The Symmetries of Quantum and Classical Information. The Ressurected “Ether" of Quantum Information
Authors: Penchev Vasil 
Published: June 2021

The paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to &ldquo;empty qubits&rdquo; (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (e.g. that of the Big Bang), which can be described exhaustively by means of 16 numbers (4 for position, 4 for velocity, and 8 for acceleration) independently of time, but in space-time continuum, and still one, 17th number is necessary for the mass of rest of the observer in it. The same 17 numbers describing exhaustively a privileged reference frame thus granted to be &ldquo;zero&rdquo;, respectively a certain violation of all the three symmetries of the Standard model or the &ldquo;record&rdquo; in a qubit in general, can be represented as 17 elementary wave functions (or classes of wave functions) after the bijection of natural and transfinite natural (ordinal) numbers in Hilbert arithmetic and further identified as those corresponding to the 17 elementary of particles of the Standard model. Two generalizations of the relevant concepts of general relativity are introduced: (1) &ldquo;discrete reference frame&rdquo; to the class of all arbitrarily accelerated reference frame constituting a smooth manifold; (2) a still more general principle of relativity to the general principle of relativity, and meaning the conservation of quantum information as to all discrete reference frames as to the smooth manifold of all reference frames of general relativity. Then, the bijective transition from an accelerated reference frame to the 17 elementary wave functions of the Standard model can be interpreted by the still more general principle of relativity as the equivalent redescription of a privileged reference frame: smooth into a discrete one. The conservation of quantum information related to the generalization of the concept of reference frame can be interpreted as restoring the concept of the ether, an absolutely immovable medium and reference frame in Newtonian mechanics, to which the relative motion can be interpreted as an absolute one, or logically: the relations, as properties. The new ether is to consist of qubits (or quantum information). One can track the conceptual pathway of the &ldquo;ether&rdquo; from Newtonian mechanics via special relativity, via general relativity, via quantum mechanics to the theory of quantum information (or &ldquo;quantum mechanics and information&rdquo;). The identification of entanglement and gravity can be considered also as a &lsquo;byproduct&rdquo; implied by the transition from the smooth &ldquo;ether of special and general relativity&rsquo; to the &ldquo;flat&rdquo; ether of quantum mechanics and information. The qubit ether is out of the &ldquo;temporal screen&rdquo; in general and is depicted on it as both matter and energy, both dark and visible.