Conservation laws, violation

SRPA restores the conservation laws (e.g. translational invariance) violated by the static mean field. Indeed, let s assume a symmetry mode with... 

No laws of physics or thermodynamics are violated in such open dissipative systems exhibiting increased COP and energy conservation laws are rigorously obeyed. Classical equilibrium thermodynamics does not apply and is permissibly violated. Instead, the thermodynamics of open systems far from thermodynamic equilibrium with their active environment—in this case the active environment-rigorously applies [2-4]. 

An important function of the conservation laws is that they allow predictions about the behav ior of a system without going into mechanical details of what happens during the course of a reaction. The laws provide a direct connection between the slate of the system before the reaction and the stale after the reaction. Also, one may conclude that any action that violates one of the conservation laws must be forbidden. 

The muon and the electron may be considered to belong to two different generations of leptons, which thus far appear to remain separate because of the independent conservation laws of muon number and of electron number. Any connection between the muon and the electron, such as a process which would violate muon number conservation, would be an important clue to the relationship... 

Violates additive conservation law for muon number, EL constant. 

These considerations have a particular reference to the dissociation of N2O in which the temperature independent factor was found to be about io times the value obtained by estimating (4). This was taken, for awhile, as an indication of the non-adiabatic nature of the reaction,2 which was suggested by the fact that it violates the spin conservation law. However, it has been shown by Zener on the basis of the interaction integrals obtained from the intensities of forbidden... 

Conservation laws occupy a special place in science and engineering. Common statements of these laws take the form of mass (energy) is neither created nor destroyed, the mass (energy) of the universe is constant, the mass (energy) of any isolated system is constant, or equivalent statements. To refute a conservation law, it would be sufficient to find just one example of a violation. 

Despite all these impressive progress, we are still too far from the ultimate theory of everything. I listed some obvious avenues for future research in particle physics and cosmology. If I am allowed to say my personal prejudice, I would say that the flavor problem is beyond our reach for years to come, but our understanding of the law of force may further be advanced by a new discovery of violation of empirical conservation laws. The Majorana nature of neutrino masses and proton decay are just manifestation of violation of lepton and baryon numbers, and in my view there is no fundamental obstacle against these being discovered in future, however remote it might be. 

A deep reason for this fanatic belief is the gauge principle. I would say that all empirical conservation laws not protected by the gauge principle are doomed to be violated at some level of strength. The only relevant question is at which energy scales these conservation laws are violated. Both theory and experiment should give definitive signatures for this energy scale. We already seem to have some hint on this. 

Additional spatial dimensions beyond the three we move in (anywhere from one extra, as in traditional Kaluza-Klein theory, up to 11 or thereabouts) imply the possibility of extra symmetries, extra conserved quantities, and a lowest-mass particle that cannot decay without violating that conservation law and which is, therefore, a possible DM candidate. Some names we caught were ... 

Kolev [46] discussed the validity of these relations for fluid particle collisions considering the obvious discrepancies resulting from the different nature of the fluid particle collisions compared with the random molecular collisions. The basic assumptions in kinetic theory that the molecules are hard spheres and that the collisions are perfectly elastic and obey the classical conservation laws do not hold for real fluid particles because these particles are deformable, elastic and may agglomerate or even coalescence after random collisions. The collision density is thus not really an independent function of the coalescence probability. For bubbly flow Colella et al [15] also found the basic kinetic theory assumption that the particles are interacting only during collision violated, as the bubbles influence each other by means of their wakes. 

These formulas are immediately generalizable to the case of transition to both nearest and next nearest neighbor levels (see Fig. 3). Here the conservation law is violated in the last two... 

The question may also be asked as to whether chemical symmetry differs from any other kind of symmetry Symmetries in the various branches of the sciences are perhaps characteristically different, and one may ask whether they could be hierarchically related. The symmetry in the great conservation laws of physics (see, e.g.. Ref. [1-28]) is, of course, present in any chemical system. The symmetry of molecules and their reactions is part of the fabric of biological structure. Left-and-right symmetry is so important for living matter that it may be matched only by the importance of left-and-right symmetry in the world of the elementary particles, including the violation of parity, as if a circle is closed, but that is, of course, a gross oversimplification. 

A moment s reflection shows that the big bang violates all of the individual conservation laws and tries to outfox the CPT theorem by sleight of hand, dressed up as Grand Unified Theories (GUT s). They find an interval, between t = and 10 seconds after the big bang, when a state of... 

In keeping with the current interest in tests of conservation laws, we collect together a Table of experimental limits on all weak and electromagnetic decays, mass differences, and moments, and on a few reactions, whose observation would violate conservation laws. The Table is given only in the full Review of Particle Physics not in the Particle Physics Booklet. For the benefit of Booklet readers, we include the best limits from the Table in the following text. Limits in this text are for CL=90% unless otherwise specified. The Table is in two parts Discrete Space-Time Symmetries, i.e., C, P, T, CP, and CPT and Number Conservation Laws, i.e., lepton, baryon, hadronic flavor, and charge conservation. The references for these data can be found in the the Particle Listings in the Review. A discussion of these tests follows. 

In strong and electromagnetic interactions, hadronic flavor is conserved, i.e. the conversion of a quark of one flavor (d, u, s, c, 6, t) into a quark of another flavor is forbidden. In the Standard Model, the weak interactions violate these conservation laws in a manner described by the Cabibbo-Kobayashi-Maskawa mixing (see the section Cabibbo-Kobayashi-Maskawa Mixing Matrix ). The way in which these conservation laws are violated is tested as follows ... 

Conservation laws represent most precious information about our system. It is not important what happens to the isolated system, what it is composed of, how complex the processes taking place in it are, whether they are slow or violent, whether there are people in the system or not, or whether they think how to cheat the conservation laws or not. Nothing can happen if it violates the conservation of energy, momentum, or angular momentum. 

Symmetries in particle physics are even more important than in chemistry or solid-state physics. Just like in any theory of matter, the inner structure of the composite particles is described by symmetries, but in particle physics everything is deduced from the symmetries (or invariance properties) of the physical phenomena or fi-om their violation the conservation laws, the interactions, and even the masses of the particles, as it will be shown later. 

A simple particle collision is described as a particle current exchanging an interaction boson with another similar current. The appearance of an extra boson is made possible by the uncertainty principle of Heisenberg which implies that for sufficiently short times and distances the conservation laws of energy and momentum can be violated AE At > hl2 and Ap Ax > h 2, where AA means a small uncertainty or deviation ia A A = E, p, t, x), Eand p are the energy and momentum of the particle, t and x are time and spatial coordinates. The smallness of the reduced (sometimes called rationalized) Planck constant, h = 1.055 x 10 Js ensures that in the macroworld the conservation laws are exactly fulfilled. The exchanged boson maybe real or virtual depending on whether or not the conservation laws are fulfilled for its creation if it is real, then it is emitted and so it can be detected if it is virtual, then it is absorbed and one can see the result of the boson exchange only, i.e., the effect of the interaction on the motion of the particles involved. 

These simple conservation laws are nevertheless not assmed, in fact they are sometimes even severely violated, in many of existing calculation methods including mean-field methods like the semiclassical Ehrenfest theory (SET). The surface hopping method circumvents the problem by adjusting the linear momenta of nuclei so as to satisfy the asymptotic energy conservation law. 

---