By D.I. Blokhintsev, Z. Smith
A manner of figuring out the legislation which govem the worId of simple particIes has no longer been chanced on but. Present-day theoretical physicists must be chuffed with compromises which, on the top, promise a few good fortune on the fee of generality and harmony. U nder those situations a severe research of the elemental options of modem quantum concept will be well timed and usefuI. it really is was hoping that the worth of such an research might be preserved whether, within the close to destiny, new methods of realizing the root of simple particIe physics are stumbled on. during this monograph one particular element of this research is handled, particularly the issues of geometry within the microworld. An out line of geometrical measurements within the macroworld was once given pre viously. those measurements appear to be c1ear sufficient for a minimum of a definite set of difficulties to be regarded as a kick off point for discussing the placement within the microworld. The options and techniques that are invaluable within the macroworld could merely not directly be carried over into the microworld they usually require a excessive measure of abstraction. In comprehending the actual content material of dynamic variables that have geometric which means, for instance, the space-time partic1e coor dinates x, y, z, t it really is of ten essential to have recourse to gedanken experiments which, even if now not possible in perform, can however be suitable with the fundamental rules of geometry and quantum mechanics.
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NIL Therefore, when making an exact measurement of the coordinates of a micropartide x, an infinitely large energy must be involved in this measurement. , from any part ofthe measuring instrument). Thus for measuring coordinates, the interference ofthe instrument with the micropartide state is both inevitable and essential. When considering this interference, it is better to speak, not of the measuring the micropartide coordinate x, but of localizing [30] the micropartide about the point x=x' as a re suIt of its interaction with the measuring device.
It is sufficient for our purpose here to limit ourselves to one dimension x. 8) xr/lx' = x'r/lx" where r/lx' is the characteristic function ofthe operator x belonging to the characteristic value x'. The explicit form of r/lx' depends on the representation selected. In the momentum representation, r/I x' is a function of Px and the operator x is equal to x =+ A 8 In-. 9) • °Px In the coordinate representation, r/lx' is a function of x and the operator is equal to x x == X. 11) and in the coordinate representation r/lx' (x) = 6(x - x').
The investigations like those performed in this work, namely which start from general concepts, serve only as a tool that does not allow the limitedness and long standing preJudices to hinder progress in the understanding of things. We stand here on the threshold of a region that belongs to another science, to physics, and now we ha ve no indication how to cross it. [1SP 6. THE PHYSICS OF ARITHMETIZATION OF THE SPACE-TIME MANIFOLD The assignment of specific coordinates to physical events is not only a mathematical process.