Lambert’s cosine law is that the intensity of a light ray hitting a surface varies by the cosine of the angle it hits at, so light hitting 90º to a plane gives all its intensity but at 0º gives none, and in-between the angle cosine gives the intensity. A light ray essentially projects its intensity onto the plane according to angle.

If ray intensity reflects the channels available across a plane, the channels light occupies vary as the cosine of its angle to the plane. The cosine law implies that two rays of light on the same axis share all the same channels because Cos(0) is one and at right angles share no channels because Cos(90) is zero, and two rays at an angle share channels by the cosine of that angle. In effect, the two rays project into each other’s channels according to angle.

Two perpendicular light rays on a plane through a node occupy every channel, as every other ray on that plane can be obtained as a projection of those rays by the cosine rule. When two light rays cross at a node point, they fill all the channels of a plane though that point. It follows that if the channel bandwidth of a line axis through a node is one, the bandwidth of a plane through a node is two. If an electron is two extreme light rays filling the channels of a line through a node, four extreme light rays are needed to fill a plane though it.

In Figure 4.9, three equal-angle extreme rays in a plane meet at a node point. How the photons in these three rays use the node channels may one day be simulated but for now it must be envisaged. If each ray fills half the bandwidth of one axis, three times that is 1.5 but the bandwidth of a plane is two. If the result is a quark, it can’t be stable because three extreme rays don’t fill the bandwidth of a plane.

Rays that aren’t at right angles will share channels at the node so each ray axis has fewer channels than a single axis. Dividing the plane bandwidth of two between three axes gives each axis a two-thirds bandwidth. Thus, filling each of the three axes in Figure 4.9 at two-thirds of an electron axis will fill the plane bandwidth, because three times two-thirds is the plane bandwidth of two. It follows that for light rays on three axes to fill all the channels of a node plane, each of the three axes must fill at two-thirds of an electron axis. Quarks must fill all the channels of a node plane to achieve stability.