Just realized in retrospect that it was a very confusing choice of terminology to use "reference frame" to refer to the frame that's used to label other frame's relative velocities--I was thinking of the idea that other frame's velocities are labeled "in reference" to this one choice of frame, but somehow it didn't occur to me that "reference frame" is a synonym for "frame of reference", which is what ALL frames are called. So I edited my post below to use the term "index frame" instead, since I'm indexing other frames by their velocity relative to this frame:
On Thu, Mar 6, 2014 at 12:51 PM, Jesse Mazer <laserma...@gmail.com> wrote: > > I don't know what you mean by "the frame view of all frame views". I agree > that for a given pair of clocks A and B that are at rest relative to each > other and synchronized in their rest frame, each frame has only ONE answer > to how much clock A is ahead of B (a number which can be zero if the frame > in question is their rest frame, and can also be negative if the frame in > question sees clock A as having a time that's behind clock B's time). But > if we want to LABEL each such frame by velocity (so we can do an integral > or sum over frames with different velocities to take the average), then we > must use some specific "index frame", and label the velocity of every other > frame relative to the index frame. So for example if a given frame X has a > velocity of 0.9c relative to a pair of clocks that are 2 light-year apart > in their own rest frame, then in X they are out-of-sync by 2*0.9 = 1.8 > years. If we use as our "index frame" the rest frame of the clocks > themselves, then X is labeled with v=0.9c since that's its velocity > relative to the index frame, and thus our "amount out of sync as a function > of v" function will have a value of 1.8 at v=0.9c. On the other hand, if we > use as our "index frame" a frame moving at 0.8c relative to the clocks, > then frame X will have to be labeled with v=0.357c since that's its > velocity relative to the new index frame--it's still the same frame X, and > it still has the same amount-out-of-sync of 1.8, but it just has a > different velocity label. So using this index frame, our "amount out of > sync as a function of v" function will have a value of 1.8 at v=0.357c. > > Point is, depending on the index frame we use to define the "v" of every > other frame, our "amount out of sync as a function of v" function will look > different, and thus if we integrate over that function to find some sort of > "average" value for the amount the clocks are out of sync, or just do an > average over a finite number of values of the function at regular intervals > of v, then we'll get different answers depending on what index frame we > chose. > > 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
