An attempt is made in this paper to analyze the purely formal nature of information-theoretic concepts. The suggestion follows that such concepts, used to supplement the logical and mathematical structure of the language of science, represent an addition to this language of such a sort as to allow the use of a unitary language for the description of phenomena. (The alternative to this approach must be certain multi-linguistic and mutually untranslatable descriptions of related phenomena, as with the various versions of Complementarity). This conception is tested for the specific case of Heisenberg's Uncertainty Principle, in order to show that, with the assumption of a suitable and intuitively satisfactory definition of the quantity of information contained in a measurement, the Heisenberg Principle becomes an informational restriction arising from the formal properties of the symbols of a given language rather than as a “law” of nature.
An attempt is made in this paper to analyze the purely formal nature of information-theoretic concepts. The suggestion follows that such concepts, used to supplement the logical and mathematical structure of the language of science, represent an addition to this language of such a sort as to allow the use of a unitary language for the description of phenomena. (The alternative to this approach must be certain multi-linguistic and mutually untranslatable descriptions of related phenomena, as with the various versions of Complementarity). This conception is tested for the specific case of Heisenberg's Uncertainty Principle, in order to show that, with the assumption of a suitable and intuitively satisfactory definition of the quantity of information contained in a measurement, the Heisenberg Principle becomes an informational restriction arising from the formal properties of the symbols of a given language rather than as a “law” of nature.
From the preceding exposition it follows that not only physics but natural science as a whole is basically dependent on ordinary language. The complementarity of quantum physics displays the fundamental interdependence of observation and description of natural phenomena, and the very objectivity of natural science relies directly on the differentiation of experiences into external and private phenomena afforded by ordinary language. Because of the extreme smallness of the quantum of action the complementarity of physical phenomena is not experienced either in daily life or in classical physics. But the interdependence of observation and description of phenomena prevails as much in classical science as in quantum physics. The very aim of experimental investigation is to perform observations in those particular ways which make possible the communication of information sufficient for the reproduction of the observed phenomena. Concordantly the elementary physical variables, which are indispensable to any systematic analysis in natural science, are defined through reference to measuring arrangements constructed so as to be unambiguously describable in ordinary language. Thus no scientific formula, law, or result of measurement can be given objective significance independent of ordinary language. Through every hierarchy of descriptions in natural science ordinary language penetrates as the unambiguity of propositions.
Niels Bohr's interpretation of quantum mechanics is often cast as positivist and sometimes explicitly claimed to be influenced by logical positivists due to some similarities in their thinking. While it is certainly the case that some logical positivists attempted to recruit Bohr, this paper argues that Bohr had interests of his own in the logical positivists. Bohr's interpretation of quantum mechanics focuses on observation, the use of classical concepts in quantum mechanics, and indeterminacy of quantum processes as opposed to uncertainty of measurement. His view thereby shares some common ground with the logical positivists' views on verification, the observation language, and anti-metaphysics. But Bohr also emphasized complementarity: that certain pairs of concepts - such as position and momentum - are mutually exclusive in quantum mechanics since they, according to Bohr, are only meaningful relative to different experimental arrangements. Bohr believed that complementary brought a general epistemological lesson for all of science that an objective description of nature is not separable from the observational and experimental conditions under which we explore nature. Motivated by the common ground between himself and logical positivism, Bohr tried to persuade the logical positivists and Carnap in particular to adopt and champion complementarity as well as part of their unity of science program. Though his efforts ultimately proved in vain, Bohr's attempts to influence logical positivism disprove the claim that his engagement with them was reluctant and purposefully limited.
Although the interpretation of the concept of information is not clear, even in the classical framework, new interpretive problems have arisen with the advent of the so-called quantum information, which combine the difficulties in understanding the concept of information with the well-known foundational puzzles derived from quantum mechanics itself. The aim of this paper is to consider some arguments traditionally put forward to support the idea that quantum information is qualitatively different from classical information. The final conclusion is that there are no reasons to admit the existence of quantum information as qualitatively different from classical information: there is only one kind of information, physically neutral, which can be encoded by means of classical or quantum states.
In this paper and a companion paper, we attempt to systematically investigate the possibility that the concept of information may enable a derivation of the quantum formalism from a set of physically comprehensible postulates. To do so, we formulate an abstract experimental set-up and a set of assumptions based on generalizations of experimental facts that can be reasonably taken to be representative of quantum phenomena, and on theoretical ideas and principles, and show that it is possible to deduce the quantum formalism. In particular, we show that it is possible to derive the abstract quantum formalism for finite-dimensional quantum systems and the formal relations, such as the canonical commutation relationships and Dirac's Poisson Bracket rule, that are needed to apply the abstract formalism to particular systems of interest. The concept of information, via an information-theoretic invariance principle, plays a key role in the derivation, and gives rise to some of the central structural features of the quantum formalism.
In last years, we are witnessing a trend, of trying to describe the laws of nature using informational tools instead of by functional tools. This change towards more abstract description of the nature, is a natural development, as from the time of the Greeks, through the time of Newton, followed by Analytical Mechanics, all the way up to General Relativity and String Theory, there was always a preference to the more abstract and general description of nature. The reason we prefer the more general and abstract descriptions, is that they give us a more objective point of view at the laws of Nature, which allow us more effectively to separate between Phenomena that are the manifestation of the deep laws of Nature, and Phenomena that are just being resulted by our very specific point of view at the universe, and the specific description that we have decided to give it. The more abstract descriptions give us a better frame of reference in our attempted to understand the origins of the laws of Physics. Informational description of the Universe is suspected to be better than the Functional description, as it is a more abstract and general point of view of the Universe, and yet, there is no complete and simple way to translate every Physical Theory to informational language. In this article I have attempted to do just that, by taking two tied Philosophical arguments, and giving them a Formal and Mathematical meaning, by so upgrading them into Physical Principals. The first Principle is the idea that the only objective thing in Nature, that does not depend at the observer point of view, is the different options that realty can exist in. This set of options of reality is meaningless and lacks structure in any way besides their combined number (cardinality), and I name these options of reality “cosmoses”. The second Principle is that there are observers, that are bound to one option of reality, but unable to separate between their cosmos to other cosmoses. This inability to completely know in what cosmos they do exist, creates a local structure. This structure, and the way it changes over time is what creates the structure of the universe that the observers (including you dear reader) measure. By using this simple language, I was able to suggest some new tools and predictions.