Pedagogically Unfortunate

Albro Swift wrote
 The assumption of spatial and mechanical isotropy in all 
 inertial frames is *empirically* incompatible with the 
 assumption of unique simultaneity in all inertial frames.
 This is the essential physical content of special relativity.

Brian Jones wrote:
 Please tell us all what SRT says explicitly about the arbitrary,
 solitary inertial observer.

I'd be happy to respond, but it isn't clear what you're asking.  
When you say  "tell us what SRT says explicitly"  it sounds as if 
you're asking for a quotation from a book, but of course SRT isn't 
a book, it's a theory, and as such it doesn't "explicitly say" 
anything.  A theory provides a means of answering a class of 
questions.  If you state a question I'll try to tell you whether 
it's in the class of questions answerable by SRT and, if so, 
what answer it gives.

On the other hand, if the above is as close as you can come to 
formulating a well-posed question, then I might be able to refer 
you to a passage from a book I believe you own, namely, Einstein's 
"Relativity, The Special and General Theory", originally written as 
a popular survey in 1916.  This little book happens to be the poorest 
presentation of relativity that Einstein ever wrote, but anyway, if
your "question" is interpreted as "Please tell us all what [Einstein's 
book] says explicitly about the arbitrary, solitary inertial observer" 
then you might review the following passage:

     "In the first place, we started out with the assumption
      that there exists a reference body K whose condition is
      such that the Galilean Law holds with respect to it: 

          A particle left to itself and sufficiently 
          far removed from all other particles moves 
          uniformly in a straight line.  

      With reference to K the laws of nature were to be as 
      simple as possible.  But in addition to K, all bodies 
      of reference K' should...be exactly equivalent to K 
      for the formulation of natural laws, provided they 
      are in a state of uniform rectilinear and non-rotary 
      motion with respect to K; all these bodies are to be 
      regarded as Galilean reference bodies."

Based on these assumptions, Einstein shows how the empirical evidence 
requires us to relinquish the convention of absolute simultaneity.  In 
other words, he showed that

   The assumption of spatial and mechanical isotropy in all 
   inertial frames is *empirically* incompatible with the 
   assumption of unique simultaneity for all inertial frames.

Since this has been stated in previous posts and you've notably 
avoided taking exception to it, I assume we're in agreement as to 
the basis of special relativity.  Of course, as Einstein observed, 
this basis contains an inherent epistemological defect (just as 
does Newtonian mechanics), which is that it requires us to assume 
an object left to itself moves uniformly in a straight line if it 
is "sufficiently far removed" from all other objects, but the only 
way we have of knowing whether an object is sufficiently far removed 
from all other objects is if it moves uniformly in a straight line.  
Thus the identification of inertial frames in SRT (as in Newtonian 
mechanics) is circular, and Einstein was acutely aware of this. 
That's why he worked so intensely between 1905 and 1915 to place 
SRT within a sound (or at least more sound) framework, arriving 
finally at general relativity, a truly beautiful theory.  

Sadly, this "relativity" newsgroup rarely even touches on Einstein's 
final version of relativity (GR), which was created largely to address 
the epistemological issues left unanswered by the early incomplete 
version of relativity (SR).  Instead, this newsgroup contains endless 
(and mostly clueless) examinations of the philosophical foundations of 
the early incomplete theory (SR) which, since 1915, really exists only 
as a utilitarian set of numerical approximations and limiting cases.

Albro Swift wrote:
 The assumption of spatial and mechanical isotropy in all
 inertial frames is *empirically* incompatible with the
 assumption of unique simultaneity for all inertial frames.

Brian Jones responded:
 There is nothing "empirical" about any assumption.

The word 'empirically' modifies 'incompatible' (not 'assumption').
This incompatibility is the heart of the matter.  Your position 
here is that there's no empirical necessity for the abandonment of 
absolute simultaneity.  That is perfectly correct.  Your numerous 
posts here about "one-way light-speed", etc., all seem to be attempts 
on your part to argue this point, but in fact there is no disagreement 
on this point at all!  No experiment can disprove the convention 
of absolute simultaneity.  This is not controversial, nor is it 
new.  It was emphasized by Poincare, Einstein, and many others.

So, you might ask, where is the disagreement?  Well, just as there 
is no experiment that can faslify the Galilean convention of absolute 
simultaneity, there is also none that can falsify the Galilean 
convention of spatial and mechanical isotropy in all inertial frames.
You've not commented on this, but you can hardly disagree with it, 
since it follows from the same arguments that rule out the 
falsification of absolute simultaneity.  They are really two 
sides of the same coin.

Now, here is the crucial point:

  No experiment can rule out absolute simultaneity, and no 
  experiment can rule out spatial isotropy in all inertial 
  frames.  HOWEVER, there ARE experiments that can rule out 
  the COMBINATION of both those assumptions.  This is what 
  we mean when we say those two assumptions are empirically 
  incompatible WITH EACH OTHER.  We're perfectly free to 
  adopt one or the other - and no experiment can prove us 
  wrong - but if we adopt BOTH of those conventions we CAN 
  be proven wrong by experiment.

To see how two individually viable conventions may be mutually 
incompatible, consider the well-known fact that we can regard the 
Earth's surface as being actually flat, with the peculiar property 
that the sizes of physical objects and time intervals become 
distorted radially, and light rays bend, as we move away from some
fixed point.  As Poincare stressed, this sort of thing is entirely 
a matter of convention.  Likewise we're free to assume an overall 
metrical uniformity of the Earth's surface, i.e., spatial and 
mechanical isotropy on some scale.  Neither of these conventions 
can be disproven by experiment.  HOWEVER, it IS possible to 
demonstrate empirically that these two conventions are *mutually 
incompatible*.  This is exactly the state of affairs with respect
to the conventions of absolute simultaneity and spatial isotropy 
for all inertial frames.

From here the discussion could proceed in one of two directions.  
You may disagree with the above, i.e., you may claim that the 
two Galilean conventions are NOT incompatible, in which case 
I could proceed to describe experiments that demonstrate the 
incompatibility.  On the other hand, it's possible that you 
actually agree with the empirical incompatibility of the two 
Galilean conventions, in which case your complaint is simply 
that the usual formalism of relativity is based on poor 
choice of conventions.   You're certainly entitled to that 
opinion, but it's really just a formal objection rather than 
a substantive one.  We can interpret SR along the lines of 
Lorentz's theory, just as we're free to interpret general 
relativity as a field theory in flat spacetime instead of 
as a metrical theory of curved spacetime.  These are just 
different ways of looking at the same thing.

So you need to decide: are you making a substantive objection
to special relativity, or merely a formal one?


Albro Swift wrote:
  ...Einstein's "Relativity, The Special and General Theory", 
 originally written as a popular survey in 1916.  This little 
 book happens to be the poorest presentation of relativity 
 that Einstein ever wrote...

Brian Jones replied:
 How many other presentations of relativity did he write, anyway?  
 Not counting his 1905 paper, only one.

You're mistaken.  Einstein wrote many accounts of relativity
theory over the years, aimed at different audiences.  Even
setting aside the several research papers on various aspects of 
relativity that he published in scholarly journals from 1905 (when 
he published TWO papers, not one, on relativity) through the 1920s, 
he wrote numerous more or less popular expositions for different 
occassions, ranging from the 1907 review article "On the Relativity
Principle...", to the 1928 article "Fundamental Concepts of Physics 
and Their Most Recent Changes", to the Oxford Lecture in 1933 "On 
the Method of Theoretical Physics", to the Glasgow lecture of the 
same year "Origins of the General Theory of Relativity".  He even 
wrote a lengthy (and quite good) exposition on space and time for 
the Encyclopedia Britannica.  In addition to these, we have his 
excellent book "The Meaning of Relativity" [Princeton], which he 
saw through five editions, and the book "The Evolution of Physics" 
written with Infeld.  Of all these, the book you have evidently
relied on is the most "cartoonish" and lowest level, meant really 
for young school children and people afraid of math.


Brian Jones wrote:
 And even in his book "Relativity," he told no lies, as far
 as we know. For example, when he stated that an inertial 
 observer found that light's speed varied per the simple 
 equation c-v, this is exactly what he meant.

You can't be serious.  Surely you're not referring to the passage
that reads 

     "w is the required velocity of light with respect
    to the carriage, and we have w=c-v.  The velocity of
    propogation of a ray of light thus comes out smaller 
    than c.
      But this result comes into conflict with the principle
    of relativity..." [snip explanation of why w does NOT
    in fact equal c-v.]

If this little literary device is what led you into your present
state of confusion then it just demonstrates that the book is 
pedagogically unfortunate.  On the other hand, the reader can't
be held entirely blameless.  It's as if you had read Galileo's
"Dialogue on the Two Chief World Systems" and came away thinking 
Simplicio was one sharp dude.