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Measurement problem and local hidden variables with entangled photons

  • Eugen Muchowski EMAIL logo
Veröffentlicht/Copyright: 29. Dezember 2017
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Open Physics
Aus der Zeitschrift Open Physics Band 15 Heft 1

Abstract

It is shown that there is no remote action with polarization measurements of photons in singlet state. A model is presented introducing a hidden parameter which determines the polarizer output. This model is able to explain the polarization measurement results with entangled photons. It is not ruled out by Bell’s Theorem.

Keywords: EPR paradox; Bell theorem; nonlocality; remote action at a distance; entanglement
PACS: 03.65.Ta; 03.65.Ud

1 Introduction

The polarization behaviour of entangled photons is widely discussed. A general overview is given by Laloe [1]. The paper of Einstein, Podolsky and Rosen (EPR) [2] had initiated a discussion whether the theory of quantum mechanics (QM) is incomplete. The EPR argument when applied to entangled photons says as follows (see also Aspect et al. [3]): suppose we have a pair of entangled photons in singlet state. Both photons are propagating in opposite directions towards polarization measuring devices A and B consisting of polarizing beam splitters and detectors. A coincidence measuring device encounters coinciding events at the two detectors. When after measurement of the polarization of one photon the polarization of the other photon can be predicted in advance with certainty, there must exist an element of physical reality corresponding to this physical quantity according to EPR.

John Bell [4] has stated that it is impossible to explain the predictions of quantum mechanics with a model based upon real local variables. QM were a nonlocal theory, many authors claim [5], and there would be action at a distance in order to have a far distant photon forced to a particular polarization upon measurement of the peer photon. This action at a distance would be faster than light as was experimentally proved by some authors including Weihs [6]. However, it was stated, that no information transport is possible through the quantum channel of entangled photons [7]. Some authors have established nonlocal models in order to explain the predictions of QM, see Leggett [8]. Branciard and others [9] have experimentally falsified Leggett’s model in agreement with QM. Englert [10] has stated “It is true that joint probabilities that result from quantum processes can have stronger correlations than those available by non quantum simulations;” and finally concludes quantum theory is a local theory. This assertion connotes that the measured value is defined before measurement. Otherwise, if the measured value would be created with the measurement, a correlation between the outcomes of measurements at different sides would demand nonlocal effects. The measurement problem is thus closely connected with the EPR paradox. This paper will help to understand the experimental results. Such an understanding is intended to rely on local effects only. An argument is given in Section 2. Following it there are no nonlocal actions involved with polarization measurements of photons in singlet state. In Section 3 a model is presented which describes the behaviour of polarized photons using a statistical parameter. Whether this is in contradiction to Bell’s theorem is also discussed in Section 3. The model will give an idea how entanglement works.

2 Photons in singlet state do not exhibit action at a distance

Suppose we have a pair of entangled photons in singlet state. Both photons are propagating in opposite directions towards polarization measuring devices consisting of polarizer P1 with detectors D1-1 and D1-2 at side 1 and polarizer P2 with detectors D2-1 and D2-2 at side 2. A coincidence measuring device encounters simultaneous events at the two detectors D1-1 and D2-1 or at D1-2 and D2-2, respectively. The polarizing angles can be adjusted at each side.

Figure 1 Temporal sequences of creating and detecting entangled photon pairs. The SEPP (source of entangled photon pairs) emits photons in singlet state |Ψ12〉=1/2(|H1V2〉-|V1H2〉)$\vert\Psi_{12}\rangle=1/\sqrt{2}(\vert{}\text{H}_{1}\text{V}_{2}\rangle\text-\vert \text{V}_{1}\text{H}_{2}\rangle) $ propagating in opposite directions towards adjustable polarizers and detectors. A coincidence measuring device not seen in the picture encounters matching events. Time axes for each photon are shown at the bottom. At time t0 the photon pair leaves the source. At time t1 photon 1 has left the polarizer P1 and is detected in the detector D1-1 at time t2. At time t3 photon 2 has left P2 and is detected at time t4. The polarization angles are defined in the x-y-plane which is perpendicular to the propagation direction of the photons. The coordinate system is left handed and the same for both sides with the x-axis in horizontal and the y-axis in vertical direction. The z-axis is in propagation direction of photon 1 and opposite to the propagation direction of photon 2.
Figure 1

Temporal sequences of creating and detecting entangled photon pairs. The SEPP (source of entangled photon pairs) emits photons in singlet state |Ψ12〉=1/2(|H1V2〉-|V1H2〉) propagating in opposite directions towards adjustable polarizers and detectors. A coincidence measuring device not seen in the picture encounters matching events. Time axes for each photon are shown at the bottom. At time t0 the photon pair leaves the source. At time t1 photon 1 has left the polarizer P1 and is detected in the detector D1-1 at time t2. At time t3 photon 2 has left P2 and is detected at time t4. The polarization angles are defined in the x-y-plane which is perpendicular to the propagation direction of the photons. The coordinate system is left handed and the same for both sides with the x-axis in horizontal and the y-axis in vertical direction. The z-axis is in propagation direction of photon 1 and opposite to the propagation direction of photon 2.

The Hilbert space for the combined system is H12 = H1⊗H2. Normalized base vectors are |H1〉 and |V1〉 for system 1 at side 1 and |H2〉 and |V2〉 for system 2 at side 2. |H1〉 and |H2〉 correspond to the x-axis and |V1〉 and |V2〉 correspond to the y-axis. Photon 1, as a convention, is measured before photon 2.

Suppose now the polarizer P1 is set to 0∘/90∘. Before photon 1 entered the polarizer P1 the pair was in the singlet state |Ψ12〉. In the following we only look at those photon 1 which are detected in detector D1-1 behind the 0∘ exit of P1. They are experimentally identified by the time stamp of the detector click of D1-1. After detecting photon 1 at time t2 in the detector D1-1 we know photon 1 was in state |H1〉 between t1 and t2. This is due to preparation by P1.

Upon hitting the detector D1-1 photon 1 has ceased to exist and the singlet state no longer describes the state of the photon pair. Photon 2 must thus be in another state. We can calculate this state from the evaluation of the experimental findings. With the polarizer P2 set to an arbitrary angle δ the probability P for photon 2 to pass the polarizer at δ after photon 1 had passed P1 at 0∘ is according to the experimental results [6] P = sin2(δ).

According to Born’s rule this is possible only if photon 2 was in state |V2〉 before measurement at P2 so that

P=cos2(δ−90∘)=sin2(δ).(1)

As there is no physical action upon photon 2 after it had left the source it is in state |V2〉 just after t0. There is no action at a distance from photon 1 upon photon 2. Nonlocality is therefore not a necessary consequence of entanglement. The abovementioned does also apply to the detection of photon 1 at any polarization angle α and the polarizer setting β at side 2 with δ = β − α because the experimental results are rotationally invariant. Photon 2 is then in state –sin(α)|H2〉 + cos(α)|V2〉 just after t0. With δ = 90∘ follows P = 1 and photon 2 is found with certainty behind the β exit of P2. How it can be understood that the setting of the polarizer at side 1 defines the polarization of photon 2 is subject of the model discussed in the following section.

3 Model describing the statistical behaviour of entangled photons

EPR [2] have stated quantum physics were incomplete as it does not account for the physical reality given by the fact that measured values can be predicted in advance to a measurement as we have seen in the previous section. See Fine [11] for a detailed discussion of the EPR paradox. Below a model is presented which describes the behaviour of polarized photons using a statistical parameter.

That such a model may be in contradiction to Bell’s theorem which forbids the existence of hidden parameters will be discussed also. The model assumptions show which conditions have to be met in order to reproduce the experimental results and to fulfil the requirements of quantum physics. The model should and does explain the following characteristics:

  1. The measured value of a polarization measurement is determined before the measurement,

  2. The QM predictions of polarization measurements with single photons according to Born’s rule,

  3. The mechanism of entanglement by a parameter,

  4. The locality of the polarization measurements with entangled photons,

  5. Rotational invariance of the polarization measurements with entangled photons,

  6. The QM predictions of polarization measurements with entangled photons,

  7. The model violates Bell’s inequality,

  8. Measurement results of subsequent measurements are not predictable.

Six model assumptions M1-M6 are made:

  1. introduces the physical entity propensity state, called p-state, determining the polarization behaviour.

  2. controls the statistical distribution of p-states.

  3. accounts for the fact that the polarization of entangled photons is unknown but is defined after a measurement at one side as shown in Section 2.

  4. establishes how the p-state depends on the statistical parameter λ.

  5. accounts for the entanglement of the singlet state.

  6. accounts for the fact that photons don’t have a memory of previous states after a measurement.

The six assumptions are described in detail in the following:

Model assumption M1

A propensity state called p-state determines which polarizer output a photon will take. A photon in p-state α would pass a polarizer set to α with certainty.

Purpose: introducing the physical entity propensity state, called p-state, determining the polarization behaviour.

Model assumption M2

A statistical parameter is introduced, the value of which determines in which of two orthogonal p-states a photon is. λ has the value range -1<λ<+1 and a normalized probability distribution ρ(λ) = ½ with∫−11dλρ(λ) =1.

Purpose: controlling the statistical distribution of p-states.

Model assumption M3

Photons from an ensemble in the same p-state have the polarization (state) given by the p-state. This assumption refers to entangled photons only where the polarization of the incoming photons is unknown. With not entangled prepared photons the polarization is determined by the preparation.

Purpose: Accounting for the fact that the polarization of entangled photons is unknown but is defined after a measurement at one side as shown in Section 2.

It is assumed that a photon can be simultaneously in different p-states depending on the value of a parameter λ and a chosen direction relative to the polarization of the photon. That means some of the photons with polarization α are also in p-state β and thus pass a polarizer set to β with certainty. As p-state and polarization are different physical entities ambiguous polarization states are excluded.

Entangled photons are generated by a common source on the side 1 with the polarization ϕ1 = 0∘ and on the side 2 with the polarization ϕ2 = 90∘ or on the side 1 with the polarization ϕ1 = 90∘ and on the side 2 with the polarization ϕ2 = 0∘. We now look at side 1 with the polarizer setting α/α+π/2: Incoming photons have the polarization ϕ1 = 0∘ or ϕ1 = 90∘. Outgoing photons leave the polarizer either through the output with the setting α or through the output with the setting α+π/2.

Let δ be the angle between the polarizer setting α and the polarization of the incoming photon. Then we get δ = α-ϕ1 and a polarization function A(δ, λ) can be defined, which indicates the p-state of the photon before a subsequent measurement. A(δ, λ) can have the values +1 and -1. The representation of the photon p-states occurs in the Bloch circle. From the projection onto the double angle 2δ, a rule can be constructed which determines whether the arriving photon of polarization ϕ1 is in p-state δ+ϕ1 corresponding to A(δ, λ) = +1 or in p-state δ+ 90∘+ϕ1 corresponding to A(δ, λ) = -1. See Figure 2. Being in p-state α = δ + ϕ1 means the photon would pass the polarizer output α with certainty.

Figure 2 Geometrical derivation of a deterministic distribution of polarized photons onto polarizer outputs. The representation of the photon states occurs in the Bloch circle. The incoming photon has a polarization of 0∘. The polarizer is set to the angle δ/δ+90∘ We are looking for a rule which determines whether the photon takes the output δ or the output δ+90∘. For this purpose, a parameter is introduced which is evenly distributed over the incoming photons in the value range -1<λ<+1. By projecting the unit vector with direction 2δ onto the horizontal, the horizontal diameter is divided into the sections of the length 1+cos(2δ) and 1-cos(2δ), or after conversion 2cos2(δ) and 2sin2(δ). Photons with λ < cos(2δ) are assigned to the polarizer output δ, while photons with λ > cos(2δ) take the output δ+90∘.
Figure 2

Geometrical derivation of a deterministic distribution of polarized photons onto polarizer outputs. The representation of the photon states occurs in the Bloch circle. The incoming photon has a polarization of 0∘. The polarizer is set to the angle δ/δ+90∘ We are looking for a rule which determines whether the photon takes the output δ or the output δ+90∘. For this purpose, a parameter is introduced which is evenly distributed over the incoming photons in the value range -1<λ<+1. By projecting the unit vector with direction 2δ onto the horizontal, the horizontal diameter is divided into the sections of the length 1+cos(2δ) and 1-cos(2δ), or after conversion 2cos2(δ) and 2sin2(δ). Photons with λ < cos(2δ) are assigned to the polarizer output δ, while photons with λ > cos(2δ) take the output δ+90∘.

Model assumption M4

For -π/2<δ<π/2:

For incoming photon 1 with polarization ϕ1 = 0∘and polarizer P1 setting α:

A(δ,λ)=+1 for −1<λ<cos⁡(2δ),(2)

meaning photon 1 is in p-state α and

A(δ,λ)=−1 for cos⁡(2δ)<λ<1,(3)

meaning photon 1 is in p-state α + π/2 with δ = α – 0 = α.

For incoming photon 1 with polarization ϕ1 = 90∘and polarizer P1 setting α + π/2

A(δ,λ)=−1 for −1<λ<cos⁡(2δ),(4)

meaning photon 1 is in p-state α+π/2 and

A(δ,λ)=+1 for cos⁡(2δ)<λ<1,(5)

meaning photon 1 is in p-state α, with δ = α+π/2 − π/2 = α.

Purpose: establishing how the p-state depends on the statistical parameter λ.

This explains property #1: The measured value of a polarization measurement is determined before the measurement.

Geometrical calculations yield 1 + cos(2δ) = 2 cos2(δ) and 1 − cos(2δ) = 2sin2(δ). Using equation (2) the horizontally polarized photon 1 is found behind the output α of the polarizer P1 with the probability

Pδ=1/2∫−1cos⁡(2δ)dλ=cos2⁡(δ).(6)

With δ = α we obtain the same Pδ for a photon in state |H〉 to be found in state cos(α)|H〉 + sin(α)|V〉 according to QM from Born’s rule.

This explains property #2: The QM predictions of polarization measurements with single photons according to Born’s rule.

With polarizers P1 and P2 orientated perpendicularly to each other measurement results at both sides are of opposite sign. Having P1 set to α means P2 is set to β = α+π/2. If the incoming photon on side 1 comes with polarization ϕ1 = 0∘ the partner photon on side 2 comes with polarization ϕ2 = 90∘. Let B(δ, λ) be the polarization function at side 2 and in this case δ = β–ϕ2 we get δ = α+π/2–π/2 = α. Here δ is again the angle between the polarizer setting and the polarization of the incoming photon.

Model assumption M5

In order to meet the experimental results with entangled photons, it is defined:

B(δ,λ)=−A(δ,λ).(7)

Purpose: accounting for the entanglement of the singlet state.

This explains property #3: The mechanism of entanglement by a parameter and property #4: The locality of the polarization measurements with entangled photons.

The rules for the distribution of the incoming photons onto the two output directions of the polarizer are also valid for the partner photon on side 2. With equation (7) it follows:

For incoming photon 1 with polarization ϕ1 = 0∘ having incoming photon 2 with polarization ϕ2 = 90∘ and polarizer P2 setting β = α + π/2 we obtain from equation (4)

B(δ,λ)=−1 for −1<λ<cos⁡(2δ),(8)

meaning photon 2 is in p-stateα+π/2 and from equation (5)

B(δ,λ)=+1 for cos⁡(2δ)<λ<1,(9)

meaning photon 2 is in p-stateα, where δ = β – π/2 = α.

For incoming photon 1 with polarization ϕ1 = 90∘ having incoming photon 2 with polarization ϕ2 = 0∘ and polarizer P2 setting β = α we obtain from equation (2)

B(δ,λ)=+1 for −1<λ<cos⁡(2δ),(10)

meaning photon 2 is in p-state α and from equation (3)

B(δ,λ)=−1 for cos⁡(2δ)<λ<1,(11)

meaning photon 2 is in p-state α + π/2, where δ = β−0∘ = α.

With equations (2) and (5) it follows A(δ, λ) = 1 for each value of δ and for –1 < λ < 1 although from different incoming photons. From equations (8) and (11) we get B(δ, λ) = –1 for –1 < λ < 1, again from different incoming photons. Photons 1 with A(δ, λ) = +1 are part of an ensemble, selected by polarizer P1, with the polarization α and the partner photons 2 with B(δ, λ) = –1 are part of an ensemble with the polarization α+π/2 coupled with photon 1 by equation (7). This follows from model assumption M3.

With photon 1 in state ϕ1= α and photon 2 in state ϕ2 = α +π/2 we can rotate the coordinate system by an angle α and get ϕ1′=ϕ1−α=α−α=0∘ and ϕ2′=ϕ2−α=α+π/2−α=90∘ and β′ = β – α.

This explains Property #5: Rotational invariance of the polarization measurements with entangled photons.

For incoming photon 1 with polarization ϕ1′=0∘ having incoming photon 2 with polarization ϕ2′=90∘ and polarizer P2 setting β′ we obtain from equation (8)

B(δ,λ)=−1 for −1<λ<cos⁡(2δ),(12)

meaning photon 2 is in p-state β′ and from equation (9)

B(δ,λ)=+1 for cos⁡(2δ)<λ<1,(13)

meaning photon 2 is in p-state β′ –π/2, with δ = β′ – π/2.

For incoming photon 1 with polarization ϕ1′=90∘ having incoming photon 2 with polarization ϕ2′=0∘ and polarizer P2 setting β′–π/2 we obtain from equation (10)

B(δ,λ)=+1 for −1<λ<cos⁡(2δ),(14)

meaning photon 2 is in p-state β′–π/2 and from equation (11)

B(δ,λ)=−1 for cos⁡(2δ)<λ<1,(15)

meaning photon 2 is in p-state β′ with δ = β′ – π/2 – 0∘.

The expectation value of a common measurement with polarizers P1 and P2 is

E(α,β)=1/2∫−11Aα,λ∗B(β,λ)dλ,(16)

where α and β are the polarizer settings at side 1 and side 2 respectively and

Aα,λ=Aδα,λ

where δ(α) = α – α = 0 and

Bβ,λ=B(δ(β),λ)

where δ(β)= β – α – π/2.

With A(0,λ) = 1 and B(β,λ) from equations(12) and (13) where δ = β′ – π/2 = β – α – π/2 it follows from equation (16)

E(α,β)=−1/2∫−1cos⁡(2δ)dλ+1/2∫cos⁡(2δ)1dλ=−cos2⁡(δ)+sin2⁡(δ)=−sin2⁡(β−α)+cos2⁡(β−α).(17)

The same result is obtained using A(α,λ) = –1 and B(β,λ) equations (14) and (15).

The probability Pα,β to measure a photon 2 polarization at β after photon 1 was measured at α can be obtained from

E(α,β)=+1∗(1−Pα,β)−1∗Pα,β(18)

yielding

Pα,β=1/2(1−E(α,β))=sin2⁡(β−α).(19)

This explains property #6: The QM predictions of polarization measurements with entangled photons.

As the expectation value E(α,β) from equation (17) does exactly match the predictions of quantum physics it also violates Bells [4] inequality. This explains property #7: The model violates Bells inequality as quantum physics does.

What is the reason for this? With δ = β – α – π/2 the value of B(β,λ) in equation (16) depends on the setting angle α of the polarizer at side 1 whereas in Bells model the measured value at side 2 does not depend on the setting of polarizer at side 1. This difference is the reason that the model presented here violates Bells inequality whereas Bells model does not. Bell thought, “the result B for particle 2 should not depend on the setting … for particle 1”. But we have seen with model assumptions M1-M6 that a local model is possible without Bells restriction cited above. Bell had cited Einstein [12] “But one supposition we should in my opinion, absolutely hold fast: the real factual situation of the system S2 is independent of what is done with the system S1, which is spatially separated from the former.” This supposition is fulfilled with the model above. With model assumption M3 the polarization of the incoming photon at side 2 depends on the setting of the polarizer at side 1 although there is no nonlocal action. As only those photons 2 are considered which match with a measured photon 1 it is not unexpected to see the result at side 2 depending on the polarizer setting at side 1. The rule that determines which polarizer exit a photon will take is the same for both sides. Dependencies between the photons on either side originate from the shared parameter λ and not from a nonlocal influence of photon 1 upon photon 2.

Model assumption M6

We assume that λ is indeterminate and uniformly distributed after a measurement.

Purpose: accounting for the fact that photons don’t have a memory of previous states after a measurement.

After a preparation the polarizer output of the next measurement is determined by the parameter λ, but it can not be predicted which polarizer output the photon will pass after a further subsequent measurement. How this indeterminacy is realized can not be said at the moment. However, this is a local effect which applies to single photons as well as to entangled photons. The ensemble of photons covers the full range –1 < λ < +1 after passing a polarizer and a photon has the polarization α after passing a polarizer with setting α. That explains property #8: Measurement results of subsequent measurements are not predictable.

From the model above we get an idea how entanglement works. From the six model assumptions M1-M6 only M3 and M5 refer to entanglement. The other four assumptions apply to single photons as well. Particularly M3 is significant. It states that an ensemble of photons with a particular polarization state can arise from two different input photons. This is the real reason for the rotational invariance of the polarization behaviour of entangled photons.

4 Results, Discussion and Conclusion

Photons in singlet state do not exhibit action at a distance. Nonlocality is therefore not a consequence of entanglement. Experimental results on entangled photons can be explained without assuming non-local effects. This means measured values are not generated upon the measurement, they already exist beforehand. If the measured value exists before the measurement, the measurement is a selection of existing states. This indicates an ensemble.

It was argued by Einstein, Podolsky and Rosen [2] quantum physics were incomplete as it does not predict the exact measurement result for each photon. A hidden parameter model was presented, able to complete the formalism of quantum physics for the case of polarized photons. It is not ruled out by Bells theorem. The reason for this was discussed. Relations between measurement results of the photons on either side do not come from nonlocal effects but rather originate from the shared parameter λ which connects them from the moment they are created by the common source. The model also made use of a propensity state which determines a subsequent polarization measurement. According to the model the quantum mechanical state again describes an ensemble. The individual parts differ by the value of a parameter.

However, the model presented above is an enhancement but no replacement of the formalism of quantum physics. Enhancement means that the model correctly describes certain phenomena in detail where QM does not give answers. These phenomena are the polarization measurements at linearly polarized photons including entangled photons where QM only describes probabilities. The model is valid if it is free of contradictions. Generally, the formalism of QM is not in question.

Acknowledgement

I would like to thank Prof. Dr. Harald Weinfurter and Prof. Dr. Robert B. Griffith for fruitful discussions on the subject.

References

[1] Laloe F., Do we really understand quantum mechanics? Strange correlations, paradoxes and theorems. American Journal of Physics, 2001, 69, 65510.1119/1.1356698Suche in Google Scholar

[2] Einstein A., Podolsky B., Rosen N., Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Phys. Rev., 1935, 47, 77710.1103/PhysRev.47.777Suche in Google Scholar

[3] Aspect A., Grangier P., Roger G., Experimental realization of Einstein-Podolsky-Rosen-Bohm Gedanken experiment: A new violation of Bell’s inequalities, Phys. Rev. Lett., 1982, 49, 91-9410.1103/PhysRevLett.49.91Suche in Google Scholar

[4] Bell J.S., On The Einstein Podolsky Rosen Paradox. Physics (Long Island City N.Y.), 1964, 1, 19510.1103/PhysicsPhysiqueFizika.1.195Suche in Google Scholar

[5] Christensen Bradley G., et al., Exploring the limits of quantum nonlocality with entangled photons. arXiv preprint arXiv:1506.01649, 201510.1103/PhysRevX.5.041052Suche in Google Scholar

[6] Weihs G., Jennewein T., Simon C., Weinfurter H., Zeilinger A., Violation of Bell’s Inequality under Strict Einstein Locality Conditions. Phys. Rev. Lett., 1998, 81, 503910.1103/PhysRevLett.81.5039Suche in Google Scholar

[7] Clauser J.F., Horne M.A., Experimental consequences of objective local theories. Phys. Rev. D, 1974, 10, 52610.1103/PhysRevD.10.526Suche in Google Scholar

[8] Leggett A.J., Nonlocal Hidden-Variable Theories and Quantum Mechanics: An Incompatibility Theorem. Found. of Phys., 2003, 33, 146910.1023/A:1026096313729Suche in Google Scholar

[9] Branciard C., et al., Experimental Falsification of Leggett’s Nonlocal Variable Model. Phys. Rev. Lett., 2007, 99, 21040710.1103/PhysRevLett.99.210407Suche in Google Scholar PubMed

[10] Englert B., On Quantum Theory. Eur. Phys. J. D, 2013, 67, 23810.1140/epjd/e2013-40486-5Suche in Google Scholar

[11] Fine A., The Einstein-Podolsky-Rosen Argument in Quantum Theory, The Stanford Encyclopedia of Philosophy (Fall 2016 Edition)Suche in Google Scholar

[12] Einstein A., in: Albert Einstein, Philosopher Scientist (Edited by P.A. Schilp) p.85, Library of Living Philosophers, Evanston Illinois (1949)Suche in Google Scholar

Received: 2017-9-19
Accepted: 2017-11-23
Published Online: 2017-12-29

© 2017 Eugen Muchowski

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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  276. Speed control of an induction motor by 6-switched 3-level inverter
https://doi.org/10.1515/phys-2017-0106
Schlagwörter für diesen Artikel
EPR paradox; Bell theorem; nonlocality; remote action at a distance; entanglement
Creative Commons
BY-NC-ND 4.0

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  201. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  202. The photon identification loophole in EPRB experiments: computer models with single-wing selection
  203. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  204. Bohr against Bell: complementarity versus nonlocality
  205. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  206. Is Einsteinian no-signalling violated in Bell tests?
  207. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  208. Bell’s “Theorem”: loopholes vs. conceptual flaws
  209. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  210. Nonrecurrence and Bell-like inequalities
  211. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  212. Three-dimensional computer models of electrospinning systems
  213. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  214. Electric field computation and measurements in the electroporation of inhomogeneous samples
  215. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  216. Modelling of magnetostriction of transformer magnetic core for vibration analysis
  217. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  218. Comparison of the fractional power motor with cores made of various magnetic materials
  219. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  220. Dynamics of the line-start reluctance motor with rotor made of SMC material
  221. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  222. Inhomogeneous dielectrics: conformal mapping and finite-element models
  223. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  224. Topology optimization of induction heating model using sequential linear programming based on move limit with adaptive relaxation
  225. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  226. Detection of inter-turn short-circuit at start-up of induction machine based on torque analysis
  227. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  228. Current superimposition variable flux reluctance motor with 8 salient poles
  229. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  230. Modelling axial vibration in windings of power transformers
  231. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  232. Field analysis & eddy current losses calculation in five-phase tubular actuator
  233. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  234. Hybrid excited claw pole generator with skewed and non-skewed permanent magnets
  235. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  236. Electromagnetic phenomena analysis in brushless DC motor with speed control using PWM method
  237. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  238. Field-circuit analysis and measurements of a single-phase self-excited induction generator
  239. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  240. A comparative analysis between classical and modified approach of description of the electrical machine windings by means of T0 method
  241. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  242. Field-based optimal-design of an electric motor: a new sensitivity formulation
  243. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  244. Application of the parametric proper generalized decomposition to the frequency-dependent calculation of the impedance of an AC line with rectangular conductors
  245. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  246. Virtual reality as a new trend in mechanical and electrical engineering education
  247. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  248. Holonomicity analysis of electromechanical systems
  249. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  250. An accurate reactive power control study in virtual flux droop control
  251. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  252. Localized probability of improvement for kriging based multi-objective optimization
  253. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  254. Research of influence of open-winding faults on properties of brushless permanent magnets motor
  255. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  256. Optimal design of the rotor geometry of line-start permanent magnet synchronous motor using the bat algorithm
  257. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  258. Model of depositing layer on cylindrical surface produced by induction-assisted laser cladding process
  259. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  260. Detection of inter-turn faults in transformer winding using the capacitor discharge method
  261. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  262. A novel hybrid genetic algorithm for optimal design of IPM machines for electric vehicle
  263. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  264. Lamination effects on a 3D model of the magnetic core of power transformers
  265. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  266. Detection of vertical disparity in three-dimensional visualizations
  267. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  268. Calculations of magnetic field in dynamo sheets taking into account their texture
  269. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  270. 3-dimensional computer model of electrospinning multicapillary unit used for electrostatic field analysis
  271. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  272. Optimization of wearable microwave antenna with simplified electromagnetic model of the human body
  273. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  274. Induction heating process of ferromagnetic filled carbon nanotubes based on 3-D model
  275. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  276. Speed control of an induction motor by 6-switched 3-level inverter
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Heruntergeladen am 9.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/phys-2017-0106/html
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