# Fresh Thinking on Entropy

There are many previously unsolved problems in physics which are or will be solved using the Neoclassical Physics and Quantum Gravity model. In this post I’ll discuss Entropy.

For NPQG basics see: Idealized Neoclassical Model and the NPQG Glossary.

Let’s start with some background information before we turn to the unsolved problem related to entropy.

WHAT IS ENTROPY?

In statistical mechanics, entropy is an extensive property of a thermodynamic system. It is closely related to the number Ω of microscopic configurations (known as microstates) that are consistent with the macroscopic quantities that characterize the system (such as its volume, pressure and temperature). Under the assumption that each microstate is equally probable, the entropy S is the natural logarithm of the number of microstates, multiplied by the Boltzmann constant.

WIKIPEDIA

Entropy, the measure of a system’s thermal energy per unit temperature that is unavailable for doing useful work.

BRITTANICA

THE SECOND LAW OF THERMODYNAMICS

The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. The total entropy of a system and its surroundings can remain constant in ideal cases where the system is in thermodynamic equilibrium, or is undergoing a (fictive) reversible process. In all processes that occur, including spontaneous processes, the total entropy of the system and its surroundings increases and the process is irreversible in the thermodynamic sense. The increase in entropy accounts for the irreversibility of natural processes, and the asymmetry between future and past.

WIKIPEDIA

We can express the second law from the perspective of the universe for any process with a change in entropy S, such that $\mathbf{\Delta S{_{U}} \geq 0}$.

“The law that entropy always increases holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations — then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation — well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.”

Sir Arthur Stanley Eddington

THE ENTROPY PROBLEM

With that background, here is an unsolved problem in physics:

Arrow of time (e.g. entropy’s arrow of time): Why does time have a direction? Why did the universe have such low entropy in the past, and time correlates with the universal (but not local) increase in entropy, from the past and to the future, according to the second law of thermodynamics?

WIKIPEDIA

ENTROPY IN NPQG

The Internatonal System (SI) of units of entropy are joules per kelvin, energy divided by temperature. The energy of a particle is directly related to its temperature. We also know that particles and energy are both conserved. When we talk about a collection of particles, if it is not in equilibrium then at least one subset of particles has higher energy and higher temperature than another subset that has lower energy and lower temperature. We also know that if we concentrate a set of particles in a volume, that superfluid temperature will also rise in that volume. It seems to me that we can tighten the second law of thermodynamics to say that the total entropy of any process or reaction remains constant when considering all particles. If entropy increases in a portion of the universe, then the remainder of the universe must experience a decrease in entropy. Specifically, any change in entropy in one group of particles is balanced by the equal and opposite change in another group of particles. This is a local process. Therefore we can refine the 2nd Law of thermodynamics and change the equation to an equality. The reason we are able to tighten the 2nd law is that GR-QM era scientists did not understand the superfluid nor black hole dynamics.

Note: The superfluid is lightly interacting. We don’t feel the 2.7 K temperature of the superfluid in the Earth’s atmosphere. Presumably this is because there is far more energy in the molecules of the atmosphere that dominates. We know that if we were exposed to superfluid in outer space that we would feel it then and our bodies would quickly shed energy.

GRAVITY, BLACK HOLES, AND ENTROPY IN NPQG

Gravity reduces entropy of matter-energy and increases the entropy of superfluid. It brings together matter-energy and concentrates the heat, compacts it, transduces it, removes degrees of freedom, and crushes it by many orders of magnitude all the way down to Planck particles. The more concentrated the matter, the more mass energy the free matter must average outstanding in the superfluid. Thermodynamic work must be done against the superfluid to accelerate a particle, and per the equivalence principle this applies to a particle being acted upon by gravity as well. Planck particles may occur in the core of a supermassive black hole (SMBH), and possibly in other high energy objects or as a result of high energy events (e.g., BH-BH mergers, BH, BH-NS mergers?, NS?). BH = black hole. NS = neutron star.

Thermodynamic work must be done against the superfluid to accelerate a particle, and per the equivalence principle this applies to a particle being acted upon by gravity as well

J Mark Morris
San Diego July 21, 2019

Planck particle phase has the lowest possible entropy, zero, and the highest possible energy density, the Planck energy density. Per the Britannica definition of entropy, Planck particles have zero energy unavailable for performing useful work. Or rather, 100% of the energy of Planck phase particles is available for useful work.

I imagine in-core Planck particles in a solid form, arranged in the densest packing possible. Perhaps face centered cubic (FCC) packing. Planck particles in a supermassive black hole (SMBH) core can be described by a single bit of information, Planck core or not Planck core. If that is true, then a Planck core has zero entropy $\mathbf{S=k_B\ln{(w=1)}}$. Under certain conditions, the SMBH will jet the Planck core as plasma. Once the plasma has escaped, the entropy of the particles begins to increase.

BLACK HOLE DYNAMICS

Bekenstein and Hawking related black hole entropy to the area of a black hole event horizon.

$\mathbf{S_\text{BH} = \frac{k_BA}{4\ell_\text{P}^2}}$

where $\mathbf{A}$ is the area of the event horizon, $\mathbf{k_B}$ is Boltzmann’s constant, and $\mathbf{\ell_\text{P} = \sqrt{G\hbar / c^3}}$ is the Planck length.

The Boltzmann constant is a physical constant which relates the average relative kinetic energy of particles in a gas with the temperature of the gas and occurs in Planck’s law of black-body radiation and in Boltzmann’s entropy formula.

WIKIPEDIA

It is fascinating that Boltzmann’s constant, which has to do with a gas, appears in the entropy equation for a black hole event horizon. What does a gas have to do with the event horizon area? Ingested matter-energy is not expected to be in a gas state at the event horizon by GR-QM era science. So what is going on here? Oh, I see, the Planck length squared is in the denominator. The surface of the Planck phase core volume, may be composed of electrino/positrino dipoles, fixed in position, storing the maximum energy possible. The surface of the Planck phase core manifold is the matching surface to the prior phase which must be a gas. That is likely why Boltzmann’s constant appears in the entropy formula.

What is that geometry of a Planck core? Parallel spherical or oblate shells that alternate electrino-positrino, fixed in position geometrically? The dipoles are not spinning in the Planck phase. It seems to me that time slowed and now stops for the Planck core, so I am thinking the electrinos and positrinos are fixed in position. And if they stopped spinning, that means the spin had to migrate somewhere else due to conservation of spin, so this must accelerate the spin of the black hole. As more layers join the core the geometry of the core will evolve.

The next step is to relate Boltzmann’s constant to a potentially evolving geometry of the Planck phase core manifold. Maybe it’s something simple, like an oblate spheroid. It’s going to be that isn’t it?

Jumpin’ Jack Flash
It’s a gas, gas, gas

The Rolling Stones

Remember, we always need to consider faults and misalignments, in the actual physical geometry position by position. Nature is not perfect! I’ve been thinking face centered cubic would play a role in NPQG, and the Planck core phase manifold makes sense.

For equal spheres in three dimensions the densest packing uses approximately 74% of the volume. A random packing of equal spheres generally has a density around 64%.

Two simple arrangements within the close-packed family correspond to regular lattices. One is called cubic close packing (or face centred cubic, “FCC”)—where the layers are alternated in the ABCABC… sequence. The other is called hexagonal close packing (“HCP”)—where the layers are alternated in the ABAB… sequence. But many layer stacking sequences are possible (ABAC, ABCBA, ABCBAC, etc.), and still generate a close-packed structure. In all of these arrangements each sphere is surrounded by 12 other spheres, and the average density is 0.74048.

Carl Friedrich Gauss proved in 1831 that these packings have the highest density amongst all possible lattice packings.

WIKIPEDIA

The formula for packing density is $\mathbf{\frac {\pi }{3{\sqrt {2}}}\simeq 0.74048}$

This suggests that the packing arrangement involves a somewhat regular structure that can grow layers. True, core density might drop a little here or there near a fault, but overall, 74% packing upper bound makes sense. There are two ideal geometrical arrangements that can reach this upper bound: hexagonal close packing (HCP) or face centered cubic (FCC). Now, which arrangement makes more sense ABCABC (FCC) or ABAB (HCP)? If you said ABCABC (FCC) and your reasoning was “because space has three dimensions,” then you had the same intuition that I did.

We can use this density formula, perhaps adusted downwards a bit for faults, to estimate the energy density of a Planck core! Geometrical simulation may be able to provide an exact solution based on number of layers.

A regular solid with 12 vertices, equally spaced on an imaginary sphere, is a cuboctahedron, which is a uniform polyhedron. I think it scales by adding a layer of spheres at a time, in the sphere model. The details about how these layers are added geometrically may be a future research area. In any case, it seems likely that nature would tend to optimize and make this figure more and more spherical as layers were added. It probably doesn’t take many layers to reach an almost ideal sphere, even if carved out of a regular cuboctahedron lattice.

So far I’ve made a primitive case for layers of FCC cuboctahedron of Planck photons, spheres of six electrinos and six positrinos each, such that when alignment happens and Planck phase is enjoined that we get alternating layers, electrino, positrino, electrino, positrino, proceeding spherically or spheroidally. I think this is somewhat appealing from a beauty and naturalness perspective, and in keeping with symmetry perhaps each dipole aligns radially to maximize the energy storage. Note: for the Planck core dipoles to align radially it must be that conserved spin has migrated to outer layers of the black hole, probably largely in a kinetic form.

It may well be that supermassive black holes self-regulate themselves. The larger the Planck core grows, the more spin is outsourced to the periphery, causing the black hole event horizon and the Planck core to to each become oblate spheroids.

If the mantle and core of the black hole were both oblate spheroids, the polar thickness of the mantle would be less than in a sphere of the same volume. Thus spin may play a regulation role. The Planck core spin is shed to the mantle, causing an oblate spheroid, which reduces the barrier toward escape for the Planck core. There may be a relationship between supermassive black hole spin rate and Planck emission initiation. Cessation would be related to spin rate, but also to remaining volume of Planck particle phase core.

None of the thinking on entropy in the GR-QM era has considered superfluid particles and their temperature, nor has it considered the correct thermodynamics of black holes.

What happens at the transition to the Planck particle phase? In this state, matter has achieved the ultimate concentration of energy. The neighborhood of the Planck core is composed of extremely high energy particles. As more energy pours into the SMBH the energy intensity of the core begins rising. General relativity still holds as long as there are no Planck particles. However, at some point, particles will occasionally hit Planck energy. Then as more energy gathers, the percentage of Planck particles will grow. Planck particles do not participate in general relativity, i.e., they do not transmit their mass, nor receive gravitational waves. This is because the electrinos and positrinos in a Planck particle are not moving. Time has stopped for the Planck particle.

RAMBLING THOUGHTS….

What about reversibility? We need to broaden our thinking on reversibility beyond reversing individual reactions and consider that particles can lose and gain energy any number of times as long as they are between zero energy (0 Kelvin) and the Planck energy (Planck temperature). Black holes can reset the energy of particles to the highest level possible. In that sense the particle entropy has been reversed from any lower energy transtions it has previously experienced.

The relation to time is that energy tends towards thermal equilibrium. Most free particles, absent any other impinging particles or laboratory preparation, have more energy than a superfluid particle. Therefore the free particle is more likely to emit radiation, i.e., shed energy, than it is to absorb energy. We observe this process occuring over time and because GR-QM era scientists did not understand the superfluid, nor black hole dynamics they have tied the concept of entropy to time.

Clearly the average temperature of the superfluid is 2.7 K, but what exactly is the composition of the superfluid? Is it purely low energy photons? Does in include low energy neutrinos? Do low energy photons combine to make a larger particle that moves slowly (a graviton?)?

When a black body radiates, a common reaction is that an electron sheds energy to a superfluid particle which becomes a photon. The electron then drops down an energy level. This is the reverse of the process that heated the material, where photons transferred energy to the particle, typically causing an electron to increase its energy level.

Matt on PBS Space Time says black holes hold most of the entropy in the universe. What insights can we derive from this knowledge?

PREDICTIONS AND HYPOTHESES

• The total entropy in the universe is constant and conserved. Some processes concentrate energy and some processes diffuse energy. We can clarify the second law from the perspective of the universe for any process as $\mathbf{\Delta S{_{U}} = 0}$.
• In-core Planck particles can be described by a single bit of information, Planck core or not Planck core. Planck particles have a single microstate.
• A Planck core has zero entropy. $\mathbf{S=k_B\ln{(w=1)}}$.
• When in-core Planck particles are exposed to a cooler and lower pressure environment, such as when penetrating the axial pole of an SMBH, the vast majority of ejecta is Planck photons and neutrinos.
• No information is “stored” on a black hole horizon.
• Information is destroyed in Planck cores of black holes.

WHAT IS THE LOWEST POSSIBLE SUPERFLUID ENERGY STATE?

What is the absolute lowest possible energy state of the superfluid? Does it correspond to maximum entropy? I am presuming that the 2.7K cosmic microwave background is the black body temperature of the superfluid.

If the universe and superfluid is continuous and infinite, then perhaps 2.7K is its lowest average energy. However, some observations have suggested colder spots in the CMB. If those are valid results, what could cause a colder region of superfluid?

If our superfluid is a bubble, rather than infinite, then the surface of the bubble may be the interface to a phase change. What lies beyond the bubble surface? Here are some possibilities to ponder as we reverse engineer nature. Keep in mind that it may be difficult or impossible to test these ideas.

• A 3D void free of electrinos, positrinos, and energy. Logically this implies that nothing can escape our bubble.
• A 3D void with other superfluid bubbles in many size scales from unpaired electrinos and positrinos all the way up to bubbles similar to ours or even larger in scale.
• Bubbles may move through the 3D void and occasionally combine.
• A frozen superfluid at near 0 Kelvin. All electrinos and positrinos have zero velocity relative to the whole. Is it a lattice of interspaced electrinos and positrinos that minimizes charge interaction?
• Some or all of the above.

Also, note that scientists have cooled free matter-energy particles to incredibly close to absolute 0 Kelvin. However, those particles are in a bath of superfluid at 2.7 K, plus any delta in temperature due to Earth’s gravity. Considering these experiments may provide additional insight.

J Mark Morris

June 15, 2019 San Diego v1
July 21, 2019 San Diego v2