The postulate in the Copenhagen interpretation is for quantum measures that in experiments from a set of operators only a subset of commuting operators can be measured simultaneously, the rest remains undetermined. As example the Stern-Gerlach measure shows for spin a 90 degree change and measures for instance spin up and down of the outcome particles only in the z-direction. The spacial xy-coordinates remain undetermined.Using octonion coordinates [1,2] for the quantum range this view can be applied to all octonion base GF triples which use the three noncommuting Pauli matrices. The coordinates are enumerated by indices 0,1,2,…,7. Entanglements of different GF are possible. Two examples are the spin-lepton cases 123 (for xyz) and 145 (1 for electrical EM charge, 4 for magnetism, 5 for leptonic mass) either in the gyromagnetic relation (EM) or the helicty (neutral leptons).A in the second case the Copenhagen interpretation is extended to a quantum interpretation for measurements of the GF. The systems and energies involved can be different. The neutrino N oscillations show that also the Heisenberg uncertainties HU play a role. Spin is aligned with the space coordinate 1 and the momentum p = mv on 6. The HU means that 1,6 cannot be measured sharp. Hence the leptonic kg measure 5 changes for p along the world line of N stochasticaly, observed as oscillation. The kg GF is 257 and has 6 possible values for leptons. The weights of the three GF coordinates are mostly positive real or complex numbers. There are seven octonion GF 123, 145, 167 (for electromagnetic interaction EMI), 246 (for heat, acoustics), 257, 347 (for rotational energy), 356 (for a nucleon inner dynamics). Beside these are for the strong interaction SI three more GF 126 as rgb-graviton , 345 for its dual Dg and 037 for a newly postulated color charge force cc.The new cc force has a different symmetry than the Pauli quaternions.The six complex cross ratios invariant under the Moebius transformations of the Riemannian sphere are discussed in relation to quantum measures.
The postulate in the Copenhagen interpretation is for quantum measures that in experiments from a set of operators only a subset of commuting operators can be measured simultaneously, the rest remains undetermined. As example the Stern-Gerlach measure shows for spin a 90 degree change and measures for instance spin up and down of the outcome particles only in the z-direction. The spacial xy-coordinates remain undetermined.Using octonion coordinates [1,2] for the quantum range this view can be applied to all octonion base GF triples which use the three noncommuting Pauli matrices. The coordinates are enumerated by indices 0,1,2,…,7. Entanglements of different GF are possible. Two examples are the spin-lepton cases 123 (for xyz) and 145 (1 for electrical EM charge, 4 for magnetism, 5 for leptonic mass) either in the gyromagnetic relation (EM) or the helicty (neutral leptons).A in the second case the Copenhagen interpretation is extended to a quantum interpretation for measurements of the GF. The systems and energies involved can be different. The neutrino N oscillations show that also the Heisenberg uncertainties HU play a role. Spin is aligned with the space coordinate 1 and the momentum p = mv on 6. The HU means that 1,6 cannot be measured sharp. Hence the leptonic kg measure 5 changes for p along the world line of N stochasticaly, observed as oscillation. The kg GF is 257 and has 6 possible values for leptons. The weights of the three GF coordinates are mostly positive real or complex numbers. There are seven octonion GF 123, 145, 167 (for electromagnetic interaction EMI), 246 (for heat, acoustics), 257, 347 (for rotational energy), 356 (for a nucleon inner dynamics). Beside these are for the strong interaction SI three more GF 126 as rgb-graviton , 345 for its dual Dg and 037 for a newly postulated color charge force cc.The new cc force has a different symmetry than the Pauli quaternions.The six complex cross ratios invariant under the Moebius transformations of the Riemannian sphere are discussed in relation to quantum measures.
Interpreting quantum mechanics is a hard problem basically because it means explaining why and how the mathematics exploited to formulate wave-particle duality are related to observations or reality in classical physics (due to Newtonian mechanics, special relativity, gravity and entropy). Here, we first prove the limitation of the Heisenberg uncertainty principle by invoking the wave-particle duality and apply it to revise and/or extend the Copenhagen postulates. In particular, even though the said uncertainty exists due to non-commuting operators, but these operators do not commute simply because one of the operators is well-defined in classical physics (particle-like), while the other is wave-like (well-defined in quantum mechanics), or the eigenvalue is not at all defined in classical physics. We also construct a new quantum mechanical postulate (Postulate 9) to deduce why the forbidden gap between discrete energy levels should exist in atoms, molecules and condensed matter phases. In fact, we tackle all the problems arising from the Copenhagen interpretation without violating established experiments and without proposing ideas that violate physical reality.
1. Amend the two postulates of the special relativity. 2. Set “the measurement is founded to change the object by destroying the original quantum coherence between the object and its environment” as the third postulate. 3. From the third postulate (new added postulate) educe: the concept of the reference system’s referenced weight and perhaps the reference system’s space is something nearby the referenced weight; time coordinate should be something as space coordinate there is not the problem to have to synchronize the clocks of the two reference systems before simultaneous time measurement; the essence of Heisenberg Uncertainty Principle; the “actual length” of the same measurement unit in different case is different; it is the reference system’s taking measurement instead of the ether or the object’s motion that changes the being measured object; two reference systems (e.g. Σ and Σa and their relative motion may be uniform or not) taking simultaneously measure of the same quantity of the same object their measurement will disturb each other and “the numerical values before Σ’s unit” ≠ “the numerical values before Σa’s unit” (only when the relative motion speed v≡0 or uniform relative speed v=0 can the sign ≠ just turn into =); even in uniform relative motion Σ and Σa still are different for the relative motion and they may have different referenced weight, in taking simultaneously measure of the same speed of relative motion the speed numerical values of Σa is v while of Σ is va11/a44. 4. From the three postulates express the relation between the numerical values of the two reference systems taking simultaneous measurement of the same speed by matrix and the same small moving particle’s mass by the element of the matrix; determine the speed of the photon which come from “in motion” light source by the photon’s speed when light source “in stationary” and the reference systems’ coordinate relation; determine two reference systems’ coordinates relation when reduced the case educe generally there is not the invariant interval and then there is not the proper time, re-reduced the case and re-re-reduced the case then educe the essence of “in motion” time dilate or contract meanwhile space contract or dilate in all directions, moving micro-particle’s time to dilate and space to contract in all directions, superluminal photonic tunneling experiment, quasar’s super-luminal expansion and fine structure constant’s lessening, took Michelson-Morley experiment with the light from the sun or quasars or high-speed (close to C) moving micro-particle all obtained zero result.
Some finite subspace models L are presented for quantum structures which replace the use of countable infinite Hilbert space H dimensions. A maximal Boolean sublattice, called block, is 24, where its four atoms directly above 0εL, base vectors of H in 24 are drawn as four points on an interval. Blocks can overlap in one or two atoms. Different kinds of operators can map one block onto another and interpretations are given such that subspaces can carry on their base vector tuple real, complex or quaternionic numbers, energies, symmetries and generate coordinate lines. Describing states of physical systems is done using L and its applications for dynamical modelling. They don‘t need the infinte dimensional vectors of H. L has in the first model 11 blocks and 24 atoms (figure 1). They correspond to the 24 elements of the tetrahedral S4 symmetry. S4 arises from a spin-line rgb-graviton whirl operator with center at the tip of a tetrahedron and a nucleon triangle base with three quarks as vertices. The triangles factor group D3 of S4 is due to the CPT Klein normal subgroup Z2 x Z2 of S4 . It has a strong interaction SI rotor for the nucleons inner dynamics which is used for integrating functions, exchanging energies of nucleon with its environment and setting barycentrical coordinates in the triangle. At their intersection B as barycenter sets a Higgs boson or field the rescaled quark mass of a nucleon. Each factor class of one element from D3 assigns to it a color charge, a coordinate, an energy vector and a symmetry. Symmetries attached can be different according to interactions involved. Every atom of L has then a specific character with different properties.Three characters are added to octonian base vectors, listed by their indices as n = 0,1,…,7, and named for the atoms of L as na, nb, nc. The structure and element attributes of the finite subspace lattices L are desribed in many examples and models which technical constructed run macroscopically. Several models are described below. Example, the color charge whirl as rgb-graviton projection operator maps the block 2c3b5a6a to 0a1a2a3a. The symmetries change dimension from 3x3- to 2x2-matrices. From SU(3) are λ1 on 3b mapped to the SU(2) x-coordinate Pauli matrix σ1, from λ2 on 5a to σ2 y-coordinate and from λ3 on 6a to σ3 z-coordinate of real Euclidean space R³. The SU(3) matrices have complex w3 = z +ict, w2 = (iy,f), w1 = (x,m) coordinates. In figure 3 is shown how a rotation of two proton tetrahedrons for fusion changes the two linearly independent wj vectors to the 1-dimensional x,y,z base vectors. In deuteron then on one coordinate line sit with Cooper paire u-d-quarks at the ends the Heisenberg coupled energy or space vector rays 15 (x,m), m mass measured in kg, x in meter, 23 (iy,E(rot)), E(rot) rotational energy measured in Joule J, y in meter, 46 (ict,f), t time measured in seconds, f = 1/∆t frequency s inverse time interval measured in Hz. The six color charges are red r on +x as octonian coordinate 1, green g on +y as 2 , blue b on -z as 6, turquoise on -x as 5, magenta on -y as 3, yellow on +z as 4.
Long ago, and almost in parallel with the “orthodox” Copenhagen/standard interpretation, other interpretations of quantum mechanics were proposed. Giving an exhaustive discussion of all points of view that have been put forward since then would probably be an impossible task. Moreover, while one can distinguish big families among the interpretations, it is also possible to combine them in many ways, with an almost infinite number of nuances. The Copenhagen/standard interpretation itself, as we have seen, is certainly not a monolithic construction, but can be declined in various forms. In this chapter, we will therefore limit ourselves to a general description of the major families of interpretations. We will begin with a brief description of some frequent attitudes observed among scientists in laboratories, who do not necessarily pay extreme attention to the foundations of quantum mechanics, even when they do experiments in quantum physics. In practice, they often use pragmatic rules, which are sufficient to interpret all their experiments, and prefer to avoid difficult questions about the very nature of the measurement process. For instance, one popular point of view is the “correlation interpretation”, which can be considered as a “minimal interpretation” – minimal but sufficient for all practical purposes; it is accepted as a valid rule by a large majority of physicists, even those who prefer to supplement it with other elements in order to reach a more precise interpretation for the whole theory. We will then proceed to discuss various families of interpretations that are less common, including additional variables, modified Schrödinger dynamics, consistent histories, Everett interpretation, etc.
The interpretation of measurements in quantum mechanics is still under discussion (Healey [84], Bell [9], Redhead [136]). Besides the Copenhagen interpretation we have the many-worlds interpretations (Everett interpretations), the modal interpretations, the decoherence interpretations, the interpretations in terms of (nonlocal) hidden variables, the quantum logical interpretations. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Some finite subspace models L are presented for quantum structures which replace the use of countable infinite Hilbert space H dimensions. A maximal Boolean sublattice, called block, is 24, where its four atoms directly above 0εL, base vectors of H in 24 are drawn as four points on an interval. Blocks can overlap in one or two atoms. Different kinds of operators can map one block onto another and interpretations are given such that subspaces can carry on their base vector tuple real, complex or quaternionic numbers, energies, symmetries and generate coordinate lines. Describing states of physical systems is done using L and its applications for dynamical modelling. They don‘t need the infinte dimensional vectors of H. L has in the first model 11 blocks and 24 atoms (figure 1). They correspond to the 24 elements of the tetrahedral S4 symmetry. S4 arises from a spin-line rgb-graviton whirl operator with center at the tip of a tetrahedron and a nucleon triangle base with three quarks as vertices. The triangles factor group D3 of S4 is due to the CPT Klein normal subgroup Z2 x Z2 of S4 . It has a strong interaction SI rotor for the nucleons inner dynamics which is used for integrating functions, exchanging energies of nucleon with its environment and setting barycentrical coordinates in the triangle. At their intersection B as barycenter sets a Higgs boson or field the rescaled quark mass of a nucleon. Each factor class of one element from D3 assigns to it a color charge, a coordinate, an energy vector and a symmetry. Symmetries attached can be different according to interactions involved. Every atom of L has then a specific character with different properties.Three characters are added to octonian base vectors, listed by their indices as n = 0,1,…,7, and named for the atoms of L as na, nb, nc. The structure and element attributes of the finite subspace lattices L are desribed in many examples and models which technical constructed run macroscopically. Several models are described below. Example, the color charge whirl as rgb-graviton projection operator maps the block 2c3b5a6a to 0a1a2a3a. The symmetries change dimension from 3x3- to 2x2-matrices. From SU(3) are λ1 on 3b mapped to the SU(2) x-coordinate Pauli matrix σ1, from λ2 on 5a to σ2 y-coordinate and from λ3 on 6a to σ3 z-coordinate of real Euclidean space R³. The SU(3) matrices have complex w3 = z +ict, w2 = (iy,f), w1 = (x,m) coordinates. In figure 3 is shown how a rotation of two proton tetrahedrons for fusion changes the two linearly independent wj vectors to the 1-dimensional x,y,z base vectors. In deuteron then on one coordinate line sit with Cooper paire u-d-quarks at the ends the Heisenberg coupled energy or space vector rays 15 (x,m), m mass measured in kg, x in meter, 23 (iy,E(rot)), E(rot) rotational energy measured in Joule J, y in meter, 46 (ict,f), t time measured in seconds, f = 1/∆t frequency s inverse time interval measured in Hz. The six color charges are red r on +x as octonian coordinate 1, green g on +y as 2 , blue b on -z as 6, turquoise on -x as 5, magenta on -y as 3, yellow on +z as 4..