In one of the letters written to the Infeld group in Warsaw Einstein wrote:
"A new manner of thinking is essential if humankind is to survive."

  

RELATIVITY IN PHYSICS. INTRODUCTION

In the present part we discuss the Physical concept of Relativity 
in the light of Relativistic Dialectic (RD). One may object that 
it involves vicious circle, RD having been founded in Physical 
Relativity ("Foundations in Physics"). However, human reflection seems 
to dwell necessarily in apparent vicious circle loops elongated along 
the time dimension into a spiral ("Reflection Spiral"). 

RD founds human Universe of Discourse in the Dialectic Dichotomy 
Situation (Subject versus Object) which is phenomenally equivalent 
("Glossary") with Texture (Continuity versus Discreteness) and Scope 
(Globality versus Locality), as well as with Future and Past aspects 
of Temporality ("Observation and Situation", "Texture", "Scope", 
"Foundations in Ontology").

Future, the domain of Subject, has the nature of Possibility and its 
order is teleological, based upon the final cause related to its goal.
Past, the domain of Object, has the nature of Contingency and its 
order is deterministic, based upon effective cause related to its 
effect.        

Let's recall from "Foundations in Physics" some essential features
of "Dichotomy":

[... "dichotomy" is often confused with "antinomy"
which denotes logical contradiction between two statements.
Dichotomy is not restricted to statements, but encompasses
all phenomena and its terms are not contradictory, but
complementary. Compass needle is not an antinomy of
contradictory poles, but a dipole (dichotomy) composed of
two complementary poles (terms).
One of the terms of Dichotomy is "Referential". For want of
a better name we shall call "Core" its counterpart, the
"principal" term on which the awareness concentrates directly.
Phenomena have no exceptional status and the choice of a
particular term as core or referential is arbitrary. To say
that a stone is moving with respect to the Pisa tower, or
indeed with respect to the earth crust is equivalent with
saying that the earth crust is moving with respect to the
stone. Stone and earth crust are two equally worthy terms
of the Dichotomy "Galileo's Experiment".
However, in most cases it's advisable to choose the more complex
term as referential. Galileo was perfectly entitled to choose
the stone as referential. However, cosmology build upon earth
crust falling on a stone would be a bit too complex. Galileo
preferred to use earth crust as referential and formulated a
simple, consistent and reliable theory: the earth crust confirmed
itself as a pertinent referential.] 

Thus, RD sees human Universe of Discourse as a structure of 
Dialectic Dichotomies - Situations ("Fundamental Dichotomies") 
whose complementary Terms are:

-SUBJECT(ivity), phenomenally equivalent with Continuity, Globality, 
 Future, Possibility, Teleological Order.
-OBJECT(ivity), phenomenally equivalent with Discreteness, Locality, 
 Past, Contingency, Deterministic Order.

Relativity consists, in the sense of RD, in considering Phenomena and 
Model Constructs in Situations defined by their Subjective and 
Objective counterparts. Thus, Discrete (Objective) Constructs should 
be considered at the background of (Subjective) Continuum and be 
mathematically represented as integrals thereof. Conversely, the 
structure of Continuum should result from #Space relations among 
neighboring elementary discrete Constructs or #Events, mathematically 
represented as differentials.

Consequently, we shall consider Physical Theories as Dichotomies 
classified in two most general types:

1."Continuous" or "Continuity based" Theories having Continuous Core 
  and Discrete Referential.
2."Discrete" or "Discreteness based" Theories having Discrete Core 
  and Continuous Referential.

We shall see that this classification is not always obvious and in 
some cases, such as Newton's Model and the Quantum Field Theory, may 
be at variance with universally accepted views. 

We shall examine Physical Theories with help of RD's criteria some of 
which  are:

-Equivalence of Causality and Local Action ("Causality")
-Equivalence of #Space and Field ("Derivation of GR Steps 1 & 2"),
-Einstein's Covering Principle ("Glossary"),
-Physical Detector as Observer's support ("Observation and Situation")
-Principle of Preponderance of Facts: for inconsistencies between 
 abstractions and facts, one should first reexamine abstractions. 
 Facts may be called in question only with respect to their Certainty 
 ("Cognitive Network").

CONCLUSIONS
Our review of several most important Physical Theories seems to show 
that only those based in Continuum satisfy our definition of Model or
Model #Space: A particular subclass of #Space which endeavors to map, 
to order and to coordinate Phenomena of PS (Phenomenon #Space) into 
consistent and coherent structures.

This seems to confirm the phenomenal equivalence of Continuity /
Discreteness respectively with Subjectivity / Objectivity. Indeed,
only Subjective (thus Continuity based) Theories are rational, i.e. 
axiomatic and factually falsifiable. Objective (thus Discreteness 
based) Theories, based by definition in some transcendental "objective 
reality", are irrational, dogmatic and not falsifiable: an 
experimental failure calls in question the experiment but never the 
dogma. Objective, discrete Theories are at best recipes of "ad hoc
crutches", procedures allowing to compute local arbitrary #Events, but 
fail to determine the Global structure of a Model #Space. It's shown
in chapters dealing with Newton Theories, Aether and Quantum Theory.
Only Subjective, Continuity based Theories, may be called "Models".

Having said that, let's recall that Continuity and Discreteness are
inseparable, complementary terms of the Dichotomy "Observation" which 
necessarily implies that a Continuous Model is Continuous AND Discrete. 
Logical contradiction, but Dialectic Complementarity: 

Subject (Continuous Core) observes Object (Discrete Referential) of
Phenomenon #Space reducible to discrete Events mapped as points into 
the subjective Continuum, or, in mathematical terms, as differentials 
determining, by integration, the subjective Continuous Model #Space.

One may object that our restriction of "Models" to Continuous Theories
skirts the distinction between, say, the Continuous General Relativity
and the Quantum Field Theory usually considered as dealing with
particles, thus Discrete. A brief inspection of Continuum shows 
however, that a Continuum based Theory may deal with particles and in
the chapter on QFT we see that, at variance with the common belief, it
is clearly a Continuous Model.

Continuum encompasses two constructs:
-Defined area of continuous structure and 
-Undefined Singularity areas (for instance Field being inverse of
distance from its source, tends to infinity and becomes mathematically 
undefined in neighborhood of this source).

Singularities are mathematically undefined discrete lumps of Continuum, 
which, however, does not lessen their physical meaning and importance. 
A Model is a Polar construct whose both Poles, continuous structures 
and discrete singularities have equal physical importance.

The common belief in QFT being Discrete does not concern its Base,
but its preponderant orientation. A consistent Model deals necessarily
with both "Continuities" and Singularities. Most famous cosmic 
Singularities, Big Bang and Black Holes have been defined by the
"continuous" General Relativity and, on the other hand, one of the
most important Continuous, #Space and Field concerning  phenomenon, 
the Casimir Effect has been predicted and confirmed by the "discrete"
QFT. 

At the risk of boring the reader we shall repeat that all rational
Models are Continuous, that they encompass both Poles, Continuous
Structures and Discrete Singularities and that they may be
preponderantly oriented towards one or the other, being then 
improperly called "continuous" or "discrete".

A few words about Einstein's pretended dislike of the Quantum Theory. 
He considered it, rightly in our opinion, as a recipe of arbitrary 
procedures misfounded in Discreteness and not a Model. Still, he was 
one of, if not the principal contributor to QT and got the Nobel Price 
not for Relativity, but for conceptual and experimental discovery of 
photons. He contributed to recipes hoping that some day next 
generations will turn them to a consistent Model.

And they did. Crutches of QT have been collected and incorporated
into the Continuum based, consistent Model, the Quantum Field Theory.

To finish, a bit on the Grand Unified Theory (GUT). In order to be
a consistent Model it would have to be Continuum based and, on the 
other hand, strongly Discreteness oriented. as majority of interesting  
Phenomena have discrete structure. QFT satisfies theoretically these 
requirements but it stumbles against two practical problems, which 
make the GUT look like unrealizable utopia:

1.At the continuous side there have been discovered four different
Fields: Gravitational, Electro-Magnetic, Week and Strong and there 
does not exist any idea how to go about unifying them in one 
Continuum. Nothing tells us that new ones will not be discovered
in future. GUT should be able to predict them as aspects of some
Grand Unified Continuum, but we are unable to conceive such Unified 
Continuum even for the existing Fields, which appear just to be
there, arbitrarily, unrelated among them.

2.At the discrete side we have to deal with Singularities of a Field
or of interacting Fields. But those lead us immediately to infinity
with which we cannot deal else than by applying some mathematical 
butchery to the integrals until we get the answer we want. Einstein
saw a possible support of GUT in some Singularity-free mathematical
description of Continuum, but did not see where and how it could
be even started. Dirac expressed a similar idea in different words:

**There must be some fundamental change in our ideas, probably a 
change just as fundamental as the passage from Bohr's orbit theory 
to quantum mechanics. When you get a number turning out to be infinite 
which ought to be finite, you should admit that there is something 
wrong with your equations, and not hope that you can get a good theory 
just by doctoring up that number**

So, even the most advanced Model, the QFT, while consistently founded
in Continuum and consistently considering particles as discrete Field 
Singularities, still processes this discrete aspects with help of
arbitrary recipes. However, this time it's no more due to physical
misconception, but to purely mathematical problems, so maybe, all
hope for a GUT is not lost.