Time reversal (physics)

The time reversal is a physical transformation of the type

{\ displaystyle T: t \ mapsto -t.}

Almost all fundamental physical laws are symmetrical with respect to a reversal of time , one also speaks of -symmetry or of time reversal invariance (not to be confused with time invariance ). A physical process is invariant in time reversal if it can in principle also take place reversed in time, i.e. backwards. Specifically, this is expressed in the fact that for every solution of a physical equation that describes a time process, a new solution can be constructed immediately by only changing the sign of the time variable in the known solution . ${\ displaystyle T}$

In any case, in 1928 Paul Dirac was able to predict the existence of the positron , the antiparticle of the electron . The positron was then detected by Anderson in 1932 as a new particle in cosmic rays .

Macroscopic Phenomena: The Second Law of Thermodynamics

Our daily experience shows us that there are irreversible phenomena: water always flows downhill, cups break when falling, and hot tea cools down to room temperature. Many phenomena, such as the relative movement of bodies with friction or the viscous flow of liquids, are based on the dissipation of energy (i.e. the conversion of kinetic energy into heat ). The conversion of energy is determined by the second law of thermodynamics in one direction ( time arrow ).

In a thought experiment , James Clerk Maxwell dealt with the second law of thermodynamics. His Maxwellian demon is a microscopic gatekeeper between two halves of a room, who only lets slow molecules through in one direction and fast molecules in the other. That way, one half of the room would heat up at the expense of the other half. It seems that the entropy is decreasing and the time arrow is reversing. However, a closer examination, including the demon, shows that the total entropy of space and demon increases .

The scientific consensus today is the interpretation of Ludwig Boltzmann and Claude Shannon , which relates the logarithm of the phase space volume to the information entropy . Here the macroscopic initial state has a very small phase space volume, since the position of the atoms is limited. If the system continues to develop under the influence of dissipation, the phase space volume increases and the entropy increases.

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

Microscopic phenomena: time reversal invariance

Classical mechanics and electrodynamics

Since most macroscopic systems are asymmetric with respect to time-reversal, it is interesting to ask which phenomena are symmetric with respect to time-reversal. In classical mechanics z. B. the speed is reversed with time reversal, while the acceleration remains unchanged. Therefore, friction effects by odd v - Terme modeled. If, however, all frictional effects can be excluded, classical mechanics is symmetrical with respect to time reversal. ${\ displaystyle {\ vec {v}}}$ ${\ displaystyle {\ vec {a}}}$

The movement of charged particles in the magnetic field is determined by the Lorentz force and does not appear to be invariant under time reversal at first glance. On closer inspection, however, it turns out that its direction also changes when the time is reversed , since a magnetic field is generated by an electric current , which also reverses its direction when the time is reversed. This means that the movement of charged particles in the electromagnetic field is symmetrical in relation to time reversal, just like the laws of gravitation . ${\ displaystyle {\ vec {B}}}$ ${\ displaystyle {\ vec {v}} \ times {\ vec {B}}}$ ${\ displaystyle {\ vec {B}}}$ ${\ displaystyle {\ vec {J}}}$

Quantum physics

In physics a distinction is made between the laws of motion, i.e. H. the kinematics and the effect of forces or interaction potentials, d. H. the dynamics . The kinematics can be characterized by the metrics of the special-relativistic Minkowski space ; this metric is time reversal invariant. On the other hand, the orbits of the particles in this space may hurt, e.g. B. in β-decay , under the influence of the interaction potentials the time reversal invariance. As in classical kinematics, which is described by Newton's laws of motion , quantum mechanical kinematics is also structured in such a way that it does not make any statements about the time-reversal invariance of the dynamics. In other words: the dynamics can violate the time invariance, although this behavior cannot be seen in the quantities that characterize the kinematics.

A fundamental violation of the time-reversal invariance for the weak interaction (β-decay, etc.) was first indirectly concluded in 1956. At that time, a slight violation of the CP invariance (= symmetry of the physical laws with a simultaneous change in the signs of charge and parity ) was observed, from which the violation of the time reversal invariance also follows, provided that the validity of the CPT theorem (= symmetry of the physical laws at simultaneous change of the sign of charge, parity and time).

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

Mathematical representation

The mathematical representation in quantum physics is subtle: Most of the time, one starts from the case that, as in non-relativistic physics, one works with a two-way spinor , i.e. describes the state of the system using two wave functions

{\ displaystyle \ psi _ {1} ({\ vec {r}}, t) = \ psi _ {\ uparrow} ({\ vec {r}}, t)}

and

{\ displaystyle \ psi _ {2} ({\ vec {r}}, t) = + \ psi _ {\ downarrow} ({\ vec {r}}, t)}

.

The "temporally inverted" two-spinor is then the size with the two components

{\ displaystyle ({\ mathcal {T}} \ psi) _ {1} ({\ vec {r}}, t) = \ psi _ {\ downarrow} ^ {*} ({\ vec {r}}, t)}

and

{\ displaystyle ({\ mathcal {T}} \ psi) _ {2} ({\ vec {r}}, t) = - \ psi _ {\ uparrow} ^ {*} ({\ vec {r}} , t)}

.

That means: it will be

the conjugate complex wave functions are formed ${\ displaystyle (\ psi \ to \ psi ^ {*})}$
up and down spin components swapped and ${\ displaystyle (\ uparrow \ Longleftrightarrow \ downarrow \,)}$
the “phase factors” +1 or −1 are attached, which corresponds to the usual “halving of the angle” when transitioning from vectors to spinors, namely

{\ displaystyle \ exp \ left (i {\ tfrac {0 ^ {\ circ}} {2}} \ right) = + 1}

and

{\ displaystyle \ exp \ left (i {\ tfrac {360 ^ {\ circ}} {2}} \ right) = - 1}

.

Individual evidence

^ Gernot Eder: Atomphysik , 2nd revised edition 1989, Wissenschaftsverlag, ISBN 3-411-03217-0 , p. 226
↑ JP Lees et al. a. Observation of Time-Reversal Violation in the B0 Meson System , Phys. Rev. Lett., Volume 109, 2012, p. 211801
↑ Dirk Eidemüller time asymmetry directly demonstrated for the first time , Pro Physik, November 2012

[1] Gernot Eder: Atomphysik , 2nd revised edition 1989, Wissenschaftsverlag, ISBN 3-411-03217-0 , p. 226

[2] JP Lees et al. a. Observation of Time-Reversal Violation in the B0 Meson System , Phys. Rev. Lett., Volume 109, 2012, p. 211801

[3] Dirk Eidemüller time asymmetry directly demonstrated for the first time , Pro Physik, November 2012