On Monday, October 29, 2018 at 1:55:27 PM UTC-5, [email protected] wrote: > > > > On Monday, October 29, 2018 at 6:36:47 PM UTC, Philip Thrift wrote: >> >> >> >> On Monday, October 29, 2018 at 11:07:41 AM UTC-5, John Clark wrote: >>> >>> On Sun, Oct 28, 2018 at 2:56 PM <[email protected]> wrote: >>> >>> > *What's your view of Zeno's paradox which implies motion is >>>> impossible.* >>> >>> >>> Zeno thought it was obvious if you added an infinite number of nonzero >>> lengths or nonzero times together you would always get something that was >>> nfinite, and that is the foundation of his paradox; but with modern >>> calculus we know that sometimes that isn't true, and when it isn't true >>> calculus can tell you exactly what the FINITE length or finite time >>> interval turns out to be. For example, the sum, of the infinite series: >>> 1+1/4+1/9+1/16+1/25 + 1/36 + .... 1/N^2 is EXACTLY equal to (PI^2)/6. >>> >>> John K Clark >>> >>> >>> >>> >> It is still a paradox as discussed in foundational physics and >> mathematical writing, when one leaves the naive calculus as taught in high >> school or college. >> >> *What if Tegmark is right, and one should banish the word "infinite" once >> and for all, so "sum of the infinite series" could not even be mentioned!* >> >> The problem is we do not know what spacetime is, really. >> >> >> https://blogs.unimelb.edu.au/sciencecommunication/2017/10/22/zenos-paradox-the-puzzle-that-keeps-on-giving/ >> >> : >> ... >> >> *So, has this puzzle been solved once and for all?* >> >> *Quantum physics has probably given us our most convincing answer to the >> paradox so far, but it is not a certainty. The question of whether space is >> continuous or made up of discrete units is still debated among physicists >> (there are experiments currently trying to test this), and quantum >> mechanics itself is known not to be a complete theory of the universe. If >> history is any indication, this isn’t the last we’ll hear of Zeno’s >> paradox.* >> >> >> - pt >> > > *Clark misstated the paradox, but it seems clear it depends on assuming > space is infinitely divisible. So the resolution MUST be that space is > discrete even though our most sensitive measurements to date have not > detected it. LC can speak to this. And the problem has nothing to do with > whether the word 'infinite" enters the analysis. One can do calculus > without ever using that word to describe limits, etc. Great! So now I know > the resolution of Zeno's paradox, and the physical fact that space must be > discrete! Gotta love it. AG* > >> >> > Spacetime is a mystery, and it's discrete vs. continuous is perhaps an oversimplification.
There are other mathematical models theorists pursue (check arXiv), e.g. fractal. Scale relativity and fractal spacetime: theory and applications Laurent Nottale <https://arxiv.org/search/physics?searchtype=author&query=Nottale%2C+L> https://arxiv.org/abs/0812.3857 - pt -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
