The Symmetry of Relative Motion - Revision history

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	A symmetrical spacetime model of relative motion is developed in relation to the hyperbola, t? − x? = 1. The model shows the Worldline of P (Inertial Frame coordinates x<span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica">P</span></span><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica">, t</span></span><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica">P</span></span><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica">) moving symmetrically away from that of Q. If a ray of light leaves P at x</span></span><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica">P </span></span><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica">= 0, t</span></span><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica">P </span></span><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica">= a-b, is reflected from an event H on Q (x</span></span><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica">Q </span></span><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica">= 0, x</span></span><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica">P </span></span><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica">= b) and returns to P at x</span></span><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica">P </span></span><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica">= 0, t</span></span><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica">P </span></span><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica">= a+b, the value t</span></span><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica">P</span></span><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica">=a is an overestimate of the time on Ps clock as H occurs. The time overestimate results in an underestimate by P of the velocity of Q relative to P. There is therefore a velocity v = x</span></span><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica">P</span></span><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica">/t</span></span><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica">P </span></span><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica">= b/a , which is less than the velocity w = x</span></span><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica">P </span></span><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica">/(time on Ps clock as H occurs) = b/(<a) derived from a symmetrical model. The former, v, the usual definition, is limited by the equations to less than the speed of light; the latter, w, is not limited. The "twin paradox" is solved.</span></span>		A symmetrical spacetime model of relative motion is developed in relation to the hyperbola, t? − x? = 1. The model shows the Worldline of P (Inertial Frame coordinates x<span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica">P</span></span><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica">, t</span></span><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica">P</span></span><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica">) moving symmetrically away from that of Q. If a ray of light leaves P at x</span></span><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica">P </span></span><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica">= 0, t</span></span><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica">P </span></span><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica">= a-b, is reflected from an event H on Q (x</span></span><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica">Q </span></span><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica">= 0, x</span></span><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica">P </span></span><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica">= b) and returns to P at x</span></span><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica">P </span></span><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica">= 0, t</span></span><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica">P </span></span><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica">= a+b, the value t</span></span><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica">P</span></span><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica">=a is an overestimate of the time on Ps clock as H occurs. The time overestimate results in an underestimate by P of the velocity of Q relative to P. There is therefore a velocity v = x</span></span><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica">P</span></span><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica">/t</span></span><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica">P </span></span><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica">= b/a , which is less than the velocity w = x</span></span><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: xx-small; FONT-FAMILY: Helvetica">P </span></span><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica"><span style="FONT-SIZE: x-small; FONT-FAMILY: Helvetica">/(time on Ps clock as H occurs) = b/(<a) derived from a symmetrical model. The former, v, the usual definition, is limited by the equations to less than the speed of light; the latter, w, is not limited. The "twin paradox" is solved.</span></span>

	[[Category:Scientific Paper]]		[[Category:Scientific Paper\|symmetry relative motion]]

	[[Category:Relativity]]		[[Category:Relativity]]

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{{Infobox paper
| title = The Symmetry of Relative Motion
| author = [[P R Asquith]]
| keywords = [[Symmetry]], [[Relative Motion]]
| published = 2004
| journal = [[General Science Journal]]
| num_pages = 24
}}

==Abstract==

A symmetrical spacetime model of relative motion is developed in relation to the hyperbola, t? − x? = 1. The model shows the Worldline of P (Inertial Frame coordinates xP, tP) moving symmetrically away from that of Q. If a ray of light leaves P at xP = 0, tP = a-b, is reflected from an event H on Q (xQ = 0, xP = b) and returns to P at xP = 0, tP = a+b, the value tP=a is an overestimate of the time on Ps clock as H occurs. The time overestimate results in an underestimate by P of the velocity of Q relative to P. There is therefore a velocity v = xP/tP = b/a , which is less than the velocity w = xP /(time on Ps clock as H occurs) = b/(<a) derived from a symmetrical model. The former, v, the usual definition, is limited by the equations to less than the speed of light; the latter, w, is not limited. The "twin paradox" is solved.  

[[Category:Scientific Paper]]

[[Category:Relativity]]