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On 2002-10-23 07:16, Verlan J. Kliewer wrote:
The point in my mathematical exercise was NOT to find how to add velocities under relativity, but rather to show a mathematical contradiction.
When you want to prove that something is false in mathematics, you start first by assuming it is true. Then you work through the math and arrive at equations or results that cannot be true. When you do that, you have established that your original assumptions were wrong. This is a very common approach in mathematical proofs.
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OK, but you have to be very careful when you make additional assumptions--it could be those additional assumptions are wrong, not your original assumption.
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I used this approach, and I started with the assumption that all frames of reference are equally valid. I proceeded with the mathematics and arrived with an equation for adding velocities. I took the position that my equation for adding velocities was not correct, and therefore, the original assumption that all frames of reference are equally valid is not correct.
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Well, your final equation is obviously invalid, but your assumption that you can multiply relative velocities is in error.
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GrapesOfWrath Bad PhD did a good job of articulating my assumption: "I think the basic error is his assumption that the dilations compound by multiplication. He assumes that if A sees B as twice as slow, and B sees C as twice as slow, then A will see C as four times as slow. That's obviously not true--just let C be the first observer A. A would see A as four times as slow?"
My assumption is that time dilations compound by multiplication. GrapesofWrath stated the assumption obviously is not true, but I do not follow the reasoning of GrapesofWrath.
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[img]/phpBB/images/smiles/icon_smile.gif[/img] I'll try again, using X, Y, and Z. If X sees Y as twice as slow, and Y sees Z as twice as slow, then X will see Z as four times as slow. That's just a rephrase, right?
Now, let X=A, Y=B, and Z=A.
In special relativity, when A sees B as twice as slow, B also sees A as twice as slow. That does not mean, though, that A sees A as four times as slow.
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<font size=-1>[ This Message was edited by: GrapesOfWrath on 2002-10-23 08:49 ]</font>