General Relativity without the Equivalence principle?

I have skimmed through this book Handbook of Spacetime:

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The following represents my impressions formulated after reading the sections about the equivalence principle.

I read this paper:

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However, Einstein did not write this wonderful passage in the letter to Robert Lawson. Here is the letter to Lawson (Einstein to Lawson, 22 January 1920):

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Einstein writes to Lawson in the above letter: “The article for Nature is almost finished, but it has unfortunately become so long that I very much doubt whether it could appear in Nature“. Indeed, in a 1920 unpublished draft of a paper for Nature, “Fundamental Ideas and Methods of the Theory of Relativity, Presented in Their Development”, Einstein wrote the above long paragraph describing him in 1907 sitting in the Patent Office. He was brooding on special relativity, and suddenly there came to him the happiest thought of his life:

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Let us analyze this passage. The man in free fall (elevator experiments): Special relativity is incorporated into general relativity as a model of space-time experienced by an observer in free fall, over short times and distances (locally):

Between 1905 and 1907, Einstein tried to extend the special theory of relativity so that it would explain gravitational phenomena. He reasoned that the most natural and simplest path to be taken was to correct the Newtonian gravitational field equation. Einstein also tried to adapt the Newtonian law of motion of the mass point in a gravitational field to the special theory of relativity. However, he found a contradiction with Galileo’s law of free fall, which states that all bodies are accelerated in the gravitational field in the same way (as long as air resistance is neglected). Einstein was sitting on a chair in my patent office in Bern and then suddenly a thought struck him: If a man falls freely, he would not feel his weight. This was the happiest thought of his life. He imagined an observer freely falling from the roof of a house; for the observer there is during the fall – at least in his immediate vicinity – no gravitational field. If the observer lets go of any bodies, they remain relative to him, in a state of rest or uniform motion, regardless of their particular chemical and physical nature. The observer is therefore justified in interpreting his state as being (locally) at rest. Einstein’s 1907 breakthrough was to consider Galileo’s law of free fall as a powerful argument in favor of expanding the special principle of relativity to systems moving non-uniformly relative to each other. Einstein realized that he might be able to generalize and extend special relativity when guided by Galileo’s law of free fall. The Galilean law of free fall (or inertial mass is equal to gravitational mass) became known as the weak principle of equivalence.

Lewis Ryder explains: “Some writers distinguish two versions of the equivalence principle: the weak equivalence principle, which refers only to free fall in a gravitational field and is stated… as The worldline of a freely falling test body is independent of its composition or structure; and the strong equivalence principle, according to which no experiment in any area of physics should be able, locally, to distinguish a gravitational field from an accelerating frame”.

There are several formulations of the weak and the strong principles of equivalence in the literature. By far the most frequently used formulation of the strong principle of equivalence is Einstein’s 1912 local principle of equivalence: In a local free falling system special relativity is valid. (See my book General Relativity Conflict and Rivalries. Einstein’s Polemics with Physicists, 2015, for further details).

Nick Woodhouse explains:

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in the chapter:

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Hence Joshi says:

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in the chapter:

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Lewis Ryder

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writes in the above paper:

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(i.e. Einstein 1911 paper: “On the Influence of Gravitation on the Propagation of Light”). He formulates the equivalence principle in the following way: “In a freely falling (non-rotating) laboratory occupying a small region of spacetime, the local reference frames are inertial and the laws of physics are consistent with special relativity”. He then writes:

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The equivalence principle enables us to find just one component g00 – of the metric tensor gmn. All components can be found (at least in principle) from the Einstein field equations. Ryder thus concludes that the equivalence principle is dispensable. I don’t quite agree with Ryder.

In my 2012 paper, “From the Berlin ‘Entwurf’ Field equations to the Einstein Tensor III: March 1916”, ArXiv: 1201.5358v1 [physics.hist-ph], 25 January, 2012 and also in my 2014 paper,  “Einstein, Schwarzschild, the Perihelion Motion of Mercury and the Rotating Disk Story”, ArXiv: 1411.7370v [physics.hist-ph], 26 Nov, 2014, I demonstrate the following:  On November 18, 1915, Einstein found approximate solutions to his November 11, 1915 field equations and explained the motion of the perihelion of Mercury. Einstein’s field equations cannot be solved in the general case, but can be solved in particular situations. Indeed, the first to offer an exact solution was Karl Schwarzschild. Schwarzschild found one line element, which satisfied the conditions imposed by Einstein on the gravitational field of the sun, as well as Einstein’s field equations from the November 11, 1915 paper. Schwarzschild sent Einstein a manuscript, in which he derived his exact solution of Einstein’s field equations. In January, 1916, Einstein delivered Schwarzschild’s paper before the Prussian Academy, and a month later the paper was published. In March 1916 Einstein submitted to the Annalen der Physik a review article, “The Foundation of the General Theory of Relativity”, on the general theory of relativity. The paper was published two months later, in May 1916. The 1916 review article was written after Schwarzschild had found the complete exact solution to Einstein’s November 18, 1915 field equations. Even so, Einstein preferred not to base himself on Schwarzschild’s exact solution, and he returned to his first order approximate solution from November 18, 1915. In the final part of the 1916 review paper Einstein demonstrated that a gravitational field changes spatial dimensions and the clock period:

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This equation is further explained in my 2012 paper (page. 56):

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Neither did Einstein use the Schwarzschild solution nor was he guided by the  equivalence principle. He was rather using an approximate solution and the metric, the line element to arrive at the same factor he had obtained by assuming the heuristic equivalence principle. He thus demonstrated that the equivalence principle was a fundamental principle of his theory, because in 1912 he formulated an equivalence principle valid only locally  (see my book: General Relativity Conflict and Rivalries. Einstein’s Polemics with Physicists, 2015, p. 184). I further explain it below.

Ryder then explains: The equivalence principle is local (a complete cancelation of a gravitational field by an accelerating frame holds locally). However, over longer distances two objects in free fall at different places in a realistic gravitational field move toward each other and this does not happen in an accelerating elevator. The cancelation of the gravitational field by an accelerating field is thus not complete. According to general relativity this effect (tidal effect) is a consequence of the curvature of space-time:

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Although the equivalence principle might have been a heuristic guide to Einstein in his route to the fully developed theory of general relativity, Ryder holds that it is now irrelevant.

I don’t agree with Ryder’s conclusion which resembles that of John Lighton Synge (and Hermann Bondi). Indeed the equivalence principle is not valid globally (i.e. for tidal effects). Although the strong equivalence principle can at best be valid locally, it is still crucial for the general theory of relativity:

  1. Einstein formulated an equivalence principle which is valid only locally. Special relativity is valid locally and space-time is locally the Minkowski space-time.
  2. The principle of equivalence is fundamental for a metric theory and for our understanding of curved space-time: Freely falling test bodies move along geodesic lines under the influence of gravity alone, they are subject to an inertio-gravitational field . The metric determines the single inertio-gravitational field (affine connection), and there is breakup into inertia and gravitation relative to the acceleration. According to the equivalence principle, the components of the affine connection vanish in local frames. John Stachel quotes a passage from Einstein’s letter to Max von Laue:

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Stachel, John, “How Einstein Discovered General Relativity: A Historical Tale with Some Contemporary Morals”, Einstein B to Z, 2002.

Indeed Ryder quotes J. L. Synge :

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Einstein’s equivalence principle was criticized by Synge:

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Synge, J. L. (1960). Relativity: The General Theory (Amsterdam, The Netherlands: North Holland Publishing Co).

And Hermann Bondi reacted to Einstein’s principle of equivalence:

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Bondi also said (‘NO SUCCESS LIKE FAILURE …’: EINSTEIN’S QUEST FOR GENERAL RELATIVITY, 1907–1920, Michel Janssen):

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Other authors contributing to the Handbook of Spacetime write the following:

Graham S. Hall in his paper:

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writes the following:

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“The choice of a geodesic path (Einstein’s principle of equivalence) reflects the results of the experiments of Eötvös and others, which suggest that the path of a particle in a pure gravitational field is determined by its initial position and initial velocity”. This is not Einstein’s equivalence principle. This is the Galilean principle of equivalence or the weak equivalence principle.

And according to Vesselin Petkov:

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the geodesic line is indeed a manifestation of Galileo’s free fall law:

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Ryder presents tests for the equivalence principle. The operation of the global positioning system, the GPS, is a remarkable verification of the time dilation. The GPS system consists of an array of 24 satellites, which describe an orbit round the earth of radius 27,ooo km, and are 7000 km apart, and every 12 hours travel at about 4km/s.  Each satellite carries an atomic clock, and the purpose is to locate any point on the earth’s surface. This is done by sensing radio signals between the satellites and the receiver on the earth, with the times of transmission and reception recorded. The distances are then calculated. Only three satellites are needed to pinpoint the position of the receiver on the earth. Relativistic effects must be taken into account arising both from special relativity (time dilation: moving clocks on the satellites run slower than clocks at rest on the surface of the earth) and from general relativity (gravitational time dilation/gravitational frequency shift: when viewed from the surface of the Earth, clocks on the satellites appear to run faster than identical clocks on the surface of the earth). The combined effect (the special relativistic correction and the general relativistic correction) is that the clocks on the satellites run faster than identical clocks on the surface of the earth by 38.4 microseconds per day. The clocks thus need to be adjusted by about 4 x 10-10s per day. If this factor is not taken into account, the GPS system ceases to function after several hours. This provides a stunning verification of relativity, both special and general.

Neil Ashby dedicates his paper to the GPS:

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and gives a critical reason why the equivalence principle is indeed relevant. Consider again the GPS (global positioning system) or generally, Global navigation satellite systems (GNNS). For the GPS or GNNS, the only gravitational potential of significance is that of the earth itself. The earth and the satellites fall freely in the gravitational field of the sun (and external bodies in the solar system). Hence, according to the equivalence principle one can define a reference system which is locally very nearly inertial (with origin at the earth’s center of mass). In this locally inertial coordinate system (ECI) clocks can be synchronized using constancy of the speed of light (remember that special relativity is incorporated into general relativity as a model of space-time experienced locally by an observer in free fall):

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One writes an approximate solution to Einstein’s field equation and obtains that clocks at rest on earth

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run slow compared to clocks at rest at infinity by about seven parts in 1010.

Unless relativistic effects on clocks [clock synchronization; time dilation, the apparent slowing of moving clocks (STR); frequency shifts due to gravitation, gravitational redshift(GTR)] are taken into account, GPS will not work. GPS is thus a huge and remarkable laboratory for applications of the concepts of special and general relativity. In addition, Shapiro signal propagation delay (an additional general relativistic effect) and spatial curvature effects are significant and must be considered at the level of accuracy of 100 ps of delay. Ashby mentions another effect on earth that is exactly cancelled:

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Wesson in this paper:

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presents the standard explanation one would find in most recent textbooks on general relativity:

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The Christoffel symbols are also used to define the Riemann tensor, which encodes all the relevant information about the gravitational field. However, the Riemann tensor has 20 independent components, and to obtain field equations to solve for the 10 elements of the metric tensor requires an object with the same number of components. This is provided by the contracted Ricci tensor. This is again contracted (taking its product with the metric tensor) to obtain the Ricci curvature scalar.  This gives a kind of measure of the average intensity of the gravitational field at a point in space-time. The combination of the Ricci tensor and the Ricci scalar is the Einstein tensor and it comprises the left hand-side of Einstein’s field equations.

At every space-time point there exist locally inertial reference frames, corresponding to locally flat coordinates carried by freely falling observers, in which the physics of general relativity is locally indistinguishable from that of special relativity. In physics textbooks this is indeed called the strong equivalence principle and it makes general relativity an extension of special relativity to a curved space-time.

Wesson then writes that general relativity is a theory of accelerations rather than forces and refers to the weak equivalence principle:

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As said above, Einstein noted that if an observer in free fall lets go of any bodies, they remain relative to him, in a state of rest or uniform motion, regardless of their particular chemical and physical nature. This is the weak principle of equivalence: The worldline of a freely falling test body is independent of its composition or structure. The test body moves along a geodesic line. The geodesic equation is independent of the mass of the particle. No experiment whatsoever is able, locally, to distinguish a gravitational field from an accelerating system – the strong principle of equivalence (see Ryder above). A freely falling body is moving along a geodesic line. However, globally space-time is curved and this causes the body’s path to deviate from a geodesic line and to move along a non-geodesic line. Hence we speak of geodesics, manifolds, curvature of space-time, rather than forces.

José G. Pereira explains the difference between curvature and torsion (and force) (see paper here):

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General relativity is based on the equivalence principle and geometry (curvature) replaces the concept of force. Trajectories are determined not by force equations but by geodesics:

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How do we know that the equivalence principle is so fundamental?  Gravitational and inertial effects are mixed and cannot be separated in classical general relativity and the energy-momentum density of the gravitational field is a pseudo-tensor (and not a tensor):

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General relativity is grounded on the equivalence principle. It includes the energy-momentum of both inertia and gravitation:

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In 1928 Einstein proposed a geometrized unified field theory of gravitation and electromagnetism and invented teleparallelism. Einstein’s teleparallelism was a generalization of Elie Cartan’s 1922 idea. Picture20

According to Pereira et al: “In the general relativistic description of gravitation, geometry replaces the concept of force. This is possible because of the universal character of free fall, and would break down in its absence. On the other hand, the teleparallel version of general relativity is a gauge theory for the translation group and, as such, describes the gravitational interaction by a force similar to the Lorentz force of electromagnetism, a non-universal interaction. Relying on this analogy it is shown that, although the geometric description of general relativity necessarily requires the existence of the equivalence principle, the teleparallel gauge approach remains a consistent theory for gravitation in its absence”.

See his paper with R. Aldrovandi and K. H. Vu: “Gravitation Without the Equivalence Principle”, General Relativity and Gravitation 36, 2004, 101-110.

Petkov explains in his paper: (see further above)

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the following:

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The bottom line is that classical general relativity is fundamentally based on the equivalence principle. One cannot reject Einstein’s route to the theory of general relativity.

 

 

 

 

 

 

 

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

Here   x

 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

See here

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