T-symmetry

The time reversal is a physical transformation of the type

Almost all the basic physical laws are symmetric with respect to a reversal of the time, one also speaks of time-reversal invariance or T- symmetry. A physical process is time-reversal invariant if it can in principle also be reversed in time, so backward run. Specifically, this manifests itself in the fact that to each solution of a physical equation describing a temporal process, once a new solution can be constructed by changing only the sign of the time variable in the known solution.

So anyway, Paul Dirac was in 1928 the existence of the positron, the antiparticle of the electron predict. The positron was detected on 1932 of Anderson as new particles in cosmic rays.

Macroscopic phenomena: the second law of thermodynamics

Our daily experience shows us that there are non-reversible phenomena: water always flows downhill, cups burst from dropping and hot tea cools down to room temperature. Many phenomena, such as the relative movement of the bodies with the friction or viscous flow of fluids, are based on the dissipation of energy (ie, the conversion of kinetic energy into heat). The conversion of energy is determined by the second law of thermodynamics to a direction.

In a thought experiment, James Clerk Maxwell sat apart with the second law of thermodynamics. His Maxwell's demon is a microscopic gatekeepers between two halves of a space that transmits the slow molecules in one direction only, the fast in the other direction. In this way, one half of the space would be at the expense of heat of the other half. It seems that the entropy decreases and reverses the arrow of time. A more detailed study involving the demon, however, shows that the total entropy of space and demon increases.

The scientific consensus today is the interpretation of Ludwig Boltzmann and Claude Shannon, who is the logarithm of the phase space volume in relation to the information entropy. Here the macroscopic initial state has a fairly low phase space volume, as the position of the atoms is limited. When the system is under the influence of dissipation further developed, the phase space volume and the entropy increases increases.

Another point is that we observe a steady increase in entropy, "only" because the initial state of the universe had a low entropy; other possible states of the universe would thus lead to a decrease of entropy. According to this view, the macroscopic irreversibility is a problem of cosmology: why the universe began with low entropy? The question of the beginning of the universe is an open question in the current physics.

Microscopic phenomena: time-reversal invariance

Classical mechanics and electrodynamics

Since most macroscopic systems are asymmetric under time reversal, it is interesting to ask what phenomena are symmetric under time reversal. In classical mechanics the speed reversed, for example, v if time is reversed in order during the acceleration a is unchanged. Therefore, friction effects are modeled by odd v -terms. However, if all friction effects can be excluded, classical mechanics is symmetric under time reversal.

The movement of charged particles in the magnetic field B is determined by the Lorentz force and appears at first sight so as not to be invariant under time-reversal. On closer inspection, however, shows that even if time is reversed B changes its direction as a magnetic field by an electric current J is generated, which also reverses its direction at time reversal. So the movement of charged particles in the electromagnetic field is symmetrical with respect to time reversal. The laws of gravity are invariant under time reversal.

Quantum physics

In physics, the so-called dynamics between the laws of motion, so-called kinematic, and the effect of forces or interaction potentials differences; for example, can be characterized by the metric of the special- relativistic Minkowski space the kinematics. This metric is time-reversal invariant. The paths of the particles in this space, however, be a violation of, for example, when β -decay, under the influence of the interaction potentials, the time-reversal invariance. As in the classical kinematics, which is described by the Newtonian laws of motion, the quantum mechanical kinematics is designed so that it makes no statement about the time-reversal invariance of the dynamics. In other words, the dynamics, the time invariance violating, although the characteristic of the kinematic variables does not consider this behavior.

On a fundamental violation of time-reversal invariance of the weak interaction ( β -decay, etc.) was first closed in 1956 indirectly. At that time, a slight violation of the so-called CP invariance was observed ( = symmetry of physical laws while changing the sign of charge and parity), which also results in the violation of time-reversal invariance follows, if one the validity of the CPT theorem ( = symmetry of the physical laws with a simultaneous change of sign of charge, parity (physics) and time) presupposes.

After the violation of CP symmetry was confirmed in the B- meson factories Babar and Belle in 2002, succeeded in 2012 from the post-analysis of old BaBar data and the direct detection of T- violation.

Mathematical representation

The mathematical representation in quantum physics is subtle: Usually one proceeds from the event that you work as in the non-relativistic physics with a Zweierspinor, so the state of the system by two wave functions and describes. The " time- inverted " Zweierspinor is then the size of the two components as well. This means that there are, first, the complex conjugate wave functions formed, secondly reversed up - and down- spin components and 1 or -1 attached thirdly, the " phase factors ", which is the usual " bisector " in the transition from vectors to spinors (exp (i 0 ° / 2) = 1; exp ( i 360 ° / 2) = -1).