The Einstein Rosen bridge and the Einstein Podolsky Rosen paradox, ER and EPR: Wormhole and entanglement

The Einstein-Rosen Bridge and the Einstein Podolsky Rosen paradox. I demonstrate that the two-body problem in general relativity was a heuristic guide in Einstein’s and collaborators’1935 work on the Einstein-Rosen bridge and EPR paradox.

In 2013 Juan Maldacena and Leonard Susskind demonstrated that the Einstein Rosen bridge between two black holes is created by EPR-like correlations between the microstates of the two black holes. They call this the ER = EPR relation, a geometry–entanglement relationship: entangled particles are connected by a Schwarzschild wormhole. In other words, the ER bridge is a special kind of EPR correlation: Maldacena and Susskind’s conjecture was that these two concepts, ER and EPR, are related by more than a common publication date 1935. If any two particles are connected by entanglement, the physicists suggested, then they are effectively joined by a wormhole. And vice versa: the connection that physicists call a wormhole is equivalent to entanglement. They are different ways of describing the same underlying reality.

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This image was published in a Nature article, Ron Cowen, “The quantum source of space-time”,  explaining the geometry–entanglement relationship and Maldacena’s and Susskind’s ER = EPR idea: Quantum entanglement is linked to a wormhole from general relativity. This representation is deterministic and embodies the many worlds interpretation: Collapse of the wave function never takes place. Instead, interactions cause subsystems to become entangled. Each measurement causes the branches of the tree to decohere; the quantum superposition being replaced by classical probabilities. The observer follows a trajectory through a tree. The entire tree, i.e., the entire wave function, must be retained and the universe is the complicated network of entanglements, branches of the tree: the wormhole bifurcating throats and mouths in the universe. See Susskind’s new paper from April 2016. Hence general relativity and quantum mechanics are linked by ER = EPR and Einstein’s soul can rest in peace because god will not play dice.

Maldacena and Susskind explain that one cannot use EPR correlations to send information faster than the speed of light.  Similarly, Einstein Rosen bridges do not allow us to send a signal from one asymptotic region to the other, at least when suitable positive energy conditions are obeyed. This is sometimes stated as saying that (Schwarzschild) Lorentzian wormholes are not traversable.

I uploaded a paper to the ArXiv: “Two-body problem in general relativity: A heuristic guide for the Einstein-Rosen bridge and EPR paradox”

In this paper I discuss the possible historical link between the 1935 Einstein-Rosen bridge paper and the 1935 Einstein-Rosen-Podolsky paper. The paper is a first version and I intend to upload a second version.

Between 1935 and 1936, Einstein was occupied with the Schwarzschild solution and the singularity within it while working in Princeton on the unified field theory and, with his assistant Nathan Rosen, on the theory of the Einstein-Rosen bridges. He was also occupied with quantum theory. He believed that quantum theory was an incomplete representation of real things. Together with Rosen and Boris Podolsky he invented the EPR paradox. In this paper I demonstrate that the two-body problem in general relativity was a heuristic guide in Einstein’s and collaborators’1935 work on the Einstein-Rosen bridge and EPR paradox.

In 1935 Einstein explained that one of the imperfections of the general theory of relativity was that as a field theory it was not complete in the following sense: it represented the motion of particles by the geodesic equation. A mass point moves on a geodesic line under the influence of a gravitational field. However, a complete field theory implements only fields and not the concepts of particle and motion. These must not exist independently of the field but must be treated as part of it. Einstein wanted to demonstrate that the field equations for empty space are sufficient to determine the motion of mass points. In 1935 Einstein attempted to present a satisfactory treatment that accomplishes a unification of gravitation and electromagnetism. For this unification Einstein and Rosen needed a description of a particle without singularity. In 1935, they joined two Schwarzschild solutions at the Schwarzschild limit and omitted part of the space-time beyond the Schwarzschild singularity. They showed that it was possible to do this in a natural way and they proposed the Einstein-Rosen bridge solution.

In the Einstein-Rosen bridges paper of 1935, Einstein negated the possibility that particles were represented as singularities of the gravitational field because of his polemic with Ludwig Silberstein. Silberstein thought he had demonstrated that general relativity was problematic. He constructed, for the vacuum field equations for the two-body problem, an exact static solution with two singularity points that lie on the line connecting these two points. The singularities were located at the positions of the mass centers of the two material bodies. Silberstein concluded that this solution was inadmissible physically and contradicted experience. According to his equations the two bodies in his solution were at rest and were not accelerated towards each other; these were nonallowed results and therefore Silberstein thought that Einstein’s field equations should be modified together with his general theory of relativity. Before submitting his results as a paper to the Physical Review, Silberstein communicated them to Einstein. This prompted Einstein’s remark, in his paper with Rosen in 1935, that matter particles could not be represented as singularities in the field.

Einstein and Rosen were trying to permanently dismiss the Schwarzschild singularity and adhere to the fundamental principle that singularities of the field are to be excluded. Einstein explained that one of the imperfections of the general theory of relativity was that as a field theory it was not complete because it represented the motion of particles by the geodesic equation. Einstein also searched for complete descriptions of physical conditions in quantum mechanics. It seems that the two-body problem in general relativity was a heuristic guide in the search of a solution to the problem that the psi function cannot be interpreted as a complete description of a physical condition of one system. He thus proposed the EPR paradox with Rosen and Podolsky.

Updated 2016

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My book: Einstein’s Pathway to the Special Theory of Relativity

2015 marks several Albert Einstein anniversaries: 100 years since the publication of Einstein’s General Theory of Relativity, 110 years since the publication of the Special Theory of Relativity and 60 years since his passing.

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What is so special about this year that deserves celebrations? My new book on Einstein: Einstein’s Pathway to the Special Theory of Relativity has just been returned from the printers and I expect Amazon to have copies very shortly.

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The Publisher uploaded the contents and intro.

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I hope you like my drawing on the cover:

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Einstein, 1923: “Ohmmm, well… yes, I guess!”

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The book is dedicated to the late Prof. Mara Beller, my PhD supervisor from the Hebrew University of Jerusalem who passed away ten years ago and wrote the book: Quantum Dialogue (Chicago University Press, 1999):

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Have a very happy Einstein year!

איינשטיין ותורת הקוונטים Einstein and the Light Quantum

In 1905 Planck, a coeditor of the Annalen der Physik, accepted Einstein’s paper on light quanta for publication, even though he disliked the idea of “light quanta”. Einstein’s relativity paper was received by the Annalen der Physik at the end of June 1905 and Planck was the first scientist to notice Einstein’s relativity theory and to report favorably on it. In the 1905 relativity paper Einstein used the notion, “light complex”, and he did not invoke his novel quanta of light heuristic with respect to the principle of relativity. He chose the language “light complex” for which no clear definition could be given. But with hindsight, in 1905 Einstein made exactly the right choice not to mix concepts from his quantum paper with those from his relativity paper. He focused on the solution of his relativity problem, whose far-reaching perspectives Planck already sensed. x

In the Electrodynamical part of the Relativity paper Einstein considers the system K. Very far from the origin of K, there is a source of electromagnetic waves. Let part of space containing the origin of coordinates 0 be represented to a sufficient degree of approximation by plane waves. Einstein asks: What characterizes the waves when they are examined by an observer at the same point 0, but at rest in the system k, moving relatively to K with constant speed v? x

Einstein applies the Lorentz transformation and transformation equations for electric and magnetic fields to the equations of the plane electromagnetic wave with respect to K. He obtains the Doppler principle, i.e., the frequency of electromagnetic waves as it appears in the system k and K: f’/f.   x

Einstein then finds the amplitude of the waves as it appears in the system k; the amplitude of the electric or magnetic waves A or A’, respectively, as it is measured in the system K or in the system k. Einstein gives the equation for the square of amplitude, Pointing vector. x

We expect that the ratio of the square of the amplitude of a given light complex “measured in motion” and “measured at rest” would be the energy if the volume of a light complex were the same measured in K and k. However, says Einstein, this is not the case.  x

Einstein thus instead considers a spherical surface of radius R moving with the velocity of light. He is interested in the light energy enclosed by the light surface. No energy passes outside through the surface of the spherical light surface, because the surface and the light wave both travel with the velocity of light. He calculates the amount of energy enclosed by this surface as viewed from the system k, which will be the energy of the light complex relative to the system k. The spherical surface – viewed in the system k – is an ellipsoidal surface. If we call the energy of the light enclosed by this surface E when it is measured in system K, and E’ when measured in system k, we obtain the equation that relates between E and E’.  x

Einstein realizes that, “It is noteworthy that the energy and the frequency of a light complex vary with the observer’s state of motion according to the same law”. x

Namely, E’/E = f’/f.     x

John Stachel read my manuscript and said that this formula corresponds to that of the light quantum hypothesis, and in hindsight this supplies extra evidence for the later hypothesis. Einstein’s aim is to show that the equation E = hv that he uses in the quantum paper takes the same form in any inertial frame. That is, E = hv is transformed to E’ = hv’ and thus the relativity postulate is not violated.  x

I wrote in my manuscript that Rynasiewicz wrote in 2005 (and even before that) that, “Einstein wraps up his derivation with what is clearly an allusion to the light quantum hypothesis”. Rynasiewicz adds that “What he does not draw attention to there is the intimate relation of this result to the relative character of simultaneity”.  x

However, Stachel told me that he was the first to notice that in his relativity paper Einstein implicitly referred to the light quantum hypothesis and he told me to delete Rynasiewicz’s comment. x

Then in light of my manuscript Stachel wrote the following paragraph, which reflects my manuscript, and also the collected papers of Einstein, which he edited

Before submitting his 1905 special relativity paper, Einstein had submitted the light quantum paper – the only one of his 1905 papers he considered truly revolutionary. “On a Heuristic Viewpoint Concerning the Generation and Transformation of Light”, sent to the Annalen on March 17th, 1905, and received by the Annalen a day afterwards. Indeed Einstein wrote Habicht in May 1905 about this paper, “It deals with the radiation and energy characteristics of light and is very revolutionary”.  x

This paper extended the range of application of Planck’s 1900 quantum hypothesis. In order to explain his law of black body radiation, which had been well-verified empirically, Planck was forced to assume that oscillators interacting with the electromagnetic field could only emit and/or absorb energy in discrete units, which he called quanta of energy. The energy of these quanta was proportional to the frequency of the oscillator: E = hv. But Planck believed, in accord with Maxwell’s theory, that the energy of the electromagnetic field itself could change continuously. x

Einstein now showed that, if this formula were extended to the electromagnetic field energy itself, a number of phenomena involving interactions between matter and radiation, otherwise inexplicable classically, could now be simply explained with the help of these light quanta. x

But, he was at work on his relativity paper too; so the question naturally arose, if the equation E = hv holds in one inertial frame of reference, will it hold in all others. If not, then Einstein’s relativity principle would be violated. Since h, the so-called quantum of action, is a universal constant, the question reduces to: Do the energy and frequency of a light quantum transform in the same way in passing from one inertial frame to another. And this is just what he demonstrates in his paper. x

Hence, not wanting to introduce a discussion of his still-quite-speculative light quantum hypothesis into a paper which he regarded as simply an extension of well accepted classical ideas from mechanics to electromagnetism and optics, he confined his proof to the classical level. x

Instead of “light quanta”, in his proof he introduced the rather awkward term “light complex”, a term that he soon dropped. x

In my paper discussing relativity and light quanta I bring both opinions and I also refer to Einstein’s Collected Papers. x

HUJI, Lucien Chavan

paper abstract

Philosophy of Physics – Quantum Mechanics פילוסופיה של הפיזיקה מכניקת הקוונטים

schrodingerscat_fullpic        Weknowmemes  (קישורים למאמרים בעברית בתוך המאמר באנגלית)

Foundations of quantum physics

Quantum time machine and quantum time travel

Einstein’s theory of general relativity allows the existence of closed timelike curves (CTCs), paths through spacetime that, if followed, allow a time traveler to interact with his/her former self. Seth Lloyd suggests that general relativistic CTCs provide one potential mechanism for time travel, but they need not provide the only one. Quantum mechanics might allow time travel even in the absence of CTCs in the geometry of spacetime. He explores a particular version of CTCs based on combining quantum teleportation (and quantum entanglement) with “postselection”. This combination results in a quantum channel to the past. The entanglement occurs between the forward- and backward going parts of the curve. Post-selection replaces the quantum measurement, allowing time travel to take place: Postselection could ensure that only a certain type of state can be teleported. The states that qualify to be teleported are those that have been postselected to be self-consistent prior to being teleported. Only after it has been identified and approved can the state be teleported, so that, in effect, the state is traveling back in time. Under these conditions, time travel could only occur in a self-consistent, non-paradoxical way. The resulting post-selected closed timelike curves (P-CTCs) provide time-travel (Quantum time machine) that avoids grandfather paradox. Entangled states of P-CTCs, allows time travel even when no space-time CTC exists. Such quantum time travel can be thought of as a kind of quantum tunneling backwards in time, which can take place even in the absence of a classical path from future to past

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 פילוסופיה של הקוונטים: מסע בזמן, טלפורטציה בזמן והחתול של שרדינגר קם לתחייה

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Wheeler’s delayed choice thought experiment

Wave-particle duality: A photon, may behave either as a particle or a wave. The way in which it behaves depends on the kind of experimental apparatus with which it is measured. Both aspects, particle and wave, which appear to be incompatible, are never observed simultaneously (complementarity, Copenhagen interpretation). It was suggested that quantum particles may know in advance to which experiment they will be confronted, via a hidden variable, and could decide which behavior to exhibit. This was challenged by Wheeler’s delayed choice thought experiment: In this variant of the double slit experiment (Mach-Zehnder interferometer + classically controlled beam-splitters), the observer chooses to test either the particle or wave nature of a photon after it has passed through the slits. Thus, the particle could not have known in advance via a hidden variable the kind of experiment it will be confronted. Wheeler’s experiment has been implemented experimentally, and quantum predictions were confirmed. Recently, quantum delayed choice experiments were proposed using a quantum beam-splitter in superposition of being present and absent, and thus the interferometer is in a superposition of being closed and open. This forces the photon to be in a superposition of particle and wave at the same time; then we can detect the photon before choosing if the interferometer is open or closed. This implies that we can choose if the photon behaves as a particle or as a wave after it has been already detected (post-selection). This negates consistent hidden-variable theories in which particle and wave are realistic properties. The upshot of the experiment can be cast in a (“realistic”) language of Schrödinger’s cat: “Long after the cat has supposedly been killed or not, one can choose to determine if it is dead or alive or determine if it is dead and alive,” says Seth Lloyd at the MIT. See refs. in this source

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Spookier than “spooky action at a distance”: Delayed choice quantum eraser and delayed choice entanglement swapping experiments

According to the famous words of Albert Einstein, the effects of quantum entanglement appear as “spooky action at a distance.” Here are experiments that are spookier than quantum entanglement. Two types of delayed choice experiments: delayed choice quantum eraser experiment and delayed choice entanglement swapping. Anton Zeilinger at the Institute for Quantum Optics and Quantum Information, the University of Vienna and authors experimentally realized the latter “Gedankenexperiment” formulated by Asher Peres in 2000.
Consider Wheeler’s delayed-choice experiment: Wheeler has pointed out that the experimentalist may delay his decision as to display wave like or particle like behavior in a light beam long after the beam has been split by the appropriate optics. A delayed-choice experiment with entangled photons pave the way for new possibilities, where the choice of measurement settings on the distant photon can be made even after the other photon has been registered. This has been shown in a delayed-choice quantum eraser experiment. The which-path information of one photon was erased by a later suitable measurement on the other photon. This allowed to a posteriori decide a single-particle characteristic, namely whether the already measured photon behaved as a wave or as a particle.
However, this delayed-choice experiment focused on wave-particle duality for single particles, there is an entanglement-separability duality for two particles. Entanglement and separability correspond to two mutually exclusive types of correlations between two particles. Even the degree to which the particles were entangled can be defined after the particles have been registered.
Consider entanglement swapping. Peres proposed an experiment, where entanglement is produced a posteriori, after the entangled particles have been measured and may no longer exist. This is Delayed choice for entanglement swapping. In realist’s language: quantum entanglement can reach into the past, future actions may influence past events.
In the proposed experiment, two distant observers, conventionally called Alice and Bob, independently prepare two sets of photons entangled with each other. Alice and Bob keep one particle of each pair and send the other particle to a third observer, Eve also arranges them in pairs (one from Alice and one from Bob). Alice and Bob sort the records of their measurements into four subsets, according to Eve’s results. It then follows that, the state of the particles that Alice and Bob kept was the same as the state later found by Eve. Even after Alice and Bob have recorded the results of all their measurements, Eve still has the freedom of deciding which experiment she will perform. It is not even necessary for Alice and Bob to know which experiments Eve will do. Hence, Eve has control over Alice and Bob’s particles. Eve is free to choose either to project her two photons onto an entangled state and thus project Alice’s and Bob’s photons onto an entangled state, or to measure them individually and then project Alice’s and Bob’s photons onto a separable state. If Alice and Bob measure their photons’ spin (or polarization) states before Eve makes her choice and projects her two photons either onto an entangled state or onto a separable state, it implies that whether their two photons are entangled (showing quantum correlations) or separable (showing classical correlations) can be defined after they have been measured; Eve can choose to take her action even after Bob and Alice may have destroyed their photons. Indeed Asher Peres wrote: “quantum effects mimic not only instantaneous action-at-a-distance but also, as seen here, influence of future actions on past events, even after these events have been irrevocably recorded”.
A recent experiment implements the two important steps necessary on the way from Wheeler’s to Peres’s gedankenexperiment: One needs to first extend Wheeler’s delayed-choice experiment to the delayed-choice quantum eraser to have the possibility that a choice (for one particle) can be after the measurement (of another particle). In a second step, one has to go from the delayed-choice quantum eraser to delayed-choice entanglement swapping to be able to a posteriori decide on a two-particle characteristic and show entanglement-separability duality

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פילוסופיה של הקוונטים חלק ב’. הפרדוקס של אשר פרס: האם העתיד גורם לעבר?

An entanglement swapping setup that generates a secrete key for quantum cryptography

The peculiar properties of quantum mechanics allow two remote parties to communicate a private secret key, which is protected from eavesdropping by the laws of physics and therefore unbreakable in theory (due to Heisenberg uncertainty principle). This is Quantum cryptography, or more precisely quantum key distribution (QKD). However, practical QKD systems could be vulnerable to side-channel attacks even if it is unbreakable in theory. Researchers from the UK have proposed a new theoretical scheme for QKD that keeps the detectors from being exposed to an untrusted third party (UTP) and, even better, uses the UTP to inadvertently generate the secrete key for the detectors. The protocol is based on an entanglement swapping setup scenario. Alice and Bob, control two private spaces, A and B, respectively. Conventionally, these spaces are assumed completely inaccessible from the outside, i.e., no illegitimate system may enter A or B. For this reason every kind of side-channel attack upon the private spaces is assumed excluded. Within its own private space, each party (Alice or Bob) has a bipartite state, which entangles two systems:  A, A’ for Alice and B, B’ for Bob. Systems A, B are kept within the private spaces, while systems A’, B’ are sent to a UTP, whose task is to perform a quantum measurement and communicate the corresponding result. At this point, Alice and Bob do not share any common quantum states with which to generate a key. But the UTP is Eve!! Eve’s aim is to eavesdrop the key, or else prevent Alice and Bob from generating the key. Eve applies a quantum instrument T to the incoming systems A’, B’ from Alice and Bob. This is a quantum operation with both classical and quantum outputs. The classical output of T can be simply represented by a stochastic variable L. The quantum output of T is represented by a system E which is correlated with Alice and Bob’s private systems A, B. E is the system that Eve will use for eavesdropping. Eve can store all the output systems E (generated in many independent rounds of the protocol) into a big quantum memory. Then, she can detect the whole memory using an optimal quantum measurement (corresponding to a collective attack). Oh my god!

Eve sends a classical communication to both Alice and Bob in order to “activate” the correlations. Here, Eve has another weapon in her hands, i.e., tampering with the classical outcomes. In order to decrease the correlations between the honest parties, Alice and Bob, Eve processes the output stochastic variable L via a classical channel and then communicates the fake variable L’ to Alice and Bob. Eve is now eavesdropping and entangled with Alice and Bob. After M rounds of the protocol, Alice and Bob will share M copies of a new fake quantum entangled state dependent on the fake variable L’. In general, Alice and Bob do not know anything about this physical process. They get M copies of an unknown state plus classical fake information L’. However, by measuring a suitable number M’ of these copies, they are able to deduce the explicit form of the fake quantum state for the remaining N = M – M’ copies (here M, M’ and N are large numbers). Then, by applying local measurements, Alice on her private systems and Bob on his, they are able to extract and derive a shared secret key. Hence, in the proposed protocol Eve allows the creation of correlations between the private systems A, B that Alice and Bob can exploit to generate a secret-key. According to the authors, eventually one is able to completely protect private space settings and detectors from probing side-channel attacks.

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Charles Bennett’s meme

A quantum eraser under Einstein’s locality condition

Anton Zeilinger and authors propose and experimentally demonstrate a quantum eraser under “Einstein’s locality condition”: The locality condition imposes that if “two systems no longer interact, no real change can take place in the second system in consequence of anything that may be done to the first system”. To experimentally realize a quantum eraser under Einstein’s locality condition, the erasure event of “which-path” information has to be relativistically space-like separated from the whole passage of the interfering system through the interferometer including its final registration. This means that in any and all reference frames no subluminal or luminal physical signal can travel from one event to the other and causally influence it.

A source in a laboratory located in La Palma, on the Canary Islands, produces path-polarization entangled photon pairs: with entanglement between two different degrees of freedom, namely the path of one photon denoted as the system photon, and the polarization of the other photon denoted as the environment photon.

The system photon is sent to an interferometer, and the environment photon is subject to polarization measurements. The environment photon is sent away from the system photon to Tenerife via a long 144 km optical fiber (connecting the La Palma laboratory and a laboratory in Tenerife).

The environment photon’s polarization carries which-path information of the system photon due to the entanglement between the two photons. According to the quantum eraser experiment, by measuring the environment photon’s polarization (horizontal or vertical), Zeilinger is able to determine the which-path information of the system photon and observe no interference, or erase the which-path information and observe interference. In the latter case, it depends on the specific outcome of the environment photon in Tenerife which one out of two different interference patterns the system photon is showing. Choices to acquire which-path information or to obtain interference of the system photons in La Palma are made so that the two systems (system photon and environment photon) are not interacting; no real change is taking place in the second system (system photon) in consequence of something done to the first system (environment photon). Hence, there are no causal influences between the system photons and the environment photons. In this arrangement in order to pass information between the environment photon in Tenerife and the system photon in La Palma, the speed of a hypothetical superluminal signal would have to be about 96 times the speed of light!

Zeilinger demonstrates and confirms that, whether the correlations between two entangled photons reveal which-path information or an interference pattern of one (system) photon depends on the choice of measurement on the other (environment) Photon; this is so even when all of the events on the two sides that can be space-like separated are space-like separated. The delayed choice quantum eraser experiment or space-like quantum eraser experiment performed here shows that it is possible to decide whether a wave or particle feature manifests itself long after—and even space-like separated from—the measurement.

Zeilinger and authors conclude, their 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, they believe that such a viewpoint should be given up entirely.

Source (January 2013).

Tripartite entanglement: three-party generalization of the 1935 Einstein-Podolsky-Rosen thought experiment (EPR)

Scholars demonstrate Entanglement between three separated particles. Three particles – photons – are created directly from a single input photon: A pump photon (a narrowband pump laser at 404 nm) will occasionally fission inside a nonlinear crystal into a pair of daughter polarized photons at 776 nm and 842 nm. The total energy in the process is conserved. The daughter photons share strong energy and time (position-momentum) correlations that are the hallmark of entanglement. The process is repeated with the 776 nm daughter photon serving as a pump and sent through a second crystal, creating a pair of granddaughter photons simultaneously at 1530 nm and 1570 nm. Again energy is conserved, and the total energy of the three photons created must sum to the energy of the pump. This process leaves the 842 nm, 1530 nm and 1570 nm photons entangled in energy and time. Hence, the three photons exhibit genuine tripartite energy-time (position-momentum) entanglement. The entanglement between the three photons is the three-party generalization of the 1935 Einstein-Podolsky-Rosen thought experiment (EPR). The new form of three-particle entanglement may prove to be a valuable part of future communications networks that operate on the principles of quantum mechanics

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Quantum communications networks? Recently entanglement has been achieved between two atomic ensembles (comprised of a large collection of identical atoms) and quantum teleportation of light to matter demonstrated. In 2005 scientists reported observations of entanglement between two atomic ensembles (quantum memories) located in distinct apparatuses separated by 3 meters. Now Chinese scientists reported they have realized the first quantum teleportation between two remote atomic-ensembles (quantum memories).  What about the Quantum Internet? How do we progress toward more complex quantum networks? Does entanglement extend across the whole network? Adopt the perspective of a quantum network as a quantum many body system and to search for more physical characteristics of the network (e.g., the scaling behavior of pair correlation functions and multipartite entanglement)? Distribution of quantum information over quantum networks: interaction of light with atomic ensembles

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EPR model can exhibit a metric that is analogous to a black hole and a wormhole

The Bohm-de Broglie (BdB) “pilot wave” hidden variable theory opened up the possibility of a new physics that lied outside the domain of quantum physics: quantum cosmology. Cosmologists applied the BdB interpretation of quantum mechanics to gravity: space-time geometry sometimes looks like (semi-classical) gravity and sometimes looks like quantum effects. In the BdB approach, it is possible to interpret the quantum effects as modifying the geometry in such a way that the scalar particles see an effective geometry.

A scholar from Brasil follows this tradition and studies the two-particle wave function of a scalar field in two dimensions under the EPR condition. He first shows that a two dimensional EPR model, in a particular quantum state and under a non-tachyonic approximating condition – EPR without assuming tachyons – can exhibit in some limited region an effective metric that is analogous to a two dimensional black hole (BH). He considers the BdB theory and concludes that, Bohm’s 1952 quantum potential generates an effective metric so that the quantum potential modifies the background geometry giving a curved space-time with the metric defining a two dimensional BH type solution. After developing a causal approach to the non-tachyonic EPR two-particle correlated system, this allows him to connect the EPR correlations with an effective wormhole geometry. For a two-dimensional static EPR model he shows that quantum effects produce an effective geometry with singularities in the metric, a key ingredient of a bridge construction or a wormhole. He therefore interprets the EPR correlations as driven by an effective wormhole, through which physical signals can propagate (no need then for tachyons to “explain” via a hidden variable theory the EPR paradox?…). The two-particle system ”sees” an effective metric with singularities, a fundamental component of a wormhole, through which the physical signals can propagate from one particle to the other.

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Personal wormhole

No-cloning theorem and teleportation

The story of FLASH—A superluminal communicator based upon a new kind of measurement. Nick Herbert proposed entanglement + cloning; faster than light communication was never mentioned. Asher Peres was the referee who approved the publication, knowing perfectly well that it was wrong. This led to the no-cloning theorem: cloning turns out not to be possible in quantum mechanics. If you can clone quantum bits (qubits), you can use this process to communicate faster than light. In fact quantum entanglement never lets you transmit information faster than light. If quantum states can be cloned then special relativity would be violated. A quantum state (quantum information) cannot be transmitted over the telephone. Suppose that Alice has an unknown quantum state. If she could send information over the telephone that was sufficient for Bob to recreate it, then Bob could recreate two copies. However, if Bob and Alice share an entangled bit in an EPR state, Alice can indeed send a qubit in an unknown state in teleportation. In teleportation Alice has destroyed the state, so the information in it is not cloned. Information is shifted from one place to another destroying the original process. Bob must wait to receive the classical outcome of Alice’s measurement, and thus teleportation cannot be used to transmit information faster than light

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Charles Bennett’s meme

משפט האי שכפול וטלפורטציה

פילוסופיה של הקוונטים ג’: האם ניתן לתקשר במהירות אינסופית באמצעות ניסוי איינשטיין-פודולסקי-רוזן (אפ”ר)?

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The “Everettian Revolution” – Many Worlds

A system in a superposition of states could in principle boost quantum computers; but measurement causes the states to collapse into a single state. Prof. Frank Tipler explains how one can find a solution to this problem by adopting the “Everettian Revolution”, Hugh Everett’s many-worlds interpretation (Relative State formulation of quantum mechanics, which became the many worlds interpretation, and then parallel universes, many minds, etc…): “The quantum computer, invented by the Everettian physicist David Deutsch, is one of the first results of parallel universe thinking. The idea of the quantum computer is simple: since the analogues of ourselves in the parallel universes are interested in computing the same thing at the same time, why not share the computation between the universes? Let one of us do part of the calculation, another do another part, and so on with the final result being shared between us all”. Do we share the computation with a parallel universe via a wormhole?…  Raphael Bousso and Leonard Susskind resort to cosmology. They say that in both the many-worlds interpretation of quantum mechanics and the multiverse of eternal inflation the world is viewed as an unbounded collection of parallel universes. Therefore they argue that the many-worlds of quantum mechanics and the many worlds of the multiverse are the same thing (same sides of the same coin…), and that the multiverse is necessary to give exact operational meaning to probabilistic predictions from quantum mechanics.

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פילוסופיה של הקוונטים ד’: החתול של שרדינגר במסע לעולם דה קוהרנטי ולעולמות מקבילים