Symmetry (physics)
Symmetry in physics refers to the principle that the laws governing the universe remain unchanged under various transformations, such as spatial rotations or changes in energy. This concept can be observed in geometric objects that maintain their appearance despite alterations, as well as in the consistent behavior of physical laws across different conditions. The roots of symmetry in physics trace back to ancient Greek philosophy, where thinkers like Pythagoras noted the orderly nature of the cosmos and its relation to geometric shapes. The modern understanding of symmetry played a significant role in the development of quantum mechanics and Einstein's theories of relativity.
Symmetry manifests in various natural forms, such as the spherical shapes of celestial bodies and the intricate designs found in snowflakes and crystals. Additionally, the Fibonacci sequence exemplifies a numerical pattern that appears in nature, illustrating symmetry in growth and structure. Einstein's theories highlighted the symmetry of mass, energy, and motion, particularly through his equation E=mc², which underscores the invariant speed of light regardless of an observer's motion. In quantum mechanics, the concept of supersymmetry posits a relationship between different types of elementary particles, suggesting that every particle has a partner with opposite characteristics. This exploration of symmetry deepens our understanding of the fundamental nature of matter and the universe.
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Symmetry (physics)
Symmetry in physics is the concept that the laws of the universe, the structure of matter, and the forces of nature remain the same even after being subjected to mathematical or physical transformations. This idea can be illustrated in a number of ways. For example, a geometric object may exhibit an orderly appearance that remains constant even if the object is rotated in a different direction. Shapes such as spheres, cubes, and snowflakes follow this pattern. Physical laws also display symmetry as their effects follow specific mathematical patterns and remain constant even if conditions undergo changes in position or energy. The idea of symmetry in nature was first developed by the ancient Greeks who saw evidence of an ordered universe in the "perfection" of geometric shapes. In the modern era, symmetry was a fundamental aspect in developing the laws of quantum mechanics and physicist Albert Einstein's theories of relativity.
Background
The ancient Greeks were one of the first human civilizations to attempt to understand the universe in a scientific manner. They used the word cosmos to describe what they saw as the ordered and harmonious nature of the natural world. In the sixth century B.C.E., the philosopher and mathematician Pythagoras noticed the world around him displayed symmetrical elements, such as the shape of the wings of a butterfly or the patterns found in the designs of gemstones. If symmetry was commonplace on Earth, then the heavens, he reasoned, must also display a symmetrical nature. He argued that instead of the sky being a dome that covered the world, the heavens must be a symmetrical sphere, as must also be Earth, the moon, and other celestial bodies. Pythagoras, and the Greek philosophers who followed him, believed that the symmetry of the cosmos could be observed in the five Platonic solids—geometrical shapes with sides that were perfect polygons. A tetrahedron, for example, had four sides that were triangles, a cube's six sides were squares, an octahedron had eight triangular sides, a dodecahedron had twelve sides that were pentagons, and an icosahedron had twenty triangular sides.
In the seventeenth century, German astronomer Johannes Kepler attempted to build on the ancient Greek idea of a cosmic geometry by trying to find a correlation between the five perfect solids and the six planets known in his time. Kepler believed that each planet moved on the boundaries of one of the five solids and the universe was made up of these nested celestial spheres in a pattern that displayed a divine symmetry. While trying to prove his model of the cosmos correct, however, Kepler could not make the mathematical calculations support his theory. He eventually discarded the notion of perfect celestial spheres and developed his three laws of planetary motion. Although it was not the kind of universal order he set out to prove, Kepler's laws displayed a different form of symmetry in that they applied to the motion of all celestial bodies no matter their size or distance from the sun.
Overview
Symmetry is commonplace in the structure of the natural world. As Pythagoras deduced, Earth and other celestial bodies are sphere shaped, as are other natural formations such as water droplets in clouds. Crystalline structures found in rocks or the intricate patterns of snowflakes display a more complex form of symmetrical pattern. A numerical pattern known as the Fibonacci sequence—named after thirteenth-century Italian mathematician Leonardo Fibonacci—can be observed in many aspects of nature. The sequence is a numerical series in which each number is the sum of the previous two numbers. (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, …). Illustrating this ratio with a series of squares forms a spiral pattern that can be seen in such diverse objects as a seashell, the face of a sunflower, the circulation of a hurricane, and a distant spiral galaxy.
The concept of symmetry in relation to the laws of physics is often attributed to twentieth-century German physicist Albert Einstein and his theories of relativity. Using nothing but thought experiments and observations of the world around him, Einstein deduced that the speed of light remains constant no matter the relative motion of an observer. This means that light will always travel at 186,000 miles per second, even if an observer is moving at a particular speed. That speed will not be added to the speed of light, nor can any form of matter "catch up" to the speed of light. Einstein's famous equation E=mc2—energy (E) is equal to mass (m) times the speed of light (c) squared—is based on the symmetry of mass, energy, and speed. He found that as an object approached the speed of light, its mass increased. With more mass, additional energy would be needed to increase the object's speed, thereby further increasing its mass. As a result, an infinite amount of energy would be needed to reach the speed of light. No matter which variable is changed, the fundamental constructs of the theory remain constant.
Symmetry is also evident in the field of quantum mechanics, the study of subatomic particles. Subatomic particles such as electrons, protons, and neutrons are the fundamental building blocks of matter. Electrons circling the protons in the nucleus of an atom adhere to some of the same laws of physics that planets do in orbiting the sun. These subatomic particles themselves are made of even smaller units called elementary particles. At this level, matter acts in strange ways, seemingly ignoring physical laws that apply to the larger world. Light, which is a form of electromagnetic radiation that moves in waves, exhibits some characteristics associated with the movement of particles, while particles exhibit characteristics of waves. A theory known as supersymmetry suggests that elementary particles exist in a symmetrical relationship with other particles with opposite characteristics. Particles called fermions and bosons are differentiated from each other by units of spin—fermions have spin measured in half units while bosons are measured in whole numbers. Supersymmetry holds that each fermion must have a partner boson and each boson a partner fermion. Scientists who adhere to the theory believe it explains why particles have mass.
Bibliography
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