On Fri, Feb 7, 2014 at 7:57 AM, Edgar L. Owen <[email protected]> wrote:
> Jesse, > > OK, here's the detailed analysis of how I see the current state of this > issue that I promised: > > > A few points: > > 1. Since you asked let me repeat my 'operational definition' of the > present moment that I used before. The twins meet, shake hands and compare > watches. That is the operation definition. > > That is essentially the same as your reflected light operational > definition with which I have no problem. > > 2. However it is important to note that that works not just for the twins > together, but for every single twin by himself. Because any twin or > observer can shake his own hand, look at his own watch, or note that the > light reflected from a mirror in his hand takes minimal time to return. > > Therefore what is true for the twins together is also true for each twin > separately, and is true for every observer in the universe as well. > > 3. So what is it that is true? You say it is "being at the same point in > spacetime". Call that relationship R1. I use the term that everyone else > does and has throughout history, namely "being in the (same) present > moment". Call that relationship R2. > > > So let's use a thought experiment to examine the difference between R1 and > R2: > > Imagine a line of a billion twins. By both our definitions every two > adjacent twins will be in what you call relationship R1 and I call R2. And > this will be true of the adjacent twins on both sides of every twin. > > In your terminology every twin will be "at the same point of spacetime" > with both the one to the right and to the left. > > In my terminology every twin will be "in the same present moment" with > both the one to the right and to the left. > > Note that these relationships are transitive, so they necessarily cascade > through the whole line of twins. What that means is that twin #1 must have > that same relationship with twin #1 billion. > > But clearly it is NOT true that twin 1 is "at the same point in spacetime" > as twin 1 billion because he not at the same point in space. However twin 1 > can be in the same present moment as twin 1 billion, because that is just a > time relationship that does not require a same space location. > > Thus our agreed operational definition leads to a contradiction with your > terminology but not mine. > Well, in my discussion I believe I alternated between two subtly different definitions--one which said the light-signal-return-time actually went to zero, and another which said that it was "negligible". The first definition was an ideal theoretical description--and if the twins in your thought-experiment were ideal point-like observers who could literally have the time delay of light signals approach zero at the moment on each of their clocks where they met, then you could have a billion of them meeting in such a way and the fact of delay time approaching zero would really be completely transitive. But the second definition was just an approximate practical one. "Negligible" is obviously a fuzzy term which depends on how precise your instruments are--if the twins are standing 0.3 meters apart and they use the light test, a sufficiently sensitive instrument will reveal it actually takes about 2 nanoseconds between emitting a light flash and getting back the reflection. Likewise if they shake hands, sufficiently good equipment would show a much larger delay between the moment their hands touch and the moment the train of nerve impulses set off by the touch reaches the brain (and the atoms of their hands don't really "touch", so there would even be some sub-nanosecond delay between a motion in an atom in the palm of one hand and its effect on the motion of an atom in the palm of the other hand). For a normal experiment like the twin paradox, we won't get any noticeably inaccurate results if we model them as meeting at the same point in spacetime when sufficiently accurate measurements might show them a light-nanosecond apart. But your row-of-twins scenario is obviously constructed in a way where we'll get wrong conclusions if we treat "negligible" the same as "zero", since if you stack up a bunch of zeros you still always get zero, but if you stack up a bunch of "negligible, unmeasurable" differences you eventually get a measurable difference. I'm sure you would run into the same problem if I asked you for a practical operational definition of "same point in space"--any such practical difference is going to ignore very small gaps that are too small for our measuring-instruments to discern (or just aren't worth worrying about in our calculations), but obviously if you stack up a sufficient number of small things with small spatial gaps you may get an arbitrarily large spatial distance between both ends of the stack. > > > Now one final point: You criticize me for relying on "conscious > experience" presumably when it comes to the twins shaking hands and > comparing watches. > No, when I talked about "conscious experience" I meant the vague qualitative sense we have that time seems to "flow", that things seem to come into existence (from our perspective at least) and go out of them. I didn't mean the perceptions of well-defined experiments that anyone can observe the result of from the outside without knowing anything about the inner experience of the person performing it, like a comparison of watches or a shaking of hands. Jesse -- 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 http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
