T-symmetry is the symmetry of physical laws under a time-reversal transformation.

Physicists distinguish time asymmetries that are intrinsic to the dynamic laws of nature, and those that are due to the initial conditions of our universe. The T-asymmetry of the weak nuclear force is of the first kind, while the T-asymmetry of the second law of thermodynamics is of the second kind.

Mathematical description of T-symmetry

In its simpler form, T-symmetry arises if one replaces t with −t and sees if the same equation arises. This will occur if all of the terms of the equation are even powers of t and if all of the derivatives are of even order. Conversely, T-symmetry will be broken if there are any odd powers of t or if there are derivatives of odd order. One consequence is that T-symmetry will exist if the equation describing the physical law involves only the acceleration (such as with Newton's laws of physics) and will be broken if the equations include any terms that involve the velocity (such as with laws which include friction).

However, velocity dependent forces do not always break T-symmetry. Magnetism is velocity dependent but T-symmetric. Some systems of first order differential equations, such as the Hamiltonian formulation of classical mechanics, and the standard formulation of QED are T-symmetric.

To further understand T-asymmetry and the effect of the initial conditions, physicists use an alternative, more sophisticated definition of T-symmetry. Physical laws can almost always be separated in 2 parts: a "static" part describing the possible state S, and a dynamic part U(t) describing the dynamics of moving from one state to another. A law is said to be time-symmetric if there is a mapping T between states so that U(−t) = T⁻¹ U(t) T. We'll see that such a mapping exists for the second law of thermodynamics.

T-symmetry violations in particle physics

There is only one observed process in particle physics in which T-symmetry appears to be violated, the decay of the neutral kaon. This was first observed as a violation of CP-symmetry in 1964 in the Brookhaven National Laboratory.

Because there are strong theoretical reasons for believing that CPT-symmetry holds, but it is experimentally observed that CP-symmetry is sometimes broken there must be a balancing T-symmetry violation in order to preserve CPT-symmetry.

In 1998, a small T-symmetry violation was directly observed in decays of neutral kaons in 1998 in the KTeV experiment of the Fermilab.

In addition, T-symmetry is also believed to be violated in some processes involving the strong nuclear force which occur at much higher energies than can be practically observed. The reason for believing this is an argument by physicist Andrei Sakharov who developed the criteria for there to be a difference in the amount of matter and anti-matter in the universe assuming that the universe did not start out with this asymmetry. One of the criteria is that CP and hence T-symmetry is violated.

Because there appears to be more matter than anti-matter in the universe, and because assuming that the universe just started out that way is theoretically ugly, it is strongly believed that there are some very high energy processes which are not T-symmetric. Incorporating these hypothetical processes in a grand unified theory is an area of active research.

In addition, in some but not all interpretations of quantum mechanics, T-symmetry is broken by the act of measurement which collapses the wavefunction. T-symmetry is thus broken in the Copenhagen interpretation of quantum mechanics, but not in the many-worlds interpretation (MWI).

Since it is impossible to experimentally distinguish between these interpretations, no observable T-asymmetry can be traced to this cause.

Second law of thermodynamics

While T-symmetry appears to hold for most microscopic laws, it often does not hold for laws describing the behavior of bulk materials, most notably the second law of thermodynamics, and the asymmetry in macroscopic laws appears not to be the result of microscopic asymmetries. Any equation which includes dissipation of energy through friction or viscosity or converts usable energy into heat will not exhibit T-symmetry.

Physicists say that we observe a constant increase of entropy only because of the initial state of our universe. Other possible states of the universe would actually result in decrease of entropy. To illustrate it simply, if the velocity of all particles was suddenly inverted, the world would go in reverse, and the second law of thermodynamics would not hold anymore (entropy would decrease).

So the apparent T-asymmetry of our world is a cosmology problem. Cosmology has to explain why the universe started with this incredibly low entropy, and does not finish with an incredibly low entropy. Indeed, thermodynamics says that a low-entropy-ending universe would be just as unlikely that a low-entropy-starting universe.

See also

• Loschmidt's paradox

External links

• http://content.aip.org/APCPCS/v549/i1/957_1.html
• PhysicsWeb: Time's arrow seen in particle decays
• Cosmic inflation and the arrow of time
• The Physical basis of the Direction of Time