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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?. Correspondence of The Principle of Maximum Entropy With other Laws of Physics. Maximum Proper Time Least Action Least Time Minimum Energy.
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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? Correspondence of The Principle of Maximum Entropy With other Laws of Physics • Maximum Proper Time • Least Action • Least Time • Minimum Energy
In a relativistic universe Atomic Clocks’ events appear at differing rates depending on the world line of the frame of reference • It’s 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
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
Contrast Free Fall with static position in Gravitational Field • At rest on ground (accelerated) In Free - Fall • Ent [Exponential Distribution] < Ent [Uniform 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
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 = M*A can be derived from Least Action Principle • Feynman derived Schrodingers Wave Equation using the Principle of Least Action as a starting point
Schrodinger’s 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!!
Correspondence of Least Energy and Maximum Entropy on the Micro Scale • As a particle is confined more it’s energy goes up • Since Schrodinger’s maximizes wavefunction entropy the energy level is minimized for a given confinement • This is analogous to a gas in a box
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”
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….
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 motion……A modified Newton’s 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