A measurement is a physical operation in space and in time. The properties of a system are described in relation to measurements at a given time, and no value of the time is intrinsically distinguished from another by the results of measurements on an isolated physical system. The operators symbolizing analogous properties at different times must be related by a unitary transformation. The propagation in time of the disturbance produced by a measurement implies that physical quantities referring to different times are incompatible, in general. The development of the fundamental dynamical variables through an infinitesimal time interval is described by an infinitesimal unitary transformation, which implies first order differential equations of motion for these variables. The necessity of an even number of variables and the possibility of dividing them into two complementary sets also appears for variables of the second kind.
A measurement is a physical operation in space and in time. The properties of a system are described in relation to measurements at a given time, and no value of the time is intrinsically distinguished from another by the results of measurements on an isolated physical system. The operators symbolizing analogous properties at different times must be related by a unitary transformation. The propagation in time of the disturbance produced by a measurement implies that physical quantities referring to different times are incompatible, in general. The development of the fundamental dynamical variables through an infinitesimal time interval is described by an infinitesimal unitary transformation, which implies first order differential equations of motion for these variables. The necessity of an even number of variables and the possibility of dividing them into two complementary sets also appears for variables of the second kind.
The uncontrollable disturbance attendant upon a measurement implies that the act of measurement is indivisible. Any attempt to trace the history of a system during a measurement process usually changes the nature of the measurement that is being performed. Hence, to conceive of a given selective measurement M(a', b') as a compound measurement is without physical implication. All algebraic relations and adjoint connections among vectors and operators are preserved by unitary transformation. Two successive unitary transformations form a unitary transformation, and the inverse of a unitary transformation is unitary-unitary transformations form a group. In discussing successive unitary transformations, it must be recognized that a transformation which is specified by an array of numerical coefficients is symbolized by a unitary operator that depends upon the coordinate system to which it is applied. The continual repetition of an infinitesimal unitary transformation generates a finite unitary transformation.
Modern physics, which had its beginnings in the inclined-plane experiments of Galileo, deals with the measurable aspects of the world about us. The laws and definitions of classical physics are, at least superficially, differential equations in which each variable represents the result of a particular kind of measurement. These variables are usually called physical quantites. Starting from a few general laws and definitions we can derive formally further relations between the physical quantities and their rates of change in space and time. If the original definitions are self-consistent and the original laws accurate, the relations we derive from them should enable us to predict what the numerical result of a certain measurement will be whenever certain other measurements have yielded specified numerical results.
The classical theory of measurement is built upon the conception of an interaction between the system of interest and the measuring apparatus that can be made arbitrarily small, or at least precisely compensated, so that one can speak meaningfully of an idealized measurement that disturbs no property of the system. In the most elementary type of measurement, an ensemble of independent similar systems is sorted by the apparatus into subensembles, distinguished by definite values of the physical quantity being measured. The use of complex numbers in the measurement algebra implies the existence of a dual algebra in which all numbers are replaced, by the complex conjugate numbers. No physical result can depend upon which algebra is employed. The measurement symbols of a given description provide a basis for the representation of an arbitrary operator by N 2 numbers, and the abstract properties of operators are realized by the combinatorial laws of these arrays of numbers, which are those of matrices.
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.
The commutation properties of the infinitesimal operator variations that are employed in the fundamental dynamical principle are such as to maintain the commutation relations obeyed by the dynamical variables. This chapter examines these special variations possess a transformation group aspect. It discusses a group of inner automorphisms - transformations, constructed from the elements of the algebra that maintain all algebraic relations and Hermitian properties. In constructing transformation functions, one must eliminate explicit reference to the operators of the physical system and express the transformation function in terms of the eigenvalues which, for variables of the second kind, are the elements of the external algebra. Although the integral notation is effective in unifying some of the formal properties of the two classes of variables, the nature of the operations is quite distinct. The symbol ∫ has the significance of differentiation for variables of the second kind, and the inverse of differentiation for variables of the first kind.
The conventional correspondence basis for quantum dynamics is here replaced by a self-contained quantum dynamical principle from which the equations of motion and the commutation relations can be deduced. The theory is developed in terms of the model supplied by localizable fields. A short review is first presented of the general quantum-mechanical scheme of operators and eigenvectors, in which emphasis is placed on the differential characterization of representatives and transformation functions by means of infinitesimal unitary transformations. The fundamental dynamical principle is stated as a variational equation for the transformation function connecting eigenvectors associated with different spacelike surfaces, which describes the temporal development of the system. The generator of the infinitesimal transformation is the variation of the action integral operator, the spacetime volume integral of the invariant lagrange function operator. The invariance of the lagrange function preserves the form of the dynamical principle under coordinate transformations, with the exception of those transformations which include a reversal in the positive sense of time, where a separate discussion is necessary. It will be shown in Sec. III that the requirement of invariance under time reflection imposes a restriction upon the operator properties of fields, which is simply the connection between the spin and statistics of particles. For a given dynamical system, changes in the transformation function arise only from alterations of the eigenvectors associated with the two surfaces, as generated by operators constructed from field variables attached to those surfaces. This yields the operator principle of stationary action, from which the equations of motion are obtained. Commutation relations are derived from the generating operator associated with a given surface. In particular, canonical commutation relations are obtained for those field components that are not restricted by equations of constraint. The surface generating operator also leads to generalized Schr\"odinger equations for the representative of an arbitrary state. Action integral variations which correspond to changing the dynamical system are discussed briefly. A method for constructing the transformation function is described, in a form appropriate to an integral spin field, which involves solving Hamilton-Jacobi equations for ordered operators. In Sec. III, the exceptional nature of time reflection is indicated by the remark that the charge and the energy-momentum vector behave as a pseudoscalar and pseudovector, respectively, for time reflection transformations. This shows, incidentally, that positive and negative charge must occur symmetrically in a completely covariant theory. The contrast between the pseudo energy-momentum vector and the proper displacement vector then indicates that time reflection cannot be described within the unitary transformation framework. This appears most fundamentally in the basic dynamical principle. It is important to recognize here that the contributions to the lagrange function of half-integral spin fields behave like pseudoscalars with respect to time reflection. The non-unitary transformation required to represent time reflection is found to be the replacement of a state vector by its dual, or complex conjugate vector, together with the transposition of all operators. The fundamental dynamical principle is then invariant under time reflection if inverting the order of all operators in the lagrange function leaves an integral spin contribution unaltered, and reverses the sign of a half-integral spin contribution. This implies the essential commutativity, or anti-commutativity, of integral and half-integral field components, respectively, which is the connection between spin and statistics.