Basic Twistor Theory, Bi-twistors, and Split-octonions - Roger Penrose

Abstract: Twistor theory was introduced in the mid 1960s as an approach to
combining quantum theory with space-time structure. A driving
force behind the introduction of Twistor Theory was to combine the
quantum-field theoretic requirement of positive frequency with the
structure of space-time. In order to achieve this, the notion of
twistor space was introduced to codify the structure of space-time in
a way which related it to the splitting of the twistor space into two
halves, one representing positive frequency, and the other
representing negative frequency. 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. The points of the space PN represent light rays in
Minkowski space-time. 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 G 2 * structure, which enables the split-
octonion algebra to be directly formulated in terms of quantized bi-
twistors, once the appropriate complex structure is incorporated.
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[proximitygaming]

I feel like this is one of those scientists/mathematicians that go down as famous for fundamental discoveries, except that Penrose is alive in our era.

[postiemania]

At 8:38 this is the field geometry of an actual engine I am building. Sir Roger Penrose and his work is very inspiring to me.

[patrickmendoza]

Roger Penrose: "But anyway, he was very useful to me."

[Killer_Kovacs]

I came to nearly the same conclusions.
Can hyperspheres be monopolar?

[SpotterVideo]

What do the Twistors of Roger Penrose and the Hopf Fibrations of Eric Weinstein and the "Belt Trick" of Paul Dirac have in common?
It takes two complete turns to get down the "rabbit hole" (Alpha Funnel 3D--->4D) to produce one twist cycle (Quantum unit).
Can both Matter and Energy be described as "Quanta" of Spatial Curvature? (A string is revealed to be a twisted cord when viewed up close.) Mass= 1/Length

[KipIngram]

You know, I SO wish I could find an introduction to this stuff that actually taught it from first principles. Everything I've been able to find is already just a little out of my reach, and I haven't been able to find the "ladder rungs" I need to cover the gap yet. 😞

[LibrawLou]

@Hyperduality : Dialectic rules under ever-onward Synthesis!

[JAYMOAP]

Ironic but Penrose complained against string theory dealing with higher dimensions, but here you are he construct 6 dimensional model haha. On the other hand, his gluing is essentially a gauging procedure so he derive gauge theory just like string theory does. He doesn't realise this but he essentially indeed in the framework of string theory.

[timohelenius]

you must think sometimes with brains, its most difficult situation in your life

[timohelenius]

in finland the more the more cloud the singer will gave loud, it is the best in finland, but i like more mozart

[KaliFissure]

Surface(cos(u/2)cos(v/2), cos(u/2)sin(v/2), sin(u)/2), u, 0, 2pi, v, 0, 4pi

I suggest applying twistor theory to the above manifold.

[gene]

Interesting, as this could describe “Worm Holes”. I’m not a physicist, but I am curious if the positive and negative hemispheres, could be obtained by the use of, synthetic materials, negative refractive indexed meta materials (left-handed electromagnetic rotation); and natural material, (right-handed electromagnetic rotation). Just a thought…

[timohelenius]

if you google robots sight from japan then follow ...

[thomasolson]

The tangent plane on the sphere is where the algebra happens. Instead of Pythagoren Theorm, it's the quadratic formula.