This is why time has a minus sign in SR. (I believe the usual way this informally is put is that the space-traveller "trades space for time".)
On 8 March 2014 13:26, Jesse Mazer <[email protected]> wrote: > > On Fri, Mar 7, 2014 at 7:20 PM, Edgar L. Owen <[email protected]> wrote: > >> Jesse, >> >> Do you understand why the world line that is depicted as LONGER in the >> typical world line diagram is ACTUALLY SHORTER? >> >> E.g. in your diagram do you understand why even though A's world line >> looks longer than C's world line, it is ACTUALLY SHORTER? >> >> Edgar >> > > Are you actually reading my posts carefully all the way through, or just > skimming them or something? I spent a whole extended section of my post > discussing just this point, read it again: > > 'It is true that if you just look at the spatial lengths of each path on > the diagram, the ratio between the spatial lengths doesn't actually match > up with the ratio between the proper times that would be calculated using > relativity. If you use any Cartesian spatial coordinate system to draw x-y > axes on the diagram, then you can use this coordinate system to assign x > and y coordinates to the endpoints of any straight blue segment, x1 and y1 > for one endpoint and x2 and y2 for the other, and then calculate the > spatial length of that segment using the Pythagorean theorem: > squareroot[(y2 - y1)^2 + (x2 - x1)^2]. Note that you ADD the squares of the > two terms in parentheses when calculating spatial length, but my earlier > equation showed that you SUBTRACT the square of the two terms in > parentheses when calculating proper time, which explains why this sort of > spatial path length on a spacetime diagram can be misleading. For example, > in spatial terms a straight line is the SHORTEST path between two points, > but in spacetime a straight (constant-velocity) worldline is the one with > the LARGEST proper time between points. > > Nevertheless, the math for calculating the invariant spatial path length > using a Cartesian coordinate system is closely analogous to the math for > calculating the invariant proper time using an inertial frame. The diagrams > show the spatial length of the paths being different despite identical red > acceleration segments, and this remains true if you actually calculate > proper time, even though in terms of proper times C > B > A which is the > opposite of how it works with spatial lengths.' > > > > >> >> >> >> >> >> On Friday, March 7, 2014 5:15:57 PM UTC-5, jessem wrote: >>> >>> >>> >>> >>> On Fri, Mar 7, 2014 at 4:02 PM, Edgar L. Owen <[email protected]> wrote: >>> >>> Jesse, >>> >>> Finally hopefully getting a minute to respond to at least some of your >>> posts. >>> >>> I'm looking at the two 2 world line diagram on your website and I would >>> argue that the world lines of A and B are exactly the SAME LENGTH due to >>> the identical accelerations of A and B rather than different lengths as you >>> claim. >>> >>> The length of a world line is the PROPER TIME along that world line. >>> Thus the length of a world line is INVARIANT. It is the length of the world >>> line according to its proper clock and NOT the length according to C's >>> clock which is what this diagram shows. >>> >>> >>> I don't understand what you mean by "the length according to C's >>> clock"--are you just talking about the numbers on the vertical time axis, >>> 2000-2020? That axis represents the coordinate time in C's rest frame, and >>> obviously the coordinate time between "2000" at the bottom of the diagram >>> and "2020" at the top is 20 years regardless of what path you're talking >>> about, so I don't see how it makes sense to call this the "length" of any >>> particular path. But you can also use C's >>> ... >> >> -- >> 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/d/optout. >> > > -- > 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/d/optout. > -- 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/d/optout.
