Yada Yada Yada...General Relativity

Albro Swift wrote:
 ...it's possible that you actually agree with the empirical 
 incompatibility of the two Galilean conventions... of absolute 
 simultaneity [and] of spatial and mechanical isotropy in all 
 inertial frames... in which case your complaint is simply that 
 the usual formalism of relativity is based on poor choice of 
 conventions.

Frank Wappler wrote:
 That's at least my complaint.  The notion of a coordinate system 
 is not intrinsic to any individual observer (for instance a pointlike 
 observer), instead individual observers have to establish "frames" 
 by some procedure...  I think that the objection _is substantive_ 
 if _the execution_ of any such procedure can vary between individual 
 observers...  this objection applies in the requirement to refer to 
 a "flat and empty" experimental area for observers who apply Einstein's 
 calibration procedure...  I propose to resolve this by identifying a 
 calibration procedure which doesn't involve _any_ "a priori scales" 
 _except_ those intrinsic in the definition of observers (namely the 
 individual ordered sets of their observational statements) and 
 _derives_ the calibration of other scales from them.

Your "observational statements" presumably represent something like the 
observed coincidences of point particles in spacetime.  You're suggesting 
that, with no a_priori "calibration", two *separate* particles have no 
way of relating themselves to each other, so it's only the "meetings" of 
particles that are definite and observable.  The introduction of a system 
of coordinates serves no other purpose than to facilitate the description 
of the totality of all such meetings.

In view of this, you might want to begin with a perfectly general set of 
coordinates x1,x2,x3,x4 that are really just labels of spacetime points, 
with nothing but the topological property that neighboring coordinate 
values are associated with neighboring points.  Otherwise these 
"coordinates" are entirely arbitrary (i.e., uncalibrated).  Thus you 
do not pre-suppose any "scales".

Now, with no preference for any particular calibration of this system of 
labels (coordinates), we should seek physical laws that have the same 
natural expression regardless of which particular calibration we choose.
(We certainly don't want a law that takes a particularly simple form in 
just one coordinate system, because that would amount to a preference 
for that particular "calibration".)

Yada yada yada, and so on to the full theory of (general) relativity.  
But why the legerdemain?  A pedegogical strategy?  Or just some kind of 
weird performance art?


Albro Swift wrote:
 ...only the "meetings" of particles are definite and observable.

Frank Wappler wrote:
 Not only those.  We can still assume that they can exchange signals
 (at least in principle).  Their observations are therefore the 
 emission (coding) of own signals and the reception (decoding) of 
 signals (own and foreign).

So your ontology includes "signals" as a separate class of 
(corporeal?) entities?  As you probably know, the usual concept 
of a signal is that it represents the transferral of some physical 
entity, such as photons, electrons, phonons, etc.  Since you reject 
this fundamental concept, it seems you have a lot of work to do
before you can even *begin* to talk about spacetime scales and
calibration.  You need to define the properties and characteristics 
of "signals" in your ontology.  Do they "travel".  If so, what are
the attributes of their propagation? i.e., do they have a direction 
and a speed?  Also, do they have finite spatial extent? etc, etc.  
More fundamentally, you probably need to address the question of 
why we should want to adopt an ontology that treats "signals" as 
something that is not the product of material interactions.

Albro Swift wrote:
 ...you might want to begin with a perfectly general set
 of coordinates x1,x2,x3,x4 that are really just labels of spacetime
 points, with nothing but the topological property that neighboring
 coordinate values are associated with neighboring points.  Otherwise
 these "coordinates" are entirely arbitrary (i.e., uncalibrated).
 Thus you do not pre-suppose any "scales".

Frank Wappler wrote:
 ...instead of using the labels "x1, x2, ..."  I suggest to use 
 "location_of_observer1, location_of_observer2, ...", and of course 
 dropping the misinterpretable property "neighboring".  How would you 
 define "neighboring" a priori?

Every property is misinterpretable (as demonstrated daily on this 
newsgroup).  The notion of "neighboring" really just signifies that 
the labels of the set of all possible locations is ordered, and that 
the labels are numerically ordered in the same sense.  In other words,
if event B is *between* events A and C, then the coordinates of B are 
numerically between the coordinates of A and C.  If you are proposing 
to dispense with the notion of definite "betweeness" for events, 
then, again, you have a  lot of work ahead of you to lay down your 
principles before you can even begin to discussion scales and 
calibration.


Albro Swift wrote:
 You need to define the properties and characteristics 
 of "signals" in your ontology.  [...] More fundamentally, you 
 probably need to address the question of why we should want 
 to adopt an ontology that treats "signals" as something that 
 is not the product of material interactions.

Frank Wappler wrote:
 Well, my idea was to keep things as universal as conceivable
 (for fear of Occam's razor :).

To introduce a new class of entities when an existing class will 
suffice violates the principle of economy, so it appears to me
you are doing the exact opposite of what you intend.  Or rather,
you *think* you are, but on closer examination we find:

Frank Wappler wrote:
 I consider collections of individual observers which are given
 as ordered sets of their "observational statements".  The addition 
 of a new statement (therefore a change of the set, i.e. a change 
 of the observer state) represents (encodes) a signal, which may 
 correlate to observations/statements of others.

Unless you're introducing yet a third class of non-material 
(not to mention undefined) entities ("observers"), the above would
have to be interpreted as contradicting your previous assertion
that signals do not consist of material processes.


Albro Swift wrote:
 ...it seems you have a lot of work to do before you can even 
 *begin* to talk about spacetime scales and calibration...

Frank Wappler wrote:
 That work consists in the formulation of a procedure by which
 those observers can relate their states to each other...

What I meant is you have a lot of work before you can even talk 
about this.  In particular, you need to define what you mean by 
"observer", since you seem to regard that as a primitive entity, 
i.e., not comprised of more fundamental entities.  The approach 
you're vaguely hinting at has historically been viewed as somewhat 
narcissistic.  As I recall, one of the plays of Aristophanes has a 
character who espouses this philosophy, i.e., the [human] observer 
[consciousnes] is the elementary unit of existence.  Many 
philosophers since then have explored the notion, but the general 
trend of the scientific tradition has been to reject that approach, 
and either posit a mind-body duality (Descartes) or else adopt an 
entirely de-personalized description of nature, with the tacit 
assumption that our consciousness is built up (in ways we don't 
fully understand) from more primitive impersonal processes.


Frank Wappler wrote:
 I hope that this "point of view" gets rid of a host of assumptions
 ("intuitive properties") which are inherent in "other ontologies":

Get's rid of, but then replaces them with a host of new assumptions.
We cannot proceed sans assumptions and/or definitions.  The trick is 
not to identify and reject assumptions - any grade school student can 
do that.  The trick is to identify a strong, elegant, and economical 
set of assumptions from which a coherent and comprehensive theory 
that connects to experience can be deduced.  So far I've seen only 
rejections of assumptions here.  That isn't progress.  Suppose we 
just stipulate right now that we do hereby reject ALL assumptions.  
Now what?  (There's a certain kind of individual who thinks that, 
merely by suggesting the rejection of some assumptions, he has done 
the heavy lifting, and he can leave to less visionary men the simple 
drudgery of filling in the details.)


Albro Swift wrote:
 The notion of "neighboring" really just signifies that the labels 
 of the set of all possible locations is ordered, and that the 
 labels are numerically ordered in the same sense.  In other words,
 if event B is *between* events A and C, then the coordinates of B 
 are numerically between the coordinates of A and C.

Frank Wappler wrote:
 I think that individual observers have a hard time to agree on
 "which order is meant by `some' order". That's why they must 
 calibrate their scales/opinions.

General relativity, for example, gives an unambiguous arrangement
of events in spacetime, about which all observers agree, but you 
evidently reject general relativity (although on what grounds is 
not clear).  Now, "order" is another assumption that you partly 
claim to reject, and yet in your previous comments you said

 I consider collections of individual observers which are given
 as ordered sets...

so it isn't clear that you're adhering to your own program.