Changes

This "transforming away" is similar to the difference between Cartesian and polar coordinates on a flat sheet of paper.  The Cartesian coordinate system is flat, and the polar system is curved.  But they are both coordinate systems on a flat sheet of paper.  However, there are surfaces ("curved surfaces"), like a sphere, that have no flat coordinate system at all.<ref>The bane of mapmakers.</ref>  In spacetime, this is equivalent to something that has no flat coordinate systems, and hence gives rise to fictitious forces that can't be transformed away.  Gravity is an example of this, a fictitious force that, unlike the centrifugal or Coriolis force, can't be transformed away.  That is, there is no place where one can stand and see gravity as just a case of people being pushed on by a floor that is accelerating upward.

This "transforming away" is similar to the difference between Cartesian and polar coordinates on a flat sheet of paper.  The Cartesian coordinate system is flat, and the polar system is curved.  But they are both coordinate systems on a flat sheet of paper.  However, there are surfaces ("curved surfaces"), like a sphere, that have no flat coordinate system at all.<ref>The bane of mapmakers.</ref>  In spacetime, this is equivalent to something that has no flat coordinate systems, and hence gives rise to fictitious forces that can't be transformed away.  Gravity is an example of this, a fictitious force that, unlike the centrifugal or Coriolis force, can't be transformed away.  That is, there is no place where one can stand and see gravity as just a case of people being pushed on by a floor that is accelerating upward.

The '''curvature of spacetime''' refers to this.  It gives rise to the "fictitious forces" that are perceived as gravity under [[General_theory_of_relativity|General Relativity]].  The Einstein Field Equations explain how that curvature arises from the presence of massive objects like the Earth or the Sun.  Analyzing the resultant gravitational fictitious force arising from massive objects obtains the same result as Newton's law of gravity for non-relativistic objects.

The '''curvature of spacetime''' refers to this.  It gives rise to the "fictitious forces" that are perceived as gravity under [[General theory of relativity|General Relativity]].  The Einstein Field Equations explain how that curvature arises from the presence of massive objects like the Earth or the Sun.  Analyzing the resultant gravitational fictitious force arising from massive objects obtains the same result as Newton's law of gravity for non-relativistic objects.

== References ==

== References ==

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[[Category: Astronomy]]

[[Category:Astronomy]]

[[Category: Cosmology]]

[[Category:Cosmology]]

[[Category: Physics]]

[[Category:Physics]]