Jesse, Yes, that is what I'm saying.
But how you don't understand that actively traveling through spacetime at c doesn't imply everything is at one and only one point in time is beyond me. It's a trivial inference. Edgar On Wednesday, February 5, 2014 5:04:36 PM UTC-5, jessem wrote: > > > > On Wed, Feb 5, 2014 at 4:41 PM, Russell Standish > <[email protected]<javascript:> > > wrote: > >> On Wed, Feb 05, 2014 at 04:21:47PM -0500, Jesse Mazer wrote: >> > On Wed, Feb 5, 2014 at 3:50 PM, Russell Standish >> > <[email protected]<javascript:> >> >wrote: >> > >> > > On Wed, Feb 05, 2014 at 07:53:16AM -0800, Edgar L. Owen wrote: >> > > > >> > > > In fact relativity itself conclusively falsifies block time as it >> > > requires >> > > > everything to be at one and only one point in clock time due to the >> fact >> > > > that everything always travels at the speed of light through >> spacetime. I >> > > > find it baffling that so many can't grasp this simple fact. >> > > > >> > > >> > > That is only true for clocks travelling along null geodesics. For all >> > > other geodesics, proper time increases at a rate of 1 second per >> > > second, or c metres per second, where c is the speed of light >> > > expressed in metres per second. >> > > >> > >> > I believe Edgar is referring to the fact that the magnitude (norm) of >> the >> > 4-velocity vector is always c, regardless of what worldline you're >> looking >> > at (Brian Greene explains that this is what he means by "speed through >> > spacetime is always c", and gives a short derivation, on p. 392 of The >> > Elegant Universe). >> > >> > But as I pointed out, this isn't a great revelation. We define >> 4-velocity >> > in natural units (c=1) as (dt/dtau, dx/dtau, dy/dtau, dz/dtau), where >> > t,x,y,z are coordinates of some inertial frame and tau is proper time. >> > Analogously, in a purely spatial scenario involving a curved wire in 3D >> > space we can define a similar vector V=(dx/dL, dy/dL, dz/dL) at every >> point >> > on the wire, where x,y,z are position coordinates and L is a parameter >> > giving distance along the wire (how far an ant would have to walk to get >> > from the end of the wire to any given point). Then the magnitude of this >> > vector V is given by the square root of (dx/dL)^2 + (dy/dL)^2 + >> (dz/dL)^2 >> > which can be rewritten as (dx^2 + dy^2 + dz^2)/dL^2, but dL^2 is just >> equal >> > to (dx^2 + dy^2 + dz^2)--if an ant moves a small distance dL along the >> wire >> > we can treat its path as a straight line segment, and by the Pythagorean >> > theorem the length of any line segment is just the square of the >> coordinate >> > differences between its endpoints--so the magnitude of V is always 1 at >> > every point on the wire, regardless of the shape or orientation of the >> > wire. Greene's derivation of the fact that the magnitude of the >> 4-velocity >> > is always c is pretty much the same, except the analogue of the >> pythagorean >> > theorem in SR spacetime is that dtau^2 = dt^2 - dx^2 - dy^2 - dz^2, and >> you >> > also have to keep track of minus vs. plus signs when you multiply a >> > 4-vector by itself to calculate its norm. >> > >> >> Yes - that is what I meant by proper time advances at 1 second per >> second. As you say, that is not a great revelation, and IIRC, is >> usually taught in introductory relativity courses. >> >> But where Edgar went wrong was to suggest that this implies that all >> points along a path traced out an object moving through space time >> have exactly the same clock time, because everything travels at >> c. This is only true for objects travelling along null geodesics, ie >> objects moving at the speed of light relative to us (or relative to any >> other >> object moving at nonluminal speeds through space). >> > > > Gotcha, I thought you meant that only things on null geodesics could be > said to be "moving through spacetime at c". I don't know if Edgar actually > meant that "all points along a path traced out by an object moving through > space time have exactly the same clock time" though, I think when he said > that everything must "be at one and only one point in clock time due" he > meant that there is an absolute present and that each object has "only one > point in clock time" at the present, not that different points along a path > of an object (or different objects) have the same clock time as one > another. But I don't follow his reasoning in thinking this idea is somehow > implied by the idea that everything "moves through spactime at c". > > 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.
