Hartle-Hawking sum over all possible metrics?

In summary, physicists Stephen W Hawking and James B Hartle proposed that the universe, in its origins, had no boundary conditions in both space and time. In order to prove that our universe was the most likely outcome, they considered a sum over all possible metrics. However, for simplicity, they focused on a subset of compact Euclidean metrics, allowing them to calculate the probability of a given universe more easily.
  • #1
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TL;DR Summary
According to Hartle-Hawking state, could we build a sum over all possible metrics (including non-compact ones)?
Physicists Stephen W Hawking and James B Hartle 1 proposed that the universe, in its origins, had no boundary conditions both in space and time.

To do that, they proposed a sum over all compact euclidean compact metrics. I have heard that they only considered these metrics in order to simplify the calculations (since their aim was to prove that our universe was the most likely outcome). Then, does that mean that they originally considered a sum over all possible metrics (not only compact euclidean ones)? Did they really considered the subset of compact Euclidean metrics just to simplify the calculations of the model (but their model was actually considering the sum over all possible metrics)?
 
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Yes, Hawking and Hartle considered a sum over all possible metrics in order to prove that our universe was the most likely outcome. However, in order to simplify the calculations, they focused on a subset of compact Euclidean metrics. This allowed them to calculate the probability of a given universe much more easily. Thus, their model does consider the sum over all possible metrics, but the focus on the subset of compact Euclidean metrics allowed them to simplify the calculations.
 

FAQ: Hartle-Hawking sum over all possible metrics?

What is the Hartle-Hawking sum over all possible metrics?

The Hartle-Hawking sum over all possible metrics is a mathematical concept proposed by physicists James Hartle and Stephen Hawking. It suggests that the universe can be described as a sum over all possible metrics, or ways of measuring the geometry of space-time. This theory is part of the larger field of quantum cosmology, which aims to explain the origin and evolution of the universe using principles of quantum mechanics.

How does the Hartle-Hawking sum over all possible metrics work?

The Hartle-Hawking sum over all possible metrics works by considering all possible ways in which the geometry of space-time could be measured. This includes both classical and quantum descriptions of space-time. The theory suggests that the universe can be described as a superposition of all these possible metrics, with each metric having a certain probability of occurring. By summing over all these possibilities, the theory aims to provide a complete description of the universe.

What is the significance of the Hartle-Hawking sum over all possible metrics?

The Hartle-Hawking sum over all possible metrics has significant implications for our understanding of the universe. It suggests that the universe may have originated from a state of pure potentiality, with no definite geometry or laws of physics. This challenges traditional notions of a singular beginning of the universe and raises questions about the role of observation and measurement in shaping the universe.

How does the Hartle-Hawking sum over all possible metrics relate to the theory of relativity?

The Hartle-Hawking sum over all possible metrics is closely related to the theory of relativity, particularly the concept of space-time curvature. The theory suggests that the geometry of space-time is not fixed, but rather a result of the sum over all possible metrics. This is in line with the principles of general relativity, which state that the curvature of space-time is determined by the distribution of matter and energy.

Are there any criticisms of the Hartle-Hawking sum over all possible metrics?

Yes, there are some criticisms of the Hartle-Hawking sum over all possible metrics. One criticism is that the theory is purely mathematical and does not provide any physical predictions that can be tested. Additionally, the theory does not address the issue of time in the universe, as it suggests that time is not a fundamental aspect of the universe. Some physicists also argue that the theory does not fully explain the origin of the universe, as it does not address the initial conditions that led to the sum over all possible metrics.

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