The First 100 Years of Quantum Physics Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College

Wave-Particle Duality The First 100 Years of Quantum Physics Wave-Particle Duality Light as Particles Particles as Waves Quantum Interference Lecture 3 Wave-Particle Duality Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College

Wave-Particle Duality The First 100 Years of Quantum Physics Light As Particles Where did things stand in 1920? Atoms were understood to consist of small heavy nuclei surrounded by electrons. Absorption and emission of light was understood to involve discrete energy wave packets obeying the formula E = hf = hc/λ. The particle nature of light itself was still a matter of considerable doubt to most physicists. Lecture 3 Wave-Particle Duality By 1920, Quantum Theory had become a baroque assortment of primitive atomic models and heuristic rules. To the Prussian Academy of Sciences: I heartily recommend Herr Einstein for Academy membership although … “he might sometimes have overshot the target in his speculations, as for example in his light quantum hypothesis…” Max Planck, 1913 Einstein was one of the few who believed in the fundamental particle nature of light. Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College

Wave-Particle Duality The First 100 Years of Quantum Physics Wave - Particle Duality Momentum: Energy: Lecture 3 Wave-Particle Duality Wavelength: Frequency: Einstein – Planck: Light (electromagnetic waves) behave, when emitted or absorbed, as particles (photons). De Broglie: Particles (electrons, etc.) behave, while in motion , as waves. Generally, high energy and momentum correspond to small wavelengths and large frequencies. Momentum: Wavelength: Energy: Frequency: Technical note: A particle’s total energy is given by the relativistic formula . A photon has no mass, so the relationship between its momentum and energy is Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College

Wave-Particle Duality The First 100 Years of Quantum Physics Wave - Particle Duality The Compton Effect (1923) Lecture 3 Wave-Particle Duality In 1923, Arthur Holly Compton demonstrated that light acted in collisions exactly as particles. Derived from the relativistic mechanics of particles, not waves. Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College

Wave-Particle Duality The First 100 Years of Quantum Physics Wave - Particle Duality The Compton Effect (1923) Lecture 3 Wave-Particle Duality In 1923, Arthur Holly Compton demonstrated that light acted in collisions exactly as particles. Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College

Wave-Particle Duality The First 100 Years of Quantum Physics Wave - Particle Duality Wave Interference Lecture 3 Wave-Particle Duality Constructive Interference How can de Broglie’s hypothesis be tested? Use a unique property of waves called “interference”. Destructive Interference Wave interference Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College

Wave-Particle Duality The First 100 Years of Quantum Physics Wave - Particle Duality Two slit interference of water waves Lecture 3 Wave-Particle Duality All waves show interference phenomena. Open 1 & 2 Close slit 2 Close slit 1 Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College

Wave-Particle Duality The First 100 Years of Quantum Physics Are Photons Particles or Waves? Lecture 3 Wave-Particle Duality Interference of light has been used for more than three hundred years as evidence that light is a wave phenomenon. Interference generated by photons – one photon at a time Photons don’t interfere with each other – they interfere with themselves! Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College

Wave-Particle Duality The First 100 Years of Quantum Physics Are Electrons Waves or Particles? Two-slit non-interference of particles Lecture 3 Wave-Particle Duality Particles do not interfere when emitted and detected singly and independently. Electrons do interfere even when emitted and detected singly and independently. 28 e- 104 e- Electron Double-Slit Experiment Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College

Wave-Particle Duality The First 100 Years of Quantum Physics Electrons as Waves Lecture 3 Wave-Particle Duality Davisson and Germer were the first to detect electron interference experimentally. Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College

Wave-Particle Duality The First 100 Years of Quantum Physics Wave - Particle Duality Lecture 3 Wave-Particle Duality Diffraction patterns are the same for light and for electrons; intensities may vary. After all, light is light and electrons are electrons. X-Ray Diffraction Electron Diffraction Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College

Wave-Particle Duality The First 100 Years of Quantum Physics Wave - Particle Duality Anton Zeilinger, et al. Lecture 3 Wave-Particle Duality All atomic sized and smaller particles exhibit quantum interference in double-slit and similar experiments. Neutron double-slit interference Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College

The Uncertainty Principle The First 100 Years of Quantum Physics The Uncertainty Principle Minimum Interference Compatible and Incompatible Observables Quantum States and Quantum Causality Lecture 4 The Uncertainty Principle Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College

The Uncertainty Principle The First 100 Years of Quantum Physics Uncertainty Principle Lecture 4 The Uncertainty Principle Werner Heisenberg Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College

The Uncertainty Principle The First 100 Years of Quantum Physics Uncertainty Principle Lecture 4 The Uncertainty Principle X position X momentum p = mv The uncertainty principle relates to the uncertainties in pairs of quantities. x Δp p Δx Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College

The Uncertainty Principle The First 100 Years of Quantum Physics Quantum States State of a Single ‘Free’ Particle in Three Dimensions y Lecture 4 The Uncertainty Principle px py pz p The motion of a particle is described by a complete set of independent quantities, called observables. x z Observables In classical physics, the state of the particle is established by knowing the values of all the independent observables. Position variables: x, y and z Independent observables Momentum variables: px, py and pz Energy, angular momentum, etc. Derived observables Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College

The Uncertainty Principle The First 100 Years of Quantum Physics Quantum States The Classical Doctrine of Determinism Lecture 4 The Uncertainty Principle “We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.” Pierre-Simon Laplace (1814) Classical physicists thought the universe was like a watch. Wind it up and let it go according to predetermined cause and effect as codified in Newton’s Laws. Pierre-Simon Laplace Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College

The Uncertainty Principle The First 100 Years of Quantum Physics Quantum States State of a Single ‘Free’ Particle in Three Dimensions y Lecture 4 The Uncertainty Principle px py pz p Classical physicists thought the universe was like a watch. Wind it up and let it go according to predetermined cause and effect as codified in Newton’s Laws. x z Newton’s Laws + Initial values of all independent variables + Exact knowledge of all forces  Precise knowledge of the future Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College

The Uncertainty Principle The First 100 Years of Quantum Physics Quantum States State of a Single Particle y Lecture 4 The Uncertainty Principle F py p px Classical physicists thought the universe was like a watch. Wind it up and let it go according to predetermined cause and effect as codified in Newton’s Laws. pz x z Classical Causality - Determinism Newton’s Laws + Initial values of all independent variables + Exact knowledge of all forces  Precise knowledge of the future Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College

The Uncertainty Principle The First 100 Years of Quantum Physics Quantum States Time Out for Some Basic Physics Lecture 4 The Uncertainty Principle Sorry, but we really do have to do this. We need to know how energy momentum angular momentum are defined. Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College

What is momentum? Momentum is the mechanical influence of a moving object. What do you mean by that? The more momentum a moving object has, the more it can affect anything it hits. How much momentum does a moving body have? If m is its mass and v is its velocity, then momentum = m x v. What happens to momentum? It is always conserved in a force-free environment, but is often transferred from one body to another.

What is angular momentum? Angular momentum is the mechanical influence of a rotating object. What do you mean by that? A rotating or spinning object can share angular momentum with other objects. How much angular momentum does a spinning body have? The amount is a function of the structure and size of the body, but it depends upon its mass and is proportional to the rate of rotation (frequency or angular velocity.) What happens to angular momentum? It is always conserved in a force-free environment, but is often transferred from one body to another.

What is energy? Energy is the ability to do work. What is work? Work is done when a force is exerted through a distance. F d How much work is done? If F is the force and d is the distance, Work = F x d. What happens to energy? It is always conserved but often changes from one form to another.

What forms of energy are there? There is energy of motion, called kinetic energy. How much kinetic energy does an object have? If an object of mass m has velocity v, it has kinetic energy equal to ½mv2 = p2/2m What other forms of energy are there? There is heat energy, which is really the kinetic energy of atoms and molecules all together in a substance. Are there other forms of energy? Yes. All other forms are called potential energy because it is stored up and waiting to be turned into kinetic energy or other forms of potential energy.

What are some examples of potential energy? There is gravitational potential energy. If you hold an object up, it has gravitational potential energy. If you drop it, the force of gravity acts to convert the gravitational potential energy to kinetic energy. Potential energy seems to be associated with forces. Is there electrical potential energy? Yes, and magnetic potential energy, too. Electrical charges move under the action of the forces each exerts on the other and magnets do the same. How about elastic forces, like in rubber bands or springs? They are really electrical forces between atoms and molecules. Stretched springs have potential energy.

Are all forms of energy kinetic or potential? According to classical physics, yes. But I showed that mass is also a form of energy. What kind of energy is mass? It is sort of a potential energy, but not due to force fields like gravitational or electrical energy are. What do you mean? An object of mass m that is not moving and not in a force field still has an energy equal to mc2, where c is the speed of light. If it is moving with speed v, its total energy is

A very important point! In addition to these definitions of dynamical physical quantities, we have also learned three key conservation laws: 1. Conservation of momentum 2. Conservation of angular momentum 3. Conservation of energy Each of these conservation laws is due to a fundamental symmetry in nature. These symmetries play vital roles in Quantum Mechanics.

Conservation of momentum is a direct consequence of the irrelevance to physical laws of where you place the origin of spatial coordinates. Conservation of angular momentum is a direct consequence of the irrelevance to physical laws to how you orient the spatial coordinate axes. Conservation of energy is a direct consequence of the irrelevance to physical laws to how you set your clock.

The Uncertainty Principle The First 100 Years of Quantum Physics Quantum States Classical states are described by specifying all possible independent quantities. Quantum states are specified by the values of a maximal set of compatible observables. Lecture 4 The Uncertainty Principle Example: For a single free particle - Compatible observables are those which do not share an uncertainty principle. Example: For a single free particle - Incompatible observables are not both knowable to arbitrary accuracy. but not - incompatible observables Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College Incompatible pairs: {x, px}, {y, py}, {z, pz}

The Uncertainty Principle The First 100 Years of Quantum Physics Quantum States Example: Hydrogen Atom Lecture 4 The Uncertainty Principle It is most often useful to take as state defining observables those which are conserved. Quantum Numbers A complete set of compatible observables: Energy (n) Total angular momentum squared (ℓ) One (any) component of angular momentum (μ) Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College

The Uncertainty Principle The First 100 Years of Quantum Physics Quantum States The End of Determinism Lecture 4 The Uncertainty Principle “…In the strong formulation of the causal law: ‘If we know exactly the present, we can predict the future,’ it is not the conclusion but rather the premise which is false. We cannot know, as a matter of principle, the present in all its details.” W. Heisenberg Quantum physics says that the future is not exactly predictable because of the fundamental inability to determine the present . Werner Heisenberg Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College

Next: Wave Functions and Probability – the New Causality The First 100 Years of Quantum Physics The Emeritus College http://www.emerituscollege.asu.edu Next: Wave Functions and Probability – the New Causality rjjacob@asu.edu http://www.public.asu.edu/~rjjacob/courses.html Dr. Richard J. Jacob Professor Emeritus of Physics Arizona State University The Emeritus College