> On 2 Jun 2020, at 03:07, Alan Grayson <agrayson2...@gmail.com> wrote: > > > > On Monday, June 1, 2020 at 3:58:01 PM UTC-6, Jason wrote: > 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 > > I don't see what measurements of similarity has to do with this issue. Fact > is that if space is continuous,
That is not a fact. The fact is that we don’t know, neither with Mechanism, nor with physics which has not yet successfully explain how to marry the quantum and GR. With mechanism, the continuum comes from the necessary random oracle of the first person posts of view. > there cannot be any exact repetitions. And not only is position continuous, > but so are other variables, which makes the case of uniqueness even stronger. > And it doesn't matter whether the universe is finite or infinite in spatial > extent. So from my perspective, every universe is unique (provided continuity > of spatial extent exists). AG Better to not assume a universe, or a god, as those things are what we need to explain. Bruno > > On Mon, Jun 1, 2020 at 4:24 PM Alan Grayson <agrays...@gmail.com > <javascript:>> 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/ > <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 everyth...@googlegroups.com <javascript:>. > 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 > <mailto:everything-list+unsubscr...@googlegroups.com>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/82b88c81-c7bb-4546-bf50-0ba773b06203%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/82b88c81-c7bb-4546-bf50-0ba773b06203%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/291CEA16-F6AC-4F2D-8D18-BBF50830D5A1%40ulb.ac.be.
