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CAUSALITY AND IMPLICATION
Intuitive causality and logic
This section recalls the main traits of the intuitive
causality and logic defined in "NATURAL MODEL".
"Physical bodies" are constructed by collecting repetitive
patterns of sense impressions into secondary images,
apparently more "real" than their originations.
Similarly, one selects some pattern of event-images
apparently always followed by another one and under names
respectively "cause"/"effect" collects them into the
secondary image under the symbolic name "causality".
Like in the case of "physical body", one attributes to
this secondary construct "causality" the unshakable "physical
reality" and certainty, unlike to its "cause/effect" instances.
And, having constructed the "physical world" by populating it
with "physical bodies", one orders it with the principal
orderer "causality".
A particular type of Reflection ("STRUCTURES OF MIND"), which
we shall call "Inference", maps events ordered by causality
into symbolic structures of expressions related "deductively"
by Implication, shortly "ER structures". Inverse operation
regresses "inductively" expressions to their territory of
events.
Due to intuiting causality as unshakably "real", deduction
appears as "necessary" or "certain".
Induction, on the contrary, retrieving the originating events
of symbolic expressions, gets affected by their uncertainty
and fuzziness.
Causality maps to the primary logical operator "implication".
Other subordinated orderers: such as "and", "or", etc. order
particular patterns of causes and effects.
Common sense taking the illusory "reality" at its face value,
considers the intuitive causality/logic as an evident rule
of practical behavior, applying it instinctively to the
day-to-day practice. One knows intuitively that hitting a nail
with a hammer will drive it into the wall and that standing
in the way of the oncoming bus will cause not a little misery.
In the social praxis people tending to stand in the way of
oncoming buses are isolated in lunatic asylums with others
who cast similar doubts on causality and logic.
However, extended over intellection, the common sense unveils
the prejudices it has gathered through the daily practice,
and rigorous rationality starts by overcoming it.
The following sections deal with causality from the point
of view of rational scientific models.
Historic overview
In the context of the physical reality causality appears as
a principle manifested by concrete instances of causation
or action of cause(s) upon effect(s). We shall use the
universally employed terms "action" and "interaction" (local,
at distance, etc.) as a strict synonyms of causation
instances.
Causality became a crucial issue of foundations of physics
as result of the discovery of quantal phenomena and involved
controversy between continuous and discrete view of the base
of physical reality.
After long discussions of Einstein with Bohr and Born,
the issue of causality, whether accepted or not, boiled
down to the Principle of Locality, shortly "Locality" and
the Principle of Separation, shortly "Separability". We shall
examine their original, rather confused formulation and some
refinements which unluckily did not succeed to eliminate the
ambiguity of both principles and of founded in them causality.
We shall try to disambiguate it in the next section.
At the outset, Einstein's rather crude formulation asserted
that by virtue of Locality an object may act only on its
immediate neighborhood. Then, taking two objects A and B
far apart in space, Separation states that external influence
on A has no direct influence on B, which is a clear corollary
of Locality. He added that Locality is used consistently only
in field theory.
***
If this axiom were to be completely abolished,
the idea of the existence of quasi enclosed systems, and
thereby the postulation of laws which can be checked
empirically in the accepted sense, would become impossible.
This view of how interactions propagate through space should
be contrasted with the primitive magical view (which is also
the view of QM(;-)) (Einstein 1948 and The Born-Einstein
Correspondence)
***
Although one tends to get the intuitive gist, the formulation
is so ambiguous that it hardly means anything. What exactly
is an "object"? Or a "system"? What's the "immediate
neighborhood"? Doubtless other objects related by what we
designate in "NATURAL MODEL" as "Contact". One does not see
how interaction of A with its neighbors may "propagate" and
in particular - propagate to B.
It would presuppose a chain of intermediary objects touching
one another between A and B and one of them failing would
annihilate the interaction. Yet, sun's gravity interacts
with earth without any intermediary objects, unless we
disenter the old billiard balls. In brief, the locality
based propagation and interaction seem no less magical than
the QM's view, BTW its magic alleged and not substantiated.
Toning down the alleged magic of the QM, Einstein asserted:
***
On the basis of quantum theory there was obtained a
surprisingly good representation of an immense variety of
facts which otherwise appeared entirely incomprehensible.
But on one point, curiously enough, there was failure:
it proved impossible to associate with these Schrodinger
waves definite motions of the mass points - and that, after
all, had been the original purpose of the whole construction.
The difficulty appeared insurmountable until it was overcome
by Born in a way as simple as it was unexpected.
The de Broglie-Schrodinger wave fields were not to be
interpreted as a mathematical description of how an event
actually takes place in time and space, though, of course,
they have reference to such an event. Rather they are a
mathematical description of what we can actually know about
the system. They serve only to make statistical statements
and predictions of the results of all measurements which we
can carry out upon the system.
It seems to be clear, therefore, that Born's statistical
interpretation of quantum theory is the only possible one.
The wave function does not in any way describe a state which
could be that of a single system; it relates rather to many
systems, to an 'ensemble of systems' in the sense of
statistical mechanics. (Einstein, 1936)
***
It hardly tones down anything. "On the basis of quantum
theory" sounds ambiguous. If it designates the QM of "these
Schrodinger waves", one hardly sees the immensity of well
represented facts. After all the objective of quantum
physics consists in postulating and empirically discovering
particles and none has been discovered by so meant QM.
All were discovered by field quantizing methods having nothing
to do with Schrodinger waves. Born's statistical interpretation
only confirms that Schrodinger waves cannot represent and
coordinate events.
So we are back at Locality, separability and their refinement
with respect to crude version we saw above.
Under the press of Bohr's repeated critiques, Einstein dove
steadily deeper in his understanding of the roots of his
commitment to separability. In a 1948 article he pointed out
that field theories like general relativity assume separability
in the most extreme possible form, since, in effect, they
regard each point of the space-time manifold as a separable
physical system, endowed with its own, independent physical
state in the form of, say, the value of the metric tensor at
that point. (Einstein 1948, 321).
It does not sound very convincing either. Abstractions have
sense for Einstein only as coordinating representations of
events. If a "system" should represent one or more events,
one hardly sees how it could be embodied by a point.
Einstein himself contradicted the idea of a "system" reduced
to a point or even to a monolithic "matter" particle. In his
letter to Lorentz of 23 May 1909 he wrote:
***
We are, to be sure, all of us aware of the situation regarding
what will turn out to be the basic foundational concepts in
physics: the point-mass or the particle is surely not among
them. the field, in the Faraday-Maxwell sense, might be, but
not with certainty.
***
Sounds like intuition of the United Theory in spite of weak
and strong interaction fields not yet being discovered.
He writes further:
***
I am not at all of the opinion that one should think of light
as being composed of mutually independent quanta localized
in relatively small spaces. This would be the most convenient
explanation of the Wien end of the radiation formula. But
already the division of a light ray at the surface of refractive
media absolutely prohibits this view. A light ray divides, but
a light quantum indeed cannot divide without change of frequency.
As I already said, in my opinion one should not think about
constructing light out of discrete, mutually independent points.
I imagine the situation somewhat as follows: ... I conceive of
the light quantum as a point that is surrounded by a greatly
extended vector field, that somehow diminishes with distance.
Whether or not when several light quanta are present with
mutually overlapping fields one must imagine a simple
superposition of the vector fields, that I cannot say. In
any case, for the determination of events, one must have
equations of motion for the singular points in addition to
the differential equations for the vector field.
***
In the same letter he reiterated his view of locality
(embodying causality):
***
... that which we conceive as existing ("real") should somehow
be localized in time and space. That is, the real in one part
of space, A, should (in theory) somehow "exist" independently
of that which is thought of as real in another part of space, B.
If a physical system stretches over the parts of space A and B,
then what is present in B should somehow have an existence
independent of what is present in A. What is actually present
in B should thus not depend upon the type of measurement carried
out in the part of space, A;
***
This causal view of physics and of quantum physics in particular
has been contested by the partisans of the rudimental QM and
of its "Copenhagen Interpretation". The physical failure and the
fatuous shamanist pseudo-philosophy of this "acausal" approach,
contrasted with the vertiginous accomplishments of contemporary
causal models, to wit the Extended Relativity and the Quantum
Field Theory are discussed in "FOUNDATIONS OF QUANTUM PHYSICS",
Any doubt that may still persist with respect to causality is
due to Einstein's ambiguous metalanguage. While he argued for
causality, his maladroit wording argued against it.
In the following section we try to clarify the still
ambiguous concept of locality and its relation to causality.
Extended Locality
In its habitual usage and even in Einstein's formulations
locality appears confused and incompatible with interaction
of spatially separated events. We shall try to repair it
by expansion to "Extended Locality" (e-locality), defined
as follows:
Two events are said to be "e-locally related" (in a Model)
when their Model's representations are connected by a geodesic
of model's SPACE Continuum to the same "location" or point of
this Continuum. E-locality is clearly Model dependent.
E-locality clarifies the confusion of "locality" with a
single point of SPACE. Even such distant bodies as Earth
and Moon are e-locally related via the SPACE-equivalent
gravity field continuum.
In order to conform with the usual terminology, we shall
further use the term 'locality', meaning by it the e-locality,
unless differently defined, in which case we shall mark it
with inverted commas, as "locality".
Causality and implication
Given locally related Events A,B we shall say that they
appear respectively as "Cause" and "Effect" if:
-A precedes B in time,
-B has never been observed without A, while A might have
been observed without B.
Thus force appears as cause of acceleration as the latter
has never been observed without the former, while force
is often observed without acceleration.
Eventtual causality relation maps into model's abstract
implication relation. Thus, we consider causality as
equivalent with implication: to say "A is cause of B" is
equivalent with "A implies B".
Weak verifiability and strong falsifiability of Implication
corresponds to the uncertainty of Causality which is
hypothetical, never verified, but at best not (yet)
falsified by eventual observation of effect lacking its
alleged cause. Taking into account the fundamental fuzziness
of events ("NATURAL MODEL") we can conclude:
CAUSALITY IS HYPOTHETICAL, FALSIFIABLE AND FUZZY.
As a necessary foundation of implicative scientific Models,
it extends over them these characteristics.
Reified causality, or "determinism"
In "STRUCTURES OF MIND" we asserted that sensations trigger
ordered "physical reality" of images and that mind's faculty
of (re)cognition guides us through their labyrinth.
"Physical bodies" have been constructed by collecting some
repeatedly occurring patterns of sensations into
secondary images, apparently more "real" than their
originations.
Similarly, one selects some pattern of event-images
apparently always followed by another one and under names
respectively "cause"/"effect" collects them into the
secondary image under the symbolic name "causality".
Like in the case of "physical body", one attributes to
this secondary construct "causality" the unshakable "physical
reality" and certainty, unlike to its "cause/effect" instances.
And, having constructed the "physical world" by populating it
with "physical bodies", one orders it with the principal
orderer "causality".
However, this "physical world" appears as a map of some
hypothetical territory - "Transcendency". And temptation
arises to regress it to this transcendental territory and
to posit thus called forth transcendency as the "real world
out there". Yet, no matter how tenacious and persistent
this temptation may be, the transcendental "reality" of
regressed mental constructs is nothing, but a "transcendental
illusion".
One may give in to the temptation and fall prey to the
transcendental illusion by regressing mental secondary
constructs - the "physical bodies" to "real objects"
of transcendency. To use the fashionable philosophical term,
the transcendental illusion is tantamount to reification.
Like the e-locality, causality is an abstract construct
pertinent exclusively to abstract models. Reified causality,
illusorily ordering phantasmal "real objects" of transcendency
is known as "determinism".
Thus, "determinism" is irrational and void of any rational
meaning. Qualifying a physical approach as "deterministic",
or, for that matter, "indeterministic", falls to the province
of pseudo-philosophy and not physics.
Extrinsic logic
Mind's faculty to support inference's ERN structures and
functions may be called intrinsic or natural "Logic".
It is the subconscious Mind's system used instinctively as
support of daily behavior. Irreplaceable as pilot of simple
activities, it may nevertheless be misleading owing to its
inadequacy to handle complex cases due to mind's limited
working memory and its incapacity to concentrate simultaneously
on numerous issues, as well as to the fuzziness of induction.
Facing shortcomings of their natural faculties, humans usually
produced compensating tools: hammer to assist striking and
extrinsic "Logical Systems" to assist intrinsic mind's
inference. Such extrinsic systems may be justified exclusively
by their capacity to extend and simulate mind's intrinsic, ERN
logic. In the chapter "ERN LOGIC" we present a properly
justified extrinsic logical system, whose applications so far
stood the verification test, i.e., which, as yet, has not been
falsified. It replaces consistently and simply the ill founded
established systems.
