Advances in Quantum Theory - download pdf or read online

By I. Cotaescu

ISBN-10: 9535100874

ISBN-13: 9789535100874

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Decoherence in a system is caused by the interaction with a macroscopic device, which in turn is embedded in an even larger environment. As a consequence, information flows out from the quantum object. As long as this information is restricted to a finite volume, there is no fundamental obstacle preventing the information from coming back into the quantum object. However, any environment is ultimately coupled to the cosmic space, being presently nearly empty and dark. This cosmic boundary condition is the reason that in the end, perhaps with some intermediate steps, the information can escape without any realistic chance for ever coming back.

Since the amplitude ψ ( p) is a complex number value and no location for the value is specified, one may choose any location, x, such as that of an observer, Ox , to assign ψ ( p) as a number value in C¯ x and the integral as an element of x . The relation between ψ ( p) and ψ ( x ) is given by the Fourier transform. The components of the space integral in ψ ( p) = eiz pz z ψ (z)dz (50) must all be mapped to a common point, x, for the integral to make sense. This gives ψ ( p) x = (eiz pz z ) x ψ (z) x dz x (51) (eiz pz z ) x = Fx,z eiz pz z = ei x p x z x is the same number in C¯ x as eiz pz z is in C¯ z .

This result is obtained by noting that for each y the local representation of H¯ y , C¯ y on H¯ x , C¯ x , r r r with scaling factor included, is H¯ xy,x , C¯ xy,x . The vector in H¯ xy,x that is the same vector as ψ (y)| y r is in H¯ y , is denoted by ψ (y)rx ·rx | yrx . Here ψ (y)rx is the same number value in C¯ xy,x as ψ (y) is r in C¯ y , and | yrx is the same vector in H¯ xy,x as | y is in H¯ y as | y x x is in H¯ x . This follows from the observation that y, yrx , and y x are the respective same numbers in R¯ 3y , ( R¯ rx )3 , and R¯ 3x .

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Advances in Quantum Theory by I. Cotaescu


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