When I Say STRAIGHT...

Wayne Price wrote:
 In trying to understand the Twin Paradox, I am not quite clear on 
 how nature knows which twin is "older" when they are brought back 
 together.  From what I understand, the twin that is moving in 
 respect to the universe will be younger.  If so, what force does 
 the universe apply in order to cause this to happen?  If it is 
 gravity, it would seem that the effects of SR would be different 
 when traveling with the expansion of the universe than against it...

John Anderson wrote:
 In special relativity, there is no preferred frame such as what you 
 are calling the _universe_.  The world lines of the two twins are 
 distinguishable.  The one that stays at rest in some inertial frame 
 has a straight world line in all frames of reference...

The above explanation doesn't directly address the issue, because 
it refers to "straightness" as if it was an unambiguous concept.  
It's well known that special relativity is based, as is Newtonian 
mechanics, on the *assumption* of a preferred set of reference 
frames (along with the further assumption that we can effectively 
identify those reference frames in any particular circumstance).  
It so happens that the preferred set of reference frames (the 
"inertial" frames) are evidently those that are in uniform motion 
(i.e., "straight") relative to the average frame of the distant 
stars.  The same is true in Newtonian mechanics.  Thus, the premise 
of the original poster's question is perfectly correct, i.e., the 
criterion of "straightness" is the overall mass of the universe.  
As to why this correspondence exists, or how it is enforced, SR 
is silent.

As Einstein observed "in the theory of special relativity there 
is an inherent epistemological defect", namely, the assumption of 
a preferred class of reference frames with no physical means of 
identification.  He pointed out the fallacy of believing we can
identify them based on "straightness", because SR doesn't provide
us with any means of determining straightness, which is after all
a relative concept.  Similarly he pointed out that we can't define 
"straightness" as the path of an object to which no forces are 
applied, because the only way we have of knowing if a particle is 
subject to forces is by seeing whether its path is straight.

Only by embedding SR within the framework of GR do we have a valid 
THEORETICAL (as opposed to computational) basis for treating the 
twins paradox.  [Needless to say, if we just want to crunch out an 
answer, and don't care why it's right, or under what circumstances 
it would be wrong, we can use SR.]  As Weinberg says in his book 
on GR

 "The question of what determines the inertial frames is
  now answered, for the only reference frames in which the
  whole universe appears spherically symmetric...are the
  frames which do not rotate with respect to the expanding
  cloud of typical galaxies.  The inertial frames are any
  reference frames that move at constant velocity, and 
  without rotation, relative to the frames in which the
  universe appears spherically symmetric."

The earliest writers on relativity clearly understood the 
philosophical (not computational) necessity of invoking general 
relativity and the origin of inertia in any meaningful treatment 
of the twins paradox.  For example, in Reichenbach's classic 
"The Philosophy of Space and Time" he says

  "The error lies in a misconception of relativity...the
   theory of gravitation shows that the theory of special
   relativity is applicable only because the distant masses
   of the fixed stars determine a particular metrical field.
   If we take account of the masses of the fixed stars [in
   a fully relativistic treatment of the twins paradox] the
   apparent equivalence between the two interpretations
   vanishes."

Max Born (in "Einstein's Theory of Relativity") makes the same 
point, and goes on to quantitatively analyze the situation from a 
fully relativistic standpoint, showing how the gravitational field 
induced by the distant stars yields the same net effect, whichever 
twin is treated as having a "straight" worldline.  Thus, the key 
distinction between the twins in not which one has an absolutely 
"straight" worldline (which is epistemologically meaningless), but 
which twin's worldline is straight relative to the fixed stars.

Of course, even general relativity fails to give a completely 
unambiguous definition of inertial frames, because the metrical 
field is fully determined by the masses in the universe only in 
certain closed cosmological models.  For open cosmologies, GR 
permits universes that are rotating relative to their centers of 
mass, and so on.  As a result, the true origin of inertia is 
still unresolved.


John Anderson replied:
 I really don't care about most of the issues you are trying
 to raise here because they are irrelevant to the point I
 was making.

The issues I raised are entirely relevant to the "point"
you were making.  In fact, one of the issues raised was 
that your "point" (defining the class of inertial frames 
as those moving uniformly relative to inertial frames) is 
meaningless.


John Anderson wrote:
 When I say _straight_, I mean that the world line of the 
 inertial twin has the space coordinates as linear functions 
 of the time coordinate...in all inertial frames...

Look closely at what you've written.  You say inertial frames 
are those that move uniformly relative to inertial frames.  This 
is the kind of patently vacuous "explanation" that fuels much 
of the sad anti-relativity phenomenon.