Order 3 tumbling of the vectors is not smooth but occurs in discrete flips. The order 3 equivalent to a photon is a gluon.
In QCD, the theory behind the nuclear strong force, quarks have a property called colour, which can be either red, green or blue, or anti-red, anti-green or anti-blue [[i]].
It might be possible that the colours are not actually constant, but cycle round, flipping between 3 states, for example a coloured particle might go “red, green, blue, red, green, blue, …”. This way particles that are far apart are pretty much identical, but when they are close the phase becomes important.
There is a nice and simple relationship between these colours and three dimensional axes:
The anti-colours point of course in the opposite direction.
So how could a gluon look like in this scheme? If a gluon spins around between three states which are equivalent to the axes of the three space dimensions then there are 8 possible types of gluon, analogous to the corners of a cube:
Building a helix in order 3 is tricky since it doesn’t curve back into the negative direction, like order 4 does in the complex plane. If an isolated pattern that is the order 3 equivalent to an electron exists, it would move at the speed of light, but at an angle to our perceived time dimension, so we would not be able to observe it. This pattern is what we see as an up or down quark. It would blink into and out of existence like a virtual particle. It would continuously fire out gluons the same way as an electron interacts with photons. This would explain quark confinement.
In order to perceive it as a stable particle we need to make sure that it persists down the dominant timeline, which is the diagonal between the three time dimensions tx,ty,tz.
There are at least two ways this can be done.
One way is to pair up each quark with its exact opposite, or anti-quark. The combined pattern is then a quark and its anti-quark connected by a stream of gluons. We call the particles that correspond to these patterns Mesons.
If we represent the direction this pattern travels through the time dimensions as (tx,ty,tz) we could notionally say that the combination of quark travelling along (1,0,0) with quark (-1,0,0) gives a pattern that corresponds to (0,0,0) and is therefore stable along the diagonal (1,1,1), the dominant time direction.
The other way is to make a pattern out of three quarks of different colours also connected by gluons. This appears to be particularly stable, since the combined pattern actively follows the dominant timeline. Using the same notional notation as above we combine (1,0,0), (0,1,0) and (0,0,1) to give (1,1,1). We call the particles that correspond to these patterns Baryons.
In this diagram the three coloured axes represent three time dimensions, and the grey arrow is the dominant timeline down the diagonal. Three quarks, each propagating down one time dimension, together remain on the grey diagonal.
[[i]] Harald Fritsch, Quarks:the stuff of matter