5-Physics-Heat-Entropy-Information Theory

information in physics

Systems have particles, which have position and momentum, and energy and time {information, physics}.

spin system

Particles can have spin up clockwise or spin down counterclockwise. Particle spin state encodes one binary choice or information bit: 0 or 1. For quanta, such as spin, state holds one quantum information bit. One kilogram of plasma in one liter of space can hold 10^31 bits.

Particles with known spins can carry input or output information. For interacting particles, quanta can entangle, and information can entangle. Particles can interact to represent computation to calculate. Bits can change electromagnetically every 10^-20 second. Signals travel 3 * 10^-12 seconds to next particle. System particles entangle and change in parallel. One kilogram of plasma in one liter of space can have 10^51 particle-spin changes each second.

system information

Information required to describe system state depends on degrees of freedom. Mole of chemical has 10^23 degrees of freedom because it has that many molecules. In regions that have no boundary and have uniform matter and energy, entropy is proportional to volume.

black hole

By Bekenstein-Hawking formula, one-kilogram black holes have radius 10^-27 meters. Event-horizon surface can hold 10^16 bits. Bits can change every 10^-35 second. Surface can have 10^51 particle-state changes each second. Light can cross black holes in 10^-35 seconds, so physical processes have time to work serially.

Observers cannot see past event horizon, so horizon surface must contain all information about region volume inside black hole. Gravity causes information bits to interact, so entanglement over surface area can have enough information states to hold information about inside volume. Black-hole entropy is directly proportional to event-horizon surface area. Planck area is 10^-66 cm^2. One Planck area has 0.25 information bit, so four Planck areas make one bit.

One-kilogram black holes emit gamma and higher-energy rays by Hawking radiation and disappear in 10^-21 second. Smaller black holes dissipate faster and emit higher energies.

Perhaps, rather than particle spins and states, branes or strings hold states.

cell size

Bit-change maximum rate is maximum clock frequency, and so time has quanta. Rate depends on gravitational constant, light speed, and Planck constant.

Space has quanta, with cell sizes. Black holes have maximum energy per volume and have definite ratio between mass and event-horizon radius, so maximum mass-energy is proportional to space-time radius. Cell size varies with radius cube root. For universe, cell diameter is 10^-15 meters.

Energy and time relate, so space cell size depends on space-time radius. The holographic principle can derive from uncertainty principle.

universe

Universe has age 1.3 * 10^10 years and so radius 1.3 * 10^10 light-years. Universe is close to maximum density, so it can hold 10^123 bits. It can have 10^106 bit changes each second, in parallel, from 10^72 joules. It has 10^92 bits of ordinary matter, which can change bits at 10^14 Hz. It has less than 10^123 bits of dark energy, which can change bits at 10^18 Hz.

generalized second law

Total entropy in universe, inside and outside black holes, cannot go down {generalized second law} (GSL).

Horowitz-Maldacena model

Information that went into black hole can come out by entanglement of two surface virtual particles, one of which interacts with original matter and information at singularity {Horowitz-Maldacena model}.

Margolus-Levitin theorem

Information bits can change no faster than quantum time. Heisenberg uncertainty principle relates energy and time. Quantum time t depends on quantum energy E {Margolus-Levitin theorem}: t >= h / (4*E), where h = Planck's constant.