Correspondence of The Principle of Maximum Entropy With other Laws of Physics

1
Correspondence of The Principle of Maximum
Entropy With other Laws of Physics
How may the Maximum Entropy Principle be used to
achieve greater understanding of much of Physics
and what can be derived from such a point of view?

• Maximum Proper Time
• Least Action
• Least Time
• Minimum Energy

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In a relativistic universe Atomic Clocks events
appear at differing rates depending on the world
line of the frame of reference

• Its the comparative rates of events that change
  in our relativistic universe
• For the following discussion I would like to use
  the concept of EVENTS to replace TIME
• The TIC of the clock is the atomic events
  E1,E2,E3

What has been done is to replace the viewpoint of
time with a viewpoint of Events to see what
arises as a result
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Principle of Maximum Proper Time

• A body in motion takes the path in space-time
  that maximizes the passage of proper time
  according to its own built in WRISTWATCH aka
  EVENTS E1,E2. This will maximize the
  Entropic Rate
• This principle is valid on a differential scale
  also
• An example is a free falling body that senses
  no force Proper time is maximized by this
  condition

By treating Proper time as a dimension where
entropy is maximized by virtue of Proper time
being maximum one can attain a new viewpoint and
solve problems
4
Contrast Free Fall with static position in
Gravitational Field

• At rest on ground (accelerated) In Free -
  Fall
• Ent Exponential Distribution Distribution (Ent entropy of operator)
• Spatial entropy is maximized in both depicted
  conditions
• Its much easier to see why inertial mass
  gravitational mass under this viewpoint

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The Principle of Least Action can be derived from
the principle of Maximum Proper time

• Least Action also maximizes the space-time for
  events and therefore maximizes entropy so it
  appears that max entropy principle extends from
  space and time to spacetime
• This principle works on the differential scale
  also
• d ( action ) K.E. -P.E. .this maximizes the
  P.E. and therefore the proper time passage is
  greatest
• F MA can be derived from Least Action
  Principle
• Feynman derived Schrodingers Wave Equation using
  the Principle of Least Action as a starting point

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Schrodingers Equation yields Maximum Entropy
solutions

• This answers a question that I have had for a
  long time
• Question Why is it valid to use a sinusoidal
  waveform when modeling physical systems such as
  atoms in a lattice or electrons in an antenna?
• Answer For a particle constrained to a given
  energy and position over interval - inf , inf
  the maximum entropy wave function is gaussian
  in the base state
• HARMONIC POTENTIAL sinusoidal!!

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Correspondence of Least Energy and Maximum
Entropy on the Micro Scale

• As a particle is confined more its energy goes
  up
• Since Schrodingers maximizes wavefunction
  entropy the energy level is minimized for a given
  confinement
• This is analogous to a gas in a box

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Principle of Least Time

• A photon knows no time because it travels at the
  speed of light.
• Emission and absorption appear to occur
  simultaneously from the point of view of the
  photon
• From the Universe around the photon Entropic rate
  will be maximized if the light takes the least
  time between emission and absorption as measured
  by those of us with rest mass that experience
  time

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Entropic Theory of Gravitation

• Above newtons law of gravity is derived by
  differentiating proper time with respect to
  distance and substituting for the Schwarzchild
  radius (with a correction factor !)
• One can see that the force of gravity on an
  object is an entropic pressure in free fall an
  object wants to HOP to the most likely next
  state and does so
• The correction factor shows the force to be
  infinite at the event horizon.

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Results

• As a result of this investigation I have been
  able to see that the physical bodies experience
  some sort of entropic pressure that governs their
  motionA modified Newtons theory of gravitation
  may be derived
• In place of time I substituted a progression of
  events in which entropy in its enumeration of
  physical states and seems to be much more useful
  in some fundamental way
• Maximum entropy method applies to space and time
  similtaneously