Everyday entropy: zero to infinity dimensions

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Hydrogen bubble chamber

Between zero and infinity, matter, space and information give a pretty good impression three dimensions in flux with time.

The information spaces are conformal in time but orthogonal at any given point, and since no plane of information is privileged, a 3d manifold appears in the convolution of 2d planes.  It’s worth bearing in mind that cartesian 3d coordinate system isn’t actually a 3d space, but three, separate, 2d planes that can be moved past one another to plot a point or vector in what we intuitively assume is 3d space.  This system only works in the abstract condition where the zero point is privileged.  You have to remember that in real space, there is no privileged zero point, so that each particle must have its own set of planes, and as it turns out, each particle is a zero point in quantum information space.  Not only that, but each point in empty space is also a zero point.

The thing about zero point energy in space, though, is that it has no vector or definite plane of polarisation or wave form, so there is no reason why the zero point energy in empty space should push two galaxies apart rather than together or sideways.

The equivalence of mass and energy is slightly misleading because it doesn’t tell us what those things are.  When you parse the definitions, it means that mass is equal to momentum, which is equal to mass times acceleration, which means that momentum was always made up of mass and acceleration, which means that as long as there is some mass and some acceleration, you can adjust either in equal measure to produce the same resulting momentum.  The significant message in e=mc2 is that rest mass can be converted into communicable heat energy, which can be converted back into rest mass somewhere else.  It is worth bearing in mind that this is unification of Boltzmann’s statistical mechanics with Planck’s oscillator basis for blackbody radiation.  This is to take nothing away from Einstein, only to caution that e=mc2 is something of a tautology that should not be taken as a definition of energy or mass.

The other important point is that energy in the absence of mass is equal to acceleration to the speed of light.  Special relativity then states that the energy propagates at the speed of light, and does not accelerate any more, because time dilates to infinity, so the energy has no more time to accelerate.

Feynman was right in that there is no answer to the questions what is matter and why is the speed of light, but he was wrong to tell students to stop asking the questions.  When you stop asking the questions, you forget the meaning of your calculations, and they degenerate first into trivia, and then into fake news based on trivia.

Statistical mechanics provides an informational map of position with respect to momentum, but not a definition of position itself.  Entropy increases because position is uncertain and momentum is conserved.  Wherever any given particle is located, it must keep moving, not just because it has momentum, but because there is no fixed place in space for it to sit, and it can’t share space with any other massive particle.  Given these constraints – position cannot be fixed, momentum cannot be diminished, and no two massive particles can occupy the same space – the momentum in a configuration will distribute itself equally over time.  Note that heavier particles settle because momentum would have to concentrate underneath them to keep them up, which is highly unlikely.

Momentum is a bit of quantum information like spin and charge, and it is certain.  For any given particle, rest mass is well known.  Position is not.  In fact, position isn’t even real.  We take for granted that there a map of the universe that is real, so we think of momentum as uncertain because we have to get information about the system before we can say that it exists anywhere, and that information costs momentum.  So we need to bleed momentum from anything we want to locate, and the quantum of energy that goes into the information and then into the entropy of our measuring device must be uncertain for the simple reason that we would have to measure the measuring device with a second device to find it, and then measure the second measuring device with a third device to find the energy that bled into the information required for the second measurement and so on ad infinitum.  We have trouble imagining a particle independent of its position in our mind-map of the universe.  But it is.

Quantum mechanics is concerned with real information that exists in the information-space of the universe.  General relativity is as perfect a system as will be devised to map the relative locations of particles in the universe.  General relativity presumes a privileged location from which to begin, and this location must be fictional, because it cannot be associated with the actual position of any particle of matter, since the position of every particle is uncertain.  General relativity is an example of an extremely useful model that is both fictional and predictive, because while no actual place exists from which to begin mapping the universe, if you plug in the zero point at an arbitrary location, you can predict the motion of any particle that has given you enough information to establish its position relative to the arbitrary zero point.  The general relativity model only functions if the zero point and the faraway object have enough mass in thermodynamic equilibrium to provide a steady stream of consistent information about their momenta.  At this scale, quantum mechanics just isn’t relevant, and even if you could count up all of the quanta in an object big enough to locate, that still wouldn’t tell you where or when the object really is.  Its position is inherently relative in both space and time.

Quantum information is real and true.  Minkowski space is a fictional model.  Quantum information can’t predict anything about relative location, but Minkowski space can.  Which is more useful depends entirely on your purpose for using them.  Things do not exist at a location in space time.  Things exist and there is space around them.  That is all.   We create maps to establish the probability that any two things will collide.  These maps cannot be arbitrarily accurate because they do not describe real space.  They are artefacts of the sharing of quantum information between things, either gluons, photons or their composite phonons.  Location, in all senses of the word, is a matter of archeology.

Let us assume that the only quantum of information in empty space, independent of massive particles, is found in photons passing between particles.  The distance between any two particles depends on your speed and the gravitational field relative to the particles, but the speed of light will appear constant.  Let us say that the passage of light is the only thing that defines the geometry of empty space so that distance and time are functions of observation.  Distance and time are the constraints on the sharing of information, not properties of space.  The architecture of space, then, is nothing but the pathways of light, and the map of the universe is a web of photon trails between communicating particles.  The length of these trails are not determined – for a photon the journey is instantaneous – so the trails’ lengths are different for every particle.

From the photons’ perspective, each photon experiences the universe as a static disc perpendicular to its pathway, but only superimposed photons experience the same discs.  The discs are two dimensional but each one is oriented differently, so that the space of the universe is an infinite-dimensional set of discs in the same way that the pathways of photons create an infinite-dimensional set of orthogonal planes of electromagnetic excitations.

When a photon fails to interact with anything, it is not so much that the information is absorbed into the substance of space, but that the length of all of the possible pathways increases by the quantum of momentum that would have been communicated, making it appear that everything has been pushed away, perhaps perpendicular to the projected pathway.

 

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