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---------------------- 2303 - Universal Beauty in Symmetry
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- These laws of physics are the same everywhere. With symmetry all frames of reference require the laws of physics to have the same result.
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- The Earth is symmetrical, well almost, if it were a perfect sphere. However, the Earth is 7,929 miles through the equator and 7,904 miles through the poles. 25 miles out of 7,929 is 0.3% distortion from a perfect sphere. With perfect symmetry a sphere looks the same from all directions.
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- Emmy Noether, one of the planet’s smartest mathematicians, in 1918 came up with a Theory of Symmetry which says for every continuous symmetry of the laws of nature, there is a conserved quantity.
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- Noether’s theorem is the math behind the Laws of Conservation of Momentum, the Conservation of Mass and Energy, the Conservation of Electric Charge, the Conservation of Spin, the Conservation of Color in the Strong Force. And, there are still more discoveries in physics to come using her theorem.
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- Following this Review is more on the biography of Emmy Noether and here brilliant theories that changed all of science.
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- In the Universe all directions, places (positions), and times are created equal. This particular invariance is considered to be symmetry in the Universe for space and time and is what Albert Einstein used to deduce the General Theory of Relativity.
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------------- The four forces of nature came from what is known as Gauge Symmetry, or Group Theory.
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------------ Newton’s Universal law of Gravitation exhibits spherical symmetry.
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------------ Kepler’s laws of planetary motion are the consequence of the conservation of angular momentum which is corresponding to rotational symmetry.
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- All states of uniform motion are equivalent to each other which is a symmetry of nature. Only relative motion can be determined. The principle of relativity is a continuous symmetry of the laws of physics.
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- We can continuously change our place and our state of motion and the laws of nature are invariant. The laws remain the same regardless of where, or when. The speed of light is invariant to all observers regardless of their state of motion. This fundamental tenant is used in deriving the theory of relativity.
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- The laws of physics are exactly the same in the anti-particle world as they are in the particle world. Anti-particles are negative energy and matter going backwards in time. When particles and anti-particles come together they annihilate each other in a powerful explosion where all things are conserved.
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- Angular momentum is always either an integer or a half-integer multiplied by Planck’s Constant / 2*pi. 2*pi represent one cycle or 360 degrees, pi represents 180 degrees or a half-cycle. Angular Momentum can change but its energy is always conserved.
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- Using the laws of symmetry scientists have developed the Standard Model with the Universe consisting of 6 Quarks (protons, neutrons), 6 Leptons (electrons), and 12 Gauge Bosons (photons, gluons, and gravitons).
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- The theory came first. Using Emmy Noether’s Symmetry Theory these particles were predicted and scientists have been trying to find the particles ever since. They have used particle accelerators to find most of them and the list is nearly complete except the graviton and the Higgs Boson in the Standard Model have yet to be discovered.
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- Continuous symmetry uses differential calculus. Mathematics has a profound place in nature. Leave it to a mathematician to define one of the most important laws in Physics, the Laws of Conservation.
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--------------------------- Time is related to energy
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--------------------------- Space is related to momentum. Momentum is space / time * mass.
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-------------------------- (Energy)^2 = (momentum)^2 * (speed of light)^2
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- In two different frames of reference the laws of physics must be the same, A and B, therefore:
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------------------------- (Energy A)^2-(momentum A)^2 * (speed of light)^2 = (Energy B)^2-(momentum B)^2 * (speed of light)^2
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------------------------- If one of the frames of reference is at rest then a mass at rest, E = mc^2, therefore:
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------------------------- (Energy)^2-(momentum)^2 * (speed of light)^2 = mass^2 * (speed of light)^4
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------------------------- Expanding this equation using differential calculus we get the series:
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------------------------- E^2 = m*c^2 + momentum^2 / 2*mass + ………………………
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------------------------- Energy at rest = m*c^2
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- The second term in the series is momentum^2 / 2*mass = mass^2*velocity^2/2*mass = ½ mv^2, which the definition of Kinetic Energy.
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- Does it get any more beautiful than that?
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- We look at the Universe with symmetry and we derive energy at rest, E=mc^2 and energy in motion, Kinetic Energy = ½ mv^2. The Symmetry in the Universe is Beautiful. But, it takes a mathematician to see it.
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- Emmy was a mathematician at a time when women were not allowed in education or in scientific research. She was born March 23, 1882, in Germany. In 1907 she earned her Ph.D. and began working at a university in 1915. In 1918 she presented her theorems on symmetry and the conservation laws to the University’s Mathematical society.
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- In 1919 she gets permission to teach a course in abstract algebra. She was not paid a full salary as a teacher until 1923. In April, 1933 the German Government under Hitler removes her position from the University not allowing women professors. In October she comes to the U.S. to teach at the College of Pennsylvania. In 1935 she dies from surgery.
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- Today her theories in relevant symmetries are used to develop gauge symmetries in particle physics. Her theory was used to define the conservation of electric charge. Noether’s theorems are tools to develop our understanding of quantum gravity linking general relativity and quantum mechanics.
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- Noether’s theorems even suggested the conservation of energy and of angular momentum. Her proposed translation symmetry means that the laws of physics remain the same throughout the Universe. Energy Conservation comes from the symmetry in “time“. Momentum Conservation comes from translation symmetry in “space“. The conservation of angular momentum comes from rotational symmetry.
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- Energy cannot be created or destroyed defines properties of the Universe. Even in particle physics describing the smallest dimensions have predicted the existence of the Higgs Boson that was not discovered until 2012.
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- March 8, 2019 682
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-------------------------- Tuesday, March 12, 2019 --------------------------
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