Harry Veeder wrote:
Harry:
The raison d'être of GR is to explain gravity.
Stephen:
That's right. But you don't need it to resolve the twins problem, which
takes place in flat space.
I am confused.
In your first response to me you started off by saying the opposite:
Harry:
That works in SR, but the solution is inconsistent with GR.
Stephen:
Wrong. In fact the full solution can only be had using techniques
commonly considered to be part of GR.
Err hmmph. Well. What I meant by that is this....
Gravity, and the attendant curved space, is unnecessary to the solution
to the twins problem. However, if you want to solve the problem from
the point of view of the traveling twin, without neglecting acceleration
(i.e., without assuming velocity changes happen "instantly"), then you
need to use techniques which are commonly treated as part of general
relativity, rather than special relativity. If one is willing to do the
actual calculations using the frame of reference of the stationary twin,
however, then there's no need to integrate over a curved path with a
non-Minkowski metric, and we can solve it, acceleration included, using
techniques from SR. See, for example:
http://www.physicsinsights.org/accelerating_twins.html
In case that was all insufficiently murky, let me add to the confusion
by explaining that the boundary between GR and SR has been a bit of a
moving target over the years. Initially SR dealt only with inertial
frames (no acceleration), and in fact the basic postulates of SR don't
really say what happens during acceleration. However, if we add the
_assumption_ that clocks are not affected by acceleration, then at the
expense of some additional complexity in the math we can solve problems
such as this one entirely within the "extended" version of SR, in either
frame of reference. From that point of view, anything _except_ gravity
is in the bailiwick of SR.
Finally, I should mention that there is a somewhat surprising error on
my accelerating twins page, linked to above. (I don't mean it's
surprising that there's an error; rather, the particular error is
surprising!) At the bottom of the page I mentioned that I hadn't yet
done the porthole view from the ship but asserted that it "contains no
new surprises". That's utterly wrong -- the porthole view from the ship
is extremely surprising, as I found when I started to work it out.
Someday I may get around to putting together an "integrated" page on all
this, showing how the pieces fit together; it's not as straightforward
as it appears at first glance. Here's a partial writeup:
http://www.physicsinsights.org/porthole_view_1.html
As someone said when I mentioned the effects discussed on that page,
"Oh, that's just aberration!". Well, yeah, it is aberration -- but I
wouldn't have said "just" aberration; I think it's highly weird...
Harry
