Reactions at High Time Energy

"This book is about time. I would have liked to have named it Time, the Forgotten Dimension..." [Ilya Prigogine]. {594}

"The notion of time may be unfolded into an independent pure science... a science ofpure time is possible." [Sir William R. Hamilton, 1837]. {595}

"...contrary to the conclusions ofclassical mechanics, there exist effects ofpotentials on charged particles, even in the region where all the fields (and therefore the forces on the particles) vanish. " [Y. Aharonov and D. Bohm] {596}.

" behavior greatly modifies the very meaning of space and time. Much of geometry and physics is based on a simple concept ofspace and time, generally associated with Euclid and Galileo. In this view, time is homogeneous. Time translations may have no effect on physical events. Similarly, space is homogeneous and isotropic; again translations and rotations cannot alter the description of the physical world. It is quite remarkable that this simple conception ofspace and time may be broken by the occurrence ofdissipative structures. Once a dissipative structure is formed, the homogeneity of time, as well as space, may be destroyed. " [Ilya Prigogine] {597}.

"As we expand our observation, we extend our concepts. Thus the simple symmetries that once seemed self-evident are no longer taken for granted. Out ofstudies ofdifferent kinds ofinteractions we are learning that symmetry in nature is some complex mixture ofchangingplus into minus, running time backward and turning things inside out. " [T. D. Lee] {598}.

"The desirable features ofa system of units in any field are convenience and clarity. For example, theoretical physicists active in relativistic quantum field theory and the theory of elementary particles find it convenient to choose the universal constants such as Planck's quantum of action and the velocity of light in vacuum to he dimensionless and of unit magnitude. The resulting system of units (called 'natural' units) has only one basic unit, customarily chosen to be length. All quantities, whether length or time orforce or energy, etc., are expressed in terms ofthis one unit and have dimensions which are powers of its dimension. There is nothing contrived or less fundamental about such a system than one involving the meter, the kilogram, and the second as basic units. It is merely a matter ofconvenience." [J. D. Jackson] {599}.

[Violation of Second Law of Thermodynamics] "We experimentally demonstrate the fluctuation theorem, which predicts appreciable and measurable violations of the second law ofthermodynamics for small systems over short time scales... Our results show entropy consumption can occur over colloidal length and time scales." [Evans et al.]287

[Implications ] "This result has profound consequences for any chemical or physical process that occurs over shorttimesandinsmallregions. "[Evans et al.]288

[Implications] "The smaller a machine is, the greater the chance that it will run backwards. " [Evans et al., ibid.]

[Implications] "Physicists knew that at atomic scales over very shortperiods oftime, statistical mechanics is pushed

287 G. M. Wang, E. M. Sevick, Emil Mittag, Debra J. Searles, and Denis J. Evans, "Experimental Demonstration of Violations of the Second Law of Thermodynamics for Small Systems and Short Time Scales," Phys. Rev. Lett, 89(5), 29 July 2002, 050601.

288 BBC News, 18 July 2002,

beyond its limit, and the second law does not apply. Put another way situations that break the second law become much more probable. ... the new experimentprobed the uncertain middle ground between extremely small-scale systems and macroscopic systems and showed that the second law can consistently be broken at micron scale, over time periods of up to two seconds." [Chalmers] 289

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