Introduction:
The relation of model and reality
is fundamental differently defined in quantum mechanics in comparison with
classical physics and epistemology. The classical model is relevant to all
available data (eventually except not many anomalies). There is an unavoidable
and finite difference between any possible model and reality, which can be
considered as relevant to any possible collection of data, even infinite. The
successive series of models should converge to reality. The collections of any
available experimental results in quantum mechanics are divergent and even
random in principle. Only the probability distribution of them converges to a
limit described by the corresponding model. Furthermore, any deformation of
that model probability distribution can be interpreted as a force field, in
which the investigated system is disposed. No way for distinguishing that
deformation from an external force for the description of the system as
isolated is fundamentally equivalent to that where the system is a part of
another and thus within some force field. This property can be deduced from the
mathematical formalism of quantum mechanics, e.g. by the “no hidden variables”
theorems. If that is the case, can that model be distinguished from reality?
Any alleged difference between any model and reality can be removed
interpreting that difference as being due to an equivalent external force
originating from the universe as whole e.g. at the expense of entanglement.
Consequently the coincidence of model and reality turns out to be provable as
an inherent property of the model in quantum mechanics. Is quantum mechanics
then a falsifiable theory in the sense of Popper? The answer seems to be
negative: It looks like as a “metaphysical theory“. That is not the case in
classical physics just for it is not holistic unlike quantum mechanics allowing
the concept of the universe as a whole.
The thesis:
The mathematical formalism of quantum mechanics allows
of an internal proof within the formalism that model and reality coincide. This
means that any theory utilizing that formalism such as quantum mechanics
involves the particular case of the coincidence of model and reality and thus
there exists at least one scientific theory experimentally very well
corroborated, which is not falsifiable in the sense of Popper.
A short comments of the thesis:
0. The mathematical formalism of
quantum mechanics implies the coincidence of model and reality in two meanings,
which can be designated correspondingly as “weak” and “strong”
0.1. The weak meaning originates
from involving a mathematical formalism, which is necessary infinite. For no
finite model can resolve the main problem of quantum mechanics of uniting
quantum leaps and smooth changes: If the model is necessarily infinite, reality
containing it can be mapped into it one to one as the property of any infinite
subset. Consequently, that model can represent absolutely exhaustedly reality
and thus coincide with it. Anyway that “weak coincidence” does not identify
model and reality.
0.2. The strong meaning is just
what identifies model and reality as a sense of complementarity. The model of
Hilbert space implies that model and reality can be the interpretations both of
Hilbert and of the dual space of it, which is mathematically identical to it.
However both being complementary to each other in a physical sense cannot be
available at the same time and in the same experiment. This can be paraphrased
so: Anything, which is investigated by quantum mechanics, can be as an element
of a model as an “element of reality” (even in the sense of Einstein, Podolsky,
and Posen), but only one of them in a given moment and a given place though
never mind which exactly for they are identical.
A few "ridiculous" corollaries from
the thesis:
1. Popper’s criterion for the
“demarcation line” between science and metaphysics seems to be both falsifiable
and false at least as to quantum mechanics.
2. The coincidence of a
mathematical model and reality can be interpreted in favor of a neo-Pythagorean
understanding of reality as mathematical.
3. That internal proof can be
considered also as an internal proof of completeness of an axiomatic system including
the positive integers (the Peano axioms) therefore contradicting to the
so-called Gödel first theorem of incompleteness.
4. All conclusions (1-3) are able
not to be accepted if the concept of the universe as a whole be refuted as an
analog of the set of all sets leading to a series of contradiction in set
theory and excluded from it for that. However the concept of the universe as a
whole underlies the cosmological model of the “Big Bang” as well as the
expanding and inflating universe, and even the Standard model in particle
physics. Then one should doubt all of them.
5. The concept of the universe as
a whole is an equivalent.
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