Does an Infinite Plane Have a Horizon?

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SUMMARY

An infinite plane does not have a traditional horizon as defined in spherical geometry. The term "horizon" typically relates to a sphere and is also used in the context of "Event Horizon," which refers to a boundary in space-time beyond which events cannot influence an outside observer. In classical geometry, a plane does not curve, making the conventional definition of horizon inapplicable. However, if one considers a curved plane in the context of space-time, the concept of horizon becomes more complex, potentially aligning with the observer's eye level.

PREREQUISITES
  • Understanding of spherical geometry and its definitions.
  • Familiarity with the concept of Event Horizon in physics.
  • Basic knowledge of classical geometry and its properties.
  • Awareness of space-time curvature due to gravity.
NEXT STEPS
  • Research the mathematical implications of infinite planes in geometry.
  • Explore the concept of Event Horizon in general relativity.
  • Study the effects of gravity on space-time curvature.
  • Examine how different geometrical models define horizons.
USEFUL FOR

This discussion is beneficial for physicists, mathematicians, and students interested in geometry and general relativity, particularly those exploring the implications of infinite planes and horizons in theoretical contexts.

ezarhadden
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Does an infinite plane Have a horizon, forgive me if I'm asking it wrong.
 
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The typical definition of horizon is:

http://en.wikipedia.org/wiki/Horizon

and involves a sphere. Horizon is also used in the phrase "Event Horizon" referring to the "boundary in space-time beyond which events cannot affect an outside observer." ( http://en.wikipedia.org/wiki/Event_horizon ). Because space-time "curve" in the presence of gravity, this term is consistent with the more traditional usage.

A "Classical plane" does not curve, and so the typical definition of "horizon" does not really apply; however, if you are assuming that a plane curves to conform with space-time then the meaning of "horizon" gets a bit complicated for my little brain, and you would need to clarify your question to attract a response from people better capable of answering that.

Fish
 
The "horizon" of an infinite plane would appear to be at "eye" level of an observer.
 

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