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Well, if he didn't undo a quality edit without bothering to even read/research it, I wouldn't have had to. 76.119.75.131 (talk) 09:03, 10 October 2011 (UTC)

A trivial refutation of one of Dingle's Fumbles (Ref: Talk:Herbert Dingle Archive)

On page 230 in this appendix to "Science At the Crossroads", Dingle writes:

(start quote)

Thus, between events E0 and E1, A advances by t1 and B by t'1 = a t1 by (1). Therefore

${\displaystyle {\frac {\color {OliveGreen}rate\ of\ A}{\color {Blue}rate\ of\ B}}={\frac {\color {OliveGreen}t_{1}}{\color {Blue}at_{1}}}={\frac {1}{a}}>1\qquad (3)}$

...

Thus, between events E0 and E2, B advances by t'2 and A by t2 = a t'2 by (2). Therefore

${\displaystyle {\frac {\color {Red}rate\ of\ A}{\color {Brown}rate\ of\ B}}={\frac {\color {Red}at'_{2}}{\color {Brown}t'_{2}}}=a<1\qquad (4)}$

Equations (3) and (4) are contradictory: hence the theory requiring them must be false.

(end quote)

Dingle should have written as follows:

(start correction)

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

${\displaystyle {\frac {\color {OliveGreen}rate\ of\ clock\ not\ present\ at\ both\ events}{\color {Blue}rate\ of\ clock\ present\ at\ both\ events}}={\frac {\color {OliveGreen}coordinate\ time}{\color {Blue}proper\ time}}={\frac {\color {OliveGreen}rate\ of\ A}{\color {Blue}rate\ of\ B}}={\frac {\color {OliveGreen}t_{1}}{\color {Blue}at_{1}}}={\frac {1}{a}}>1\qquad (3)}$

...

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

${\displaystyle {\frac {\color {Brown}rate\ of\ clock\ not\ present\ at\ both\ events}{\color {Red}rate\ of\ clock\ present\ at\ both\ events}}={\frac {\color {Brown}coordinate\ time}{\color {Red}proper\ time}}={\frac {\color {Brown}rate\ of\ B}{\color {Red}rate\ of\ A}}={\frac {\color {Brown}t'_{2}}{\color {Red}at'_{2}}}={\frac {1}{a}}>1\qquad (4)}$

Equations (3) and (4) are consistent: hence there is no reason to say that the theory requiring them must be false.

(end correction)

DVdm 12:18, 6 August 2007 (UTC)