Can we project a 4D object onto the 3D world?

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SUMMARY

The discussion centers on the projection of a 4D object, specifically the LightCone, into a 3D world. It is established that the LightCone, when considering the third dimension of space, manifests as a sphere expanding from a point in both forward and backward time. The inherent limitation of 3D space prevents the full embedding of 4D objects, necessitating the use of 2D cross sections for representation. Consequently, the concept of "seeing" a 4D object in 3D is fundamentally flawed, as true visualization is impossible.

PREREQUISITES
  • Understanding of 4D geometry
  • Familiarity with the concept of LightCone in physics
  • Basic knowledge of spatial dimensions
  • Experience with visual representation techniques in mathematics
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  • Research the mathematical principles of 4D geometry
  • Explore visual representation methods for higher-dimensional objects
  • Study the implications of LightCone in theoretical physics
  • Learn about dimensionality and its effects on perception and visualization
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This discussion is beneficial for physicists, mathematicians, and educators interested in the complexities of higher-dimensional spaces and their representations.

neutrino
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The LightCone in the "3D"

How does the light"cone" appear if we include the 3rd dimension of space into the picture?
 
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As a sphere growing from a point at present in both forward and backward time. The "cone" with a 3-D cross section is now a 4-D object, and you can't embed it in 3-space. That's why we do the 2-D cross section in diagrams.
 
What do you mean by "appear"? You can't draw 4 dimensions in 3 dimensional space so you can't "see" it in that sense.
 

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