Neil Turok

speaker

2,693 appearances 2 recordings 1 series first heard Apr 2025 last heard 22 Jun

Neil Turok’s voice in public audio — every appearance, attributed to the second.

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Recordings per month over the last 12 months — 1 in all, peaking in Jun 2026 with 1.

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The way you do it is with projection operators.

Even if I'm in Minkowski space, every vector can be uniquely expressed as a linear combination of, let's say, space-like and time-like vectors.

There's nothing singular about it.

And the way you project, you can still project a vector onto its components, space-like or time-like.

So you can do the same thing in this Hilbert space.

But what you have to do is replace the Born rule.

In quantum mechanics, the probability for an event is the inner product between an initial state and a final state squared.

Okay.

And now, if you were going to normalize this, so normally we think of those states as being normalized.

You know, integral of wave function squared is one.

But imagine you can't normalize now because you're in this more general space.

So what you do is you replace the Born formula, I, then some kind of matrix transitioning you from I to F. This is some time evolution operator.

So IF, IS, that's called the S matrix, ISF squared would be the normal procedure.

So let's replace the initial state.

So we've got two copies of the initial state because we have this thing squared.

Replace the II with dividing by its norm.

Now you have a projection operator.

So a completely equivalent formulation of the Braun rule is to say, project onto initial state,

evolve with the S matrix, project onto the final state, evolve with the S dagger complex conjugate, and trace the answer.

Trace means sum over all states.

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