--------- #1409 - Equations that Affect Your World ?
- Attachments : E = mc^2
- Equations are observations that are put in mathematical terms. Equations are discoveries. Math is an invention, a powerful invention. Equations allow you to predict accurately future results. Equations are used in the design of most all the technology around you from GPS, computers, cell phones, earthquakes studies, satellites, telescopes, radar, ….. etc.
- It all starts with a mathematical derivation of an observation. The ancient Greeks were fascinated by observing a violin string. They discovered that the string’s vibrations up and down varies with the strengths length and tension. When two strings have lengths equal to the simple ratios, like 2:1 , 3:2, they produced a harmonious tone together.
- In 1727 a mathematical discovery was made that the simplest shape for a vibrating string was the sine wave. If a sine curve fits in the length of the string it produces a harmonious tone.
- In 1747 an elegant equation was discovered that describes how the shape of the vibrating string changes over time. It is called the WAVE EQUATION. It defines the acceleration of any small segment of the string to be proportional to the tension on the strength.
- Today the same wave equations are used to analyze complex waves such as earthquakes. Using these equations seismologists can map the Earth’s tectonic plates far beneath the ground.
- In 1850 Maxwell took the wave equations a step further and applied them to electromagnetic waves.
- In 1830 Faraday established the basics physics of electromagnetism. In 1850 MAXWELLS EQUATIONS formulated the math for Faraday’s theories. Faraday had postulated that electricity and magnetism were not “forces” like gravity was thought to be, but, were “fields” . Fields pervade space and change over time and can be detected by the forces they in turn produce. Maxwell took Faraday’s magnetic field lines and treated them as mathematical fluid flow. In 1914 he published his 4 equations that defined electromagnetic wave behavior. His equations stated that an electric field created by a moving charge created a magnetic field and a magnetic field in turn created an electric field.
- One amazing result fell out of his equations He recognized that one of the terms was the speed of light squared. The reciprocal of magnetic permeability and electric permittivity of free space was the speed of light squared, 9 * 10^16 meters^2 / second^2. He therefore concluded that light was an electromagnetic wave. ( The velocity of light is 3*10^8 meters / second. Squared it is 9*10^16)
- A further discovery from his equations was that there was no limit to the length of wavelengths. There must be electromagnetic radiation with longer and shorter wavelengths than light. The colors were wavelengths from 400 nanometers to 700 nanometers, blue to red. Longer wavelengths were soon discovered to be radio waves. Maxwell predicted the whole electromagnetic spectrum existed long before it was discovered.
- In 1887 the first radio transmission was demonstrated. Tesla and Marconi discovered how to put a signal on the wave and introduced modern radio communications. The same equations are used to design the cell phones of today.
- Maxwell’s equations for waves ran into conflict with photoelectric effect experiments. Equations to describe how a light shines on a metal and create an electric current required the light to act as a particle , not as a wave.
- In 1927 SCHRODINGER’S EQUATIONS wrote down the concept of particle - wave duality and he called them Quantum Waves. Schrodinger’s equations required fundamental particles such as an electron to be a “ probability cloud”., both a particle and a wave at the same time. In his concept an electron had a clockwise spin and a counter-clockwise spin at the same time until it hit something or was detected when it became one or the other. But, you did not know which it was until it was detected. This generated weirdness in which cats were both dead and alive at the same time. Or, there existed a parallel Universe where Hitler won the second world war.
- Modern technology today relies on this weirdness in order to predict behavior and to design new technology that works in the real world. It is called Quantum Mechanics. It is math equations that are used in designing computers, cell phones, memory chips, even memory dots called Quantum Dots that are used in biological imaging. ( See a future review on this topic). New applications are busy creating reality out of Quantum Mechanic’s weirdness. Lasers and Quantum Computing are today using wave equations and probability clouds in order to progress their designs.
- Another aspect of wave analysis started in 1807 when Fourier derived an equation for heat flow. How temperature changes over along thin rod. FOURIER EQUATIONS solved this behavior by representing a complex heat wave as a combination of simple sine waves with different wavelengths. He proved that “any” continuous wave cold be written as a infinite series of sine waves. Fourier did not get much recognition in mathematical circles because his equations involved and “infinite series“. Math does not like infinity. He finally got recognition with his FOURIER TRANSFORM. An equation that transforms a time- varying signal into a sine wave of specific amplitude and frequencies. It allowed a transformation from the time domain to the frequency domain, and vice versa.
- Today these same equations are used to earthquake-proof buildings. Engineers make sure the resonant frequencies of the building’s oscillations are different that the earthquakes wave frequencies. You do not want harmonics. Harmonics can bring down buildings and bridges. Another use of Fourier transforms is how your cell phone crams 10 times as much data into your digital camera memory card. ( JPEG data compression).
- There two equations in our world we would really like to unify. RELATIVITY EQUATIONS and QUANTUM MECHANICS EQUATIONS Relativity works on the macro world and Quantum Mechanics works in the micro world. But, neither works in the other’s world. We are missing something? I will bet it ends up being another equation. An announcement will be made shortly, stay tuned.
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707-536-3272, Thursday, February 16, 2012
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