Relax Your Mind

Note: At first, the ideas may appear disparate, but in fact all illustrate the necessity to view systems as ontically open.

Note: At first, the ideas may appear disparate, but in fact all illustrate the necessity to view systems as ontically open.

but has simultaneously involved the recognition of limits to the Newtonian paradigm. Below, we deal with some important findings in physics from the 20th century such as the Heisenberg uncertainty principle, the Compton effects, and the relaxation of systems that may have future parallels in ecology.

The Heisenberg uncertainty relation tells that we cannot know exactly both the position and the velocity of an atom at the same time. At the instant when position is determined, the electron undergoes a discontinuous change in momentum. This change is greater the smaller the wavelength of the light employed. Thus, the more precise the position is determined, the less precise the momentum is known, and vice versa (see Box 3.1).

Box 3.1 The Heisenberg uncertainty principle or principle of indeterminacy

The basic proof shows that the product of position and momentum will always be larger than Planck's constant. This is given explicitly by the following mathematical terms:

Where, s refers to space, p the momentum, and h the Planck's constant (6.626 X 10-34 Js).

The Compton effect deals with the change in wavelength of light when scattered by electrons. According to the elementary laws of the Compton effect, p1 and A1 stand in the relation:

where p1 is the momentum of the electron, Ai1 the wavelength increase due to the collision, E1 the energy, and T1 the time.

Equation 3.1 corresponds to Equation 3.2 and shows how a precise determination of energy can only be obtained at the cost of a corresponding uncertainty in the time (see Box 3.2).

Spin relaxation is possible because the spin system is coupled to the thermal motions of the "lattice", be it gas, liquid, or solid. The fundamental point is that the lattice is at thermal equilibrium; this means that the probabilities of spontaneous spin transitions up and down are not equal, as they were for rf-induced transitions (see Box 3.3).

Box 3.2 The Compton effect and directionality |
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