Chapter 9, 28 Modern Physics Introduction to Relativity and Quantum Physics

Before 1905 Albert Einstein was an unknown 25-year-old clerk in the Swiss patent office. Newton’s laws ruled supreme in the past 200 years. Many people were of the opinions that anything worth discovering in Physics had been discovered.

Two Postulates 1.The principle of relativity: All the laws of physics are the same in all inertial reference frames. 2.The constancy of the speed of light: The speed of light in vacuum has the same value in all inertial frames, regardless of the velocity of the observer or the velocity of the source emitting the light. From these two simple postulates Einstein constructed special relativity and started a revolution in physics.

Relativity 1.Events that are simultaneous for one observer may not be simultaneous for another. 2.When two observers measure a time interval or a length, they may not get the same results. 3.Newton’s Laws and equations for kinetic energy needs to be revised. 4.The equivalence of energy and mass ( E=mc 2 ) 5.Space and time are no longer considered separate entities, and is combined into four-dimensional space-time. 6.Expansion or contraction of the universe. 7.The existence of exotic objects like black holes, worm holes.

Time Dilation Sally Sam

Twins Paradox

Length Contraction

An exploding chicken Calculate the total energy released if a 1kg chicken is converted into energy completely.

Black Holes If the concentration of mass becomes very great, a black hole may form In a black hole, the curvature of space-time is so great that, within a certain distance from its center, all light and matter become trapped

Expansion of Universe The cosmological constant “The greatest blunder of my life.” Einstein

Quantum Mechanics and Planck’s constant (1900) h is the Planck’s constant: All quantum calculations involves h.

Wave Properties of Particles  Louis de Broglie postulated that because photons have both wave and particle characteristics, perhaps all forms of matter have both properties  The de Broglie wavelength of a particle is

Electron Diffraction, Set-Up

Electron Diffraction, cont If the detector collects electrons for a long enough time, a typical wave interference pattern is produced This is distinct evidence that electrons are interfering, a wave-like behavior The interference pattern becomes clearer as the number of electrons reaching the screen increases

Werner Heisenberg 1901 – 1976 Developed matrix mechanics Uncertainty Principle Noble Prize in 1932

The Uncertainty Principle, Introduction In classical mechanics, it is possible, in principle, to make measurements with arbitrarily small uncertainty Quantum theory predicts that it is fundamentally impossible to make simultaneous measurements of a particle’s position and momentum with infinite accuracy The inescapable uncertainties do not arise from imperfections in practical measuring instruments The uncertainties arise from the quantum nature of matter

Schrödinger Equation The (time-independent) Schrödinger equation of a particle of mass m in a potential energy well V(x) is given by: The complex function ψ is called the wave function. It determines the probability of all experimental outcomes.

Wave function and probability

Schrödinger’s Cat