We introduced in other pages the Modern version of the Principle of Superposition and related Theory of Measurement, conceived in 1957. 


   A first glimpse to the true nature of the Measurements: the fabric of a 2-brane is a web of bifurcations and interferences.  Measurements are both topologic changes, bifurcations or interferences, experienced by the topologic variety, whose character is visibly multiply-connected (image credit M. Green, 1986)

Does the new version of the Principle of Superposition applies to the subset of Binary Classifiers named Electronic Inspection systems?  


Strictly.  The new scenario was conceived for systems equipped and behaving the same identical way a common Electronic Inspection system, or Binary Classifier, is equipped.  

Devices with memory and capability to process measurements values incoming by sensors and data into its memory, to decide future actions.  In the following, we’ll directly quote Everett’s words (in DeWitt, 1973, page 64) to clear this relevant point:  


“As models for observers we can, if we wish, consider automatically functioning machines, possessing sensory apparata and coupled to recording devices capable of registering past sensory data and machine configurations. We can further suppose that the machine is so constructed that its present actions shall be determined not only by its present sensory data, but by the contents of its memory as well.   Such a machine will then be capable of performing a sequence of observations (measurements), and furthermore of deciding upon its future experiments on the basis of past results. We note that if we consider that current sensory data, as well as machine configuration, is immediately recorded in the memory, then the actions of the machine at a given instant can be regarded as a function of the memory contents only, and all relevant experience of the machine is contained in the memory.  

For such machines we are justified in using such phrases as the machine has perceived A or the machine is aware of A if the occurrence of A is represented in the memory, since the future behavior of the machine will be based upon the occurrence of A. In fact, all of the customary language of subjective experience is quite applicable to such machines, and forms the most natural and useful mode of expression when dealing with their behavior, as is well known to individuals who work with complex automata”.   

What before can be depicted in an intuitive image, one where the minkowskian world-sheet introduced in the starting sections of this web page, is swept out by stringlike particles as they move and interact in spacetime (see figure above at right side). 


 The modern version of the Principle of Superposition is a straight explanation of the process of measurement and of the deriving superposition of states, withouth anything else added.  It is firmly based and continously reconfirmed by an impressive amount of experiments and practical technological applications.  Each spectrum of light evidences quantum superposition


“...a logic gate switching does more than satisfy all of the requirements of a branching:  

it is the living example of a bifurcation"

What above had been proved in the most stable way: theorems.  What is the effect of the quantum superposition of states over an entire Bottling Control, composed of so many subsystems, is a question whose answer is time consuming. To really understand what is going on, it is vital to apply the cartesian view about the necessity to clear our inner scenario before to acquire new ideas, finally perceiving unknown facts for what they are: facts.    As an example, there is not a widespread comprehension that a logic gate switching does much more than satisfy all of the requirements of a branching (or its apparent opposite, the merging): 

  1. it is the living example of a bifurcation;
  2. its inherent information flow, structures the Multiverse. 



       David Deutsch 

The Structure of the Multiverse

In 2001 these ideas were object of a deep mathematical insight by the physicist prof. David E. Deutsch, Clarendon Laboratory, University of Oxford, at Oxford, United Kingdom, over the beneficial revolution started by Schroedinger in 1927 and continued by H. Everett in 1957.  Further details in the PDF document on right side.  A document whose consultation is strongly recommended to electronics and instrumentation engineers. It looks at the common logic gates of the every day Electronics, as seen from the vantage point of the most modern Physics.  There, with the formalism and notation appearing in the couple of graphics below, the Author introduces his point of view, today one winning increasing support, quoted below:   

“…..have explained the power of quantum computation in terms of ‘quantum parallelism’ (many classical computations occurring in parallel).  

However, if reality – which in this context is called the multiverse – is indeed literally quantum-mechanical, then it must have a great deal more structure than merely a collection of entities each resembling the universe of classical physics.  For one thing, elements of such a collection would indeed be ‘parallel’: they would have no effect on each other, and would therefore not exhibit quantum interference.   

For another, a ‘universe’ is a global construct – say, the whole of space and its contents at a given time – but since quantum interactions are local, it must in the first instance be local physical systems, such as qubits, measuring instruments and observers, that are split into multiple copies, and this multiplicity must propagate across the multiverse at subluminal speeds.  

And for another, the Hilbert space structure of quantum states provides an infinity of ways of slicing up the multiverse into ‘universes’, each way corresponding to a choice of basis. This is reminiscent of the infinity of ways in which one can slice (‘foliate’) a spacetime into spacelike hypersurfaces in the general theory of relativity.  Given such a foliation, the theory partitions physical quantities into those ‘within’ each of the hypersurfaces and those that relate hypersurfaces to each other. 

In this paper I shall sketch a somewhat analogous theory for a model of the multiverse. The quantum theory of computation is useful in this investigation because, as we shall see, the structure of the multiverse is determined by information flow, and the universality of computation ensures that by studying quantum computational networks it is possible to obtain results about information flow that must also hold for quantum systems in general. This approach was used (…) to analyse information flow in the presence of entanglement. 

   History of a computation, as seen by the classic perspective.  b is a parameter whose value is referred to the time parameter t, and whose initial state is b(0) = β.   A bidimensional graph  represents correctly the occurring computation 

 History of a computation, as seen by a quantum perspective.  A 2-D graph cannot fully represent it.  It is replaced by an infinitely wider space, a 3-D including a 2-D slice which is the classic perspective. Here, the information flow structures the graph Topology (credit Deutsch, 2001)

In that analysis, as in this one, no quantitative definition of information is required; the following two qualitative properties suffice:

Information Flow structure Topology
  • Property 1:  A physical system S contains information about a parameter b if (though not necessarily only if) the probability of some outcome of some measurement on S alone depends on b.
  • Property 2:  A physical system S contains no information about b if (and for present purposes we need not take a position about ‘only if’) there exists a complete description of S that is independent of b.

 Prof. David E. Deutsch, FRS, physicist at the Clarendon laboratory, Oxford University, founder of Quantum Computation

(…) an entity S qualifies as a ‘physical system’ if (but not necessarily only if) it is possible to store information in S and later to retrieve it. That is to say, it must be possible to cause S to satisfy the condition of Property 1 for containing information about some parameter b. It is implicit in this, and in Properties 1 and 2, that b must be capable of taking more than one possible value, so there must exist some suitable sense in which if S contained different information it would still be the same physical system.   

This condition raises interesting questions about the counter-factual nature of information which it will not be necessary to address here. It is also necessary that S be identifiable as the same system over time. This is particularly straightforward if S is causally autonomous – that is to say, if its evolution depends on nothing outside itself.”  

The Reader may infer the rationale lying behind the words pronounced above by David E. Deutsch also by cobordism. Cobordism basic generators (see figre below) and their relations allow to sight basic examples of bifurcations and interferences, satisfying a wide spectra of mathematical relations.  A direct step from Topology and Differential Geometry at the Quantum level, to the Quantum Computation applications.  

Cobordism basic generators and relations allow to see part of the rationale of the words quoted above by David Deutsch.  The basic bifurcations and interferences allow and satisfy a wide spectra of mathematical relations.  An immediate direct step from the Topology at the Quantum level to the Quantum Computation 

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