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Elaborations Quantum Mechanics (QM) is a theory of epistemology because of the probability articulation of its objects of discourse. Quanton is a generic term for atomic and subatomic particles. Particle is a name for a complex set of relations focused on pseudo objects such as electron or proton or gluon, etc. When we speak of a quanton, we do not mean an object in the classical sense of a thing with an existential boundary, but instead an identifiable subset of relations with a behavior that is filed under a name such as an electron, a proton, etc. QM predicts the probabilities of events as they relate to quanton phenomena. This means that QM is first a theory of probability, a hybrid theory of probability, but a probability theory nevertheless. What are known in QM are probabilities, not physical reality as in classical theory. The role of probability is to enable a conversation about knowing, explaining and deciding. It is the basis of epistemology, as we know it. The way we know a thing is by our inference to some degree that the thing is reproducible. Thing here refers to physical reality. Physical reality is observable, but ideas are pre-things. Thus, we are always knowing knowing, and in a similar way, explaining explaining. Deciding is the formation of objects with existential boundaries. It is the radical construction of objects. Why should a practitioner of Cybernetics be interested in quantum epistemology? QM does not work with objects with existential boundaries, and it suggests that reality is not composed of objects but of relations that are linked to all relations always evolving and known within themselves not by an observer, but by logical realists, i.e., practitioners of cybernetics. Cybernetics encourages an investigation into being without boundaries and is the proper theater for QM inquiry. Classical logical positivism and/or realism, the pillars of analytical philosophy are inadequate systems for quantum epistemology because they work with objects of existential boundaries. Cybernetics works with relations without boundaries, and objects of existential boundaries, so that it can develop an epistemology that not only satisfies quantum mechanics, but classical physical theory as well. Strategy We go to a place where the essence of QM is found. This is the famous EPR Paradox or Einstein-Podolosky-Rosen challenge to the completeness of QM. We give a synopsis from the abstract of the original EPR paper: In a complete theory there is an element corresponding to each element of reality. A sufficient condition for the reality of a physical quantity is the possibility of predicting it with certainty. In quantum mechanics in the case of two physical quantities described by noncommuting operators, the knowledge of one precludes the knowledge of the other . . . or(2) these two quantities cannot have simultaneous reality . . . if (2) is also false. One is thus led to the conclusion that the description of reality given by the wave function is not complete. What was bothering Einstein was not QM, but that there was not an intuitive causal collection of reasons why quantum phenomena existed. He did not deny the existence; he just felt that something was missing because QM had no explanation. It just was. That is, quantum phenomena jumped from the laboratory to mathematical formulation, i.e., probabilistic articulation, without any conceptual model in between. Classical analytical philosophy called for a conceptual mode. That is how objects of physical reality were understood. But in QM this was missing. Therefore, he posited that QM was somehow incomplete and with his collaborators presented the EPR paradox. Implication: if EPR was false, then QM was a complete theory without a conceptual mode. This is not just revolutionary physics. It is revolutionary epistemology. The EPR Paradox Heisenberg had established the Uncertainty Principle, namely, that the values of two observables of a quanton, such as momentum, position, energy, the projection of spin on an axis, duration, cannot be determined simultaneously. In QM, an observable is a variable of a quanton that can take on multiple values. Quantons also have intrinsic characteristics that never change such as mass or charge. EPR concerns itself with observable. It is a thought experiment. It says consider two stations, say A and B. Make sure they are spatially separated in a meaningful way. EPR has two stipulations: (1) completeness of a physical theory. Every element of the physical reality must have a counter part in the physical theory. And (2) a definition of reality: If, without in any way disturbing a system, we can predict with certainty (i.e., probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity. A and B have interacted in the past and now have moved apart, thus, A + B is known. By measuring the position of A and the position of B, we can have the quantity, Φ = qa - qb. Likewise, measuring the momentum of A and B, we derive the quantity ϖ =pa + pb. Then playing some mathematical games on the quantity [Φ, ϖ], and invoking EPR’s two stipulations, we conclude that the position and momentum on B can be known with certainty without disturbing B, meaning A does not disturb B in any way. This violates the Uncertainty Principle and is thus impossible. So it must be that QM is incomplete. [To say that QM is incomplete or that the description of reality given by the wave function is incomplete is to say the same thing.] When we speak of a wave function, think of it as a probability indicator containing all the predicting information about the quanton we would need. There are some other issues involved with EPR. One is the notion of locality. This means that station A cannot signal station B without violating Special Relativity. That is, A cannot communicate with B faster than the speed of light. Thus, spontaneity is not possible under EPR. The other is local realism. Namely, that reality is independent of observation. The third issue is Separability. This is connected to realism. There was a view that the wave function of the two quantons, A and B, remained intact and only appeared to collapse when a measurement was made. The idea here was that two particles never really separated but were part of one wave function. EPR counters this by positing that the two particles separated into two different wave functions and that this separation becomes local reality. Summing EPR, we see that EPR pose that quantons are separated and that QM is incomplete. It also reaffirms that probability enables epistemology, since reality is a function of prediction. We pause here to remind ourselves that if EPR is shown false, then quantons are not separated and we are in a reality of everything is everything, clearly, the playground of cybernetics. Further Commentary on EPR The conclusion of EPR that QM is incomplete can be stated another way that there are variables accounting for quantum phenomena that QM has not captured. This has led to a series of Local Hidden Variable propositions. We will see below that they are shown to be inconsistent with QM. For what follows, when we speak of quantum phenomena, we will be referring to the correlation of spin projections measured along the same axes for paired quantons. In other words, a quanton has spin orientation, up or down, we will be speaking of whether the spin orientations of two paired quantons are both up or down or opposite. Bell’s Theorem, Hidden Variables and EPR There are several Bells’ Theorems, but let us join them under one heading. We give Bell’s own rendition of what EPR posits: The paradox of Einstein, Podolosky and Rosen was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables. These additional variables were to restore causality and locality. In this note that idea will be formulated mathematically and shown to be incompatible with the statistical predictions of quantum mechanics. It is the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty. Bell’s Strategy Bell creates a mathematical formulation of EPR specifying locality and hidden variable conditions. His focus is on quanton correlation. He develops in closed form the “probability marker” associated with this quanton correlation. [ Note well, that this probability marker is a function of hidden variables λ. The probability distribution is ρ(λ). The probability marker is in terms of expectation.] He argues as follows: if EPR is correct that QM is incomplete, the probability marker of EPR should equal the probability marker of QM without the hidden variables. In other words, the incompleteness of QM is not that the probabilities predicted by QM are wrong, but that QM needs more variables to account for QM results. QM results are not in contention. Think of EPR probability as EPR(λ) and QM probability as simply ΡQM. The point is that if EPR is correct then EPR(λ) =ΡQM. Bell shows that they do not equal. Thus, EPR no longer holds. Interpretation No probability model of QM has hidden variables or is consistent with local realism and Einsteinian Separability. Thus, QM is complete without causality. The World of Physics: Mermin’s Experiment affirming Bell Any theorem in physics requires experimentation for affirmation. There have been a number experiments developed to test Bell’s theorem. In general, they have solidly supported Bell. There have been some obscure experiments that supported EPR, but they have been treated with great skepticism in the community. What we would like to do now is present an experiment by David Mermin that is very clear and palatable. Mermin imitates Bell strategy by first postulating/deducing what an EPR(λ) would be in his experiment. In this experiment, Bell’s Theorem is cast as follows: If EPR holds, then EPR(λ) ≥ 5/9. EPR(λ) ≥ 5/9 means that the probability of same color is ≥ 5/9. If EPR is correct then ΡQM ≥5/9. He then calculates ΡQM and empirically demonstrates that they are not equal, in particular it is less than EPR(λ). Specifically, the experiment concerns the correlations of a pair of quantons from a single source. They are sent to Stern-Gerlach detectors equidistantly placed. The detectors are looking for the spin orientation of the quantons. The detectors are set so that when either a spin up or a spin down is detected, a red or green color is recorded. The detectors are set up to give the same color with opposite orientations. This means that if the detector A records a spin up and the color red, and detector B records a spin down, B will register a color red also. The detectors are set to register spin orientations at 0, 120 and 240 degrees. Those are the three positions. There are also two colors, red and green. The detectors rotate randomly. Consider the schematic below: Stern Gerlach Laser Stern Gerlach Quanton Quanton Sample Spaces of Mermin Experiment and Data Sample Space of Mermin’s Experiment ASSUMING INDEPENDENCE AT BOTH DETECTORS: BOTH DETECTORS TREATED AS INDEPENDENT RANDOM VARIABLES 1R 2R 3R 1G 2G 3G TOTAL 1R 11RR 12RR 13RR 11RG 12RG 13RG 2R 21RR 22RR 23RR 21RG 22RG 23RG .166 3R 31RR 32RR 33RR 31RG 32RG 33RG .166 1G 11GR 12GR 13GR 11GG 12GG 13GG .166 2G 21GR 22GR 23GR 21GG 22GG 23GG .166 3G 31GR 32GR 33GR 31GG 32GG 33GG .166 .166 .166 .166 .166 .166 1.00 TOTAL .166 .166 ALL MARGINAL PROBABILITIES ARE EQUAL SINCE WE HAVE EQUAL PROBABILITY IN ALL CELLS. Ρr Same Color) = ½ (18/36) < 0.556 (5/9) EPR(λ) >ΡQM Sample Space of Mermin’s Experiment WITH QUANTUM PROBABILITY CONSTRAINTS OF SPIN CORRELATIONS OF PAIRED QUANTONS 1R 2R 3R 1G 2G 3G TOTAL 1R 11RR 12RR 13RR 0 12RG 13RG 2R 21RR 22RR 23RR 21RG 0 23RG TBD 3R 31RR 32RR 33RR 31RG 32RG 0 TBD 12GR 13GR 11GG 12GG 13GG TBD 1G 0 TBD 2G 21GR 0 23GR 21GG 22GG 23GG TBD 3G 31GR 32GR 0 31GG 32GG 33GG TBD TBD TBD TBD TBD TBD TBD 1.00 TOTAL MARGINAL PROBABILITIES NEED TO BE DETERMINED BY EXPERIMENT. QUANTUM MECHANICS PREDICTS THAT PAIRED QUANTONS MEASURED AT THE SAME ANGLE AT THE DETECTOR WILL BE PERFECTLY CORRELATED, THUS, THERE WILL NOT BE ANY MIXED COLORS AT IDENTICAL POSITIONS. Data from one run of Mermin’s Experiment WITH QUANTUM PROBABILITY CONSTRAINTS OF SPIN CORRELATIONS OF PAIRED QUANTONS 1R 2R 3R 1G 2G 3G TOTAL .156 1R .04 .013 .013 0 .036 .054 2R .027 .054 .027 .027 0 .04 .174 3R .009 .004 .049 .049 .022 0 .134 1G 0 .027 .054 .063 .018 .004 .165 2G .04 0 .054 .022 .063 .022 .201 3G .031 .063 0 .018 .004 .054 .170 TOTAL .147 .161 .196 .179 .143 .174 1.00 Ρr(Same Color) = ∑ Χi,j,kk (Cell Probabilities indexed by i,j from 1 to 3, and kk being either R or G) = 0.504<0.556 [There are some very minor rounding errors and this is only one run. What happens over the many runs is that the Pr(Same Color) converges to 0.50, clearly, less than 5/9. Thus, Mermin has produced empirical evidence supporting Bell’s theorem. Further discussion on the epistemic reality posed by EPR, Bell and you. There are many ongoing developments in QM that do not hold such strong opinions as I have interpreted Bell to mean. Yet, the question of causality seems to be at rest. QM does not need causality to be articulated. The epistemic model using conceptual causality is clearly challenged by Bell and while the issues are still being debated, causality in QM would refute Bell. That is impossible to do, thus causality if it were to gain some stature would be of something heretofore not seen. In this vein, we move to focus more on formal epistemology construction. On Causality, Probability and Epistemology. The idea of a thing is its existence and its existence is known through its replication, thus, its predictability. This does not preclude the naming of seemingly unique things such as works of art of special combinations of materials. For in such unique things, the components are known in the replicable sens. Thus, unique things are composed of known things. However, here should be caution: all things are unique. A pen in your hand is not as any other pen. It is not as grand as the Mona Lisa, but it is unique nevertheless. So then, all things are unique. This makes sense since a thing is never by itself. A thing is known by its predictability. Thus, a thing comes into being by its own construction. Its construction is from all that is. Viewing things this way, we are able to see that quanton correlations are quite natural. What may give us difficulty is why we exist. That question aside, what would a suitable epistemology for QM that also allowed for traditional logical realism? How would we construct such a system? How would we know that such a system was viable? Would we need incremental proof, validating one theorem after another? What would constitute knowing knowing? Would it be an appeal to comfort or reductionism? Could we actually form a system without causality? Would we be creating hidden contradictions? Would multivalued logics be employed? Or would we be looking for sweeping generalizations incorporating categories of theorems? Before we venture there, we reflect on how cybernetics views knowing, namely knowing knowing and explaining explaining. Knowing knowing and explaining explaining To know a thing is to measure a thing. To measure a thing means that a property attributed to the thing is observable. To observe, i.e., to observe a thing is to observe a property attributed to the thing. To observe a property attributable to the thing is to attribute a change in the system created to observe the property attributable to the thing when observing the thing. A change in the system created to observe the property attributable to the thing is anything so described by the observer, and if required, by a collection of observers within a theater of what is commonly described as organised science of any kind. An organisation is any collection of two or more conscious beings including the observer. Hence, observation, measurement and change are words used to know a thing. As observation, measurement and change change, then so does the thing since a thing is known in the act of knowing. Thus, we speak of knowing knowing. In a related manner, one can speak of explaining explaining. We have already posited that to know a thing is to measure a thing. Now, we will try to explain what we mean by explaining a thing. To explain a thing is not to know a thing. To know a thing and to explain a thing are different things. To explain a thing is to show how to know a thing. To show how to know a thing is to prescribe a set of instructions to arrive at the property attributable to the thing that has been observed by the giver of the set of instructions. One knows a wall by all the properties attributed by the observer to what which she or he designates is a wall and we say, “We know a wall.” We do not say, “How do we know a wall?” It is the set of instructions that becomes the wall. When we speak this way, we imply that we have the essence of the wall in our sentence of knowing what a wall is. We are in conversation with the wall. How have we explained the wall? The wall is in conversation with us in conversation about what the wall is. I.e., these properties attributable to our wall are what converses with the wall so that we can observe the wall in conversation with us. This conversation is private, thus, we write or otherwise show an approximation this conversation and we call this approximation, instructions. To know a thing is to know it systematically. To explain a thing is to approximate. The instructions are then translated, i.e., interpreted by the user. The user can be the observer. Hence, the explanation of a thing applying her/his instructions for interpreting instructions is at least a second order explanation of a thing. Thus, we speak of explaining explaining. This process can recursively continue ad infinitum, but humans being macro objects converge the iteration to a working limit. It is a characteristic of non-quantum living. Underlying the relation that enables knowing is the leap of consciousness in knowing: conversations are private, thus human-to-human communication requires a receptivity to approximations. This idea may be incorrect. We may all be in the same wave function, but need Einsteinian Separability for purposes heretofore unknown to us. It could be a punishment from the gods, consider, Genesis, Chapter Three, 22-24: 22 And the Lord God said, Behold, the man is become as one of us, to know good and evil; and now lest he put forth his hand, and take also of the tree of life, and eat and live for ever: 23 Therefore the Lord God sent him forth from the garden of Eden, to till the ground from whence he was taken. 24 So he drove out the man, and he placed at the east of the garden of Eden, the Cherubim, and the flame of a sword which turned every way, to keep the way of the tree of life. 25 And to assure that man would not circumvent the Cherubim, Cybernetics was invented. (Smile) Nevertheless, we put forth a cybernetic epistemology that to address QM, EPR and the issues of causality and local realism therewith. We call it logical realism. It has the following characteristics: 1. 2. 3. 4. 5. 6. Probability theory is a language construction whose purpose is explaining what is known so that what is known is knowable. Knowable things are based on measurement, observation, change and conversation. These are observable guided by the cybernetic notions of knowing knowing and explaining explaining. Independent is a word that implies that an object has an existential boundary. Every method of proof that yields objects is valid. A proof is anything wherein the cause of the object lies in the existence of the object. Universal constants and their implications, such as locality, hold until they can be discarded.