What is spin? Thomas Pope and Werner Hofer. School of Chemistry Newcastle University. Web: wernerhofer.eu

Transcription

1 What is spin? Thomas Pope and Werner Hofer School of Chemistry Newcastle University Web: wernerhofer.eu 1

2 Overview Introduction 2

3 Overview Introduction Standard model 3

4 Overview Introduction Standard model Spin in extended electrons 4

5 Overview Introduction Standard model Spin in extended electrons Conclusions 5

6 Introduction A simple question: How do electrons actually work? Standard theory: Alternative theory: Electrons are objects in mathematical space (same status as wavefunctions or spins) Electrons have properties only in distinct experiments Electrons are not material objects Electrons are objects in real space (wavefunctions contain physical objects) Electrons have physical properties at all times Electron properties change in experiments 6

7 Introduction August 11, 1997 August 5,

8 Introduction

9 Introduction

10 Introduction

11 Introduction

12 Introduction

13 Introduction

14 Introduction David Mermin (1989): If I were forced to sum up in one sentence what the Copenhagen Interpretation says to me it would be: Shut up and calculate! How does an electron actually work? How does a point-like electron interact with a point-like photon? Why does the electron change its wavelength when it changes its velocity? Why does the hydrogen electron not fall into the nucleus? How does spin, which is isotropic, become a magnetic moment, which is a vector, in a Stern-Gerlach experiment? Why are photon experiments at two polarizers fully correlated when they are random at single polarizers? 14

15 Introduction David Mermin (1989): If I were forced to sum up in one sentence what the Copenhagen Interpretation says to me it would be: Shut up and calculate! How does an electron actually work? How does a point-like electron interact with a point-like photon? Why does the electron change its wavelength when it changes its velocity? Why does the hydrogen electron not fall into the nucleus? How does spin, which is isotropic, become a magnetic moment, which is a vector, in a Stern-Gerlach experiment? Why are photon experiments at two polarizers fully correlated when they are random at single polarizers? 15

16 Standard Model Stern-Gerlach experiments: Silver atoms, with no orbital magnetic moment, are deflected by magnetic fields in Stern-Gerlach experiments 1 This is due to the spin of the outer electron 1. Walter Gerlach and Otto Stern (1922) 16

17 Standard Model What is spin? Spin is a vector: Spin is affected by a magnetic field, therefore it has the properties of a magnetic moment, therefore it is a vector. Spin is isotropic: The results of the Stern-Gerlach experiment are the same if the magnetic field is rotated, therefore spin is isotropic, therefore it is not a vector. Problems: How can spin be isotropic before the measurement? How does spin become a vector in the measurement? 17

18 Standard Model Pauli Matrices Spin is modelled with the help of Pauli Matrices: With corresponding eigenvectors for the eigenvalues +/-1: Which act on spinors: 18

19 Standard Model Stern-Gerlach experiments explained When the spin of this particle is measured with respect to a given axis, a=x, y, z, the probability that a spin of ±1/2 will be measured is, Spin can have one of two values because the Pauli matrices span the space of observables of the 2-dimensional Hilbert space. The wavefunction collapses on the eigenvector, which leads to the two trajectories in the Stern-Gerlach experiments. 19

20 Standard Model Consecutive measurements If a new measurement is performed on axis b, the probability of measuring the same spin value is, and the probability of measure the opposite spin value is, This is due to the non-commutativity of the Pauli matrices 20

21 Standard Model Problem with this explanation: No physical explanation what a collapse of the wavefunction actually means, therefore a host of theoretical speculation in terms of mathematical models: 1. Ghirardi-Rimini-Weber model: wavefunction amplitudes change with distance 2. Penrose interpretation: link between quantum effects and spacetime curvature 3. Copenhagen Interpretation: there is no causality in physics, so not really a problem 4. De Broglie-Bohm approach: wavefunctions change instantaneously, and over arbitrary distances, if experimental conditions change 5. Everett: every measurement leads to a different universe 6. Dowe: backwards causation 7. many more attempts to solve the measurement problem Missing: a physical model which determines the cause of a particular trajectory in a Stern-Gerlach experiment 21

22 Standard Model The Einstein-Podolsky-Rosen problem: In the EPR thought experiment 1, a source emits an electron pair. Two measurements are performed, which depend on one another. Because of the non-commutativity of the Pauli matrices: measurements performed on the same axis are correlated measurements performed on different axes are uncorrelated Problem: How does the second electron know what axis was chosen measuring the first? 1. Albert Einstein, Boris Podolsky and Nathan Rosen, Physical Review 47, 777 (1935) 22

23 Extended electrons Geometric algebra In three space dimensions, in geometric algebra the three directions are described by three perpendicular unit vectors, e 1, e 2, e 3. Multiplying vectors is anti-commutative and gives a so-called bivector, which is a two-dimensional area: Multiplying all 3 vectors together gives a pseudoscalar, which is equal to the imaginary unit: i=e 1 e 2 e 3 Multiplying a vector with a pseudoscalar gives the bivector composed of the two other unit vectors: The algebra of unit vectors in geometric algebra is the same as the algebra of Pauli matrices. 23

24 Extended electrons Spin densities and wavefunctions The electron has field components, e E and e H that are perpendicular to the vector of motion, e v, and one another. Because e H e E =-e E e H, we define the spin unit vector, which is parallel or antiparallel to the vector of motion, The electron is described by a wavevector in three dimensional space containing mass and spin densities and a spin bivector: 24

25 Extended electrons Spin vectors The spin vector is defined as: Spin is either parallel or antiparallel to the direction of motion The spin vector is contained in the bivector term of the wavefunction Spin is isotropic in relation to rotations in the bivector plane A statistical manifold of equal number spin-up and spin-down electrons is isotropic 25

26 Extended electrons Stern-Gerlach experiments In a magnetic field, the direction of the spin vector changes: Modified Landau Lifschitz equation 26

27 Extended electrons Stern-Gerlach experiments In a magnetic, the direction of the spin vector changes: The induced spin vector, S', is: Stern-Gerlach experiments measure the spin induced by magnetic fields 27

28 Extended electrons Einstein-Podolsky-Rosen experiments The measurements performed today on photons contain rotations of electromagnetic fields in the plane perpendicular to the direction of motion, which are described by a rotor: To account for the two rotations, we take the product of the rotors for each photon: The correlation probability is then: Full agreement with experimental results. 28

29 Extended electrons Advantages Spin has vector properties and is isotropic, Stern-Gerlach experiments are well explained in terms of cause and effect, Anti-commutativity of spin measurements is well understood, No spooky action at a distance in EPR experiments, No need for many worlds or retrocausality. Thomas Pope, Werner Hofer, Spin in the extended electron model, Frontiers of Physics 12, (2017) 29

30 The Real Quantum Revolution 30

31 The Real Quantum Revolution 31

32 The Real Quantum Revolution: Published in Chinese and English

33 The Real Quantum Revolution: Elevator pitch Today, the conventional story in physics is that modern physics was developed by faultless geniuses and that Nature at the atomic scale turns out to be bizarre and incomprehensible. The story told in this book is that modern physics is full of contradictions and logical errors, and that once these errors have been corrected, Nature turns out to be logical, comprehensible, and fairly simple. 33

34 The Real Quantum Revolution: Review 34

35 The Real Quantum Revolution: Review 35

36 Thank you! 36