Print ISBN: 978-0-7503-5265-9
Online ISBN: 978-0-7503-5269-7
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An absolutely exact measurement of momentum p is physically impossible... In this regard, the 'all values' spread in the coordinate, as feared by EPR, is not allowed... Hence, the EPR conclusion that 'the quantum mechanical description of physical reality... is not complete' can be dismissed.
Page 3-4
As noted previously Bell's theorem is completely disconnected from the physics leading to |ψ>+ , |ψ>- , |ψ>+ , and |ψ>- .
Page 10-6
What's important to highlight is that the derivation of the quantum entanglement probability amplitude, à la Dirac, flows naturally, it is transparent and straightforward. The are no 'paradoxes' in the physics of quantum entanglement.
Page 17-5
Nature appears to be very efficient and there is indeed an optimum finesse determining the smallness necessary to gain full and complete representation of the interferometric reality.
Page 29-15
A theory that does not observe Born's rule is not a quantum mechanical theory... Thus, it is logical to conclude that the hidden variable theory introduced by Bohm is not a quantum mechanical theory.
Page 30-3
Contemporaneous criticisms of quantum mechanics fail to mention that, in praxis, there is no measurement problem in quantum mechanics... quantum measurements in the interferometric and polarization domains, can be described without resorting to the concept of the collapse of the wave function or the collapse of the probability amplitude.
Page 30-7
The main impact of Bell's theorem is from a philosophical-historical perspective: it reinforces, outside the physics of quantum entanglement, the incompatibility of hidden variable theories with quantum mechanics.
Page 30-8
From an interferometric perspective, there are no mysteries... and no paradoxes... in the physics of quantum entanglement.
Page 30-14
1.1 Introduction
1.2 Foundations of quantum mechanics
1.2.1 The mathematical bases of quantum mechanics
1.2.2 The photon from a quantum perspective
1.3 Ward’s observations
1.4 History of quantum entanglement
1.4.1 The philosophical path
1.4.2 The physics path
1.5 The field of quantum entanglement
1.6 Fundamentals of quantum entanglement
1.7 Intent
Problems
References
2.1 Introduction
2.2 Dirac’s pair theory
2.3 Dirac’s notation
2.4 Dirac’s notation in N-slit interferometers
2.5 Expanded series of N-slit quantum interference probabilities
2.6 The interferometric probability in 2D and 3D
2.7 Semi-coherent interference
2.8 From quantum probabilities to measurable intensities
2.9 Interferometric calculations and quantum coherence
2.10 Dirac’s identities
2.10.1 Indistinguishability identities
2.10.2 Extending the emission identities
Problems
References
3.1 Introduction
3.2 EPR’s doubts on quantum mechanics
3.2.1 EPR’s definition of a correct theory
3.3 Transparent resolution of the EPR ‘paradox’
3.3.1 EPR and the uncertainty principle
Problems
References
4.1 Introduction
4.2 The first Schrödinger paper
4.3 The second Schrödinger paper
References
5.1 Introduction
5.2 Wheeler’s paper significance to quantum theory
5.3 Wheeler’s paper significance to quantum experiments 5.4 A theoretical opportunity
References
6.1 Introduction
6.2 The Pryce–Ward paper
6.2.1 Theoretical legacy of the Pryce–Ward paper
6.2.2 Experimental legacy of the Pryce–Ward paper
6.3 Ward’s doctoral thesis
6.4 Summary
Problems
References
7.1 Introduction
7.2 The quantum entanglement experiment
7.3 Historical notes
Problems
References
8.1 Introduction
8.2 The first three quantum entanglement experiments
8.3 Further significance of the annihilation experiments
Problems
References
9.1 Introduction
9.2 Significance to the development of quantum entanglement research
9.3 Philosophy and physics
Problems
References
10.1 Introduction
10.2 von Neumann’s
10.3 Bell’s theorem or Bell’s inequalities
10.4 Example
10.5 An additional perspective on Bell’s theorem
10.6 More philosophy and physics
Problems
References
11.1 Introduction
11.2 Probability amplitudes via Hamiltonians à la Feynman
11.3 Arrival to quantum entanglement probability amplitudes
11.4 Hyperfine splitting
11.5 Discussion
Problems
References
12.1 Introduction
12.2 Salient features
12.3 Bell’s theorem and hidden variables
References
13.1 Introduction
13.2 Testing for local hidden variable theories
13.3 Early optical experiment
13.4 Observations and discussion
References
14.1 Introduction
14.2 The Aspect experiments
14.2.1 The first Aspect experiment
14.2.2 The second Aspect experiment
14.2.3 The third Aspect experiment
14.3 Observations and discussion
Problems
References
15.1 Introduction
15.2 The quantum entanglement probability amplitude 1947–1992
15.2.1 1947–1949
15.2.2 1948
15.2.3 1951
15.2.4 1957
15.2.5 1965
15.2.6 1975
15.2.7 1990
15.2.8 1992
15.3 Observations and discussion
Problems
References
16.1 Introduction
16.2 The GHZ probability amplitudes
16.3 Observations and discussion
References
17.1 Introduction
17.2 The meaning of the Dirac–Feynman probability amplitude
17.3 The derivation of the quantum entanglement probability amplitude
17.4 Identical states of polarization
17.5 Beyond single quanta-pair quantum entanglement
17.6 Discussion
Problems
References
18.1 Introduction
18.2 The quantum entanglement probability amplitude for n = N = 4
18.3 The quantum entanglement probability amplitude for n = N = 8
18.4 The quantum entanglement probability amplitude for n = N = 16
18.5 The quantum entanglement probability amplitude for n = N = 21, 22, 23, 24, … 2r
18.6 Discussion
Problems
References
19.1 Introduction
19.2 The quantum entanglement probability amplitude for n = N = 3
19.3 The quantum entanglement probability amplitude for n = N = 6
19.4 Discussion
Problems
References
20.1 Introduction
20.2 Reversibility: from entanglement to interference
20.3 Schematics
20.4 Experimental and theoretical perspectives
20.4.1 Experimental perspective
20.4.2 Theoretical perspective
20.4.3 Derivation of the Dirac–Feynman principle
20.5 Interference for N slits and n = 1
Problems
References
21.1 Introduction
21.2 Probability amplitudes
21.3 Quantum polarization
21.4 Quantum probabilities and Bell’s theorem
21.5 Application to Bell’s theorem
21.6 All-quantum approach
21.7 Discussion
Problems
References
22.1 Introduction
22.2 The probability amplitudes of quantum entanglement
22.3 Dirac’s ket vectors and Pauli matrices
22.4 Quantum entanglement in Pauli matrix notation
22.4.1 Mechanics of Pauli matrices
22.5 Quantum entanglement and the Hadamard gate
22.6 Complete set of matrices derived from the probability amplitudes of quantum entanglement
22.7 Polarization rotators for quantum entanglement
22.8 Quantum mathematics with polarization rotators
22.9 Quantum mathematics with the Hadamard gate
22.10 Interconnectivity in quantum mechanics
Problems
References
23.1 Introduction
23.2 Measurement protocol based on Bell’s theorem
23.2.1 Experiments
23.3 All-quantum measurement protocol
Problems
References
24.1 Introduction
24.2 The mechanics of teleportation
24.3 Technology
Problems
References
25.1 Introduction
25.2 Entropy
25.3 Qbits
25.4 Quantum entanglement and Pauli matrices
25.5 Pauli matrices and quantum entanglement
25.6 Quantum gates
25.6.1 Pauli gates
25.6.2 The Hadamard gate
25.7 The Hadamard matrix and quantum entanglement
25.8 Multiple entangled states
25.9 Technology
Problems
References
26.1 Introduction
26.2 Space-to-space configurations
26.3 Experiments
26.3.1 The space-to-earth experiment
26.3.2 The International Space Station experiment
26.4 Further horizons
Problems
References
27.1 Introduction
27.2 The generalized N-slit quantum interference equations
27.3 The generation and transmission of interferometric characters
27.4 The inherent quantum security mechanism
27.5 Discussion
Problems
References
28.1 Introduction
28.2 Positron–electron annihilation
28.3 Atomic Ca emission
28.4 Type I spontaneous parametric down-conversion
28.5 Type II spontaneous parametric down-conversion
28.6 Quantum description of parametric down-conversion
28.7 Alternative quantum pair sources
28.8 Further horizons
Problems
References
29.1 Introduction
29.2 Fundamental principles of quantum mechanics
29.3 Nonlocality of the photon
29.4 Indistinguishability and Dirac’s identities
29.5 Quantum measurements
29.5.1 Probability amplitudes
29.5.2 Quantum probabilities
29.5.3 Quantum entanglement measurements
29.5.4 Quantum time and entropy
29.5.5 The quantum measurer
29.6 Quantum entanglement at the foundations of quantum mechanics
29.7 On the origin of the Dirac–Feynman principle
29.7.1 Optimum finesse
29.7.2 Further refinements
29.8 Discussion
Problems
References
30.1 Introduction
30.2 Philosophical aspects of quantum entanglement
30.2.1 The perspectives of EPR and Schrödinger on quantum entanglement
30.2.2 Hidden variable theories
30.3 Quantum critical
30.3.1 On ‘The moral aspects of quantum mechanics’
30.3.2 On ‘Against measurement’
30.3.3 On Bell’s criticisms of quantum mechanics
30.4 Conceptual ‘problems’ in quantum mechanics
30.4.1 The ‘measurement problem’
30.4.2 Particle–wave duality
30.4.3 Quantum reality
30.4.4 Unnecessary concerns
30.5 Quantum luminaries
30.6 The pragmatic perspective
30.7 The Dirac–Feynman–Lamb doctrine
30.8 The all-important probability amplitude
30.9 The quantumness derived from the nonlocality of the photon
30.10 The best interpretation of quantum mechanics
30.11 Discussion
Problems
References
A.1 Introduction
A.2 Exciting times and extreme succinctness
A.3 Conclusion
References
B.1 Introduction
B.2 The classical interference equation
B.3 The N-slit quantum interference equations
B.4 From quantum interference to classical interference
Problems
References
C.1 Introduction
C.2 Interferometers
C.2.1 The Mach-Zehnder interferometer
C.2.2 The Michelson interferometer
C.2.3 The Sagnac interferometer
C.2.4 The N-slit interferometer
C.3 Beam splitter matrices and Dirac’s bra ket notation
C.3.1 The beam splitter and the Hadamard gate
C.3.2 The Hanbury Brown-Twist interferometer
C.3.3 The HOM interferometer
Problems
References
D.1 Introduction
D.2 Wave plates
D.3 Rhomboid polarization rotators
D.4 Multiple-prism collinear polarization rotators
Problems
References
E.1 Introduction
E.2 Vector basics
E.3 Vector products
E.3.1 Dot product
E.3.2 Cross product
E.3.3 The ket bra product
E.3.4 Vector direct product
E.3.5 Vector outer product
E.4 Matrix algebra
E.4.1 The identity matrix
E.4.2 The inverse matrix
E.4.3 Matrix determinant and trace
E.4.4 Eigenvalues and eigenvectors
E.5 Unitary matrices
E.6 The tensor product
E.7 Equivalence in vector notation for entangled polarizations
Problems
References
F.1 Trigonometric identities
Problems
References
G.1 Introduction
G.2 Certainly not classical
G.3 Multiplication of probability amplitudes
G.4 On the Dirac identity for quantum entanglement
References
H.1 Introduction
H.2 From quantum interference to generalized diffraction
H.3 From generalized diffraction to generalized refraction
H.4 From generalized refraction to reflection
H.5 From quantum interference to Heisenberg’s uncertainty principle
H.6 The cavity linewidth equation
H.7 Generalized multiple-prism dispersion
H.8 Discussion
Problems
References
I.1 Introduction
I.2 Complex conjugates
I.3 Basic quaternion identities
Problems
References
J.1 Introduction
J.2 Planck’s constant
J.3 The fine structure constant
J.4 The extreme weakness of gravity in the quantum domain
J.5 Quantum consciousness
J.6 Fundamental physics constants
Problems
References
Index
ISBN: 978-0-7503-2226-3
Fundamentals of Quantum Entanglement (Institute of Physics, Bristol, 2019) at Amazon
Fundamentals of Quantum Entanglement (Institute of Physics, Bristol, 2019) at IoP
"(|x, y> - |y, x>)... was my first lesson in quantum mechanics, and in a very real sense my last, since all the rest is mere technique, which can be learnt from books" (Ward 2004).
Page 1-3
What's important to highlight is that the derivation of the quantum entanglement probability amplitude, à la Dirac, flows naturally; it is transparent and straightforward.
Page 17-5
Watch talk on Fundamentals of Quantum Entanglement in youtube
1.1 Introduction
1.2 A few words on quantum mechanics
1.2.1 The photon from a quantum perspective
1.3 Ward’s observation
1.4 History of quantum entanglement
1.4.1 The philosophical path
1.4.2 The physics path
1.5 The field of quantum entanglement
1.6 Fundamentals of quantum entanglement
1.7 Intent
References
2.1 Introduction
2.2 Dirac’s pair theory
2.3 Dirac’s notation
2.4 Dirac’s notation in N-slit interferometers
2.5 Semi coherent interference
2.6 From quantum probabilities to measurable intensities
2.7 Dirac’s identities
References
3.1 Introduction
3.2 EPR doubt’s on quantum mechanics
3.3 EPR’s landmark definition of a correct theory
References
4.1 Introduction
4.2 The first Schrödinger paper
4.3 The second Schrödinger paper
References
5.1 Introduction
5.2 Wheeler’s paper significance to quantum theory
5.3 Wheeler’s paper significance to quantum experiments
References
6.1 Introduction
6.2 The Pryce-Ward paper
6.2.1 Theoretical legacy of the Pryce-Ward paper
6.2.2 Experimental legacy of the Pryce-Ward paper
6.3 Ward’s doctoral thesis
6.4 Summary
References
7.1 Introduction
7.2 The quantum entanglement experiment
7.3 Historical notes
References
8.1 Introduction
8.2 The first three quantum entanglement experiments
8.3 Further significance of the annihilation experiments
References
9.1 Introduction
9.2 Significance to the development of quantum entanglement research
9.3 Philosophy and physics
References
10.1 Introduction
10.2 von Neumann’s
10.3 Bell’s theorem or Bell’s inequalities
10.4 An additional perspective on Bell’s theorem
10.5 Example
10.6 More philosophy and physics
References
11.1 Introduction
11.2 Probability amplitudes via Hamiltonians à la Feynman
11.3 Arrival to quantum entanglement probability amplitudes
11.4 Discussion
References
12.1 Introduction
12.2 Salient features
12.3 Bell’s theorem and hidden variables
References
13.1 Introduction
13.2 Testing for local hidden variable theories
13.3 Early optical experiment
13.3 Observations and discussion
References
14.1 Introduction
14.2 The Aspect experiments
14.2.1 The first Aspect experiment
14.2.2 The second Aspect experiment
14.2.3 The third Aspect experiment
14.3 Observations and discussion
References
15.1 Introduction
15.2 The quantum entanglement probability amplitude 1947-1992
15.3 Observations and discussion
References
16.1 Introduction
16.2 The GHZ probability amplitude
16.3 Observations and discussion
References
17.1 Introduction
17.2 The meaning of the Dirac-Feynman probability amplitude
17.3 The derivation of the quantum entanglement probability amplitude
17.4 Identical states of polarization
17.5 Discussion
References
18.1 Introduction
18.2 The quantum entanglement probability amplitude for n = N = 4
18.3 The quantum entanglement probability amplitude for n = N = 8
18.4 The quantum entanglement probability amplitude for n = N = 16
18.5 The quantum entanglement probability amplitude for n = N = 21 22, 23… 2r
18.6 Discussion
References
19.1 Introduction
19.2 The quantum entanglement probability amplitude for n = N = 3
19.3 The quantum entanglement probability amplitude for n = N = 6
19.4 Discussion
References
20.1 Introduction
20.2 Reversibility: from entanglement to interference
20.3 Schematics
20.4 Experimental and theoretical perspectives
20.4.1 Experimental perspective
20.4.2 Theoretical perspective
20.5 Interference for N slits and n = 1
References
21.1 Introduction
21.2 Probability amplitudes
21.3 Quantum polarization
21.4 Quantum probabilities and Bell’s theorem
21.5 Example
21.6 Discussion
References
22.1 Introduction
22.2 Measurement protocol
22.3 Experimental
References
23.1 Introduction
23.2 The mechanics of teleportation
23.3 Technology
References
24.1 Introduction
24.2 Entropy
24.3 Qbits
24.4 Quantum entanglement and Pauli matrices
24.5 Pauli matrices and quantum entanglement
24.6 Quantum gates
24.6.1 Pauli gates
24.6.2 The Hadamard gate
24.7 The Hadamard matrix and quantum entanglement
24.8 Multiple entangled states
24.9 Technology
References
25.1 Introduction
25.2 Free-space configurations
25.3 The space-to-Earth experiment
25.4 Further horizons
References
26.1 Introduction
26.2 The generalized N-slit quantum interference equations
26.3 The generation and transmission of interferometric characters
26.4 The inherent quantum security mechanism
26.5 Discussion References
27.1 Introduction
27.2 Positron-electron annihilation
27.3 Atomic Ca emission
27.4 Type I parametric down conversion
27.5 Type II spontaneous parametric down conversion
27.6 Further horizons
References
28.1 Introduction
28.2 Consequences of the EPR paper
28.3 Hidden variable theories
28.4 The perspectives of EPR and Schördinger
28.5 Indistinguishability and Dirac’s identities
28.6 Photon non-locality
28.7 Discussion
References
29.1 Introduction
29.2 Quantum critical
29.2.1 On “The moral aspects of quantum mechanics”
29.2.2 On “Against ‘measurement’’
29.3 Pragmatic perspective
29.4 Fundamental principles
29.5 The Dirac-Feynman-Lamb doctrine
29.6 The importance of the probability amplitude
29.7 The best interpretation of quantum mechanics
29.8 Discussion
References
A.1 Introduction
A.2 EPR and the Uncertainty Principle
A.3 Conclusion
References
B.1 Introduction
B.2 Exciting times and extreme succinctness
B.3 Conclusion
References
C.1 Introduction
C.2 The classical interference equation
C.3 The N-slit quantum interference equations
C.4 The difference between classical and quantum interference
References
D.1 Introduction
D.2 Interferometers
D.2.1 The Mach-Zehnder interferometer
D.2.2 The Michelson interferometer
D.2.3 The Sagnac interferometer
D.2.4 The N-slit interferometer
D.3 Beam splitter matrices
References
E.1 Introduction
E.2 Wave plates
E.3 Rhomboids and prismatic rotators
References
F.1 Introduction
F.2 Vector products
F.2.1 Dot product
F.2.2 Cross product
F.2.3 Density matrix
F.2.4 Vector direct product
F.2.5 Vector outer product
F.2.6 Kronecker product or tensor product
F.3 Equivalence in vector notation for entangled polarizations
References
G.1 Trigonometric identities
H.1 Introduction
H.2 Certainly not classical
H.3 Multiplication of probability amplitudes
References
I.1 Introduction
I.2 From quantum interference to generalized diffraction
I.3 From generalized diffraction to generalized refraction
I.4 From generalized refraction to reflection
I.5 From quantum interference to Heisenberg’s uncertainty principle
I.7 The cavity linewidth equation
I.6 Generalized multiple-prism dispersion
I.8 Discussion
References
J.1 Introduction
J.2 Basic quaternion identities
References
Fundamentals of Quantum Entanglement: corrigendum
Page published on the 12th of October, 2019
Updated on the 24th of September, 2022