In a previous Junk Science blog, I posited that things that might travel at the limit of speed (light rays in a perfect vacuum for instance) appear to have infinite acceleration at time zero (at the instant of creation) and zero acceleration thereafter. I will try here to rationalize this conclusion.
The formula for acceleration is d/(t**2) or distance divided by time squared. This can be also expressed as (d/t)*(1/t). Now, at time zero plus the minutest amount, light will be traveling at 186,000 miles per second. Also substituting in the second part of this formula, 1/0.1 = 10, 1/0.001 =1000, 1/0.000001=1,000,000, etc. Therefore, as the time interval decreases to nothing (gets infinitely small), the second part of this formula gets infinitely large. And, anything times infinity is infinity. Ergo, the acceleration of light at time zero is infinite.
Of course, one may then use the same logic to argue that the acceleration of anything is infinite at time zero. However, most other entities have virtually zero speed at time zero (plus the minutest amount). Therefore, zero times infinity is not infinity.
Wednesday, October 11, 2006
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