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 · last 12 monthsRecordings per month over the last 12 months — 1 in all, peaking in Jun 2026 with 1.
Appearances
Now, the disaster that happens in the quantum theory is slightly different than the classical.
what you find is that the space of quantum states does not have a positive inner product.
It has what we call negative inner product, and states of negative norm are called ghosts, traditionally in physics.
What people have often said, and what we realized is wrong, is that a state with negative norm corresponds to a negative probability.
Okay?
And you'll find this argument everywhere in the literature, or many places in the literature, that, whoops, we can't allow negative norms, they're unphysical, they correspond to negative probabilities.
That's just not true, because a quantum state is nothing but a label for a system.
Its norm is neither here nor there.
You can't observe the norm of a quantum state, okay?
So you've got these labels.
Some of your vectors in this abstract space of state have positive length squared, let's say, and some have negative.
So it's like in Minkowski spacetime.
We have distances which are space-like or time-like, and one of them is negative and the other's positive, and some are null.
There's some null directions.
Then the question we wanted to address is, can you live with a quantum theory in a space of states which has these three possibilities, positive, null, negative, norm state?
Mathematicians were studying this, and this is called a Krine space.
It's a generalization of Hilbert space.
And what we found is that provided there is a certain discrete symmetry in your theory, which we call ghost parity symmetry, and it's a very trivial thing.
It's an operator, which when you act on a negative norm state gives you minus one, and acting on a positive norm state gives you plus one.
If you have a theory where that operator is a symmetry of the theory, you can now define transition probabilities without ever normalizing the state.
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