Quantum Mechanics has taught us a lesson that goes well beyond a set of new physical laws. It has provided us with genuine “theorems of epistemology”. We now know that there are situations when the observation of the world cannot be considered as the mere reading of a reality pre-existing the observation, whereas there are circumstances where the knowledge of the whole do not corresponds to the knowledge of the parts (holism). We know that there are incompatible properties that are complementary. We know that there exist properties of the whole that are incompatible with any property of each part. The notion of “object” defined in terms of its “properties ” is in contrast with its mereologic connotation according to which objects can be composed to form new objects. The particle ontology as localizable unity is in contrast with the Malament theorem in quantum field theory. To the above add the fact that the two more general fundamental theories in physics – the quantum theory of fields and the general relativity of Einstein – are logically incompatible. In order to reconcile the logical coherence of the observations with their theoretical explanation we need a radical change of paradigm. The solution here proposed is to abandon the vision of the world as a “mechanism” and to substitute it with that of “algorithm”. This is the paradigm of the “universe as a huge computer” that have been latent within the community since Richard Feynman, and nowadays is resurrecting in physics, showing its full theoretical power. In the new algorithmic vision the “mechanics” becomes an emergent phenomenology. Without the need of physical primitive, the new “informational” program allows us to found physics on solid axiomatic grounds. The quantum theory of abstract systems along with the free quantum field theory are derived from information-theoretic axioms. The axioms of quantum theory all have an epistemological connotation, and pertain the possibility of falsifying the propositions of the theory. They reconnect holism with reductionism, probabilism and falsifiability, substituting the notion of “object” with that of “system” and of “event”, and logically implying the theorem of quantum theory without the need of using the abstract Hilbert-spaces toolkit. The free quantum field theory (Weyl, Dirac e Maxwell) is obtained by adding axioms of minimization of algorithmic complexity. The informational framework well separates the notions of “experiment”and “theory”: the theory connects input with output, the experiment being identified with the collection of input, output, and objective intermediate events. The objective reality (experiment) is made of “icons” with which we interact: the theory is the underlying algorithm. The paradigm describes the tapestry of reality as pure software, “software”. “Software without hardware”: the dematerialization of physics. “Reality without realism” means pure logical coherentism.
Quantum Mechanics has taught us a lesson that goes well beyond a set of new physical laws. It has provided us with genuine “theorems of epistemology”. We now know that there are situations when the observation of the world cannot be considered as the mere reading of a reality pre-existing the observation, whereas there are circumstances where the knowledge of the whole do not corresponds to the knowledge of the parts (holism). We know that there are incompatible properties that are complementary. We know that there exist properties of the whole that are incompatible with any property of each part. The notion of “object” defined in terms of its “properties ” is in contrast with its mereologic connotation according to which objects can be composed to form new objects. The particle ontology as localizable unity is in contrast with the Malament theorem in quantum field theory. To the above add the fact that the two more general fundamental theories in physics – the quantum theory of fields and the general relativity of Einstein – are logically incompatible. In order to reconcile the logical coherence of the observations with their theoretical explanation we need a radical change of paradigm. The solution here proposed is to abandon the vision of the world as a “mechanism” and to substitute it with that of “algorithm”. This is the paradigm of the “universe as a huge computer” that have been latent within the community since Richard Feynman, and nowadays is resurrecting in physics, showing its full theoretical power. In the new algorithmic vision the “mechanics” becomes an emergent phenomenology. Without the need of physical primitive, the new “informational” program allows us to found physics on solid axiomatic grounds. The quantum theory of abstract systems along with the free quantum field theory are derived from information-theoretic axioms. The axioms of quantum theory all have an epistemological connotation, and pertain the possibility of falsifying the propositions of the theory. They reconnect holism with reductionism, probabilism and falsifiability, substituting the notion of “object” with that of “system” and of “event”, and logically implying the theorem of quantum theory without the need of using the abstract Hilbert-spaces toolkit. The free quantum field theory (Weyl, Dirac e Maxwell) is obtained by adding axioms of minimization of algorithmic complexity. The informational framework well separates the notions of “experiment”and “theory”: the theory connects input with output, the experiment being identified with the collection of input, output, and objective intermediate events. The objective reality (experiment) is made of “icons” with which we interact: the theory is the underlying algorithm. The paradigm describes the tapestry of reality as pure software, “software”. “Software without hardware”: the dematerialization of physics. “Reality without realism” means pure logical coherentism.
In the present note I will briefly report recent results on the novel field theory based on the information-theoretical paradigm. This program continues the previous one on the axiomatic derivation of quantum theory from information-theoretical principles, of which I presented a note on January 31st 2008. The passage from the quantum theory of abstract systems to the theory of fields is achieved by adding to the axioms of quantum theory new general principles for the network of interation among a denumerable set of quantum systems. Such principles can be synthesized with the requirement of minimal complexity of the quantum algorithm describing the physical law. From general principles such as homogeneity, isotropy, locality, linearity, and unitarity of the interaction network, along with minimal dimension of the field vector, one derives the free quantum field theory, namely Weyl, Dirac, and Maxwell fields. The principles lead to a description in terms of a quantum cellular automaton on the Cayley graph of a group. The advantages of the new theory are numerous. For example the theory tautologically solves all the problems originating from the continuum, such as the ultraviolet divergencies, the localization problem, and causality violations. The mechanics itself is not assumed, but it is a consequence of the principles, and the theory is quantum ab initio, namely it does not need quantization of a classical field theory. Lorentz covariance is not assumed, but follows itself from the principles, in the relativistic limit of small wavevectors. The notion of reference system is restated in terms of irreducible representation of the quantum automaton. Finally, the new theory, derived from purely mathematical principles–whence with adimensional variables–contains itself the units of measure for distance, time, and mass, which are given in terms of extremal values of the variables, which are in principle experimentally detectable. Also effects with GR flavor emerge from the automaton theory, such as an upper bound for the Dirac particle rest-mass (from the unitariety condition), where the dispersion relation becomes completely flat, in strict analogy with the notion of mini black hole.
Based on a number of experimentally verified physical observations, it is argued that the standard principles of quantum mechanics should be applied to the Universe as a whole. Thus, a paradigm is proposed in which the entire Universe is represented by a pure state wavefunction contained in a factorisable Hilbert space of enormous dimension, and where this statevector is developed by successive applications of operators that correspond to unitary rotations and Hermitian tests. Moreover, because by definition the Universe contains everything, it is argued that these operators must be chosen self-referentially; the overall dynamics of the system is envisaged to be analogous to a gigantic, self-governing, quantum computation. The issue of how the Universe could choose these operators without requiring or referring to a fictitious external observer is addressed. The processes by which conventional physics might be recovered from this fundamental, mathematical and global description of reality are particularly investigated. Specifically, it is demonstrated that by considering the changing properties, separabilities and factorisations of both the state and the operators as the Universe proceeds though a sequence of discrete computations, familiar notions such as classical distinguishability, particle physics, space, time, special relativity and endo-physical experiments can all begin to emerge from the proposed picture. A pregeometric vision of cosmology is therefore discussed, with all of physics ultimately arising from the relationships occurring between the elements of the underlying mathematical structure.
I will discuss realism of classical and quantum theories, assessing the untenability of the object ontology, and proposing its substitution with the notion of system used in operational theories, notion that represents a theoretical connection between two events. Within operational theories the distinction between theory and objective reality is well defined: the theory provides the mathematical description of systems and events, and predicts the joint probability of the events; objective reality is identified with the collection of events that actually occurred. I then analyse some cases of realification of the theory – namely the fallacy of identifying theory with reality. In particular, the cases of the notion of causality and causal connection between events are analysed, emphasising their purely theoretical nature, contrarily to the widespread connotation of objectivity. I re-establish the role of causality in physics as a theorem of quantum theory, and hence also of classical theory (which is a restriction of quantum theory), showing how it represents a probabilistic generalisation of the same concept used in special relativity, and discussing why such notion may trivialise in the classical case. I end with a critique of David Albert’s Past Hypothesis about the nature of time, and of the resulting Block Universe vision of space-time, to reaffirm Reality of Time.
What does not satisfy me in that theory [quantum mechanics], from the standpoint of principle, is its attitude towards that which appears to me to be the programmatic aim of all physics: the complete description of any (individual) real situation (as it supposedly exists irrespective of any act of observation or substantiation). Albert Einstein, Reply to Criticisms [This] implies the impossibility of any sharp separation between the behaviour of atomic objects and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear . In fact, the individuality of the typical quantum effects finds its proper expression in the circumstance that any attempt of subdividing the phenomena will demand a change in the experimental arrangement introducing new possibilities of interaction between objects and measuring instruments which in principle cannot be controlled. Consequently, evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be regarded as complementary in the sense that only the totality of the phenomena exhausts the possible information about the objects. Indeed the finite interaction between object and measuring agencies conditioned by the very existence of the quantum of action entails – because of the impossibility of controlling the reaction of the object on the measuring instruments, if these are to serve their purpose – the necessity of a final renunciation of the classical idea of causality and a radical revision of our attitude towards the problem of physical reality. […]
A composite quantum system has properties that are incompatible with every property of its parts. The existence of such global properties incompatible with all local properties constitutes what I call "mereological holism"--the distinctive holism of Quantum Theory. Mereological holism has the dramatic conceptual consequence of making untenable the usual understanding of the "quantum system" as being a "physical object", since composed objects have properties compatible with those of its parts. The notion of "property" can be extended in a unique way to the whole class of operational probabilistic theories (shortly OPTs), of which the most relevant cases are Quantum Theory and Classical Theory. Whereas Classical Theory is not mereologically holistic, we can now search for other OPTs that are so. Within the OPT framework the role of the "system" is that of an input-output connection between two objective events. In non holistic theories, such as Classical Theory, the system can still be regarded as an "object". On the contrary, in holistic theories interpreting "system" as "object" constitutes an hypostatization of a theoretical notion.
The personal viewpoint of a theoretical physicist about the relation between reality and physical science is exposed, starting from his personal experience in the context of quantum foundations and quantum information theory. The effectiveness of an axiomatic approach is argued as a navigation system between the abstract landscape of quantum theory and the reality of facts, along a road that is intrinsically unaccessible to classical conceptual maps. The present approach requires physics to accept the notion of information at its deepest level, in place of matter and space-time, that are recovered only as an effective description of phenomena on a secondary level. As a result of the above operation, a simplified conceptual scenario is achieved, where new possibilities are available for facing the open challenges of theoretical physics.