Crash Course: Quantum Mechanics

Crash Course: Quantum Mechanics

Crash Course: Quantum Mechanics

Introduction

Quantum mechanics is the body of scientific laws that describe the wacky behavior of photons, electrons and the other particles that make up the universe. Quantum mechanics is the branch of physics relating to the very small. It results in what may appear to be some very strange conclusions about the physical world. At the scale of atoms and electrons, many of the equations of classical mechanics, which describe how things move at everyday sizes and speeds, cease to be useful. In classical mechanics, objects exist in a specific place at a specific time. However, in quantum mechanics, objects instead exist in a haze of probability; they have a certain chance of being at point A, another chance of being at point B and so on.

Three revolutionary principles

Quantum mechanics (QM) developed over many decades, beginning as a set of controversial mathematical explanations of experiments that the math of classical mechanics could not explain. It began at the turn of the 20th century, around the same time that Albert Einstein published his theory of relativity, a separate mathematical revolution in physics that describes the motion of things at high speeds. Unlike relativity, however, the origins of QM cannot be attributed to any one scientist. Rather, multiple scientists contributed to a foundation of three revolutionary principles that gradually gained acceptance and experimental verification between 1900 and 1930. They are:

-Quantized properties: Certain properties, such as position, speed and color, can sometimes only occur in specific, set amounts, much like a dial that "clicks" from number to number. This challenged a fundamental assumption of classical mechanics, which said that such properties should exist on a smooth, continuous spectrum. To describe the idea that some properties "clicked" like a dial with specific settings, scientists coined the word "quantized."

-Particles of light: Light can sometimes behave as a particle. This was initially met with harsh criticism, as it ran contrary to 200 years of experiments showing that light behaved as a wave; much like ripples on the surface of a calm lake. Light behaves similarly in that it bounces off walls and bends around corners, and that the crests and troughs of the wave can add up or cancel out. Added wave crests result in brighter light, while waves that cancel out produce darkness. A light source can be thought of as a ball on a stick being rhythmically dipped in the center of a lake. The color emitted corresponds to the distance between the crests, which is determined by the speed of the ball's rhythm.

-Waves of matter: Matter can also behave as a wave. This ran counter to the roughly 30 years of experiments showing that matter (such as electrons) exists as particles.

The uncertainty principle

In 1927, Heisenberg made a major contribution to quantum physics. He reasoned that since matter acts as waves, some properties, such as an electron's position and speed, are "complementary," meaning there's a limit (related to Planck's constant) to how well the precision of each property can be known. Under what would come to be called "Heisenberg's uncertainty principle," it was reasoned that the more precisely an electron's position is known, the less precisely its speed can be known, and vice versa. This uncertainty principle applies to everyday-size objects as well, but is not noticeable because the lack of precision is extraordinarily tiny. According to Dave Slaven of Morningside College (Sioux City, IA), if a baseball's speed is known to within a precision of 0.1 mph, the maximum precision to which it is possible to know the ball's position is 0.000000000000000000000000000008 millimeters.

Onward

The principles of quantization, wave-particle duality and the uncertainty principle ushered in a new era for QM. In 1927, Paul Dirac applied a quantum understanding of electric and magnetic fields to give rise to the study of "quantum field theory" (QFT), which treated particles (such as photons and electrons) as excited states of an underlying physical field. Work in QFT continued for a decade until scientists hit a roadblock: Many equations in QFT stopped making physical sense because they produced results of infinity. After a decade of stagnation, Hans Bethe made a breakthrough in 1947 using a technique called "renormalization." Here, Bethe realized that all infinite results related to two phenomena (specifically "electron self-energy" and "vacuum polarization") such that the observed values of electron mass and electron charge could be used to make all the infinities disappear.

Since the breakthrough of renormalization, QFT has served as the foundation for developing quantum theories about the four fundamental forces of nature: 1) electromagnetism, 2) the weak nuclear force, 3) the strong nuclear force and 4) gravity. The first insight provided by QFT was a quantum description of electromagnetism through "quantum electrodynamics" (QED), which made strides in the late 1940s and early 1950s. Next was a quantum description of the weak nuclear force, which was unified with electromagnetism to build "electroweak theory" (EWT) throughout the 1960s. Finally came a quantum treatment of the strong nuclear force using "quantum chromodynamics" (QCD) in the 1960s and 1970s. The theories of QED, EWT and QCD together form the basis of the Standard Model of particle physics. Unfortunately, QFT has yet to produce a quantum theory of gravity. That quest continues today in the studies of string theory and loop quantum gravity.

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