Re: Superstrings cannot be 'fundamental'

Posted by alen on July 07, 2002 at 06:22:26:

In Reply to: Re: Superstrings cannot be 'fundamental' posted by Mike2 on July 06, 2002 at 08:57:03:

I would like firstly to mention that what I have to say is no threat to the usefulness of continuous functions. The concept of continuity is really a concept of arbitrarily small increments, and it is to this arbitrariness that the term 'continuity' really refers.

If you wish to calculate the rate of change of a function f(x), for example, along an axis x, you will use the formula df(x)/dx which, of course, involves subtracting the value f(x) at x from the value f(x+dx) at x+dx. While dx can be arbitrarily small, you will nonetheless have to assign to it an actual value, dx > 0, in order to carry out a concrete calculation.

The same necessity applies if you intend to establish, or plot, the values of such a function along an actual axis x. You will have to select finite values of dx. Is there an alternative?

I say that what, in this way, is a necessity for you as a person is no less so in Nature. Thus, if there is an actual scalar field distributed in space, which has a value F at point P(x,y,z) different from a value F+dF at point P`(x+dx,y+dy,z+dz), this can occur only if 'Nature' selects a finite value ds (dx,dy,dz) that separates P and P`, as well as a finite value dF that separates the values F and F+dF. An actual field cannot be established by means of values dF = 0, ds = 0, but only dF > 0, ds > 0. Thus, any actual field must always have a fundamentally discrete implementation or, that is to say, the implementation must be grounded, in the end, as I said previously, in the concept of the 'particle'.

This does not affect the mathematical manipulation of continuous functions, where values like ds, dt, etc. can remain arbitrary and unspecified. It does, however, have significance for how such functions can be seen to be implemented as actual realities.


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