Jesse, OK, this is some progress.
Now you've gone from saying there is NO correlation at all, to the ages ARE CORRELATED WITHIN SOME LIMIT. In other words we DO know that for any set of twins we can always say that their ages ARE the same within some limits. Correct? This is a VERY BIG CHANGE in your stated position, from NO correlation at all to SOME correlation... You though continue to claim that all frames are equally valid, even if they DO NOT preserve the actual age changing acceleration effects between the twins, while I claim that IF we properly choose a frame that DOES preserve the actual age changing acceleration effects that we narrow that limit to zero resulting in an EXACT 1:1 age correlation. You, in fact, have previously agreed that IF we choose the frame in which the symmetric accelerations were preserved that we DO get an exact 1:1 correlation, you just disagree that that frame is privileged because it preserves the actual age changing symmetric accelerations like I claim. So I suggest that for the moment we ASSUME we should choose that frame, and then see if it can be consistently applied in a transitive manner to achieve a common age correlation between ALL observers. If it can't my theory is falsified. If it can then we can still agree to disagree about how frames should be applied to analyze specific physical relationships. Edgar On Monday, March 3, 2014 11:39:10 AM UTC-5, jessem wrote: > > > > On Mon, Mar 3, 2014 at 10:03 AM, Edgar L. Owen <[email protected]<javascript:> > > wrote: > > Jesse, > > Your position becomes more and more absurd. > > > "My position" is simply that for any question on which different frames > give different answers, there is no physical basis for judging one frame's > judgments to be "reality" while others are not. I guarantee you that any > physicist would agree with this. > > > > You claim they DO have a unique 1:1 correlation of their ages when they > are together but they DON'T when they separate. > > So how far do they have to separate before this correlation is lost? 1 > meter? 1 kilometer, 1 light year? > > > Any finite number--one trillionth of a nanometer, say. The theory says > that no matter how small the distance D you choose, if you have an inertial > frame where two clocks are at rest and synchronized a distance D apart, > then in another inertial frame where the two clocks are moving along the > axis between them at speed v, at any given moment in this new frame one > clock's time will be ahead of the other's by vD/c^2. There is a maximum to > how far their times can be out-of-sync since v must be smaller than c, this > implies that no inertial frame will see them as being out-of-sync by a time > greater than or equal to D/c (so if the two clocks are 1 light-second apart > in their rest frame, or 299792458 meters apart, any other frame will see > them out-of-sync by less than a second). And this means that if you are > rounding ages off at some point, in practice you may not have to worry > about disagreements in simultaneity between frames--if two people are > precisely the same age in their rest frame and are standing only a meter > apart in their inertial rest frame, all other frames will say their ages > differ by less than 1/299792458 of a second, so obviously if you're > rounding their ages to the nearest second you'll still say they're the > "same age" no matter what inertial frame you're using. But if you want to > talk about "physical reality" rather than mere practical approximations, > the fact remains that different frames will disagree somewhat on which ages > are simultaneous for ANY finite separation, and in relativity there can > NEVER be a physical basis for saying that one frame's judgments are a true > representation of "physical reality" while other's are not. > > > > > > And is the correlation lost all at once as they separate or gradually? And > if all at once, what is the threshold distance where correlation is lost? > > And if gradually what is the relativistic formula that determines how much > the correlation falls off with distance? > > > See above, if the clocks are at rest a distance D apart and synchronized > in their own rest frame, then in another frame moving at speed v along the > axis between the two clocks, at any given moment in this new frame the > clocks are out-of-sync by vD/c^2. This can be derived directly from the > Lorentz transformation which tells you the coordinates of any event in > frame #2 if you already have its coordinates in frame #1. > > > > > > > The fact is that both twins DO HAVE AN ACTUAL AGE AT ALL TIMES. You've > already agreed to this obvious fact. Thus there absolutely MUST be an > actual correlation of those ages. That is pure logic, not relativity. > > > > That isn't "logical" at all, in fact it's a complete non sequitur (note > that you make no attempt to actually explain the 'logic' that leads you > from the premise to the conclusion here). > > Once again I would mention the geometric analogy: > > --If you have two spatial paths between points A and B on a 2D plane, then > at any given point P on a specific path, there is an actual distance along > the path between point A and point P, which could be measured by a flexible > measuring tape laid along the path. This "distance along the path from A to > P"--call it the "proper path distance" from A to P--is totally > coordinate-independent, in the sense that if different Cartesian coordinate > systems have different coordinate descriptions of the same path, they can > each use their own coordinates to calculate this "proper path distance" > from A to P and they will all get the same answer. But if you use different > Cartesian coordinate systems to assign x,y coordinates to points on the > plane, two points P1 and P2 on *different* paths may have the same > y-coordinate in one coordinate system, but different y-coordinates in > another coordinate system. So the question "do two points on different > paths share a common y-coordinate?", unlike the question "what is the > proper path distance between two points on a single path?", is one that > different Cartesian coordinate systems answer differently. But I don't > think anyone would ever claim that one Cartesian coordinate system's answer > to the latter question would be "physically correct" while other coordinate > systems are objectively "physically wrong"--the notion of separated points > in space having the "same y-coordinate" is an INTRINSICALLY > coordinate-based idea, it HAS no physical reality independent of an > arbitrary choice of coordinate system. > > All of this is exactly analogous to the situation with the twins and > proper time vs. simultaneity. Here, I will simply cut and paste the above > paragraph and change a few words: > > --If you have two worldlines between events A and B in 4D spacetime, then > at any given event E on a specific worldline, there is an actual time along > the worldline between event A and event E, which could be measured by a > clock traveling along the worldline. This "time along the worldline from E > to P"--call it the "proper time" from E to P--is totally > coordinate-independent, in the sense that if different inertial frames have > different coordinate descriptions of the same worldline, they can each use > their own coordinates to calculate this "proper time" from E to P and they > will all get the same answer. But if you use different inertial frames to > assign x,y,z,t coordinates to points in spacetime, two points P1 and P2 on > *different* worldlines may have the same t-coordinate in one coordinate > system, but different t-coordinates in another coordinate system. So the > question "do two points on different worldlines share a common > t-coordinate?", unlike the question "what is the proper time between two > points on a single worldline?", is one that different inertial frames > answer differently. But I don't think any physicist would ever claim that > one inertial frame's answer to the latter question would be "physically > correct" while other inertial frames are objectively "physically > wrong"--the notion of separated points in spacetime having the "same > t-coordinate" is an INTRINSICALLY coordinate-based idea, it HAS no physical > reality independent of an arbitrary choice of coordinate system. > <di > ... -- 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.
