In order to understand Maxwell’s demon, you have to believe that space and information are real things that exist in the universe, not just in your imagination, even though they are immaterial. I know this is crazy, but bear with me. It’s very beautiful. The life of a photon is sudden. From its perspective, moving at the speed of light, time dilation is infinite, so light doesn’t age. For a photon, birth and death occur at the same time, just in different places. This experience creates two superimposed universes, one at birth and one at death, with nothing in between. So what happens when a photon veers off into empty space with nothing to interact with at the other end? It would only have one universe – its birth universe, and the photon would have to cease to exist in the birth universe as well. The photon represents a quantum of information that cannot disappear according to quantum mechanics. This leaves a quantum of information in the birth universe with no physical manifestation. If the information were transformed into a quantum of empty space, the space in the universe would expand, and the rate of expansion would accelerate as the avenues for zero interaction photons increased. Space is a python, squeezing the information out of mass-energy.
If you imagine a spiral galaxy, you can see how radiation from matter at the edges would be more likely to escape into free space than radiation near the middle, so that the space at the fringes of the galaxy would expand in a way that would appear to accelerate the outer arms faster than a Newtonian orbit and simultaneously prevent them from flying outwards. Conservation of momentum would account for the spin and compactness of spiral galaxies, while conservation of information would account for the shape of the spiral arms and cosmological expansion. Random variations would cause seams to appear, and in these seams there would be more free photons, and the space there would expand faster than the space in matter-rich “arms” of the galaxy. The rate of expansion would be proportional to the free space, which would increase exponentially with distance from the centre. This would explain why spiral galaxies are the same shape as nautilus shells and hurricanes, approximating a golden ratio spiral (the generative ratio, where each generation is equal to the sum of the previous two generations), and why galaxies spin faster than gravitational orbits should allow. There is also new research that shows that the rotation rate of a galaxy correlates with its radiating mass, without regard to its dark matter component, which would make sense if the excess speed were associated with its light rather than its dark matter. This is not a scientific theory. I have no proof other than the fact that a free photon in empty space would represent the loss of information, which is not allowed in quantum mechanics. Whether this is true or not, it is a beautiful way of looking at the relationship between information, matter and space, and it is so elegant it makes me want to cry.
I know this is crazy, but look at bubbles being squeezed out of a water column and ask: does that look like a photon? Spacetime is not a thing with mass and energy, but imagine it squeezing everything equally, and where there is enough mass-energy clumped together, there is a tendency for the squeezing to move more mass-energy in that direction, like the bubbles being squeezed upward through the water column, and let’s call that gravity. It isn’t terribly important whether you think of space as a constricting snake or a loving parent squeezing the information out of its creation, either way, it grows when it swallows a photon or engrosses a black hole.
The vacuum energy provides a strange basis for the squeezing of the python, and if you consider that the vacuum is massless, its energy is the inverse of a photon, so that the vacuum energy provides the impetus for the photon’s speed irrespective of the observer’s frame of reference. The energy itself – the squeezing – has no direction, and so instead of being anti-gravitational, it looks anti-informational, either pushing things together or apart depending on their information, and weakly squeezing together anything that is neutral or bundled.
The photon itself is important for entropy because it is the only physical manifestation of Shannon information. It represents the lossless transmission of a quantum of information from one particle to another. A photon is not described by the Schrödinger equation and it isn’t subject to quantum uncertainty because it is massless and its speed is absolute. If a free photon directed into empty space were to collapse into a quantum of spacetime, it would illustrate how energy can transform from mass and momentum into Shannon information and commute into space. It seems the temptation to invest in information and property at the expense of meaning and community is universal, not just a human foible.
One interesting wrinkle in Hawking-Beckenstein black hole entropy is that because the mass of a black hole is concentrated at a single point and its surface is two-dimensional, its physical entropy, its configuration, actually resembles Shannon information more than the entropy of earthly matter. The configuration of a black hole is quantised in a way that matter outside of a black hole is not.