tag:blogger.com,1999:blog-8666091.post112177138940732571..comments2021-07-18T19:54:06.055+02:00Comments on The Reference Frame: Measuring the depth of ideasLuboš Motlhttp://www.blogger.com/profile/17487263983247488359noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-8666091.post-1121872681370640862005-07-20T17:18:00.000+02:002005-07-20T17:18:00.000+02:00Lobos said:"In my opinion, the very bare statement...Lobos said:<BR/>"In my opinion, the very bare statement that everything in physics should be discrete is not deep at all. It is a program of fundamentalism. It seems that we have known discrete and continuous features of the real world for quite some time. There are many observables in the real world that look completely continuous and the discrete people can't offer any replacement - at least not a replacement that would preserve all physical consistency rules as well as the "amount of beauty" - as represented by the symmetries, for example. In this situation, the call to abandon all continuous theoretical constructs is a call to throw away a huge portion of our vital current knowledge. It is unrealistic fundamentalism, not unsimilar to the Islamic one among others - not a deep idea."<BR/><BR/>The great debate between discreteness and continuity has nothing to do with islamic fundamentalism or other ideology, Lubos. It's known, and no dispute that all of our observables are discrete. The dispute is regarding whether the "real nature" behind observables, is it discrete or continuous in nature?<BR/><BR/>In my opinion, admitting a continuous nature beyond the discreteness we observe, is to admit something beyond observation. And that's un-physical, because physics strictly deal with observables only.<BR/><BR/>But it goes beyond the mere observational facts that the universe is discrete instead of continuous in nature. A deep reason is that it only takes a funite amount of information to describe something discrete, but it would take an infinite amount of information to describe a continuous system, even one that is finite in size!!!<BR/><BR/>To illustrate this, let's imagine a perfect stick of exactly one meter long. In real physical world you really can't have something perfect due to all the discreteness. But let's say it's a continuous world, and the stick is perfect and absolutely continuous. <BR/><BR/>Now there is just one little tiny infinitely small imperfection within the stick. It's exact location is 0.35342548576985776787529.... meter from one end. Well it's a perfect continuous world so you can expand the fraction to any arbitrary precision. And all the digits carry information. So to describe the precise position of that imperfectness, you would have to carry a lot of information, an amount of information far exceeds all human knowledge summed up. Actually it would be infinite amount of information should you allow the precision to go to arbitrarily precise figure, in a continuous world. You could carry the information of the whole universe, by a precisely positioned dot on this perfect stick!!!<BR/><BR/>But in the real world, the amount of information a system can contain is fixed, not an infinite. And that finiteness is what caused quantum mechanics to exist in the first place.<BR/><BR/>You might have thought that if the Creator is allowed to start over again using a set of re-designed physics laws, He might have created a universe that is completely classical and no QM exists. But the truth is that's impossible. A system that can contain infinite amount of information is impossible. So any conceiveable universe a Creator can create, must always be a quantum world, not a continuous world.<BR/><BR/>And the other end of the discreteness is finiteness, which means finited spacetime. And that leads to curved spacetime and gravity. A universe where no gravity exists is just as unthinkable as one where everything is continuous, or one where spacetime extends to infinity. All of them require an infinite amount of information, and that rules them out.<BR/><BR/>And that deep idea of the finiteness of information leads to precise prediction of the correct value of G to within 2% of the not so precisely known current value, something hinted by Paul Dirac but one that he never figured out totally.<BR/><BR/>QuantokenQuantokenhttps://www.blogger.com/profile/08057876770160255308noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-1121858321990994572005-07-20T13:18:00.000+02:002005-07-20T13:18:00.000+02:00If money can be used as a ruler, I'd vote to study...If money can be used as a ruler, I'd vote to study conformal invariance first.<BR/><BR/>Two old webpages about Physics of Ownership.<BR/><BR/><A HREF="http://dftuz.unizar.es/~rivero/research/ecnotes.html" REL="nofollow">Random notes</A><BR/><BR/><A HREF="http://dftuz.unizar.es/~rivero/research/ownership.html" REL="nofollow">Bibliography</A>Leucipohttps://www.blogger.com/profile/14505549871207858030noreply@blogger.com