Zero electromagnetic fields, quantum

A chemical interconversion requiring an intermediate stationary Hamiltonian means that the direct passage from states of a Hamiltonian Hc(i) to quantum states related to Hc(j) has zero probability. The intermediate stationary Hamiltonian Hc(ij) has no ground electronic state. All its quantum states have a finite lifetime in presence of an electromagnetic field. These levels can be accessed from particular molecular species referred to as active precursor and successor complexes (APC and ASC). All these states are accessible since they all belong to the spectra of the total Hamiltonian, so that as soon as those quantum states in the active precursor (successor) complex that have a non zero electric transition moment matrix element with a quantum state of Hc(ij) these latter states will necessarily be populated. The rate at which they are populated is another problem (see below). 

The modern point of view is that, for every particle that exists, there is a corresponding field with wave properties. In the development of this viewpoint, the particle aspects of electrons and nuclei were evident at the beginning and the field or wave aspects were found later (this was the development of quantum mechanics). In contrast, the wave aspects of the photon were understood first (this was the classical electromagnetic theory of Maxwell) and its particle aspects only discovered later, From this modern viewpoint, the photon is the particle corresponding to the electromagnetic field. It is a particle with zero rest mass and spin one. 

Another example of zero-point energy arises in the detailed quantum theory of the electromagnetic field, known as quantum electrodynamics. The empty vacuum with no photons present is actually the zero-point level with n = 0. The non-zero energy of this state cannot be measured directly, but does have some observable consequences. The vacuum is really a state of fluctuating electric and magnetic fields that are significant at the atomic level. Without them, there would be no mechanism for the spontaneous emission of photons from excited states. There also have very small effects on the energy levels of atoms (see Section 4.4). 

In our first simple example the electrostatic potential set up by CsCl is almost but not quite a minimal surface [10]. The reason is that the Coulomb electrostatic energy is only a part of the whole electromagnetic field. Two body, three and higher order, non-additive van der Waals interactions contribute to the complete field, distributed within the crystal. This leads one to expect that the condition that the stress tensor of the field is zero, as for soap films, yields the condition for equilibrium of the crystal. Precisely that condition is that for the existence of a minimal surface. Strictly speaking the minimal surface might be defined by the condition that the electromagnetic stress tensor is zero. But in any event, we see in this manner that the occurrence of minimal surfaces, should be a consequence of equilibrium (cf. Chapter 3,3.2.4). Indeed a statement of equilibrium may well be equivalent to quantum statistical mechanics. 

It is not heretical to consider the electromagnetic vacuum as a physical system. In fact, it manifests some physical properties and is responsible for a number of important effects. For example, the field amplitudes continue to oscillate in the vacuum state. These zero-point oscillations cause the spontaneous emission [1], the natural linebreadth [5], the Lamb shift [6], the Casimir force between conductors [7], and the quantum beats [8]. It is also possible to generate quantum states of electromagnetic field in which the amplitude fluctuations are reduced below the symmetric quantum limit of zero-point oscillations in one quadrature component [9]. 

The theory for the van der Waals interactions presented in the previous section applies to macroscopic media only in a qualitative sense. This is because (i) the additivity of the interactions is assumed — i.e., the energies are written as sums of the separate interactions between every pair of molecules (ii) the relationship of the Hamaker constant to the dielectric constant is based on a very oversimplified quantum-mechanical model of a two-level system (iii) finite temperature effects on the interaction are not taken into account since it is a zero-temperature description. Here, we present a simplified derivation of the van der Waals interaction in continuous media, based upon arguments first presented by Ninham et al a more rigorous treatment can be found in Ref. 4. The van der Waals interactions arise from the free energy of the fluctuating electromagnetic field in the system. For bodies whose separations... 

The name pseudo-Casimir force for the fluctuation-induced interaction is due to the analogy with the Casimir effect [63] at T = 0 quetntum fluctuations of the electromagnetic field in a cavity yield a weak yet measurable attraction between the walls of the cavity. Because the force between the walls is determined by a derivative of the free energy of a system rather than by a derivative of its energy, a similar effect is expected above absolute zero where the interaction is not just due to quantum but also due to thermal fluctuations. In liquid crystals, the fluctuation-induced interaction is due to thermal fluctuations of the order parameter field instead of the electromagnetic field. 

As discussed in Paresegian s recent book, the modern view of dispersion interactions has its roots in the the Casimir effect. " Rather than charge fluctuations, the phenomenon can be viewed in terms of zero-point electromagnetic-field fluctuations in the vacuum as allowed by the Heisenberg uncertainty principle (AEAt>b/ln). Atoms and molecules can absorb some of these frequencies, namely those frequencies that are resonant with transitions between the quantum mechanical energy levels of the system as determined by its electronic structure. This absorption of the electromagnetic fluctuations gives rise to attractive forces between two bodies. 

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