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By John Casey

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Additional info for A treatise on the analytical geometry of the point, line, circle, and conic sections, containing an account of its most recent extensions, with numerous examples

Sample text

We shall show that it might be related to the time-like vector as considered in relativistic stochastic metric tensor. 90) where, z, = LX and L denotes Poincare transformation which bodily rotates or translates the whole physical system in space-time. Again we know that S-operator is a functional of the field and it must be the same functional form for all Lorentz frames, otherwise their equivalence is violated. But the question arises whether this frame dependence is compatible with established physical principles.

4) Within this framework, it is possible to establish the following uncertainty principle for position and momentum observables q and p respectively. 5) In quantum mechanics, the wave function contains more information rather than the probability density. The wave function contains the phase which is very important in describing the interference phenomena. But here, in the frame of stochastic space-time we are dealing directly with P(z, t). So, it appears to be problematic to explain the interference phenomena within this framework.

Karolyhazy emphasized that the amount of uncertainty incorporated into the structure of classical space-time is the apporopriate amount needed to destroy the coherence of the quantum states of macroscopic bodies, whereas the coherence of the states of microsystems will be practically unaffected [Frenkel 1995]. j where A = ~ 1O-33cm is the Planck length. Here, 6QT denotes not only the quantum uncertainty 6:1: in the position of a body, but also the uncertainty 6K v6p in the kinetic energy. This 6K contribute to the uncertainty of the structure of space-time and consequently of the length ofT.

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