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Laraudogoitia’s supertask

  1. Jul 28, 2009 #1
    http://philosophy.ucsd.edu/faculty/ccallender/index_files/Phil 146/a beautiful supertask.pdf

    It seems to me that the very fact that particles have finite size defeats this argument, as you could not have an infinite series of particles arranged in the manner described by Laraudogotia, because eventually the distance between particles would be smaller than the radius of the particle in question; i.e., there must be some finite number of particles. Is there a flaw in this reasoning?
  2. jcsd
  3. Jul 28, 2009 #2
    I didn't read the whole article (about half-way through page 2), but I agree with you. In "reality" this doesn't make sense at all b/c of what you said.

    However, let's see what the theoretical side of this says, since a theoretical truth doesn't imply a "reality" truth. According to the author, this idea holds for particles even of "finite" size although he uses "point" particles specifically in the sections I read. Now, go ahead and pick a particle of any constant and finite size (e.g. say, 1/(2^100)) . Using the authors own definitions for the positions of the infinite particles, we see that there is a contradiction here as well, similar to what you stated in "reality"; the particles would have to be of decreasing and decreasing radius as the position index increases, so as not to overlap, but I see no mention of this "nutty" idea (EDIT: actually, I do. So, the author is suggesting that the first particle can be many many orders of magnitude larger in radius than particles of higher indexes, while still retaining the same mass -- I wonder if he considered the effect of the critical density needed to form a black hole. :biggrin:).

    So far, the author's work makes sense for point particles, but of what practical use is it? I don't know the answer to this (EDIT: And, my interest is now decimated).
    Last edited: Jul 28, 2009
  4. Jul 28, 2009 #3
    Well, the idea of decreasing radius necessarily does imply increasing density to retain the same mass, you are correct. However, the formation of one of these particles into a black hole would not alter the problem, as the gravitational force is dependent simply upon mass and distance, and if we were neglecting gravitational forces to begin with, there would be no reason to include it simply because something had the necessary density to become a black hole - it would still exert the same force on all objects a given distance away (at least, in classical Newtonian mechanics). However, there are two "realistic" problems with this approach; the first is that in reality, we know that point particles cannot exist, and there is some minimum radius that objects can have (even if that's the Planck length, or the length of a string in string theory). The second, related, point, is that this would imply densities reaching infinity as we get farther along the axis, and arbitrarily high densities are similarly not allowed, as far as I know.

    Of course, in Newtonian mechanics we consider space to be a continuum, not divided up discretely as in some formulations of quantum mechanics. Nevertheless, it seems physically impossible to generate particles with arbitrarily high densities.
  5. Jul 29, 2009 #4
    I wasn't even thinking of the gravitational force between other particles, but you could look at it from this angle if you wish. I was thinking about an "elastic" collision between black holes.

    Of course, we must realize that this problem is Laraudogoitia’s playground and that he sets the rules to play the game. However, mother nature doesn't play her game by the same rules.
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