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== A trivial refutation of one of Dingle's Fumbles (Ref: [http://en.wikipedia.org/wiki/Talk:Herbert_Dingle/Archive_5#A_trivial_refutation Talk:Herbert Dingle Archive]) == |
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On page 230 in [http://users.telenet.be/vdmoortel/dirk/Physics/Dingle/Dingle_Appendices.pdf this appendix] to [http://users.telenet.be/vdmoortel/dirk/Physics/Dingle/Dingle_SCIENCE_At_the_Crossroads.pdf "Science At the Crossroads"], Dingle writes: |
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: (start quote) |
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: ''Thus, between events E0 and E1, A advances by t1 and B by t'1 = a t1 by (1). Therefore'' |
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::: <math>\frac{\color{OliveGreen}rate\ of\ A}{\color{Blue}rate\ of\ B} = \frac{\color{OliveGreen}t_1}{\color{Blue}a t_1} = \frac{1}{a} > 1 \qquad (3)</math> |
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: ... |
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: ''Thus, between events E0 and E2, B advances by t'2 and A by t2 = a t'2 by (2). Therefore'' |
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::: <math>\frac{\color{Red}rate\ of\ A}{\color{Brown}rate\ of\ B} = \frac{\color{Red}a t'_2}{\color{Brown}t'_2} = a < 1 \qquad (4)</math> |
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: '' '''Equations (3) and (4) are contradictory: hence the theory requiring them must be false.''' '' |
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: (end quote) |
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Dingle should have written as follows: |
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: (start correction) |
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: ''Thus, between events E0 and E1, A, which is '''not present''' at both events, advances by t1 and B, which is '''present''' at both events, by t'1 = a t1 by (1). Therefore'' |
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::: <math>\frac{ \color{OliveGreen} rate\ of\ clock\ not\ present\ at\ both\ events}{ \color{Blue}rate\ of\ clock\ present\ at\ both\ events} = \frac{\color{OliveGreen}coordinate\ time}{\color{Blue}proper\ time} = \frac{\color{OliveGreen}rate\ of\ A}{\color{Blue}rate\ of\ B} = \frac{\color{OliveGreen}t_1}{\color{Blue}a t_1} = \frac{1}{a} > 1 \qquad (3)</math> |
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: ... |
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: ''Thus, between events E0 and E2, B, which is '''not present''' at both events, advances by t'2 and A, which is '''present''' at both events, by t2 = a t'2 by (2). Therefore'' |
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::: <math>\frac{\color{Brown}rate\ of\ clock\ not\ present\ at\ both\ events}{\color{Red}rate\ of\ clock\ present\ at\ both\ events} = \frac{\color{Brown}coordinate\ time}{\color{Red}proper\ time} = \frac{\color{Brown}rate\ of\ B}{\color{Red}rate\ of\ A} = \frac{\color{Brown}t'_2}{\color{Red}a t'_2} = \frac{1}{a} > 1 \qquad (4)</math> |
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: '' '''Equations (3) and (4) are consistent: hence there is no reason to say that the theory requiring them must be false.''' '' |
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: (end correction) |
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[[Image:DingleRefutation.png|center]] |
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[[User:DVdm|DVdm]] 12:18, 6 August 2007 (UTC) |
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Revision as of 10:28, 8 November 2011
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