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Revision as of 15:17, 3 June 2013 view sourceDVdm (talk | contribs)Autopatrolled, Extended confirmed users, New page reviewers, Pending changes reviewers, Rollbackers138,475 editsm A trivial refutation of one of Dingle's Fumbles (Ref: Talk:Herbert Dingle Archive): ForestGreen (and corrected a few typos)← Previous edit Revision as of 12:55, 30 June 2013 view source Dixtosa (talk | contribs)Extended confirmed users910 edits XDNext edit →
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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 t 1 {\displaystyle \color {ForestGreen}{t_{1}}} and B by t 1 = a t 1 {\displaystyle \color {Blue}{t'_{1}=at_{1}}} by (1). Therefore
rate of A rate of B = t 1 a t 1 = 1 a > 1 (3) {\displaystyle {\frac {\color {ForestGreen}{\text{rate of A}}}{\color {Blue}{\text{rate of B}}}}={\frac {\color {ForestGreen}{t_{1}}}{\color {Blue}{at_{1}}}}={\frac {1}{a}}>1\qquad {\text{(3)}}}
...
Thus, between events E0 and E2, B advances by t 2 {\displaystyle \color {Brown}{t'_{2}}} and A by t 2 = a t 2 {\displaystyle \color {Red}{t_{2}=at'_{2}}} by (2). Therefore
rate of A rate of B = a t 2 t 2 = a < 1 (4) {\displaystyle {\frac {\color {Red}{\text{rate of A}}}{\color {Brown}{\text{rate of B}}}}={\frac {\color {Red}{at'_{2}}}{\color {Brown}{t'_{2}}}}=a<1\qquad {\text{(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 t 1 {\displaystyle \color {ForestGreen}{t_{1}}} and B, which is present at both events, by t 1 = a t 1 {\displaystyle \color {Blue}{t'_{1}=at_{1}}} by (1). Therefore
rate of clock not present at both events E0 and E1 rate of clock present at both events E0 and E1 = coordinate time of E1 proper time of E1 = rate of A rate of B = t 1 t 1 = t 1 a t 1 = 1 a > 1 (3) {\displaystyle {\frac {\color {ForestGreen}{\text{rate of clock not present at both events E0 and E1}}}{\color {Blue}{\text{rate of clock present at both events E0 and E1}}}}={\frac {\color {ForestGreen}{\text{coordinate time of E1}}}{\color {Blue}{\text{proper time of E1}}}}={\frac {\color {ForestGreen}{\text{rate of A}}}{\color {Blue}{\text{rate of B}}}}={\frac {\color {ForestGreen}{t_{1}}}{\color {Blue}{t'_{1}}}}={\frac {\color {ForestGreen}{t_{1}}}{\color {Blue}{at_{1}}}}={\frac {1}{a}}>1\qquad {\text{(3)}}}
...
Thus, between events E0 and E2, B, which is not present at both events, advances by t 2 {\displaystyle \color {Brown}{t'_{2}}} and A, which is present at both events, by t 2 = a t 2 {\displaystyle \color {Red}{t_{2}=at'_{2}}} by (2). Therefore
rate of clock not present at both events E0 and E2 rate of clock present at both events E0 and E2 = coordinate time of E2 proper time of E2 = rate of B rate of A = t 2 t 2 = t 2 a t 2 = 1 a > 1 (4) {\displaystyle {\frac {\color {Brown}{\text{rate of clock not present at both events E0 and E2}}}{\color {Red}{\text{rate of clock present at both events E0 and E2}}}}={\frac {\color {Brown}{\text{coordinate time of E2}}}{\color {Red}{\text{proper time of E2}}}}={\frac {\color {Brown}{\text{rate of B}}}{\color {Red}{\text{rate of A}}}}={\frac {\color {Brown}{t'_{2}}}{\color {Red}{t_{2}}}}={\frac {\color {Brown}{t'_{2}}}{\color {Red}{at'_{2}}}}={\frac {1}{a}}>1\qquad {\text{(4)}}}
Equations (3) and (4) are consistent and say that any event's coordinate time is always larger than its proper time:

hence there is no reason to say that the theory requiring them must be false.

(end correction)

DVdm 12:18, 6 August 2007 (UTC)