Standard twistor theory involves a complex projective
3-space PT which naturally divides into two halves PT+
and PT–, joined by their common 5-real-dimensional
boundary PN. However, this splitting has two quite
different basic physical interpretations, namely
positive/negative helicity and positive/negative
frequency, which ought not to be confused in the
formalism, and the notion of “bi-twistors” is introduced
to resolve this issue. It is found that quantized bi-
twistors have a previously unnoticed G2* structure,
which enables the split-octonion algebra to be directly
formulated in terms of quantized bi-twistors, once the
appropriate complex structure is incorporated.