Indeterminism principle

First of all, let us note that short-range coulombic repulsion exists, due to the homologous nature of the electronic charges of the two atoms at short distances from each other. However, the main repulsive force is quantum-mechanistic and is a manifestation of Heisenberg s indetermination principle. The more electrons are confined in a limited region of space, the more their angular momentum and hence their kinetic energy increases (of section 1.18). 

On the basis of their origin, errors may usually be classified as determinate or indeterminate. The first are those having a value which is (in principle at least) measurable and for which a correction may be made. The second fluctuate in a random manner and do not have a definite measurable value. 

Clearly the problem is indeterminate, and it is possible to devise an infinity of solutions. (For example, the die only gives i=5 or i=4 with equal probabilities). The ME principle, however, generates a unique solution which, in the jargon of the subject, is maximally unbiased, has a minimum... 

When rational choice is indeterminate, some other mechanism must take up the slack. That could be the principle of "satisficing," of choosing something that is good enough. The explanatory burden is then shifted to the notion of an aspiration... 

The picture of prime matter as a stuff that in itself is indeterminate but that is made determinate by various limiting principles, is reinforced by another passage Sokolowski cites within Aristode s discussion of place in Physics IV 2. Aristode says ... 

Finally, the spin quantum number, describes the direction of spin of the electron. It might be argued that it would be impossible to say how an electron is spinning if the uncertainty principle says that its position is indeterminate. This problem> however, may be considered to be very crudely analogous to a spinning top that is darting about so fast that its position appears blurred the operator who sets the top in motion knows its direction of spin even though he may be unsure of its position. 

In view of the results just given, we might guess that local average rates of chemical heat release in turbulent diffusion flames are calculable in some fashion from P(Z). However, this is not possible even in principle for equilibrium flows. As equilibrium is approached, the chemical production terms in the equations for species conservation become indeterminate, involving differences of large numbers that cancel (for example, see Section B.2.5.2). A more circuitous route is therefore needed to find the average rate of heat release [15], [20], [27], [28]. The necessary expressions will be developed here. 

Acceleration of a reaction, 418.—308. Comparison of the fundamental principle of chemical dynamics and the principle of dynamics properly so called, 418.—309. Influence of the composition of the system on the velodty of reaction, 416.—310. Every isothermal reaction is a moderated reaction, 416.— 3x1. The acceleration of a mod- erated reaction is negative, 416. 31 a. Influence of temperature on the velocity of reaction, 416.-—3x3. Example Phenomena of etherlfl-cation, 416.-3x4. Variation of the velocity due to a small change of composition and temperature, 418.-3x5. Return to isothermal reactions, 418.— 3x6. Adiabatic reactions, 418.—3x7. An adiabatic reaction may have a positive acceleration, 430.-3x8. Reactions with positive acceleration and explosive reactions, 430.-3x9. Conditions In order that an adiabatic reaction be explosive, 421.—320. Indetermination of the temperature which renders a reaction explosive, 421.—3ax. Stability and instability of limiting false equilibria, 421.—32a. Eveiy state of false equilibrium which is not limited is indifferent, 428.—... 

An inevitable consequence of de Broglie s standing-wave description of an electron in an orbit around the nucleus is that the position and momentum of a particle cannot both be known precisely and simultaneously. The momentum of the circular standing wave shown in Figure 4.18 is given exactly hj p = h/, but because the wave is spread uniformly around the circle, we cannot specify the angular position of the electron on the circle at all. We say the angular position is indeterminate because it has no definite value. This conclusion is in stark contrast with the principles of classical physics in which the positions and momenta are all known precisely and the trajectories of particles are well defined. How was this paradox resolved ... 

Strictly speaking, the relative contribution of bound states within the collisionless models is in principle indeterminate, which is, eventually, the consequence of the time-reversibility of Vlasov equation. The matter is that the stationary solutions of the Vlasov equation are dependent on the way of formation of the steady state of the system. Thus, to tackle this problem, one has to employ additional considerations or principles for evaluating the number of trapped ions. 

As with the trends previously mentioned, proposals have been promulgated for internal and external constraints. At first pass, it is tempting to account for relations between life history variables almost purely on the basis of fundamental allometric constraints. Metabolic rate, lifespan, fecundity, age at maturity, and maternal investment all vary with body mass as power functions. In fact, relations are invariant between some of these variables. For example, lifespan scales with body mass by a 1/4 power, and heart rate (or the rate of ATP synthesis) scales with body mass by a — 1/4 power. The product yields an approximately constant number of metabolic events in mammal species, independent of body mass or lifespan. Age at maturity / lifespan, and annual maternal investment / lifespan (for indeterminate growers), are also invariant ratios (Chamov, 1993 Chamov et al., 2001 Steams, 1992). West and Brown (2004) point out that invariant ratios, and universal quarter-power allometric trends in general, suggest underlying physical first principles. They employ their model to explain these life history relations (Enquist et al., 1999 Niklas and Enquist, 2001 West et al., 2001). 

The value of Q in relation to K serves as an index how the composition of the reaction system compares to that of the equilibrium state, and thus it indicates the direction in which any net reaction must proceed. For example, if we combine the two reactants A and B at concentrations of 1 mol L-1 each, the value of Q will indeterminately large(l/0). If instead our mixture consists only of the two products C and D, Q = 0-s-l = 0. It is easy to see (by simply application of the LeChatelier principle) that the ratio of Q/K immediately tells us whether, and in which direction, a net reaction will occur as the system moves toward its equilibrium state ... 

Powders Estimation of the effective surface area of powders with an indeterminate number and size of particles is a complicated problem. This quantity can, in principle, be determined by the BET method. However, decomposition of a powder is not uniform in space. Because of self-cooling, internal layers of powdered samples are heated more weakly than the surface layers and, therefore, make a lower contribution to the total decomposition effect. 

---