Let's say time and space are continuous. Now lets design a stop watch that works as follows:
1. *Start button:* shoots a photon with a wavelength of 300 nanometers down the length of a ruler. 2. *Stop button:* raises the ruler so that the photon hits it at a certain point that we can measure. Question: Even if space and time are continuous can this stop watch provide measurements of continuous/unlimited precision? Answer: Due to the uncertainty principle, the location the photon cannot be determined to a location finer than the photon's wavelength. Accordingly, even if space/time are continuous, such a stop watch has a discrete time-resolution of (300 nanometers / speed of light ) ~= 10^-15 seconds. So for all practical purposes, there's no difference between this stop-watch 1.000000000000000000001 and 1.000000000000000000002 seconds after pressing "Start". Given this, can we be so sure that reality is continuous? David Deutsch has speculated that the appearance of a continuum may be an artifact of living within an infinite ensemble of independently discrete realities. As we see a continuous variable evolve to reach some final state, it may be an increasing fraction of realities evolving to reach that state (with each one discretely changing). This would explain why a photon might seem to have an arbitrary polarization, or an electron some arbitrary fraction of spin, but when measured it only have one of two possible values. In summary, I agree with you that a continuous reality rules out exact duplicates. But I would add that quantum mechanics says two regions of space can be so similar to each other that no one, and no experiment, even in theory, could tell the difference between them. Jason On Mon, Jun 1, 2020 at 4:24 PM Alan Grayson <agrayson2...@gmail.com> wrote: > > > On Monday, June 1, 2020 at 1:43:09 PM UTC-6, Jason wrote: >> >> >> >> On Mon, Jun 1, 2020 at 8:31 AM Alan Grayson <agrays...@gmail.com> wrote: >> >>> >>> >>> On Monday, May 18, 2020 at 9:20:36 PM UTC-6, Jason wrote: >>>> >>>> I recently wrote an article on the size of the universe and the scope >>>> of reality: >>>> https://alwaysasking.com/how-big-is-the-universe/ >>>> >>>> It's first of what I hope will be a series of articles which are >>>> largely inspired by some of the conversations I've enjoyed here. It covers >>>> many topics including the historic discoveries, the big bang, inflation, >>>> string theory, and mathematical realism. >>>> >>>> Jason >>>> >>> >>> You claim, >>> "Every very finite sequence recurs an infinite number of times precisely >>> because Pi goes on forever." Can you prove it? AG >>> >>> "Similarly, should space go on forever then every possible finite >>> arrangement of matter occurs in an infinite number of locations." Even >>> in a finite universe, assuming space is infinitely divisible, this is false >>> IMO. For example, if we live in a finite 4 dimensional hypersphere with >>> only one particle, it can be placed in infinitely different locations and >>> no repeats is plausible. AG >>> >>> >>> >> You are right, if there are continuous variables of unlimited precision >> then repeats are infinitely unlikely. >> >> Where this assumption appears to break down, however, is that quantum >> mechanics implies an upper bound on the number of distinguishable (in >> principle) states for a given quantity of mass/energy distributed across a >> given volume of space. So while you could suppose that two similar-seeming >> regions are in fact in different states, there would be no test you could >> perform to distinguish between the two. (Given the quantum bounds on >> information storage). >> >> Jason >> > > The spectrum for an unbound particle, such as a free electron, is > continuous (not discrete). Thus, if the background space is finite OR > infinite in extent, there will be no repeats of such a universe since the > initial position of any particle, is uncountable. Although it might not be > possible to distinguish two distinct initial states by measurement, I don't > see how their existence can be denied. AG > > -- > 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 everything-list+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/c8af8793-5a22-4fc2-b721-41f29ab45e78%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/c8af8793-5a22-4fc2-b721-41f29ab45e78%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- 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 everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CA%2BBCJUiiKTqBHwz%2BjDttY2BRxzuxf7XUrGMpkFco9P4GPa3mVw%40mail.gmail.com.
