Pavlovian Relativity

Albro Swift wrote:
 I think it's important to point out that the twins paradox (i.e.,
 the privliged status of inertial frames) IS an epistemological
 problem for *special* relativity, and was one of the main
 considerations that motivated Einstein to abandon SR as a
 viable theoretical framework for physics...

John Anderson wrote:
 Bullshit!  You can explain this so-called paradox quite
 easily in SR when you consider relativity of simultaneity
 as well as time dilation.  You need to consider the acceleration
 of the non-inertial twin, but this can be done within SR.
 You don't need GR to deal with the kinematic effects of 
 accelerations.

When teaching freshmen Physics 101 it's very important to convey the 
fact that we can compute the lapse of proper time along arbitrary 
worldlines using the flat Minkowski metric, so we say "You do NOT, 
repeat, NOT need general relativity to handle accelerated frames", 
and we make everyone write that on the blackboard 20 times so they 
never forget it.  The same point is stressed in every elementary text
on special relativity, and to illustrate the point authors often 
mention the "naive twins paradox", which is really just a fancy name 
for failure to understand what the equation ds^2 = dt^2 - dx^2 means.
That's the "paradox" that is evidently the intended subject of this 
thread.

However, when someone loudly proclaims that "There is no twins
paradox!" he invites people to point out the fact that there is a 
more profound issue of epistemology that is also associated with
the name "twins paradox", one that has nothing to do with questioning 
the logical consistency of the Minkowski spacetime metric.  This is 
the grown-up version of the paradox that troubled Einstein, and that 
led him to reject special relativity as a fully coherent theory.  
The essence of this "paradox" is simply the lack of justification 
for the preferential treatment given to one particular set of world 
lines (the inertial worldlines).

The naive twins paradox doesn't concern itself with this issue, 
because it accepts uncritically the concept of absolute acceleration
and the a_priori identifiability of inertial worldlines.  However, as
explained by Einstein in my previous post, the Equivalence Principle 
compells us to relinquish this naive point of view, because it shows 
that *even in regions of flat spacetime* the metric is established 
by the imposition of boundary conditions that are ultimately linked 
to "other" masses (i.e., other than the two twins in the naive 
statement of the problem).  Thus, it becomes necessary at the very 
least to construct a relativistic theory of gravity to place the 
results of SR within a coherent epistemological context.

Now, you might legitimately question whether these "weighty arguments 
from epistemology" (to use Einstein's wry phrase) are relevant to a 
discussion of the *naive* twins paradox, which is the topic of this 
thread.  I will grant you that this is a point on which reasonable 
people can differ, but it is my bold thesis that you crank-battlers 
would actually have MORE success if you approached the problem from 
the standpoint of what is, unarguably, a more logically coherent
theory (GR).  This is true in spite of the fact that even GR does
not give an unambiguous answer as to the origin of inertia; what
GR DOES provide is a context within which clear boundary conditions
can be specified, thereby making it conceptually clear how we have
actually built in the inertial asymmetry to the background "flat
metric" of spactime in our cosmology, a fact that is completely
disguised in the context of special relativity.

You may think that people who have a problem with the naive twin 
paradox don't really care about epistemology, and that they are 
simply failing to grasp the relativity of simultaneity.  While I 
do not doubt that they fail to comprehend the implication of non-
unique surfaces of simultaneity, I also believe that lurking deep 
underneath their confusion and unwillingness to learn lies a 
instinctive dissatisfaction over how we justify picking out the 
inertial world lines to begin with.

I recall a previous discussion of this point, in which you claimed 
that the identification of inertial worldlines was unproblematical 
because "Inertial world lines are those that are straight when 
measured from any inertial frame"(!)  With patently circular 
explanations of that kind, you stand little chance of convincing 
any anti-relativity person that you have a genuine grasp of the 
conceptual issues, which is after all what he really cares about 
(as opposed to passing an exam on the Minkowski metric).  As long 
as he senses that your understanding covers only the naive twins 
paradox, and that you don't even recognize the existence of the 
grown-up twins paradox, i.e., the question of what singles out a 
preferred class of world lines as "inertial" (the question that led 
Einstein to general relativity), he is not likely to listen to your 
explanations of the Minkowski metric.  That's why I think these 
"weighty issues" actually ARE relevant (in fact, crucial) to a 
meaningful discussion of the naive paradox.  Surely even you 
yourself can't be satisfied with your explanation that inertial 
worldlines are those that are straight relative to inertial 
worldlines.


Tom Roberts wrote:
 A discussion of the epistemological foundations of SR is
 totally unrelated to a discussion of the "twin paradox".

You're referring here to the "naive twin paradox", i.e., the 
inability to figure out how a formula like ds^2=dt^2-dx^2 works.
I agree that this inability is not particularly relevant to a 
discussion of the foundations of relativity.  In fact, it's not 
relevant to *anything* except perhaps the need for remedial education.  

However, this thread asked for a description of a real twins paradox, 
which opens the door to things like this:

  The usual statement of the twin paradox doesn't specify what the 
  other matter in the universe is doing.  It just talks about the 
  Earth, the two twins, and maybe one distant star.  So we're free to
  say that all the other mass in the universe is moved in parallel 
  along with the travelling twin, and only the earth, the earthbound 
  twin, and the one distant star are stationary.  This is fully within 
  the bounds of the original problem statement, and SR gives the same 
  answer as before, because the spacetime metric in SR isn't affected 
  by accelerating the other mass in the universe, but now GR (under 
  most cosmological models) gives the *opposite* answer, because the 
  metric IS influenced by the acceleration of the other masses.

Scenarios like this attack the naive conception of what constitutes
an inertial frame.  To innoculate yourself against tactics like this 
you have to be more explicit in your statement of what you consider 
to be an acceptably naive twin paradox, i.e., you can't just specify 
what the twins are doing relative to some circularly-defined "inertial 
frame", because that doesn't constrain the context sufficiently to 
ensure that SR and GR give the same answer.  You have to specify what 
all the matter in the universe is doing...and even then the answer that 
GR gives is ambiguous, since it depends on your cosmology and/or 
boundary conditions.  Also, note that accelerometers don't help,
in view of the Equivalence Principle.

Basically I think you guys have experienced "mission creep", in
the sense that you started out to defend relativity against a
bunch of naive anti-relativity nonsense, but you're now defending
special relativity against general relativity, which is a losing
proposition.  I think you're in this position mainly because of a 
certain Pavlovian response for which people like myself are not 
entirely blameless:  Whenever you see or hear the terms "twin 
paradox" and "GR" within a mile of each other, you instantly 
respond with "GR is NOT needed to handle the twin paradox!  You
can integrate proper time along accelerated worldlines using the
flat Minkowski metric.  I loved it.  Much better than Cats.  I'm
going to see it again and again.".  That cliche knee-jerk post-
hypnotic response does not bespeak a great sensitivity to the 
real conceptual issues of space, time, and spacetime.

I honestly believe you would be more effective in your crank-
bashing (aka taunting the village idiots) if you elevated the 
discussion and dealt frankly with the philosophical issues of
relativity rather than trying to duck them.  Even if you should
succeed in getting a crank to understand how Minkowski spacetime
works, it won't matter if he doesn't understand the basis we
have for associating those abstract numerical relations with 
observable phenomena.