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Symmetry is an expression for things being equal, or the same from all
directions. Symmetry in the Universe is
invariant under transformations in space and time. With symmetry all frames of reference the
laws of physics have the same result. Emmy Noether, one of the planet’s smartest
mathematicians, in 1918 came up with a Theory of Symmetry.
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------------------------ 2052
- Universal Beauty in Symmetry
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Symmetry is an expression for things being equal, or the same from all
directions. Symmetry in the Universe is
invariant under transformations in space and time. Regardless of when or what its position is,
it is the same. The laws of physics are
the same everywhere. With symmetry all
frames of reference the laws of physics 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.
This 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 this theorem.
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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. 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. (See Review
#648 Relativity Explained)
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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 in which 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). The theory came first. Using Emmy Noether’s Symmetry Theory these
particles were predicted and scientists have been trying to find all 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 was only recently
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 = mass * velocity.
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--------------- Momentum is space / time * mass.
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------------- (Energy)^2
= (momentum)^2 * (speed of
light)^2
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E^2 = (m *v)^2
* c^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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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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it get any more beautiful than that? 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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Some reviews are at:
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http://jdetrick.blogspot.com -----
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to: ------- jamesdetrick@comcast.net ------
“Jim Detrick” -----------
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------------------------- Sunday, April 8, 2018
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