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 <[email protected]> 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 [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.
