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Yanniru, A Quick Note!

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Posted by Richard D. Stafford, Ph.D. on May 10, 2002 13:56:49 UTC

Hi Richard,

I was thinking some more about your complaint that the arguments of the Dirac delta function sum are defined to avoid the possibility of any result but zero and how to make it clear to you that you are misunderstanding things. Go read the section near the end of Chapter 1 which begins with :

Their exists one more additional constraint ...

Includes eqn(1.18) and eqn(1.19)

And ends with:

... we can deduce that the following equation must be true for all arguments.

Which of course refers to eqn(1.20): i.e., F*psi = 0.

This should make it clear that constraint number 4 in the set displayed in (1.25) does not at all depend on constraining the arguments to any allowed set.

Perhaps it was a mistake on my part to stick my proof (that any rule could always be expressed through a proper selection of "unknowable" data if F is taken to be a sum over Dirac delta functions of differences) between (1.20) and (1.25) as it seems to have lead you to forget about eqn(1.20).

The reason, did it in that order is that the deduction referred to in eqn(1.20) is much more universal than my particular use as it applies to any conceivable function F, not just the one constructed of Dirac delta functions. To do them in opposite order would not have been nearly as powerful a statement. Certainly, if you follow what I have done, you must admit that the constraint expressed in (1.25) does not limit the arguments (x, tau)i in any way. The ranges available for these arguments are entirely open!

It follows that all four constraints expressed in (1.25) are absolutely universal and apply to any conceivable set of "knowable" numbers. That is, no matter what the "knowable" numbers are, there always exists a set of "unknowable" numbers which will make those 4 equations true!

Why do you think the invention of new "particles" always plays such a big roll in explaining forces? They are just touching on an issue which I have shown to be absolutely universal.

Looking to hear from you -- Dick

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