0
$\begingroup$

In Hawking's no boundary proposal he assumed that the the amplitude for a state A (such as a given 3-manifold) is the sum of all amplitudes for histories starting at a special big-bang-state (like the south pole of a sphere) to the state A.

What if we instead we said the amplitude for a state A is the sum of all amplitudes starting at any-possible state B and ending at state A?

Would this make sense?

I think it would look like our Universe if the amplitudes for states starting at a small hot Universe like the Big Bang, outweighed most of the other amplitudes. (Such as starting almost identical to A). But none of these histories would ever have to include a state of zero-size. And you would not need a Euclidean section or imaginary time.

In Hawking's case we would be summing over closed 4-spheres. (Or the square of two hemi-4-spheres). Whereas in the second case we would be summing over $S_1\times S_3$ manifolds. (Or the square of cylinders).

We would have to assume that the amplitude for a state starting and ending at the same state is not simply 1.

$\endgroup$

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.