A question about Hawking's path integral methods

[Fredrik]

Hawking's path integral methods seem to rely on the assumption that superpositions of different metrics are meaningful. (If I'm wrong about this, let me know). But are they? Aren't these superpositions destroyed by decoherence. And aren't they also in contradiction with Penrose's claim that there is no well-defined time evolution operator on a superposition of two spacetimes, and that such superpositions should therefore be highly unstable?

 

[humanino]

Since nobody answered yet, I give my opinion, but be warned : I might be wrong too since I am not a specialist. I think there is no coherent superposition of topologically dinstinct metrics. If I understood correctly, there is coherent superposition only of topologically similar metrics. You should use one of the other threads where discussions already began on this problem.

 

[Fredrik]

The reason I started a new thread is that my question is not really about Hawking's recent result about black holes. It's about the method he used to obtain that result and many others. I hope this will be a discussion about superpositions, and not about spacetime geometry and topology.

Let me explain more clearly what I mean.

When we use path integral methods to compute the probability of an event, we don't include amplitudes for both "the cat's dead" and "the cat's alive".

The reason is that it's not possible to construct a superposition between two very different states of a macroscopic object. Some people would blame this on decoherence caused by interactions with the environment. Others (especially Roger Penrose) would blame it on a quantum gravity effect. Penrose claims that gravity makes macroscopic superpositions impossible.

If we don't add the amplitudes for "the cat's dead" and "the cat's alive" because a cat's big and heavy, why would it make sense to add amplitudes for two different distributions of matter throughout the entire universe over a period of 13.7 billion years?!

 

[Chronos]

Add degrees of freedom and your problem is solved. Hawking is very smart. He is not infallible.

 

[Fredrik]

Add degrees of freedom and your problem is solved.

I have no idea what you're trying to say here. What degrees of freedom? And why? How does it solve the problem?