- #1
MathematicalPhysicist
Gold Member
- 4,699
- 371
hi, i encountered this term in julian barbour webpage and i will like it if someone can tell me more about them?
loop quantum gravity said:hi, i encountered this term in julian barbour webpage and i will like it if someone can tell me more about them?
jeff said:I couldn't find this term on barbour's site or by googling.
well let's see if we are speaking about the same page.jeff said:I couldn't find this term on barbour's site or by googling. But knowing what he works on, by a "stratified" space he may have meant what is more commonly referred to as a "foliated" space, which roughly speaking is a space that has been expressed as a union of disjoint hypersurfaces, very much like a salami as a union of slices. In the context of the physics of spacetime, these hypersurfaces represent surfaces of simulteneity, with different observer's seeing the universe as being sliced up - foliated - in different ways. If this turns out not to be what he meant by "stratified", never mind.
I also plan to post on this website a paper explaining the rather brief remarks on p. 344 of my The End of Time about stratified manifolds, which are models of my central notion of Platonia (as explained in that book). Stratified manifolds occur widely in theoretical physics, and a question that has long interested me is the effect, if any, that the strata of these manifolds exert on classical dynamical trajectories and quantum wave functions defined on such manifolds.
Stratified manifolds are mathematical structures that describe the possible configurations of a system at different points in time. They are used in the study of dynamics and can represent complex systems such as the universe.
Julian Barbour is a British physicist and philosopher who has made significant contributions to the study of time and the nature of reality. His research on stratified manifolds has provided new insights into the foundations of physics and our understanding of the universe.
By exploring the possible configurations of a system over time, stratified manifolds allow us to better understand the dynamics of complex systems like the universe. They provide a framework for studying how the universe evolved and how it may continue to evolve in the future.
Stratified manifolds have practical applications in fields such as cosmology, quantum mechanics, and computer science. They can be used to model and predict the behavior of complex systems, and have been applied to problems in areas such as engineering, finance, and biology.
While stratified manifolds have proven to be a valuable tool in understanding complex systems, there is still ongoing debate and controversy surrounding their use. Some critics argue that they may not accurately represent the true nature of reality and that there are limitations to their applicability. However, many scientists continue to use and expand upon stratified manifolds in their research to gain further insights into the workings of the universe.