- #1

Spinnor

Gold Member

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## Main Question or Discussion Point

Consider a compressible fluid such as air. Assume we can neglect viscosity. We might describe such a fluid at some small region with a set of numbers. Three numbers would give the components of the velocity vector of the air at that small region and two more numbers would give the density and temperature of the air in that same small region.

Now suppose we have continuous functions of position and time that give the velocity, density, and temperature of air in some large region of interest. If we evaluate these functions at a "point" we must be clear that these functions only make sense if the "point" is in fact a region that is macroscopically small but large in the sense that the region contains many molecules. So we have continuous vector and scalar fields that describe the state of air which on a large scale can be thought of as a continuous compressible substance when in fact air is made up of numerous particles.

In a similar manner can one envision a multitude of discrete "things" (points, lines, or surfaces ect. with extra properties as needed to solve the problem) such that a very small region (say 10^-60 m^3) would contain many of these "things" so that for all practical purposes one would have a continuous field made up of discrete things that sit in spacetime (or are spacetime?) that would be properly described by a spinor field? Can we "build" some "structure" that sits in spacetime and we can visualize that is properly described by spinors?

If there is a small compact extra dimension, does this help solve my problem?

Thank you for any thoughts.

Now suppose we have continuous functions of position and time that give the velocity, density, and temperature of air in some large region of interest. If we evaluate these functions at a "point" we must be clear that these functions only make sense if the "point" is in fact a region that is macroscopically small but large in the sense that the region contains many molecules. So we have continuous vector and scalar fields that describe the state of air which on a large scale can be thought of as a continuous compressible substance when in fact air is made up of numerous particles.

In a similar manner can one envision a multitude of discrete "things" (points, lines, or surfaces ect. with extra properties as needed to solve the problem) such that a very small region (say 10^-60 m^3) would contain many of these "things" so that for all practical purposes one would have a continuous field made up of discrete things that sit in spacetime (or are spacetime?) that would be properly described by a spinor field? Can we "build" some "structure" that sits in spacetime and we can visualize that is properly described by spinors?

If there is a small compact extra dimension, does this help solve my problem?

Thank you for any thoughts.