T-symmetry

However, quantum noninvasive measurements are predicted to violate time symmetry even in equilibrium,[1] contrary to their classical counterparts, although this has not yet been experimentally confirmed.

The name comes from a thought experiment described by James Clerk Maxwell in which a microscopic demon guards a gate between two halves of a room.

The current consensus hinges upon the Boltzmann–Shannon identification of the logarithm of phase space volume with the negative of Shannon information, and hence to entropy.

In this notion, a fixed initial state of a macroscopic system corresponds to relatively low entropy because the coordinates of the molecules of the body are constrained.

As the system evolves in the presence of dissipation, the molecular coordinates can move into larger volumes of phase space, becoming more uncertain, and thus leading to increase in entropy.

This view, supported by cosmological observations (such as the isotropy of the cosmic microwave background) connects this problem to the question of initial conditions of the universe.

The laws of gravity seem to be time reversal invariant in classical mechanics; however, specific solutions need not be.

An object can cross through the event horizon of a black hole from the outside, and then fall rapidly to the central region where our understanding of physics breaks down.

The event horizon of a black hole may be thought of as a surface moving outward at the local speed of light and is just on the edge between escaping and falling back.

The event horizon of a white hole is a surface moving inward at the local speed of light and is just on the edge between being swept outward and succeeding in reaching the center.

For example, according to the gauge–gravity duality conjecture, all microscopic processes in a black hole are reversible, and only the collective behavior is irreversible, as in any other macroscopic, thermal system.

[citation needed] In physical and chemical kinetics, T-symmetry of the mechanical microscopic equations implies two important laws: the principle of detailed balance and the Onsager reciprocal relations.

However, it was proved that it is possible to find other time reversal operations which preserve the dynamics and so Onsager reciprocal relations;[3][4][5] in conclusion, one cannot state that the presence of a magnetic field always breaks T-symmetry.

(Despite this, it is still useful to consider the time-reversal non-invariance in a local sense when the external field is held fixed, as when the magneto-optic effect is analyzed.

This allows one to analyze the conditions under which optical phenomena that locally break time-reversal, such as Faraday isolators and directional dichroism, can occur.)

This section contains a discussion of the three most important properties of time reversal in quantum mechanics; chiefly, The strangeness of this result is clear if one compares it with parity.

For instance, quantum-mechanical time reversal was used to develop novel boson sampling schemes[7] and to prove the duality between two fundamental optical operations, beam splitter and squeezing transformations.

[8] In formal mathematical presentations of T-symmetry, three different kinds of notation for T need to be carefully distinguished: the T that is an involution, capturing the actual reversal of the time coordinate, the T that is an ordinary finite dimensional matrix, acting on spinors and vectors, and the T that is an operator on an infinite-dimensional Hilbert space.

All three of these symbols capture the idea of time-reversal; they differ with respect to the specific space that is being acted on: functions, vectors/spinors, or infinite-dimensional operators.

One important property of an EDM is that the energy shift due to it changes sign under a parity transformation.

This is correct; if a quantum system has degenerate ground states that transform into each other under parity, then time reversal need not be broken to give EDM.

Experimentally observed bounds on the electric dipole moment of the nucleon currently set stringent limits on the violation of time reversal symmetry in the strong interactions, and their modern theory: quantum chromodynamics.

Experimental bounds on the electron electric dipole moment also place limits on theories of particle physics and their parameters.

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.

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.

Strong measurements (both classical and quantum) are certainly disturbing, causing asymmetry due to the second law of thermodynamics.

[1] This type of asymmetry is independent of CPT symmetry but has not yet been confirmed experimentally due to extreme conditions of the checking proposal.

In 2024, experiments by the University of Toronto showed that under certain quantum conditions, photons can exhibit "negative time" behavior.

Using the cross-Kerr effect, the team measured atomic excitation by observing phase shifts in a weak probe beam.

The results showed that atomic excitation times varied from negative to positive, depending on the pulse width.