Human experience is based in the existence of an arrow of time. Engineering, history, and others sciences as chemistry, biology, or cosmology are firmly based in that arrow. Still, since Newtonian epoch, the physical laws are formulated in a time neutral form, with the thermodynamic arrow of time –the celebrated second law– unjustly relegated to a phenomenological level.
We do not know any experimental violation of the second law; in contrast to the limited validity for the laws of electrodynamics, Newtonian mechanics, or special relativity, the arrow of time is one of our best-tested laws of nature.
Each certain time, authors claim the observation of some kind of experimental violation for the second law of thermodynamics. An example that received some coverage in media was Experimental Demonstration of Violations of the Second Law of Thermodynamics for Small Systems and Short Time Scales by , , , , and , published in Physical Review Letters in 2002. However, further analysis done by other authors revealed that experimental data obtained was compatible with the second law
The authors of the Physical Review Letters article based their claim in a misunderstanding of the second law that has self-perpetuated in textbooks during more than a century. Many textbooks state that the second law of thermodynamics is a statistical law and, therefore, it is continuously violated in small systems due to fluctuations, which is not true.
The second law is not violated by fluctuations because the law refers to the behavior for the physical average 〈S〉. The second law of thermodynamics, as the Newtonian force equation or the Maxwell equations on electromagnetism describe the behavior of the physical ensemble –do not confound with Gibbs ensembles of statistical mechanics–. Moreover, the fluctuation data can be analized and compared with the thermodynamics theory for δS. It was proven that the data on above article was in complete agreement with the thermodynamics of fluctuations –which the authors of the 2002 paper ignored–.
It is also generally ignored that thermal science is not restricted to the macroscopic regime. Visit nanothermodynamics for additional data on giga and nanothermodynamics.
One of fundamental problems in modern physics is the incompatibility between classical mechanics and quantum theory, at the one hand, and thermodynamics at the other; this is the old problem of the arrow of time
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Thermodynamics describes the irreversibility and dissipation we observe on Nature, whereas mechanics is both conservative and time reversible. already studied modifications of time-reversible laws for explaining the dissipative motion of fluids, but he did not advance much. In successive years, dissipative problems were carefully 'eliminated' from the target of theoreticians and mathematicians; the aim was mainly aesthetic but also related to technical difficulties.
Canonical science generalizes mechanics by an adequate description of dissipative processes. In absence of dissipation, or when its effects are so small that can be neglected, canonical science reduces to mechanics. For instance, in the classical formulation in term of brackets this reduction can be represented as the limit
The canonical theory generalizes mechanics and kinetics, explains dissipative phenomena and is free of the paradoxes and technical difficulties traditionally associated to the field of the science of irreversibility.
For instance, the canonical theory let us the derivation of generalized H-theorems without the uncritical mixing of dynamical, probabilistic, and ad hoc assumptions that characterized physics and has limited the development of a general and consistent irreversible statistical mechanics during decades.
The traditional physicists' approach has been to derive the irreversible equations tested in laboratory from microscopic time-reversible laws assuming a universal validity. During more than a century this approach has failed as noticed by many authors on literature. emphasized both the mathematical and conceptual incompatibility between mechanics and thermodynamics and resumed the failure on his remarkable quote One cannot escape from this fact by any amount of mathematical funambulism.
Canonical science solves the incompatibility between mechanics and thermodynamics but does at a new conceptual and technical level, generalizing mechanics for including dissipation.
Chemistry, biology, and geology deal with irreversible phenomena. Most authors take an pragmatic attitude and use phenomenological equations available; for instance, engineers use the laws of chemical kinetics, biologists use the equation for diluted gases, and so on.
However, the empirical limits of validity of those equations are often unknown and, when applied outside their empirical range of validity, the experimental discrepancies generate hot debates on specialized literature. A few decades ago physicists thought a -like equation with a generalized coefficient would be enough for explaining phenomena in plasmas, but the entire research program failed. The equation is local and does not address dynamical bubbles arising in plasmas; the possibility of nonlocal collisions was overlooked by the empirical equations until the first rigorous theoretical frameworks proved the possibility of such one phenomena. The irreversible theory defines the limit of applicability of the equation and let us derive equations for the plasma regime: e.g. the equation.
Similar thoughts apply to other empirical laws used in biology, chemistry, or geology. We need to know their limits of applicability and we need to derive new laws for phenomena do not covered by old laws. Those equations are irreversible and cannot be derived from reversible mechanics. The search of the microscopic roots of the arrow of time is then a primary program of research.
Using canonical theory we can model both reversible and irreversible phenomena; we can obtain generalized hydrodynamics; we compute transport coefficients for dense fluids, predict thermoviscous coupling; we can go beyond standard / theory in the study of shock waves, etcetera.
Formulas for systems far from equilibrium like
derived by are not available on formulations of statistical mechanics founded on the traditional reversible equations of mechanics. postulated a generalized evolution equation is not reducible to Newtonian or Schrödinger dynamics. equation can be seen as a special case from canonical science.
The canonical theory embraces phenomenological and theoretical equations developed and proposed in the last 100 years from very different communities: laser community, astrophysicists, physical chemists, mathematical physicists, and others.
It would be remarked again that reversible physics arises as an approximation from the canonical theory. E.g. The equation of quantum mechanics arises when dissipation terms are ignored in the canonical equation.
Special relativity and quantum mechanics are both incompatible. The difficulties to merge special relativity in quantum theory were partially eliminated via a relativistic quantum field theory. But fundamental issues with relativistic quantum field theory remained and worried to physicists as , , or . Contrary to the common view on particle physics community, we cannot accept relativistic quantum field theory completely. emphasized the fundamental difficulties with relativistic quantum field theory during the last part of the 70s:
Most physicists are very satisfied with this situation. They argue that if one has rules for doing calculations and the results agree with observation, that is all that one requires. But it is not all that one requires. One requires a single comprehensive theory applying to all physical phenomena. Not one theory for dealing with non relativistic effects and a separate disjoint theory for dealing with certain relativistic effects. [...] For these reasons I find the present quantum electrodynamics quite unsatisfactory.
We may agree with that relativistic quantum field theory would be considered a preliminary step in the formulation of a complete and consistent relativistic quantum mechanics.
Recent experiments –reported for both classical and quantum systems– seem to be not in agreement with standard relativistic thoughts: anomalies in tomahawk plasmas, tunneling effects in atoms, longitudinal forces measured in Hg, quantum electrodynamics of multielectronic systems, multi-clock time dilation...
Another difficulty on theoretical physics is the long six decades failure to quantize general relativity. Attempts to directly quantize general relativity confronts us with the famous problem of the absence of time, the / equation, HΨ = 0.
The theory achieved at the Center solves difficulties with time and may be free of all experimental difficulties mentioned above. This novel formulation verifies early intuitive 's thoughts about the preliminary status of relativistic quantum field theory. The perspective opened by the new quantum gravity approach is very promising.
Standard relativistic theories define time like another dimension in a four-geometry, which is not technically satisfactory.
Relativists as have postulated time is totally 'spatialized' at the initial Big Bang, and becomes indistinguishable from the spatial dimensions. However, nobody has proposed a detailed mechanism which time splits from a hypothetical 'spacetime foam' and acquires the properties we observe.
Canonical science solves this dilemma. Matter is able to generate a canonical 'force' that continuously transmits chronons of time between past and future. This generates the advance of the present, t → t + ζ, and the subsequent increasing of the past. In this model, the past could not be infinite because then the time-flow would stop as corresponding to a static universe. Thus, a finite age for the universe is expected.
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Emergence of time from an atemporal word. Matter generates a time evolves in an endless process. |
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