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

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In summary, when we include the 3rd dimension of space, the lightcone appears as a sphere growing from a point at present in both forward and backward time. However, since it is a 4-D object, it cannot be embedded in 3-space and therefore cannot be drawn or seen in the same way as a 3D object. It is not possible to project a 4D object onto the 3D world, even onto a sheet of paper, as explained by George Gamow in his book 1,2,3 Infinity.
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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.
 
  • #3
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.
 
  • #4
Is it so?

As we can project the an 3D image on a sheet of paper, can we project a 4D object to the 3D world, not atleast to a sheet of paper. I have heard that George Gamow gave some notes about that in his book 1,2,3 infinity
 

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

What is the lightcone in 3D?

The lightcone in 3D refers to the region of space that can be reached by light emitted from a single point in three-dimensional space. It is the three-dimensional analog of a two-dimensional lightcone, which is often used to visualize special relativity.

How is the lightcone in 3D calculated?

The lightcone in 3D is calculated by tracing the path of light rays emitted from a single point in space. This is typically done using mathematical equations and computer simulations.

What is the significance of the lightcone in 3D?

The lightcone in 3D is important in understanding the behavior of light and the fundamental principles of special relativity. It also helps us visualize and study the structure of the universe.

Can anything travel faster than the speed of light in the lightcone?

According to the theory of special relativity, nothing can travel faster than the speed of light. Therefore, nothing can travel outside of the lightcone, as it would require traveling faster than the speed of light.

How does the lightcone in 3D change in different reference frames?

The lightcone in 3D remains the same in all reference frames, as it is a fundamental property of space and time. However, the perception of the lightcone may vary depending on the relative motion of the observer.

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