Is electromagnetic pressure (stress energy tensor) positive or negative in the direction of the electric field (assuming $B=0$)?

Question

Suppose we have an electric field pointing along the $x$-axis, and $B = 0$. The diagonal spatial components of the stress-energy tensor will all have the same magnitude, but the $y$ and $z$ components will have the opposite sign of the $x$ component. Which ones are positive? I am seeing conflicting information in different sources, and Wikipedia even says that this is a sign convention. Surely whether a pressure in a given direction is positive or negative cannot be a sign convention.

Answer 1

Both electric and magnetic fields carry a tension (i.e. a negative pressure) along the field direction. They also carry a positive pressure in the directions perpendicular to the field. So in Faraday's heuristic understanding of fields in terms of field lines, the field lines carry tension like strings but repel adjacent field lines.

A parallel plate capacitor is a simple example. If you consider the left capacitor plate, it feels a force towards the right plate, and you can compute that force by considering the pressure carried by field lines. There's zero field on the left side of the left plate, and nonzero field on the right side of the left plate, so to get the right direction we must assign the field a tension.

When people talk about the sign of elements of $T_{ij}$ being convention-dependent, they clearly don't mean that the sign of pressure is convention-dependent. They mean that $T_{ii}$ may either equal the pressure $p_i$ along the $i$ direction, or $-p_i$, depending on the convention. For more discussion of the origins of the different conventions, see this answer.

Answer 2

This can easily be found out by measuring a radio wave. According to Wikipedia:

The wave's magnetic field is perpendicular to the electric field, and the electric and magnetic field are oriented in a right hand sense with respect to the direction of radiation.

However, experimental facts should be checked. Because it also contains nonsense:

The polarization of radio waves is determined by a quantum mechanical property of the photons called their spin.

It is more of a chirality. Looking in the direction of motion, there are - as described by you - theoretically possible right-handed or left-handed electric and magnetic field components standing on top of each other. In reality, there can only be one variant for the EM radiation of electrons. Otherwise there would be no magnetic antennas. It can be assumed that an anti-matter antenna, operated with positrons, has the complementary chirality.

The argument with the sign convention can also be found here in the forum. This is actually incomprehensible, because the choice of directions for the magnetic and electric fields is historically a convention. But once standardized, both signs (plus-minus or north pole-south pole) are clearly defined. To relativize the two theoretically possible chiralities of the magnetic and electric field components of radio waves is too short-sighted.