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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Appearances
If the equations of motion have more than two derivatives, then the energy, or Hamiltonian, is what we call unbounded below.
You can have configurations of arbitrarily negative energy in this higher derivative system.
Now that, on the face of it, looks like a disaster because if you brought such a system into contact with the real world, where generally the energy is positive,
This system could interact with everything else and its energy could go down and the energy of everything else would go up.
So it's an infinite source of energy.
And we don't see such things in nature.
And they might be wildly unstable.
So this is called the Ostrogradsky instability.
In general, it's true.
If you tried to write down a high derivative system, you will find it's unstable.
In general, there are exceptions, but in general, that's a problem.
So people got very worried about this and often when people were building quantum field theories, and actually the first person, as far as I know, the first person to try to use a higher derivative quantum field theory,
was Homi Bhabha, who was an Indian nuclear physicist.
And people were trying to understand nuclear forces, so they're trying all kinds of models and field theories.
And Bhabha and Heisenberg and many other field theorists played with high derivative theories.
The reason they played with them
is they thought it would make quantum field theory more convergent.
It would reduce the infinities.
And it's related to the fact that gravity with four derivatives is renormalizable.
So it's a similar reason.
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