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Posted by Bruce on May 14, 2002 14:50:57 UTC

The response they gave was warranted. The post by Stafford was a complete display of ignorance with respect to how time is used in relativity. At the same time he mads a ridiculous comment that 'high school students' wouldn't make the mistake Einstein made. Skip the first part of this example because it is just the derivation for a time time equation I'm going to use to make a point.

If you put the derivative of the effective potential term (from the equation of motion) into quadratic form (to find critical values) you get

r*^2 - L*^2r + 3L*^2 = 0


r* = r/M, and L* = L/mM

Divide through by L*^2 and manipulate to get

r*^2/L*^2 = r* - 3 [saving this for a later substitution]

Setting dr = 0 in the Schwarzchild metric and substituting dphi = (L*/r*^2)dTau the metric becomes

dTau^2 = (1 - 2/r*)dt^2 - (L*^2/r*^2)dTau^2

To find the ratio dTau^2/dt^2 divide through by the bookkeeper time dt^2 and simplify to

(dTau/dt)^2 = (1 - 2/r*) / (1 + L*^2/r*^2)

Now substitute 1/ (r*-3) for L*^2/r*^2 and simplify to

dTau/dt = (1 - 3M/r)^1/2

This is a time travel equation. What is the ratio dTau/dt when r is a very large number? It is ~ 1. In other words dTau ~ dt when r is very large. What if I take my rocket ship and free fall to r = 3.000001 M and maintain a knife edge orbit for
172,800 seconds (2 days) measured with my wristwatch and I call this dTau. Then I
use this time travel equation to predict how much time was measured on a wristwatch back on Earth, while I was in orbit at r = 3.000001M, and I call this dt.
It turns out that the prediction would be ~ 9.48 years had elapsed on the Earth
wristwatch while 2 days had elapsed on the rocket ship wristwatch. The important thing to note is what dTau and dt represent. Both measure wristwatch time in a specific frame of reference. Go back and read Staffords post and then figure out why Anderson and Preby said it was a crock of Language Removed that doesn't have anything to do
with physics. Saying Einstein made a mistake by not choosing dTau to measure time
in relativity is just ignorant.

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