What is spin?

Thomas Pope and Werner HoferSchool of Chemistry

Newcastle University

Web: wernerhofer.eu

Email: werner.hofer@ncl.ac.uk1

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• Introduction

Overview

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• Introduction

• Standard model

Overview

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• Introduction

• Standard model

• Spin in extended electrons

Overview

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• Introduction

• Standard model

• Spin in extended electrons

• Conclusions

Overview

Introduction

A simple question:

How do electrons actually work?

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Standard theory:

Electrons are objects in mathematical space(same status as wavefunctions or spins)

Electrons have properties only in distinct experimentsElectrons are not material objects

Alternative theory:

Electrons are objects in real space(wavefunctions contain physical objects)

Electrons have physical properties at all timesElectron properties change in experiments

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Introduction

August 11, 1997 August 5, 1997

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Introduction

2002

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Introduction

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2011

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Introduction

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2011 2012

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Introduction

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2011 20122012

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Introduction

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2011 20122012 2014

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Introduction

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2011 20122012 20142017

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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?

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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?

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Standard Model

Stern-Gerlach experiments:Silver atoms, with no orbital magnetic moment, are deflected by magnetic fields in Stern-Gerlach experiments1

1. Walter Gerlach and Otto Stern (1922)

This is due to the spin of the outer electron

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Standard Model

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?

What is spin?

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Standard Model

Pauli Matrices

Spin is modelled with the help of Pauli Matrices:

With corresponding eigenvectors for the eigenvalues +/-1:

Which act on spinors:

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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.

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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

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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 distance2. Penrose interpretation: link between quantum effects and spacetime

curvature3. Copenhagen Interpretation: there is no causality in physics, so not really a

problem4. De Broglie-Bohm approach: wavefunctions change instantaneously, and over

arbitrary distances, if experimental conditions change5. Everett: every measurement leads to a different universe6. Dowe: backwards causation7. … 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

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In the EPR thought experiment1 , 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 chosenmeasuring the first?

Standard Model

The Einstein-Podolsky-Rosen problem:

1. Albert Einstein, Boris Podolsky and Nathan Rosen, Physical Review 47, 777 (1935)

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Geometric algebraIn three space dimensions, in geometric algebra the three directions are described by three perpendicular unit vectors, e1, e2, e3. 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=e1e2e3

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.

Extended electrons

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Extended electrons

Spin densities and wavefunctions

The electron has field components, eE and eH that are perpendicular to the vector of motion, ev, and one another.

Because eHeE=-eEeH, 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:

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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

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Extended electrons

Stern-Gerlach experiments

In a magnetic field, the direction of the spin vector changes:

Modified Landau Lifschitzequation

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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

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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.

• 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.

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Extended electrons

Advantages

Thomas Pope, Werner Hofer, Spin in the extended electron model,Frontiers of Physics 12, 128503 (2017)

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The Real Quantum Revolution

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The Real Quantum Revolution

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The Real Quantum Revolution:Published in Chinese and English 2018

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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.

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The Real Quantum Revolution:Review

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The Real Quantum Revolution:Review

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Thank you!