Everyday entropy: chord progressions

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Topologies

Entropy evolves while information progresses.  Information goes through progressions like chords in a song from one interaction or measurement to the next.  Between interactions, there are no changes.  Only the entropy, the actual configuration, evolves.  The information in DNA is a good example of progression, which occurs each time a new organism is born.  But when we think of evolution, we are thinking about the expression of those genes in the actual configuration of the organism’s body, which is determined by its environment as well as the information in its DNA.  The entropy and information of inorganic particles also evolve and progress in fundamentally different spaces.

Considering that the fundamental particles of matter never touch one another, the full description of the information in the universe is contained in the topology of space at its boundary with matter, and not at its boundary with infinity (compare, supertranslations).  In terms of matter in space, space has an area, but the information is topological in the sense that 3d distance and time are irrelevant, which is why the multiverse of information is real in terms of space, but unreal in terms of matter.  Gravity is not a function of information, but of the interaction between space and matter, which would explain why it can’t be reconciled with quantum information.  The multiverse of information space has no gravity, distance or time.

“The nature of the transition from low temperature states (where vortex pairs form) to high temperature states (where the pairs become independent) obeys the Kosterlitz-Thouless phase transition rules. Combining quantum physics with topology leads to a number of physically interesting things happening in discrete, integer steps. The conductance of a thin, electrically conductive material occurs in these steps. Chains of small magnets behave topologically. The phase transition rules apply universally to all types of materials in two dimensions. In the 1980s, Kosterlitz himself discovered the conductance relation, while Duncan Haldane discovered the topological properties of small magnet chains. Although the applications now extend into other areas of physics — statistical mechanics, atomic physics, and hopefully soon into electronics and quantum computers — the physics underlying this discrete behavior of matter in lower dimensions is governed by the same topological rules as any mathematical system.”

Ethan Siegel, in Forbes

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If you think of information space is a set of two-dimensional topologies consisting of every possible interaction that is consistent with the existing information, you can see how there is a quantum of information in each particle boundary and in the total area of the two-dimensional surface.  This seems to work well with the vector field topologies illustrated above, and the curved field lines of the space between charged particles, which can be seen as planes of information space.  The number of information space multiverses is very large, but if you imagine that an information space bends in 3d space, you can see how it isn’t necessary for each field line to have its own information space, but that each particle will interact with an information space that bends to its current position in 3d space.  As soon a new measurement occurs, all inconsistent multiverses cease to exist, and a new set appears.  It is necessary for all inconsistent information spaces to disappear so that the total information is preserved.

There is no time dimension, only static shifts from one set to the next.  Time is not a dimension, but a function of distances between particles separated by the multiverses of information space.  Time can only be “measured” because certain interactions between particles and information space are highly periodic.  In particular, the oscillation of the caesium atom at the moment of transition from one energy level to the next provides an extremely consistent periodic motion that can be replicated anywhere to establish earth time.  Earth time is extremely useful for predicting and coordinating events that are also periodical, but it is not really a fundamental element of information space or material existence.  Information is real.  Momentum is real.  Time is a heuristic for keeping track of them.

The information in a free photon is converted to the increase in the topology of space, just as the information that goes into a black hole contributes to the area of the information boundary, while the momentum of the energy in the photon is transferred to the emitting particle to contribute to galactic spin and compactness.  Momentum and information are both conserved, just in different spaces.  Here, it might be worth quoting something about Maldacena, Susskind and Van Raamsdonk:

“Much of this work rests on a discovery2 announced in 1997 by physicist Juan Maldacena, now at the Institute for Advanced Study in Princeton, New Jersey. Maldacena’s research had led him to consider the relationship between two seemingly different model universes. One is a cosmos similar to our own. Although it neither expands nor contracts, it has three dimensions, is filled with quantum particles and obeys Einstein’s equations of gravity. Known as anti-de Sitter space (AdS), it is commonly referred to as the bulk. The other model is also filled with elementary particles, but it has one dimension fewer and doesn’t recognize gravity. Commonly known as the boundary, it is a mathematically defined membrane that lies an infinite distance from any given point in the bulk, yet completely encloses it, much like the 2D surface of a balloon enclosing a 3D volume of air. The boundary particles obey the equations of a quantum system known as conformal field theory (CFT).

Maldacena discovered that the boundary and the bulk are completely equivalent. Like the 2D circuitry of a computer chip that encodes the 3D imagery of a computer game, the relatively simple, gravity-free equations that prevail on the boundary contain the same information and describe the same physics as the more complex equations that rule the bulk.”

Nature – Ron Cowen 16 November 2015

The once quibble I have is with the notion of an infinite distance, which is philosophically meaningless.  Better to say no distance from any point on the bulk and eliminate the bubble altogether.  The renormalisation of infinities is, as far as I can tell, essential to the rational functioning of quantum mechanics.  Then there is simply a boundary between space and matter with one surface, two dimensional bulk information and no distance value from any given point.

I am reminded of two horrifically inconsistent statements about the event horizon of a black hole.  On the one hand, I’ve read that the tidal force at the event horizon of a very large black hole is less violent that the force at earth’s surface.  On the other hand, Strominger notes that the frame at the event horizon is collapsing inward at the speed of light, leaving light rays hanging at the boundary, which means essentially that there is no space to fall into past the event horizon.  For special relativity to hold, one of these assumptions has to be incorrect, or you would see light moving slower than c as you pass through the horizon.

chord-prog_-sankey-1
Chord progressions for 5000 songs

 

 

 

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