Einstein s Theory Relativistic 0 < v < c. No Absolute Time. Quantization, Zero point energy position & momentum obey Heisenberg uncertainity rule

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1 Lecture: March 27, 2019 Classical Mechanics Particle is described by position & velocity Quantum Mechanics Particle is described by wave function Probabilistic description Newton s equation non-relativistic v << c Einstein s Theory Relativistic 0 < v < c No Absolute Time Schrodinger s equation non-relativistic v << c Dirac Theory Relativistic 0 < v < c Quantization, Zero point energy position & momentum obey Heisenberg uncertainity rule Electrons have spin, have anti-particle and vacuum is complicated TWO QUESTIONS: (1) Why we NEED quantum physics??? World we live in is very different from the world our grand parents lived. Science that led to all new discoveries like computers, cell phones are all rooted in quantum theory. At fundamental level, we we need quantum physics to explain observations such as (a) radiations coming from hot objects, (b) photo-electric effect (c) Compton effect (d) Atomic spectrum (e) Stability of atom 1

2 (f) Zero point energy (g) Radioactivity (1)Why do we need equations describing particles close to speed of light?? (a) Although both in classical and quantum world, most particles ( including particles like electrons inside the atom ) move very slowly compared to speed of light, particles in cosmic rays that come from outer space move close to speed of light. Also, there are experiments in the laboratory where scientist study collision between particles that move close to speed of light. (b) Very high precision measurements require talking relativistic effects small corrections. Note that even though electrons in the atom move with speed that is one percent the speed of light, there are small corrections to Bohr energy levels ( called fine structure of levels ) due to this and high precision measurement can measure this. Dirac Equation continued... Dirac wave function has four components. What does it Mean??? An electron can exist in four different forms (1) Electron with spin up, (2) Electron with spin down, (3) Electron with positive charge ( now called positron) with spin up and, (4) Positron with spin down. SUMMARY of predictions of Dirac Equation (1) Electrons have spin- an intrinsic degree of freedom. It emerges if we impose basic symmetries of Nature. In other words, Dirac theory does not require electron to be a spinning top. 2

3 It has some intrinsic character that make it behave as if it is spinning (2) Electrons have partners- anti-particles- particles that are exactly like electrons but have positive charge. When electrons and positrons collide, the annihilate each other, creating photons ( x-rays). At that time, No such particles have been known. (3) Electrons act like little magnets whose strength is characterized by what is known as the g-factor. Dirac predicted that g = 2 and this was in agreement with the experiment. (4) Fine structure of atomic spectra (5) Vacuum is very complicated ( WE WILL NOT DISCUSS THIS). POSITRON DISCOVERY Carl David Anderson was an American physicist who discovered positron in 1932, an achievement for which he received the 1936 Nobel Prize in Physics. At the time of his discovery, he did not know Dirac s prediction. Anti-Matter It is believed that in the early part of the universe, there were equal number of particles and their antiparticles. Why, no antiparticles left in the universe is a mystery. What about neutral particles?? It turns out that they also have an anti-particle, which for fermion is different from particle in other properties..like there is anti-neutron and anti-neutrino which are different from neutron and neutrino. Quantum Field Theory (QFD) The Ultimate Theory of Quantum Particles < Firstly, trying to picture electron as a wave causes lot of headaches... These waves are clearly not ordinary waves they are not like ripples on the surface of water... Despite all this, Schödinger wave theory has been very successful. However, at end of 1920, physicist realized that it told only part of the truth... 3

4 (a) It only describes how particles move. It does describe correctly how particles interact and in particular, It cannot handle physics when particles are created and destroyed. Like, when electron and positron annihilate each other, creating photons... (b) Physicist Rabi s precise measurement of g-factor showed that g is ONLY APPROXIMATELY equal to 2. He found the g value to be equal to g = He know the precise error bars of his experiment and was certain that g equal to 2 is only an approximation. Dirac equation also pointed towards such problems... This led to the notion of Quantum Fields. In this description, instead of talking about particles, one talks about quantum fields. That is, when you think of electrons, you think about some field associated with it that pervades the entire space, like the electric, the magnetic field or the gravitational field. QFD treats particles as excited states, also called quanta, of their underlying fields, which are in a sense more fundamental than the basic particles. WHAT IS QED??? Richard Feynman called it the jewel of physics for its extremely accurate predictions of quantities like the the g-factor of the electron. This explained the fine structure of H-spectrum known as and the Lamb shift. In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons. However, as Feynman points out, it fails totally to explain why particles such as the electron have the masses they do. There is no theory that adequately explains these numbers. We use the numbers in all our theories, but we don t understand them what they are, or where they come from. I believe that from a fundamental point of view, this is a very interesting and serious 4

5 problem. FEYNMAN DIAGRAM Interactions between particles can be visually represented by Feynman diagrams. Creation and destruction of particles is adding or removing quanta from the field. Earlier versions of quantum field theory had lot of problems... like infinity occurs due to electrons interacting with its own electromagnetic field... Then physicists realized that this problem can be solved and theory provides a new way to understand forces between two particles... like repulsion between two electrons. 5

6 In 1932, Bethe and Fermi suggested that repulsion between two electrons is due to exchange of photons between two electrons. These photon cannot be observed and are called virtual photons. This is wonderful... photon is not only simply the quantum particle of light or electromagnetic waves, it is the carrier of the electromagnetic force. QED & Nobel Prize Three physicists independently developed the complete theory of QED the quantum electrodynamics. They are two American physicists Richard Feynman and Julian Schwinger and Japanese physicist Sin-Itiro Tomonaga. Interestingly, these theories that on the surface looked very different were shown to be equivalent by Freeman Dyson. These 3 physicists shared Nobel prize in Let us understand this using Feynman s way... Imagine two electrons interacting, shown with the Feynman diagram... The wavy line shows the exchange of photons between this. This is a way to describe the interaction between two electrons. Electron also interacts with its own electromagnetic field. This corresponds to electron absorbing a photon. if you take this second diagram and calculate the magnetic moment of the electron, it gives the g-factor equal to 2. Now comes the real magic: If we add more photons, it increases the value of this g-factor. More photons you add, bigger the g gets, but this increase occurs at higher decimal places. Roughly, to with every decimal place, you add another photon... Well, this way, you can predict g to as many decimal places as you like. Here is the ultimate test of the theory: g = measured in the experiment. And every decimal place is predicted correctly by the theory... 6

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