single-photon interference. Versions of the quantum eraser using entangled photons, however, are intrinsically non-classical. Because of that, in order to avoid any possible ambiguity concerning the quantum versus classical interpretation, most experimenters have opted to use nonclassical entangled-photon light sources to demonstrate quantum erasers with no classical analog.

Furthermore, use of entangled photons enables the design and implementation of versions of the quantum eraser that are impossible to achieve with single-photon interference, such as the delayed choice quantum eraser which is the topic of this article.

The experiment of Kim et al. (1999)

Figure 2. Setup of the delayed choice quantum eraser experiment of Kim et al. Detector D₀ is movable

The experimental setup, described in detail in Kim et al.,^[1] is illustrated in Fig 2. An argon laser generates individual 351.1 nm photons that pass through a double slit apparatus (vertical black line in the upper left hand corner of the diagram).

An individual photon goes through one (or both) of the two slits. In the illustration, the photon paths are color-coded as red or light blue lines to indicate which slit the photon came through (red indicates slit A, light blue indicates slit B).

So far, the experiment is like a conventional two-slit experiment. However, after the slits, spontaneous parametric down conversion (SPDC) is used to prepare an entangled two-photon state. This is done by a nonlinear optical crystal BBO (beta barium borate) that converts the photon (from either slit) into two identical, orthogonally polarized entangled photons with 1/2 the frequency of the original photon. The paths followed by these orthogonally polarized photons are caused to diverge by the Glan-Thompson Prism.

One of these 702.2 nm photons, referred to as the "signal" photon (look at the red and light-blue lines going upwards from the Glan-Thompson prism) continues to the target detector called D₀. During an experiment, detector D₀ is scanned along its x-axis, its motions controlled by a step motor. A plot of "signal" photon counts detected by D₀ versus x can be examined to discover whether the cumulative signal forms an interference pattern.

The other entangled photon, referred to as the "idler" photon (look at the red and light-blue lines going downwards from the Glan-Thompson prism), is deflected by prism PS that sends it along divergent paths depending on whether it came from slit A or slit B.

Somewhat beyond the path split, the idler photons encounter beam splitters BS_a, BS_b, and BS_c that each have a 50% chance of allowing the idler photon to pass through and a 50% chance of causing it to be reflected. M_a and M_b are mirrors.

Figure 3. x axis: position of D₀. y axis: joint detection rates between D₀ and D₁, D₂, D₃, D₄ (R₀₁, R₀₂, R₀₃, R₀₄). R₀₄ is not provided in the Kim article, and is supplied according to their verbal description.

 

Figure 4. Simulated recordings of photons jointly detected between D₀ and D₁, D₂, D₃, D₄ (R₀₁, R₀₂, R₀₃, R₀₄)

The beam splitters and mirrors direct the idler photons towards detectors labeled D₁, D₂, D₃ and D₄. Note that:

• If an idler photon is recorded at detector D₃, it can only have come from slit B.
• If an idler photon is recorded at detector D₄, it can only have come from slit A.
• If an idler photon is detected at detector D₁ or D₂, it might have come from slit A or slit B.
• The optical path length measured from slit to D₁, D₂, D₃, and D₄ is 2.5 m longer than the optical path length from slit to D₀. This means that any information that one can learn from an idler photon must be approximately 8 ns later than what one can learn from its entangled signal photon.

Detection of the idler photon by D₃ or D₄ provides delayed "which-path information" indicating whether the signal photon with which it is entangled had gone through slit A or B. On the other hand, detection of the idler photon by D₁ or D₂ provides a delayed indication that such information is not available for its entangled signal photon. Insofar as which-path information had earlier potentially been available from the idler photon, it is said that the information has been subjected to a "delayed erasure".

By using a coincidence counter, the experimenters were able to isolate the entangled signal from photo-noise, recording only events where both signal and idler photons were detected (after compensating for the 8 ns delay). Refer to Figs 3 and 4.

• When the experimenters looked at the signal photons whose entangled idlers were detected at D₁ or D₂, they detected interference patterns.
• However, when they looked at the signal photons whose entangled idlers were detected at D₃ or D₄, they detected simple diffraction patterns with no interference.

Significance

This result is similar to that of the double-slit experiment since interference is observed when it is not known which slit the photon went through, while no interference is observed when the path is known.

Figure 5. Distribution of signal photons at D₀ can be compared with distribution of bulbs on digital billboard. When all the bulbs are lit, billboard won't reveal any pattern of image, which can be 'recovered' only by switching-off some bulbs. Likewise interference pattern or no-interference pattern among signal photons at D₀ can be recovered only after 'switching-off' (or ignoring) some signal photons and which signal photons should be ignored to recover pattern, this information can be gained only by looking at corresponding entangled idler photons in detectors D₁ to D₄.

However, what makes this experiment possibly astonishing is that, unlike in the classic double-slit experiment, the choice of whether to preserve or erase the which-path information of the idler was not made until 8 ns after the position of the signal photon had already been measured by D₀.

Detection of signal photons at D₀ does not directly yield any which-path information. Detection of idler photons at D₃ or D₄, which provide which-path information, means that no interference pattern can be observed in the jointly detected subset of signal photons at D₀. Likewise, detection of idler photons at D₁ or D₂, which do not provide which-path information, means that interference patterns can be observed in the jointly detected subset of signal photons at D₀.

In other words, even though an idler photon is not observed until long after its entangled signal photon arrives at D₀ due to the shorter optical path for the latter, interference at D₀ is determined by whether a signal photon's entangled idler photon is detected at a detector that preserves its which-path information (D₃ or D₄), or at a detector that erases its which-path information (D₁ or D₂).

Some have interpreted this result to mean that the delayed choice to observe or not observe the path of the idler photon changes the outcome of an event in the past. Note in particular that an interference pattern may only be pulled out for observation after the idlers have been detected (i.e., at D₁ or D₂).

The total pattern of all signal photons at D₀, whose entangled idlers went to multiple different detectors, will never show interference regardless of what happens to the idler photons.^[19] One can get an idea of how this works by looking at the graphs of R₀₁, R₀₂, R₀₃, and R₀₄, and observing that the peaks of R₀₁ line up with the troughs of R₀₂ (i.e. a π phase shift exists between the two interference fringes). R₀₃ shows a single maximum, and R₀₄, which is experimentally identical to R₀₃ will show equivalent results. The entangled photons, as filtered with the help of the coincidence counter, are simulated in Fig. 5 to give a visual impression of the evidence available from the experiment. In D₀, the sum of all the correlated counts will not show interference. If all the photons that arrive at D₀ were to be plotted on one graph, one would see only a bright central band.

Implications

Possibility of retrocausality

Delayed choice experiments raise questions about time and time sequences, and thereby bring our usual ideas of time and causal sequence into question.^{[note 1]} If events at D₁, D₂, D₃, D₄ determine outcomes at D₀, then effect seems to precede cause. If the idler light paths were greatly extended so that a year goes by before a photon shows up at D₁, D₂, D₃, or D₄, then when a photon shows up in one of these detectors, it would cause a signal photon to have shown up in a certain mode a year earlier. Alternatively, knowledge of the future fate of the idler photon would determine the activity of the signal photon in its own present. Neither of these ideas conforms to the usual human expectation of causality. However, knowledge of the future, which would be a hidden variable, was refuted in experiments.^[20]

Does delayed choice violate causality?

Experiments that involve entanglement exhibit phenomena that may make some people doubt their ordinary ideas about causal sequence. In the delayed choice quantum eraser, an interference pattern will form on D₀ even if which-path data pertinent to photons that form it are only erased later in time than the signal photons that hit the primary detector. Not only that feature of the experiment is puzzling; D₀ can, in principle at least, be on one side of the universe, and the other four detectors can be "on the other side of the universe" to each other.^[21]:197f

However, the interference pattern can only be seen retroactively once the idler photons have been detected and the experimenter has had information about them available, with the interference pattern being seen when the experimenter looks at particular subsets of signal photons that were matched with idlers that went to particular detectors.^[21]:197

Moreover, the apparent retroactive action vanishes if the effects of observations on the state of the entangled signal and idler photons are considered in the historic order. Specifically, in the case when detection/deletion of which-way information happens before the detection on D₀, the standard simplistic explanation says "The detector D_i, at which the idler photon is detected, determines the probability distribution at D₀ for the signal photon". Similarly, in the case when D₀ precedes detection of the idler photon, the following description is just as accurate: "The position at D₀ of the detected signal photon determines the probabilities for the idler photon to hit either of D₁, D₂, D₃ or D₄". These are just equivalent ways of formulating the correlations of entangled photons' observables in an intuitive causal way, so one may choose any of those (in particular, that one where the cause precedes the consequence and no retrograde action appears in the explanation).

The total pattern of signal photons at the primary detector never shows interference (see Fig. 5), so it is not possible to deduce what will happen to the idler photons by observing the signal photons alone. The delayed choice quantum eraser does not communicate information in a retro-causal manner because it takes another signal, one which must arrive via a process that can go no faster than the speed of light, to sort the superimposed data in the signal photons into four streams that reflect the states of the idler photons at their four distinct detection screens.^{[note 2][note 3]}

In fact, a theorem proved by Phillippe Eberhard shows that if the accepted equations of relativistic quantum field theory are correct, it should never be possible to experimentally violate causality using quantum effects.^[22] (See reference^[23] for a treatment emphasizing the role of conditional probabilities.)

In addition to challenging our common sense ideas of temporal sequence in cause and effect relationships, this experiment is among those that strongly attack our ideas about locality, the idea that things cannot interact unless they are in contact, if not by being in direct physical contact then at least by interaction through magnetic or other such field phenomena.^[21]:199

Against consensus

Despite Eberhard's proof, some physicists have speculated that these experiments might be changed in a way that would be consistent with previous experiments, yet which could allow for experimental causality violations.^[24][25][26]

Other delayed choice quantum eraser experiments

Many refinements and extensions of Kim et al.'s delayed choice quantum eraser have been performed or proposed. Only a small sampling of reports and proposals are given here:

Scarcelli et al. (2007) reported on a delayed-choice quantum eraser experiment based on a two-photon imaging scheme. After detecting a photon which passed through a double-slit, a random delayed choice was made to erase or not erase the which-path information by the measurement of its distant entangled twin; the particle-like and wave-like behavior of the photon were then recorded simultaneously and respectively by only one set of joint detectors.^[27]

Peruzzo et al. (2012) have reported on a quantum delayed choice experiment, based on a quantum controlled beam-splitter, in which particle and wave behaviors were investigated simultaneously. The quantum nature of the photon's behavior was tested via a Bell inequality, which replaced the delayed choice of the observer.^[28]

The construction of solid state electronic Mach-Zehnder interferometers (MZI) has led to proposals to use them in electronic versions of quantum eraser experiments. This would be achieved by Coulomb coupling to a second electronic MZI acting as a detector.^[29]

Entangled pairs of neutral kaons have also been examined and found suitable for investigations using quantum marking and quantum erasure techniques.^[30]