## Cones

Cones

Height is always a time unit

#### Light cone

Light cone

Projection of cone onto spatial graph is c t

#### Branch cone (“Quantum branch cone”)

Branch cone (“Quantum branch cone”)

Is projection of cone onto branchial state graph iℏ ?

#### Rule cone

Rule cone

Projected distance is unit of computational translation effort

[ Previously non-measured computational conversion effort / distance ; cf. constant in algorithmic complexity ]

## Hilbert space

Hilbert space

The distance in branchial space is between states (e.g. strings or hypergraphs)

What kind of a space is this?

Does it have a real norm or something else?

Consider even distances between strings. Or graphs.

What kind of a space is this?

Does it have a real norm or something else?

Consider even distances between strings. Or graphs.

What is a discrete approximation to Hilbert space?

## Quantum amplitudes

Quantum amplitudes

To get from one quantum state to another, requires follows branches on multiway system

Linearity from combining paths

Actual bra-ket requires projecting from one set of states to another: approximated by distance on the branchial state graph.

Linearity from combining paths

Actual bra-ket requires projecting from one set of states to another: approximated by distance on the branchial state graph.

## Quantum reality

Quantum reality

Invariance of multiway causal network under projections into different branches

## Quantum computing

Quantum computing

We have non-determinism in the sense of NDTMs, but not in the sense of randomness

Does this mean we can solve NP problems? No, because of causal invariance. There is a tradeoff between objective reality in QM and the ability to do NP computations.

What is the relation between NDTMs and confluent systems?

What is the relation between NDTMs and confluent systems?

Physically realizable NDTMs are confluent ones?