On Mon, Mar 3, 2014 at 10:03 AM, Edgar L. Owen <[email protected]> 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. So you can see there is an analogy between every aspect of the "two different worldlines through 4D spacetime" scenario and the "two different paths through 2D space" scenario (as I have asked many times in the past, please point out if you think there is any aspect of the first scenario that FAILS to have a direct analogue in the second). Thus even if you did actually try to present a logical argument for the idea that "both twins do have an actual age at all events on their worldline (i.e. an actual proper time between their birth and that event)" implies "there absolutely MUST be an actual correlation of those ages (i.e., a truth about which ages of different twins occur at the 'same time')", I could change a few terms in your argument to construct an analogous argument that purports to prove that since "both paths do have an actual 'proper path length' between the start of the path and any other point on the path", this implies "there absolute MUST be an actual correlation of the those proper path lengths (i.e., a truth about which proper path lengths of different paths occur at the 'same y')". But this conclusion is clearly absurd, so it's safe to predict there would be some flaw in the logic of your argument--if you ever actually presented one, rather than just jumping from premise to conclusion and shouting "logic!" > All you are saying is that relativity does not give a unique answer for > what that correlation is. Sure, I agree completely. > > But my point is that if we choose the correct frame that preserves the > relationship between ONLY the twins themselves we do get a unique > unambiguous answer. And so that is the only correct answer. And it is > consistent and transitive among all observers. Therefore it qualifies as an > actual physical fact. > > All you are saying is that relativity doesn't have a way to calculate an > age correlation. But not having a way to calculate something DOES NOT MEAN > it doesn't actually exist, it just means it can't be calculated. Do you > agree with that? > Sure, I have already agreed in the past that it's possible there is some metaphysical truth about simultaneity which cannot be determined by physical experiment (in this case you couldn't say that one frame's judgments about simultaneity were more PHYSICALLY correct than any other's, but one frame might be METAPHYSICALLY correct while others are metaphysically incorrect). Even if there was, you have no basis other than your own aesthetic preferences for thinking absolute simultaneity follows the particular rule you have described about symmetrical accelerations guaranteeing that ages will remain synchronized in absolute terms. Plenty of people who advocate an absolute present would disagree that it works that way--the common presentist response to relativity is to suggest that there is some unique reference frame whose definition of simultaneity agrees with absolute simultaneity, but we just can't determine which frame that is. You have presented no "logical" argument for saying they are wrong and you are right. And of course, there's also the teensy little matter that I've already proved that this assumption, when combined with two fairly "obvious assumptions" that I assume any presentist would agree with (the assumption of transitivity and the assumption that events that coincided at the same space and time coordinates in some inertial frame were simultaneous in absolute terms), leads directly to a contradiction where two different ages of the same observer have to be judged "simultaneous". > > So to falsify p-time you can't just say a correlation can't be calculated, > you have to actually prove there is an actual CONTRADICTION between p-time > and relativity. You haven't yet done that and I don't think you can... > I am not trying to falsify p-time, I don't favor the idea of an absolute present myself but I recognize it as a logical possibility (and I have already said the same thing in several previous posts). I am just trying to argue against your apparent belief that relativity itself somehow dictates how p-time simultaneity MUST work. > > > Note also that the GPS system DOES establish actual 1:1 correlations of > proper times between satellites and ground based receivers both moving > relative to each other and at distance from each other. if it didn't, it > couldn't work. So even relativity tells us this is possible. > It only establishes this in a particular Earth-centered coordinate system which the designers found CONVENIENT to use in order to establish a standard, they never claimed that this coordinate system's judgments about simultaneity are more "physically correct" than any other coordinate system. 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