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It is also important to note that the definition of inertial reference frame (defined as one in which a free particle travels in a straight line at constant speed) does not include a requirement that the inertial reference frame must exist in three dimensional Euclidean space. This was another of Newton's assumptions which would later be disproven. As an example of why this is important, let us consider the [[Non-Euclidean geometry]] of a sphere. In this geometry, two free particles may begin at the same point on the sphere, travelling with the same constant velocity in different directions. After a length of time, the two particles will collide at the opposite side of the sphere. Both free particles were travelling with a constant velocity and no forces were acting. No acceleration occurred and so Newton's first law held true. This means that the particles were in inertial frames of reference. Since no forces were acting, it was the geometry of the situation which caused the two particles to meet each other again. In a similar way, it is now believed that we exist in a four dimensional geometry known as [[spacetime]]. It is believed that the curvature of this 4D space is responsible for the way in which two bodies with mass will meet together even if no forces are acting. In Newtonian mechanics, this is explained by a force known as gravity. [http://en.wikipedia.org/wiki/Frame_of_reference]

It is also important to note that the definition of inertial reference frame (defined as one in which a free particle travels in a straight line at constant speed) does not include a requirement that the inertial reference frame must exist in three dimensional Euclidean space. This was another of Newton's assumptions which would later be disproven. As an example of why this is important, let us consider the [[Non-Euclidean geometry]] of a sphere. In this geometry, two free particles may begin at the same point on the sphere, travelling with the same constant velocity in different directions. After a length of time, the two particles will collide at the opposite side of the sphere. Both free particles were travelling with a constant velocity and no forces were acting. No acceleration occurred and so Newton's first law held true. This means that the particles were in inertial frames of reference. Since no forces were acting, it was the geometry of the situation which caused the two particles to meet each other again. In a similar way, it is now believed that we exist in a four dimensional geometry known as [[spacetime]]. It is believed that the curvature of this 4D space is responsible for the way in which two bodies with mass will meet together even if no forces are acting. In Newtonian mechanics, this is explained by a force known as gravity. [http://en.wikipedia.org/wiki/Frame_of_reference]

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[[Category: General Reference]]

[[Category: General Reference]]