Delayed-choice quantum eraser

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https://en.wikipedia.org/wiki/Delayed-choice_quantum_eraser

A delayed-choice quantum eraser experiment, first performed by Yoon-Ho Kim, R. Yu, S. P. Kulik, Y. H. Shih and Marlan O. Scully, and reported in early 1998, is an elaboration on the quantum eraser experiment that incorporates concepts considered in John Archibald 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 that 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. Accordingly, if the experimental apparatus is changed while the photon is in mid‑flight, the photon may have to revise its prior "commitment" 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 situation established millions or even billions of years earlier.

While delayed-choice experiments might seem to allow measurements made in the present to alter events that occurred in the past, this conclusion requires assuming a non-standard view of quantum mechanics. If a photon in flight is instead interpreted as being in a so-called "superposition of states"—that is, if it is allowed the potentiality of manifesting as a particle or wave, but during its time in flight is neither—then there is no causation paradox. This notion of superposition reflects the standard interpretation of quantum mechanics.

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 (far enough for light from both slits to overlap), 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. By decreasing the brightness of the source sufficiently, individual particles that form the interference pattern are detectable. 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. 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. This which-way experiment illustrates the complementarity principle that photons can behave as either particles or as waves, but cannot be simultaneously observed to be both a particle and a wave. However, technically feasible realizations of this experiment were not proposed until the 1970s.

Which-path information and the visibility of interference fringes are complementary quantities, meaning that information about a photon's path can be observed, or interference fringes can be observed, but they cannot both be observed in the same trial. In the double-slit experiment, conventional wisdom held that observing the particles' path inevitably disturbed them enough to destroy the interference pattern as a result of the Heisenberg uncertainty principle.

In 1982, Scully and Drühl pointed out a workaround alternative to this interpretation. They proposed to save the information about which slit the photon went through - or, in their setup, from which atom the photon was re-emitted - in the excited state of that atom. At this point the which-path information is known and no interference is observed. However, one can "erase" this information by making the atom to emit another photon and fall to the ground state. That on its own will not bring the interference pattern back, the which-path information can still be extracted from an appropriate measurement of the second photon. However, if the second photon is measured at a place where it could get to equally likely from any of the atoms, that successfully "erases" the which-path information. The original photon would now show the interference pattern (the position of its fringes depends on where exactly the second photon was observed, so that in the total statistics they average out and no fringes are seen). Since 1982, multiple experiments have demonstrated the validity of this so-called quantum "eraser".

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.

If the rate of photon production is reduced so that only one photon enters 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. This is similar to envisioning one photon in a two-slit apparatus: even though it is one photon, it still somehow interacts with both slits.

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, it seems as though the trajectories of the photons are known: If a photon emerges from the top of the apparatus, it seems as though it had to have come by way of the blue path, and if it emerges from the side of the apparatus, it seems as though it had to have come by way of the red path. However, it is important to keep in mind that the photon is in a superposition of the paths until it is detected. The assumption above—that it 'had to have come by way of' either path—is a form of the 'separation fallacy'.

In the bottom diagram, a second beam splitter is introduced at the top right. It recombines the beams corresponding to the red and blue paths. By introducing the second beam splitter, the usual way of thinking is that the path information has been "erased." However, we have to be careful, because the photon cannot be assumed to have 'really' gone along one or the other path. Recombining the beams 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. It is important to keep in mind however that the illustrated interferometer effects apply only to a single photon in a pure state. When dealing with a pair of entangled photons, the photon encountering the interferometer will be in a mixed state, and there will be no visible interference pattern without coincidence counting to select appropriate subsets of the data.

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. 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.

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, the 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., 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 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 extracted according to phase value (R₀₁ or R₀₂). Note that the phase cannot be measured if the photon's path (the slit through which it passes) 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 does not 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. 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

Retrocausality

Delayed-choice experiments raise questions about the causal connections between the events. If events at D₁, D₂, D₃, D₄ determine outcomes at D₀, then the effects might seem to precede their causes in time.

Consensus: no retrocausality

However, the interference pattern can only be seen retroactively once the idler photons have been detected and the detection information used to select subsets of signal photons.

Moreover, it's observed that the apparent retroactive action vanishes if the effects of observations on the state of the entangled signal and idler photons are considered in their 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. In a paper by Johannes Fankhauser, it is shown that the delayed choice quantum eraser experiment resembles a Bell-type scenario in which the paradox's resolution is rather trivial, and so there really is no mystery. Moreover, it gives a detailed account of the experiment in the de Broglie-Bohm picture with definite trajectories arriving at the conclusion that there is no "backwards in time influence" present. The delayed-choice quantum eraser does not communicate information in a retro-causal manner because it takes another signal, one which must arrive by 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.

A theorem proven by Phillippe Eberhard shows that if the accepted equations of relativistic quantum field theory are correct, faster than light communications is impossible.

Other delayed-choice quantum-eraser experiments

Many refinements and extensions of Kim et al. 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 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.

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 with a Bell inequality, which replaced the delayed choice of the observer.

Rezai et al. (2018) have combined the Hong-Ou-Mandel interference with a delayed choice quantum eraser. They impose two incompatible photons onto a beam-splitter, such that no interference pattern could be observed. When the output ports are monitored in an integrated fashion (i.e. counting all the clicks), no interference occurs. Only when the outcoming photons are polarization analysed and the right subset is selected, quantum interference in the form of a Hong-Ou-Mandel dip occurs.

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.

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

A quantum eraser has been proposed using a modified Stern-Gerlach setup. In this proposal, no coincident counting is required, and quantum erasure is accomplished by applying an additional Stern-Gerlach magnetic field.

Superluminal communication

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Superluminal_communication

Superluminal communication is a hypothetical process in which information is conveyed at faster-than-light speeds. The current scientific consensus is that faster-than-light communication is not possible, and to date it has not been achieved in any experiment.

Superluminal communication other than possibly through wormholes is likely impossible because, in a Lorentz-invariant theory, it could be used to transmit information into the past. This would complicate causality, but no theoretical arguments conclusively preclude this possibility.

A number of theories and phenomena related to superluminal communication have been proposed or studied, including tachyons, neutrinos, quantum nonlocality, wormholes, and quantum tunneling.

Proposed mechanisms

Spacetime diagram showing that moving faster than light implies time travel in the context of special relativity. A spaceship departs from Earth from A to C slower than light. At B, Earth emits a tachyon, particle that travels faster than light but forward in time in Earth's reference frame. It reaches the spaceship at C. The spaceship then sends another tachyon back to Earth from C to D. This tachyon also travels forward in time in the spaceship's reference frame. This effectively allows Earth to send a signal from B to D, back in time.

Tachyons

Tachyonic particles are hypothetical particles that travel faster than light, which could conceivably allow for superluminal communication. Because such a particle would violate the known laws of physics, many scientists reject the idea that they exist. By contrast, tachyonic fields – quantum fields with imaginary mass – do exist and exhibit superluminal group velocity under some circumstances. However, such fields have luminal signal velocity and do not allow superluminal communication.

Quantum nonlocality

Quantum mechanics is non-local in the sense that distant systems can be entangled. Entangled states lead to correlations in the results of otherwise random measurements, even when the measurements are made nearly simultaneously and at far distant points. The impossibility of superluminal communication led Einstein, Podolsky, and Rosen to propose that quantum mechanics must be incomplete (see EPR paradox).

However, it is now well understood that quantum entanglement does not allow any influence or information to propagate superluminally.

Practically, any attempt to force one member of an entangled pair of particles into a particular quantum state, breaks the entanglement between the two particles. That is to say, the other member of the entangled pair is completely unaffected by this "forcing" action, and its quantum state remains random; a preferred outcome cannot be encoded into a quantum measurement.

Technically, the microscopic causality postulate of axiomatic quantum field theory implies the impossibility of superluminal communication using any phenomena whose behavior can be described by orthodox quantum field theory. A special case of this is the no-communication theorem, which prevents communication using the quantum entanglement of a composite system shared between two spacelike-separated observers.

Wormholes

If wormholes are possible, then ordinary subluminal methods of communication could be sent through them to achieve effectively superluminal transmission speeds across non-local regions of spacetime. Considering the immense energy or exotic matter with negative mass/negative energy that current theories suggest would be required to open a wormhole large enough to pass spacecraft through, it may be that only atomic-scale wormholes would be practical to build, limiting their use solely to information transmission. Some hypotheses of wormhole formation would prevent them from ever becoming "timeholes", allowing superluminal communication without the additional complication of allowing communication with the past.

Fictional devices

Tachyon-like

The Dirac communicator features in several of the works of James Blish, notably his 1954 short story "Beep" (later expanded into The Quincunx of Time). As alluded to in the title, any active device received the sum of all transmitted messages in universal space-time, in a single pulse, so that demultiplexing yielded information about the past, present, and future.

Superluminal transmitters and ansibles

The terms "ultrawave" and "hyperwave" have been used by several authors, often interchangeably, to denote faster-than-light communications. Examples include:

• E. E. Smith used the term "ultrawave" in his Lensman series, for waves which propagated through a sub-ether and could be used for weapons, communications, and other applications.
• In Isaac Asimov's Foundation series, "ultrawave" and "hyperwave" are used interchangeably to represent a superluminal communications medium. The hyperwave relay also features.
• In the Star Trek universe, subspace carries faster-than-light communication (subspace radio) and travel (warp drive).
• The Cities in Flight series by James Blish featured ultrawave communications which used the known phenomenon of phase velocity to carry information, a property which in fact is impossible. The limitations of phase velocity beyond the speed of light later led him to develop his Dirac communicator.
• Larry Niven used hyperwave in his Known Space series as the term for a faster-than-light method of communication. Unlike the hyperdrive that moved ships at a finite superluminal speed, hyperwave was essentially instantaneous.
• In Richard K. Morgan's Takeshi Kovacs novels human colonies on distant planets maintain contact with earth and each other via hyperspatial needlecast, a technology which moves information "...so close to instantaneously that scientists are still arguing about the terminology".

A later device was the ansible coined by Ursula K. Le Guin and used extensively in her Hainish Cycle. Like Blish's device it provided instantaneous communication, but without the inconvenient beep.

The ansible is also a major plot element, nearly a MacGuffin, in Elizabeth Moon's Vatta's War series. Much of the story line revolves around various parties attacking or repairing ansibles, and around the internal politics of ISC (InterStellar Communications), a corporation which holds a monopoly on the ansible technology.

The ansible is also used as the main form of communication in Orson Scott Card's Ender's Game series. It is inhabited by an energy based, non-artificial sentient creature called an Aiúa that was placed within the ansible network and goes by the name of Jane. It was made when the humans realized that the Buggers, an alien species that attacked Earth, could communicate instantaneously and so the humans tried to do the same.

Quantum entanglement

• In Ernest Cline's novel Armada, alien invaders possess technology for instant "quantum communication" with unlimited range. Humans reverse engineer the device from captured alien technology.
• In the Mass Effect series of video games, instantaneous communication is possible using quantum-entanglement communicators placed in the communications rooms of starships.
• In the Avatar continuity, faster-than-light communication via a subtle control over the state of entangled particles is possible, but for practical purposes extremely slow and expensive: at a transmission rate of three bits of information per hour and a cost of $7,500 per bit, it is used for only the highest priority messages.
• Charles Stross's books Singularity Sky and Iron Sunrise make use of "causal channels" which use entangled particles for instantaneous two-way communication. The technique has drawbacks in that the entangled particles are expendable and the use of faster-than-light travel destroys the entanglement, so that one end of the channel must be transported below light speed. This makes them expensive and limits their usefulness somewhat.
• In Liu Cixin's novel The Three-Body Problem, the alien Trisolarans, while preparing to invade the Solar System, use a device with Ansible characteristics to communicate with their collaborators on Earth in real time. Additionally, they use spying/sabotaging devices called 'Sophons' on Earth which by penetration can access any kind of electronically saved and visual information, interact with electronics, and communicate results back to Trisolaris in real-time via quantum entanglement. The technology used is "single protons that have been unfolded from eleven space dimensions to two dimensions, programmed, and then refolded" and thus Sophons remain undetectable for humans.

Psychic links

Psychic links, belonging to pseudoscience, have been described as explainable by physical principles or unexplained, but they are claimed to operate instantaneously over large distances.

In the Stargate television series, characters are able to communicate instantaneously over long distances by transferring their consciousness into another person or being anywhere in the universe using "Ancient communication stones". It is not known how these stones operate, but the technology explained in the show usually revolves around wormholes for instant teleportation, faster-than-light, space-warping travel, and sometimes around quantum multiverses.

In Robert A. Heinlein's Time for the Stars, twin telepathy was used to maintain communication with a distant spaceship.

Peter F. Hamilton's Void Trilogy features psychic links between the multiple bodies simultaneously occupied by some characters.

In Brandon Sanderson's Skyward series, characters are able to use "Cytonics" to communicate instantaneously over any distance by sending messages via an inter-dimensional reality called "nowhere".

Other devices

Similar devices are present in the works of numerous others, such as Frank Herbert and Philip Pullman, who called his a lodestone resonator.

Anne McCaffrey's Crystal Singer series posited an instantaneous communication device powered by rare "Black Crystal" from the planet Ballybran. Black Crystals cut from the same mineral deposit could be "tuned" to sympathetically vibrate with each other instantly, even when separated by interstellar distances, allowing instantaneous telephone-like voice and data communication. Similarly, in Gregory Keyes' series The Age of Unreason, "aetherschreibers" use two-halves of a single "chime" to communicate, aided by scientific alchemy. While the speed of communication is important, so is the fact that the messages cannot be overheard except by listeners with a piece of the same original crystal.

Stephen R. Donaldson, in his Gap cycle, proposed a similar system, Symbiotic Crystalline Resonance Transmission, clearly ansible-type technology but very difficult to produce and limited to text messages.

In "With Folded Hands" (1947) and The Humanoids (1949), by Jack Williamson, instant communication and power transfer through interstellar space is possible with rhodomagnetic energy.

In Ivan Yefremov's 1957 novel Andromeda Nebula, a device for instant transfer of information and matter is made real by using "bipolar mathematics" to explore use of anti-gravitational shadow vectors through a zero field and the antispace, which enables them to make contact with the planet of Epsilon Tucanae.

In Edmond Hamilton's The Star Kings (1949), the discovery of an unknown form of electromagnetic radiation called sub-spectrum rays moves faster than light. The fastest of these are those of the Minus-42nd Octave, which allows for real time telestereo communication with anyone within the galaxy.

In Cordwainer Smith's Instrumentality novels and stories, interplanetary and interstellar communication is normally relayed from planet to planet, presumably at superluminal speed for each stage (at least between solar systems) but with a cumulative delay. For urgent communication there is the "instant message", which is effectively instantaneous but very expensive.

In Howard Taylor's web comic series Schlock Mercenary, superluminal communication is performed via the hypernet, a galaxy-spanning analogue to the Internet. Through the hypernet, communications and data are routed through nanoscopic wormholes, using conventional electromagnetic signals.

Superluminal motion

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Superluminal_motion

Superluminal motion

In astronomy, superluminal motion is the apparently faster-than-light motion seen in some radio galaxies, BL Lac objects, quasars, blazars and recently also in some galactic sources called microquasars. Bursts of energy moving out along the relativistic jets emitted from these objects can have a proper motion that appears greater than the speed of light. All of these sources are thought to contain a black hole, responsible for the ejection of mass at high velocities. Light echoes can also produce apparent superluminal motion.

Explanation

Superluminal motion occurs as a special case of a more general phenomenon arising from the difference between the apparent speed of distant objects moving across the sky and their actual speed as measured at the source.

In tracking the movement of such objects across the sky, a naive calculation of their speed can be derived by a simple distance divided by time calculation. If the distance of the object from the Earth is known, the angular speed of the object can be measured, and the speed can be naively calculated via:

apparent speed = distance to object × angular speed.

This calculation does not yield the actual speed of the object, as it fails to account for the fact that the speed of light is finite. When measuring the movement of distant objects across the sky, there is a large time delay between what has been observed and what has occurred, due to the large distance the light from the distant object has to travel to reach us. The error in the above naive calculation comes from the fact that when an object has a component of velocity directed towards the Earth, as the object moves closer to the Earth that time delay becomes smaller. This means that the apparent speed as calculated above is greater than the actual speed. Correspondingly, if the object is moving away from the Earth, the above calculation underestimates the actual speed.

This effect in itself does not generally lead to superluminal motion being observed. But when the actual speed of the object is close to the speed of light, the apparent speed can be observed as greater than the speed of light, as a result of the above effect. As the actual speed of the object approaches the speed of light, the effect is most pronounced as the component of the velocity towards the Earth increases. This means that in most cases, 'superluminal' objects are travelling almost directly towards the Earth. However it is not strictly necessary for this to be the case, and superluminal motion can still be observed in objects with appreciable velocities not directed towards the Earth.

Superluminal motion is most often observed in two opposing jets emanating from the core of a star or black hole. In this case, one jet is moving away from and one towards the Earth. If Doppler shifts are observed in both sources, the velocity and the distance can be determined independently of other observations.

Some contrary evidence

As early as 1983, at the "superluminal workshop" held at Jodrell Bank Observatory, referring to the seven then-known superluminal jets,

Schilizzi ... presented maps of arc-second resolution [showing the large-scale outer jets] ... which ... have revealed outer double structure in all but one (3C 273) of the known superluminal sources. An embarrassment is that the average projected size [on the sky] of the outer structure is no smaller than that of the normal radio-source population.

In other words, the jets are evidently not, on average, close to the Earth's line-of-sight. (Their apparent length would appear much shorter if they were.)

In 1993, Thomson et al. suggested that the (outer) jet of the quasar 3C 273 is nearly collinear to the Earth's line-of-sight. Superluminal motion of up to ~9.6c has been observed along the (inner) jet of this quasar.

Superluminal motion of up to 6c has been observed in the inner parts of the jet of M87. To explain this in terms of the "narrow-angle" model, the jet must be no more than 19° from the Earth's line-of-sight. But evidence suggests that the jet is in fact at about 43° to the Earth's line-of-sight. The same group of scientists later revised that finding and argue in favour of a superluminal bulk movement in which the jet is embedded.

Suggestions of turbulence and/or "wide cones" in the inner parts of the jets have been put forward to try to counter such problems, and there seems to be some evidence for this.

Signal velocity

The model identifies a difference between the information carried by the wave at its signal velocity c, and the information about the wave front's apparent rate of change of position. If a light pulse is envisaged in a wave guide (glass tube) moving across an observer's field of view, the pulse can only move at c through the guide. If that pulse is also directed towards the observer, he will receive that wave information, at c. If the wave guide is moved in the same direction as the pulse, the information on its position, passed to the observer as lateral emissions from the pulse, changes. He may see the rate of change of position as apparently representing motion faster than c when calculated, like the edge of a shadow across a curved surface. This is a different signal, containing different information, to the pulse and does not break the second postulate of special relativity. c is strictly maintained in all local fields.

Derivation of the apparent velocity

A relativistic jet coming out of the center of an active galactic nucleus is moving along AB with a velocity v, and is observed from the point O. At time ${\displaystyle t_1}$ a light ray leaves the jet from point A and another ray leaves at time ${\displaystyle t_2=t_1+\delta t}$ from point B. An observer at O receives the rays at time ${\displaystyle t_1^{\mathrm{\prime }}}$ and ${\displaystyle t_2^{\mathrm{\prime }}}$ respectively. The angle ${\displaystyle \varphi }$ is small enough that the two distances marked ${\displaystyle D_L}$ can be considered equal.

${\displaystyle AB=v\delta t}$

${\displaystyle AC=v\delta t\cos \theta }$

${\displaystyle BC=v\delta t\sin \theta }$

${\displaystyle t_2-t_1=\delta t}$

${\displaystyle t_1^{\prime }=t_1+\frac{D_L+v\delta t\cos \theta }{c}}$

${\displaystyle t_2^{\prime }=t_2+\frac{D_L}{c}}$

${\displaystyle \delta t^{\prime }=t_2^{\prime }-t_1^{\prime }=t_2-t_1-\frac{v\delta t\cos \theta }{c}=\delta t-\frac{v\delta t\cos \theta }{c}=\delta t(1-\beta \cos \theta )}$, where ${\displaystyle \beta =v/c}$

${\displaystyle \delta t=\frac{\delta t^{\prime }}{1-\beta \cos \theta }}$

${\displaystyle BC=D_L\sin \varphi \approx \varphi D_L=v\delta t\sin \theta \Rightarrow \varphi D_L=v\sin \theta \frac{\delta t^{\prime }}{1-\beta \cos \theta }}$

Apparent transverse velocity along ${\displaystyle CB}$, ${\displaystyle v_{\text{T}}=\frac{\varphi D_L}{\delta t^{\prime }}=\frac{v\sin \theta }{1-\beta \cos \theta }}$

${\displaystyle {\beta }_{\text{T}}=\frac{v_{\text{T}}}{c}=\frac{\beta \sin \theta }{1-\beta \cos \theta }.}$

The apparent transverse velocity is maximal for angle (${\displaystyle 0<\beta <1}$ is used)

${\displaystyle \frac{\mathrm{\partial }{\beta }_{\text{T}}}{\mathrm{\partial }\theta }=\frac{\mathrm{\partial }}{\mathrm{\partial }\theta }\left[\frac{\beta \sin \theta }{1-\beta \cos \theta }\right]=\frac{\beta \cos \theta }{1-\beta \cos \theta }-\frac{(\beta \sin \theta {)}^2}{(1-\beta \cos \theta {)}^2}=0}$

${\displaystyle \Rightarrow \beta \cos \theta (1-\beta \cos \theta {)}^2=(1-\beta \cos \theta )(\beta \sin \theta {)}^2}$

${\displaystyle \Rightarrow \beta \cos \theta (1-\beta \cos \theta )=(\beta \sin \theta {)}^2\Rightarrow \beta \cos \theta -{\beta }^2{\cos }^2\theta ={\beta }^2{\sin }^2\theta \Rightarrow \cos {\theta }_{\text{max}}=\beta }$

${\displaystyle \Rightarrow \sin {\theta }_{\text{max}}=\sqrt{1-{\cos }^2{\theta }_{\text{max}}}=\sqrt{1-{\beta }^2}=\frac{1}{\gamma }}$, where ${\displaystyle \gamma =\frac{1}{\sqrt{1-{\beta }^2}}}$

${\displaystyle \therefore {\beta }_{\text{T}}^{\text{max}}=\frac{\beta \sin {\theta }_{\text{max}}}{1-\beta \cos {\theta }_{\text{max}}}=\frac{\beta /\gamma }{1-{\beta }^2}=\beta \gamma }$

If ${\displaystyle \gamma \gg 1}$ (i.e. when velocity of jet is close to the velocity of light) then ${\displaystyle {\beta }_{\text{T}}^{\text{max}}>1}$ despite the fact that ${\displaystyle \beta <1}$. And of course ${\displaystyle {\beta }_{\text{T}}>1}$ means that the apparent transverse velocity along ${\displaystyle CB}$, the only velocity on the sky that can be measured, is larger than the velocity of light in vacuum, i.e. the motion is apparently superluminal.

History

The apparent superluminal motion in the faint nebula surrounding Nova Persei was first observed in 1901 by Charles Dillon Perrine. “Mr. Perrine’s photograph of November 7th and 8th, 1901, secured with the Crossley Reflector, led to the remarkable discovery that the masses of nebulosity were apparently in motion, with a speed perhaps several hundred times as great as hitherto observed.” “Using the 36-in. telescope (Crossley), he discovered the apparent superluminal motion of the expanding light bubble around Nova Persei (1901). Thought to be a nebula, the visual appearance was actually caused by light from the nova event reflected from the surrounding interstellar medium as the light moved outward from the star. Perrine studied this phenomenon using photographic, spectroscopic, and polarization techniques.”

Superluminal motion was first observed in 1902 by Jacobus Kapteyn in the ejecta of the nova GK Persei, which had exploded in 1901. His discovery was published in the German journal Astronomische Nachrichten, and received little attention from English-speaking astronomers until many decades later.

In 1966, Martin Rees pointed out that "an object moving relativistically in suitable directions may appear to a distant observer to have a transverse velocity much greater than the velocity of light". In 1969 and 1970 such sources were found as very distant astronomical radio sources, such as radio galaxies and quasars, and were called superluminal sources. The discovery was the result of a new technique called Very Long Baseline Interferometry, which allowed astronomers to set limits to the angular size of components and to determine positions to better than milli-arcseconds, and in particular to determine the change in positions on the sky, called proper motions, in a timespan of typically years. The apparent velocity is obtained by multiplying the observed proper motion by the distance, which could be up to 6 times the speed of light.

In the introduction to a workshop on superluminal radio sources, Pearson and Zensus reported

The first indications of changes in the structure of some sources were obtained by an American-Australian team in a series of transpacific VLBI observations between 1968 and 1970 (Gubbay et al. 1969). Following the early experiments, they had realised the potential of the NASA tracking antennas for VLBI measurements and set up an interferometer operating between California and Australia. The change in the source visibility that they measured for 3C 279, combined with changes in total flux density, indicated that a component first seen in 1969 had reached a diameter of about 1 milliarcsecond, implying expansion at an apparent velocity of at least twice the speed of light. Aware of Rees's model, (Moffet et al. 1972) concluded that their measurement presented evidence for relativistic expansion of this component. This interpretation, although by no means unique, was later confirmed, and in hindsight it seems fair to say that their experiment was the first interferometric measurement of superluminal expansion.

In 1994, a galactic speed record was obtained with the discovery of a superluminal source in the Milky Way, the cosmic x-ray source GRS 1915+105. The expansion occurred on a much shorter timescale. Several separate blobs were seen to expand in pairs within weeks by typically 0.5 arcsec. Because of the analogy with quasars, this source was called a microquasar.