What Precisely Does Preferred Foliation Mean?

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In summary, preferred foliation is a representation of the space as an infinite set of parallel (but possibly curved) 2-dimensional surfaces. It is a way of avoiding the problem of preferred frame in relativity. The principle of relativity suggests that no foliation of 4-dimensional spacetime should be preferred. By contrast, the theories with a preferred foliation of spacetime suggest that that spacetime has a (hidden) onion structure that does not depend on the observer.
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What Precisely Does "Preferred Foliation" Mean?

https://www.physicsforums.com/showthread.php?p=2921342#post2919489", Demystifier wrote:
Demystifier said:
The only (currently known) way to avoid preferred foliation is the evolution with respect to a scalar parameter s.

What precisely does "preferred foliation" mean? I've seen the term used here in the QM section quite a bit but never explained. I tried googling it but didn't find any definitions just plenty of usage.

I have a very very rough idea what a foliation in mathematics means but don't understand the term "preferred foliation."

It seems to be something related to "preferred frame" and causal relationships over time. Any suggestions or pointers for further research would be greatly appreciated.
 
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In a 3-dimensional world, foliation is a representation of the space as an infinite set of parallel (but possibly curved) 2-dimensional surfaces. Like an onion. In fact, any 3-dimensional object (like an apple) can be foliated in an infinite number of different ways. But for an onion, there is a preferred foliation - the foliation defined by the physical leafs themselves.

In the 4-dimensional world (associated with relativity) the idea is the same, but now the leafs are 3-dimensional hypersurfaces which can be thought of as spaces with constant time. The principle of relativity suggests that no foliation of 4-dimensional spacetime should be preferred. By contrast, the theories with a preferred foliation of spacetime suggest that that spacetime has a (hidden) onion structure that does not depend on the observer.
 
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Thanks for the definition Demystifier.

Demystifier said:
In the 4-dimensional world (associated with relativity) the idea is the same, but now the leafs are 3-dimensional hypersurfaces which can be thought of as spaces with constant time.

Does this mean that time represents the transition between the leaves in the foliation represent the movement of time?

Demystifier said:
The principle of relativity suggests that no foliation of 4-dimensional spacetime should be preferred.

Does this mean that there would be different valid foliations existing at the same time and their validity would be equal under relativity in much the same way that there is no preferred frame in relativity?

Demystifier said:
By contrast, the theories with a preferred foliation of spacetime suggest that that spacetime has a (hidden) onion structure that does not depend on the observer.

What is it about the theories that causes them to require a preferred foliation? What are the implications of a theory having a preferred foliation?

Finally, is this related to the issues of quantum gravity since quantum mechanics seems to have a sense of fixed time while relativity does not?
 

Related to What Precisely Does Preferred Foliation Mean?

1. What is meant by "preferred foliation"?

"Preferred foliation" refers to a specific orientation or arrangement of layers in a geological or biological sample that is considered to be the most informative or useful for analysis. It is the preferred or ideal way of looking at the sample in order to gain the most insight into its structure or composition.

2. How is the preferred foliation determined?

The preferred foliation is determined through various methods such as observation, laboratory analysis, or mathematical modeling. It is often based on the dominant or most prominent features of the sample, such as the direction of mineral alignment or the orientation of sedimentary layers.

3. Why is understanding the preferred foliation important in scientific research?

Understanding the preferred foliation is important because it provides valuable information about the history and formation of a sample. It can also give insights into the physical or chemical processes that have occurred in the sample, and can aid in the interpretation of data and results.

4. Can the preferred foliation change over time?

Yes, the preferred foliation can change over time due to various factors such as external forces, changes in environmental conditions, or the natural aging of the sample. This is why it is important for scientists to document and analyze the preferred foliation at different stages of a sample's development.

5. How does the concept of preferred foliation apply to other fields of study?

The concept of preferred foliation is not limited to geology or biology, but can also be applied to other fields such as engineering, materials science, and archaeology. In these fields, the preferred foliation may refer to the ideal orientation or arrangement of components in a structure or material, or the most informative way of examining and interpreting artifacts or historical objects.

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