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K. Kleinknecht and U. Uwer
9.2.1.2 Time Reversal T
This operation consists in reversing the sign of the time axis t. Under this operation
t → −t, the velocity
v, the momentum
p and the angular momentum
J change sign,
while the force
F remains unchanged under T . From the fact that the Coulomb and
Lorentz forces are invariant, we derive the result that
E →
E and
B →
B under T ;
for the potentials, V → V but
A → −
A.
9.2.1.3 Dipole Moments
Elementary particles with spin may have electric or magnetic dipole moments.
The spin
s has the dimensions of an angular momentum, and therefore remains
unchanged under parity and changes sign under time reversal.
The potential energy of an electric or magnetic dipole in an external field is
proportional to the scalar product of the electric or magnetic moment with the
strength of the external electromagnetic field. Since the moments must be parallel
to the spin, the potential energy is given by
− d e
s ·
E for the electric case
(9.4)
and
− d m
s ·
B for the magnetic case
(9.5)
Here d e and d m are the electric and magnetic dipole moments, respectively. If we
consider the transformation properties of
s,
E and
B under P and T , it turns out
that for both operations d m → d m and d e → −d e . This means that observation of a
nonvanishing electric dipole moment would violate any invariance under parity and
time-reversal transformations.
In classical physics, all processes are invariant under parity and under time
reversal. In the case of mirror symmetry, this means that a physical experiment
will lead to the same result as a mirror-imaged experiment, since the equations of
classical physics are left-right symmetric. In a similar way, the classical motion of
one particle can be reversed, e.g. by playing a film backwards, and this inversion
of the motion corresponds formally to time reversal. Again, the laws of motion are
invariant under T , and the reversed motion follows the same path backwards as
forwards.
Of course, this is no longer the case if many particles move and interact with
each other; in this case the second law of thermodynamics ensures that entropy is
increasing, thus defining an arrow of time.
K. Kleinknecht and U. Uwer
9.2.1.2 Time Reversal T
This operation consists in reversing the sign of the time axis t. Under this operation
t → −t, the velocity
v, the momentum
p and the angular momentum
J change sign,
while the force
F remains unchanged under T . From the fact that the Coulomb and
Lorentz forces are invariant, we derive the result that
E →
E and
B →
B under T ;
for the potentials, V → V but
A → −
A.
9.2.1.3 Dipole Moments
Elementary particles with spin may have electric or magnetic dipole moments.
The spin
s has the dimensions of an angular momentum, and therefore remains
unchanged under parity and changes sign under time reversal.
The potential energy of an electric or magnetic dipole in an external field is
proportional to the scalar product of the electric or magnetic moment with the
strength of the external electromagnetic field. Since the moments must be parallel
to the spin, the potential energy is given by
− d e
s ·
E for the electric case
(9.4)
and
− d m
s ·
B for the magnetic case
(9.5)
Here d e and d m are the electric and magnetic dipole moments, respectively. If we
consider the transformation properties of
s,
E and
B under P and T , it turns out
that for both operations d m → d m and d e → −d e . This means that observation of a
nonvanishing electric dipole moment would violate any invariance under parity and
time-reversal transformations.
In classical physics, all processes are invariant under parity and under time
reversal. In the case of mirror symmetry, this means that a physical experiment
will lead to the same result as a mirror-imaged experiment, since the equations of
classical physics are left-right symmetric. In a similar way, the classical motion of
one particle can be reversed, e.g. by playing a film backwards, and this inversion
of the motion corresponds formally to time reversal. Again, the laws of motion are
invariant under T , and the reversed motion follows the same path backwards as
forwards.
Of course, this is no longer the case if many particles move and interact with
each other; in this case the second law of thermodynamics ensures that entropy is
increasing, thus defining an arrow of time.