Causality, principle

The presence of an infinitesimal, purely imaginary addition in the GF denominator turns out to be very important and to have a deep physical meaning. Its origin is related to the theta-function in Eq. (A 1.13) that represents the causality principle The reaction of a system can be caused only by perturbations at preceding instants. 

The first concerns my appeal, in the last section, to a causal principle that there are no "silent," or causally impotent, properties. I appealed to that principle in my 1994 article, but managed to give a rather unfortunate statement of it, as follows "If a property is intrinsic, then it has characteristic causal consequences an intrinsic difference makes a causal difference" (Le Poidevin, 1994, p. 83). Nerlich, entirely reasonably, objected to this ... 

This argument is based on tlie implicit but plausible assumption of validity of the causality principle. 

The two-atom scheme of the Hertz experiment with multipole photons, in which the radiation field is described by a superposition of outgoing and incoming waves focused on the emitting and detecting atoms respectively, obeys the causality principle even though the path of detecting photons is indefinite. 

The local representation of multipole photons is compatible with the Mandel operational definition of photon localization [20]. In addition to the localization at photodetection, it permits us to describe a complete Hertz-type experiment with two identical atoms used as the emitter and detector (Section VI.A). Although the photon path is undefined from the quantum-mechanical point of view, the measurement process in such a system obeys the causality principle (Section IV.B). The two-atom Hertz experiment can be realized for the trapped... 

Equation (4.51) refers to the causality principle owing to which the induction at time t is determined only by the field at times t < t. 

Here, as also in (4.54), the causality principle holds, owing to which the induction at time t is determined only by the present field and the field at previous times /, t" < t. Applying now the Fourier transformation we obtain the following relation between vectors D(r, t) and E(r, t)... 

Hence, in the light of our both accounts of causality, the molecular dynamics model represents causal processes or chains of events. But is the derivation of a molecule s structure by a molecular dynamics simulation a causal explanation Here the answer is no. The molecular dynamics model alone is not used to explain a causal story elucidating the time evolution of the molecule s conformations. It is used to find the equilibrium conformation situation that comes about a theoretically infinite time interval. The calculation of a molecule s trajectory is only the first step in deriving any observable structural property of this molecule. After a molecular dynamics search we have to screen its trajectory for the energetic minima. We apply the Boltzmann distribution principle to infer the most probable conformation of this molecule.17 It is not a causal principle at work here. This principle is derived from thermodynamics, and hence is statistical. For example, to derive the expression for the Boltzmann distribution, one crucial step is to determine the number of possible realizations there are for each specific distribution of items over a number of energy levels. There is no existing explanation for something like the molecular partition function for a system in thermodynamic equilibrium solely by means of causal processes or causal stories based on considerations on closest possible worlds. 

Because of the causality principle, Eq. (11), in which x is the electric susceptibility, t the time, and z the delay must be verified ... 

Weslake s position is that once we accept an interventionist theory of causation, we ll never be led to accept the thesis of exclusion. Nothing about the causal principles within an interventionist framework will make the exclusion principle plausible. 

Bunge M (1959) Causality the place of the causal principle in modem science. Harvard University Press, Cambridge, MA... 

Let us try to examine these phenomena from the angle of causality principle. Taking the example of thermo-osmosis (Chapter 3), temperature difference is the starting cause, the effect of which is thermo-osmotic fluid flow, which in turn generates another cause, viz. pressure difference under specific circumstances (e.g. experimental set-up), the effect of which is hydrodynamic fluid flow in the reverse direction. Normally, both these causes and effects operate simultaneously. However, when two opposing flows are balanced, a steady state is reached. Similar type of situation occurs in other steady-state phenomena discussed in Chapters 4-6 including mechano-caloric effect. 

In quite a few cases, chaos can be predicted based on appropriate mathematical model (Lorenz or Rosselor) (Chapter 12). The strange attractor obtained in such cases signifies Deterministic Chaos . Such models exhibit cross-catalysis and inhibition. Experimentally observed deterministic chaos can be easily ascertained using definite criteria, although prediction of complex time order is quite difficult in many cases. In terms of causality principle, the complexity in the system arises due to complex interdependence of a number of causes and effects. 

Mathematically, integral Kramers-Kronig relations have very general character. They represent the Hilbert transform of any complex function s(co) = s (co) + s"(co) satisfying the condition s (co) = s(—co)(here the star means complex conjugate). In our particular example, this condition is applied to function n(co) related to dielectric permittivity s(co). The latter is Fourier transform of the time dependent dielectric function s(f), which takes into account a time lag (and never advance) in the response of a substance to the external, e.g. optical, electric field. Therefore the Kramers-Kronig relations follow directly from the causality principle. 

As underlined by Ingegnoli (2002), scientists have to avoid two representations of nature which tend to a world of alienation (1) the deterministic one, with no possibility of novelty and creation, (2) the stochastic one, which leads to an absurd world with no causality principle and without any ability to forecast. Possibly, the major incentive toward a new conception of nature comes from scientists like W. Ashby (1962), Von Bertalanffy (1968), Weiss (1969), Lorenz (1978, 1980), Popper (1982, 1996) and Piigogine (1977, 19%), who observed how nature creates its most fine, sensitive and complex structures through non-reversible processes which are time oriented (time arrow). No doubt that thermodynamics becomes the most important physical discipline when complex adaptive systems exchanging energy, matter and information are involved with life processes. 

An important characteristic of the optical constants is that they fall in a broad class of generalized susceptibilities with the fundamental property that their real and imaginary parts are connected by Kramers-Kronig (KK) integral relations (Landau and Lifshitz 1992). For the case of linear response, KK relations are model independent since they rely only on the causality principle and analytical properties of the complex susceptibilities. The physical reasoning behind the KK relations is that dissipation of energy of the... 

The first issue to challenge the Middle Platonists was the precise relationship between fate and providence. Apuleius and Pseudo-Plutarch had s olved the problem of evil by relegating heimarmene to a lower aspect of the divine principle of pronoia. Yet the farther one moved from the divine source in the chain of cosmic emanations, the more room that opened up for the capricious or even deleterious effects of planetary gods and daimones upon humans. To complicate the issue further, Platonist philosophers needed to define and reconcile heimarmene and pronoia with the related causal principles of chance (tuxv)), and necessity (dvdcyxy)). 

The physical background of Eq. (5.27) is easily seen. The integral relation just follows from the two basic properties of linear systems, namely the causality principle and the validity of the superposition principle ... 

In fact, these properties are not specific to the Debye-process, but have a deeper basis which extends their validity. According to the Kramers-Kronig relations, J and J" are mutually dependent and closer inspection of the equations reveals that it is impossible, in principle, to have a loss without a simultaneous change in J. Both effects are coupled, the reason being, as mentioned above, the validity of the causality principle. 

The causality principle is tied in with the rules of State Responsibility enunciated by the International Law Commission and Article 51 of the United Nations Charter which states that nothing in the Charter will impair the inherent right of individual or collective self-defense if an armed attack occurs against a Member of the United Nations, until the Security Council has taken measures necessary to maintain international peace and security. The provision goes on to say that measures taken by Members in the exercise of this right of self-defense will be immediately reported to the Security Council and will not in any way affect the authority and respOTisibiUty of the Security Council under the present Charter to take at any time such actimi as it deems necessary in order to maintain or restore international peace and security. 

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