The direction of time that we can remember is called “the past”.

We cannot remember both directions, for if we can, we will remember infinite things.

— Me@2011.07.16

2011.08.10 Wednesday (c) All rights reserved by ACHK

Time reversal of the known dynamical laws

Particle physics codified the basic laws of dynamics into the standard model. This is formulated as a quantum field theory that has CPT symmetry, i.e., the laws are invariant under simultaneous operation of time reversal, parity and charge conjugation. However, time reversal itself is seen not to be a symmetry (this is usually called CP violation). There are two possible origins of this asymmetry, one through the mixing of different flavours of quarks in their weak decays, the second through a direct CP violation in strong interactions. The first is seen in experiments, the second is strongly constrained by the non-observation of the EDM of a neutron.

It is important to stress that this time reversal violation is unrelated to the second law of thermodynamics, because due to the conservation of the CPT symmetry, the effect of time reversal is to rename particles as antiparticles and vice versa. Thus the second law of thermodynamics is thought to originate in the initial conditions in the universe.

— Wikipedia on T-symmetry

2011.07.22 Friday ACHK

Another way of dealing with Loschmidt’s paradox is to see the second law as an expression of a set of boundary conditions, in which our universe’s time coordinate has a low-entropy starting point: the Big Bang.

— Wikipedia on Loschmidt’s paradox

.

.

2011.07.20 Wednesday ACHK

Loschmidt’s paradox 2

In kinetic theory in physics, molecular chaos is the assumption that the velocities of colliding particles are uncorrelated, and independent of position. This assumption, also called in the writings of Boltzmann the Stosszahlansatz (collision number hypothesis), makes many calculations tractable.

In particular, the assumption of molecular chaos was a key element, although initially unrecognised, in Boltzmann’s H-theorem of 1872, which attempted to use kinetic theory to show that the entropy of a gas prepared in a state of less than complete disorder must inevitably increase, as the gas molecules are allowed to collide.

This drew the objection from Loschmidt that it should not be possible to deduce an irreversible process from time-symmetric dynamics and a time-symmetric formalism: something must be wrong (Loschmidt’s paradox).

The resolution (1895) of this paradox is that the velocities of two particles after a collision are no longer truly uncorrelated. By asserting that it was acceptable to ignore these correlations in the population at times after the initial time, Boltzmann had introduced an element of time asymmetry through the formalism of his calculation.

— Wikipedia on Molecular chaos

2011.07.18 Monday ACHK

Eddington then gives three points to note about this arrow:

1. It is vividly recognized by consciousness.

2. It is equally insisted on by our reasoning faculty, which tells us that a reversal of the arrow would render the external world nonsensical.

3. It makes no appearance in physical science except in the study of organization of a number of individuals.
   
— Wikipedia on Arrow of time

2011.07.17 Sunday ACHK

Loschmidt’s paradox

Loschmidt’s paradox, also known as the reversibility paradox, is the objection that it should not be possible to deduce an irreversible process from time-symmetric dynamics.

This puts the time reversal symmetry of (almost) all known low-level fundamental physical processes at odds with any attempt to infer from them the second law of thermodynamics which describes the behavior of macroscopic systems.

Both of these are well-accepted principles in physics, with sound observational and theoretical support, yet they seem to be in conflict; hence the paradox.

— Wikipedia on Second law of thermodynamics

2011.07.13 Wednesday ACHK