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Do the full inhomogeneous Maxwell equations obey parity (P) and time reversal (T) symmetry separately or only the full CPT symmetry?

I believe the homogeneous Maxwell equations obey parity and time reversal symmetry separately - is that right? The homogeneous Maxwell equations reduce to a wave equation in which space and time appear as second order derivatives.

Here's my effort at answering my first question.

In the first inhomogeneous equations one has:

$$\mathbf{\nabla . E} = \frac{\rho}{\epsilon_0}$$

If I change the sign of x,y,z, in $\mathbf{\nabla . E}$ then I must change the sign of $\rho$ to balance it.

In the third equation one has:

$$ \mathbf{\nabla \times E} = - \frac{\partial \mathbf{B}}{\partial t}$$

As the sign of x,y,z has changed then the sign of t must change to balance it.

Thus we must have CPT symmetry. This can be checked in the last equation:

$$\mathbf{\nabla \times B} = \mu_0 \mathbf{j} + \frac{1}{c^2}\frac{\partial \mathbf{E}}{\partial t}$$

The sign of x,y,z in $\mathbf{\nabla \times B}$ has changed. This is balanced by a sign change of t in $\frac{1}{c^2}\frac{\partial \mathbf{E}}{\partial t}$. The sign of $\mathbf{j}$ has changed because the charge has changed sign.

Thus the inhomogeneous Maxwell equations obey CPT symmetry rather than C,P or T alone.

Is this reasoning right?

Do the full inhomogeneous Maxwell equations obey parity (P) and time reversal (T) symmetry separately or only the full CPT symmetry?

I believe the homogeneous Maxwell equations obey parity and time reversal symmetry separately - is that right? The homogeneous Maxwell equations reduce to a wave equation in which space and time appear as second order derivatives.

Here's my effort at answering my first question.

In the first inhomogeneous equations one has:

$$\mathbf{\nabla \cdot E} = \frac{\rho}{\epsilon_0}$$

If I change the sign of x,y,z, in $\mathbf{\nabla . E}$ then I must change the sign of $\rho$ to balance it.

In the third equation one has:

$$ \mathbf{\nabla \times E} = - \frac{\partial \mathbf{B}}{\partial t}$$

As the sign of x,y,z has changed then the sign of t must change to balance it.

Thus we must have CPT symmetry. This can be checked in the last equation:

$$\mathbf{\nabla \times B} = \mu_0 \mathbf{j} + \frac{1}{c^2}\frac{\partial \mathbf{E}}{\partial t}$$

The sign of x,y,z in $\mathbf{\nabla \times B}$ has changed. This is balanced by a sign change of t in $\frac{1}{c^2}\frac{\partial \mathbf{E}}{\partial t}$. The sign of $\mathbf{j}$ has changed because the charge has changed sign.

Thus the inhomogeneous Maxwell equations obey CPT symmetry rather than C,P or T alone.

Is this reasoning right?

Do the full inhomogeneous Maxwell equations obey parity (P) and time reversal (T) symmetry separately or only the full CPT symmetry?

I believe the homogeneous Maxwell equations obey parity and time reversal symmetry separately - is that right?

Here's my effort at answering my first question.

In the first inhomogeneous equations one has:

$$\mathbf{\nabla . E} = \frac{\rho}{\epsilon_0}$$

If I change the sign of x,y,z, in $\mathbf{\nabla . E}$ then I must change the sign of $\rho$ to balance it.

In the third equation one has:

$$ \mathbf{\nabla \times E} = - \frac{\partial \mathbf{B}}{\partial t}$$

As the sign of x,y,z has changed then the sign of t must change to balance it.

Thus we must have CPT symmetry. This can be checked in the last equation:

$$\mathbf{\nabla \times B} = \mu_0 \mathbf{j} + \frac{1}{c^2}\frac{\partial \mathbf{E}}{\partial t}$$

The sign of x,y,z in $\mathbf{\nabla \times B}$ has changed. This is balanced by a sign change of t in $\frac{1}{c^2}\frac{\partial \mathbf{E}}{\partial t}$. The sign of $\mathbf{j}$ has changed because the charge has changed sign.

Thus the inhomogeneous maxwell equations obey CPT symmetry.

Is this reasoning right?

Do the full inhomogeneous Maxwell equations obey parity (P) and time reversal (T) symmetry separately or only the full CPT symmetry?

I believe the homogeneous Maxwell equations obey parity and time reversal symmetry separately - is that right? The homogeneous Maxwell equations reduce to a wave equation in which space and time appear as second order derivatives.

Here's my effort at answering my first question.

In the first inhomogeneous equations one has:

$$\mathbf{\nabla . E} = \frac{\rho}{\epsilon_0}$$

If I change the sign of x,y,z, in $\mathbf{\nabla . E}$ then I must change the sign of $\rho$ to balance it.

In the third equation one has:

$$ \mathbf{\nabla \times E} = - \frac{\partial \mathbf{B}}{\partial t}$$

As the sign of x,y,z has changed then the sign of t must change to balance it.

Thus we must have CPT symmetry. This can be checked in the last equation:

$$\mathbf{\nabla \times B} = \mu_0 \mathbf{j} + \frac{1}{c^2}\frac{\partial \mathbf{E}}{\partial t}$$

The sign of x,y,z in $\mathbf{\nabla \times B}$ has changed. This is balanced by a sign change of t in $\frac{1}{c^2}\frac{\partial \mathbf{E}}{\partial t}$. The sign of $\mathbf{j}$ has changed because the charge has changed sign.

Thus the inhomogeneous Maxwell equations obey CPT symmetry rather than C,P or T alone.

Is this reasoning right?

Do the full inhomogeneous Maxwell equations obey parity (P) and time reversal (T) symmetry separately or only the full CPT symmetry?

I believe the homogeneous Maxwell equations obey parity and time reversal symmetry separately - is that right?

Do the full inhomogeneous Maxwell equations obey parity (P) and time reversal (T) symmetry separately or only the full CPT symmetry?

I believe the homogeneous Maxwell equations obey parity and time reversal symmetry separately - is that right?

Here's my effort at answering my first question.

In the first inhomogeneous equations one has:

$$\mathbf{\nabla . E} = \frac{\rho}{\epsilon_0}$$

If I change the sign of x,y,z, in $\mathbf{\nabla . E}$ then I must change the sign of $\rho$ to balance it.

In the third equation one has:

$$ \mathbf{\nabla \times E} = - \frac{\partial \mathbf{B}}{\partial t}$$

As the sign of x,y,z has changed then the sign of t must change to balance it.

Thus we must have CPT symmetry. This can be checked in the last equation:

$$\mathbf{\nabla \times B} = \mu_0 \mathbf{j} + \frac{1}{c^2}\frac{\partial \mathbf{E}}{\partial t}$$

The sign of x,y,z in $\mathbf{\nabla \times B}$ has changed. This is balanced by a sign change of t in $\frac{1}{c^2}\frac{\partial \mathbf{E}}{\partial t}$. The sign of $\mathbf{j}$ has changed because the charge has changed sign.

Thus the inhomogeneous maxwell equations obey CPT symmetry.

Is this reasoning right?