After an introduction into some aspects of the motivation of research and researchers in general and the motivation of our research on the topic of this paper in particular we first introduce the basics of the physical definition and measurement of time intervals with atomic and molecular clocks. We then discuss the question of the definition and experimental determination of the direction of time. Time reversal symmetry (T) is introduced among a set of discrete, fundamental symmetry operations in physics (C, P, T). We briefly mention the relations between symmetries, conservation laws and fundamentally “non observable” quantities as well as the three concepts of spontaneous, de facto, and de lege symmetry breaking. In this context we cover in particular also the question of the space inversion symmetry (P) in relation to molecular chirality and charge conjugation (C), the symmetry between matter and antimatter, as well as the analogies between these symmetries.
Irreversibility in molecular kinetics is first to be understood as a de facto breaking of time reversal symmetry. Some experimental results on the molecular short time quantum dynamics on the femtosecond to nanosecond time scale demonstrate the increase with time of entropy in single isolated molecules in the gas phase. Nevertheless, these processes show, in principle, time reversal symmetry. However, one finds fundamentally different dynamical behaviour for the quantum vibrational motion of molecules depending upon anharmonicity — at the same level of “quantization” — which is an important experimental result of our more recent research.
Not all forces of nature (strong nuclear force, weak nuclear force, electromagnetic force and gravitational force) show the separate discrete symmetries C, P, T. Indeed, the weak nuclear force leads to de lege parity violation (violation of space inversion symmetry) and in recent experiments from high energy physics also de lege violation of time reversal symmetry was proven. These symmetry violations are important for our understanding of molecular chirality and we show, how an “absolute molecular clock” measuring absolute time direction and time intervals could be constructed with chiral molecules provided that the combined symmetry CPT were violated de lege. According to our current knowledge CPT symmetry seems, however, to be maintained.
In a speculative final section of this article we address the consequences of our findings in molecular kinetics for a hypothetical molecular quantum psychology, which is a new concept introduced here, which relates to the possible molecular origin of the formation of thoughts and decisions in our brain, depending upon the type and symmetry of the dynamics relevant for actual molecular processes. This complements molecular biology in our understanding of life. The question of free decision and free will is discussed from the physical-chemical point of view of this molecular quantum psychology. We conclude with some personal recollections of Per-Olov Löwdin as a teacher.
- Time reversal symmetry
- molecular kinetics
- quantum chemistry
- parity violation
- CPT symmetry
- free will
- Per-Olov Löwdin
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English Translation: Who I am, I know not. Whence I come, I know not. Whither I go, I know not. Yet this astonishing joy! Angelus Silesius
P.-O. Löwdin, Some Aspects on the Research Process in the Natural Sciences in Scientists at work: Festschrift in honour ofHerman Wold, edited by T. Dalenius, G. Karlsson, and S. Malmquist (Almqvist & Wiksell, Stockholm, 1970), pp. 112.
P.-O. Löwdin, Advances in Quantum Chemistry 8, 323 (1967).
M. Quack, Die Symmetrie von Zeit und Raum und ihre Verletzung in molekularen Prozessen in Jahrbuch 1990–1992 der Akademie der Wissenschaften zu Berlin (W. de Gruyter Verlag, Berlin, 1993), pp. 467, (printed version of the 8th public academy lecture, Berlin 4.10.1990); there exists also a slightly changed English version: M. Quack, The symmetries of time and space and their violation in chiral molecules and molecular processes, pp. 172, in Conceptual Tools for Understanding Nature. Proc. 2nd Int. Symp. of Science and Epistemology Seminar, Trieste April 1993, edited by G. Costa, G. Calucci, M. Giorgi, (World Scientific Publ., Singapore, 1995).
M. Quack, Molecular femtosecond quantum dynamics between less than yoctoseconds and more than days: Experiment and theory, Chapter 27 in Femtosecond chemistry, Proc. Berlin Conf. Femtosecond Chemistry, Berlin (March 1993), edited by J. Manz and L. Woeste (Verlag Chemie, Weinheim, 1995), pp. 781.
M. Quack and S. Jans-Bürli, Molekulare Thermodynamik und Kinetik, Teil 1: Chemische Reaktionskinetik. (Verlag der Fachvereine, Zürich, 1986), (Neuauflage M. Quack and J. Stohner in Vorbereitung 2004).
D. Luckhaus and M. Quack, Gas Phase Kinetics Studies in Encyclopedia of Chemical Physics and Physical Chemistry, edited by J. H. Moore and N. Spencer (IOP publishing, Bristol, 2001), Vol. 2 (Methods), chapter B 2.5, pp. 1871.
R. Marquardt and M. Quack, Energy Redistribution in Reacting Systems in Encyclopedia of Chemical Physics and Physical Chemistry, edited by J. H. Moore and N. Spencer (IOP publishing, Bristol, 2001), Vol. 1 (Fundamentals), chapter A 3.13, pp. 897.
D. Luckhaus and M. Quack, Gas Phase Kinetics in Encyclopedia of Chemical Physics and Physical Chemistry, edited by J. H. Moore and N. Spencer (IOP publishing, Bristol, 2001), Vol. 1 (Fundamentals), chapter A 3.4, pp. 653.
M. Quack, Multiphoton Excitation in Encyclopedia of Computational Chemistry, edited by P. von Ragué Schleyer, N. Allinger, T. Clark, J. Gasteiger, P. A. Kollman, H. F. Schaefer, and P. R. Schreiner (John Wiley & Sons, 1998), Vol. 3, pp. 1775.
M. Quack, Reaction dynamics and statistical mechanics of the preparation of highly excited states by intense infrared radiation, Advances in Chemical Physics, edited by K. Lawley, I. Prigogine, and S. A. Rice (1982), Vol. 50, pp. 395.
M. Quack, Chimia 55, 753 (2001).
M. Quack, Chimia 57 (4), 147 (2003).
M. Quack, Akademie-Journal der Union der deutschen Akademien der Wissenschaften (Themenschwerpunkt Chemie) (1), 38 (2003).
M. Quack, Angewandte Chemie 114, 4812 (2002), Angew. Chem. Int. Ed. English 41, 4618 (2002).
See also M. Quack, Angew. Chem. Int. Ed. English 28 (5), 571 (1989), Angew. Chem. 101, 588 (1989).
Löwdin-Föreläsningar 1996, contributions by M. Quack, Specialiderade föreläsningar Onsdagen den 2 oktober “The primary processes of intramolecular quantum motion and energy transfer”, and Allmänna föreläsningar, Torsdagen den 3 october: “The symmetries of time and space and their violations in molecular processes”, unpublished (the other lectures were given by Peter Fulde and by Franco A. Gianturco).
M. Quack, Telluride public lecture, Telluride 1995, unpublished.
M. Quack, Zeit und Zeitumkehrsymmetrie in der molekularen Kinetik, Berlin Brandenburg (formerly Prussian) Academy of Sciences, October/November 2002
Albert Einstein translated: “Time is what you read from your clock”; see also A. Einstein, Grundzüge der Relativitätstheorie. (Vieweg, Wiesbaden, 1922, Nachdruck 1984).
W. Klein, Der Mythos vom Sprachverfall in Jahrbuch der BBA (1999), pp. 139.
E. Schrödinger, Annalen der Physik IV. Folge 81, 109 (1926).
F. Hund, Z. Physik 43, 788 (1927); see also ibid. 40, 742 (1926).
R. Berger, M. Gottselig, M. Quack, and M. Willeke, Angewandte Chemie-International Edition 40 (22), 4195 (2001),
R. Berger, M. Gottselig, M. Quack, and M. Willeke, Angew. Chem. 113, 4342 (2001)
C. N. Hinshelwood, The Kinetics of Chemical Change, 4th ed. (Clarendon Press, Oxford, 1940).
M. Quack, Nova Acta Leopoldina 81 (Neue Folge (No. 314)), 137 (1999).
M. Quack, Annual Review of Physical Chemistry 41, 839 (1990).
M. Quack and J. Stohner, Journal of Physical Chemistry 97 (48), 12574 (1993).
A. Beil, D. Luckhaus, M. Quack, and J. Stohner, Berichte der Bunsen-Gesellschaft fuer Physikalische Chemie 101 (3), 311 (1997).
English Translation: “There are thus two types of Cartesian coordinate systems, which are called “right-handed” and “left-handed” systems. The difference between the two is familiar to every physicist and engineer. It is interesting that an absolute geometric definition of the right or left handedness is impossible, only the relationship of opposition between the two can be defined.” (see ref. )
M. Quack, Molecular Physics 34, 477 (1977).
M. Quack, Detailed symmetry selection rules for chemical reactions, in Symmetries and properties of non-rigid molecules: A comprehensive survey. Studies in Physical and Theoretical Chemistry 23, 355–378 (Elsevier Publishing Co., Amsterdam, 1983).
K. Mainzer, Symmetrien der Natur: ein Handbuch zur Natur- und Wissenschaftsphilosophie. (de Gruyter, Berlin, 1988).
English Translation: If the principles of life are chiral, then because of chiral cosmic forces at their orgin; this I think, is one of the links between life on earth and the cosmos, or the totality of forces in the universe.
English Translation: “Everything should be made as simple as possible, but not simpler.”
Text from Guiseppe Giacosa and Luigi Illica and Music by Giacomo Puccini, English Translation: “Time flies (the hour has escaped) and I die in despair.”
G. Roth, Fühlen, Denken, Handeln. (Suhrkamp Verlag, Frankfurt, 2001).
English Translation: “Our thoughts are free, who would guess them? They fly by like shadows in the night. No one can know them, no hunter can shoot them. It’s true and must be: our thoughts are free!
In the short story The Amulet by Conrad Ferdinand Meyer one can find a very nice discussion at a crucial point in the story at the beginning of the third chapter just before the first mentioning of the “medaillon”, which discusses the relevant issues from a theological point of view. The English translation of this short story is available: The Complete Narrative Prose of Conrad Ferdinand Meyer, Translated from the German by George F. Folkers, David B. Dickens, Marion W. Sonnenfeld, 2 Volumes, Bucknell University Press, Lewisburg, 1976.
J. Calvin, On the explanation of the biblical texts. (The original is in Latin, but I have available (and base myself) on the German translation: Johannes Calvins Auslegung der Heiligen Schrift in deutscher Übersetzung. (Verlag der Buchhandlung des Erziehungsvereins Neukirchen Kreis Moers, ca. 1910), (siehe besonders Hauptartikel zum Gesetz etc, 2.–5. Buch Mose, 2. Hälfte S. 3 – 441 und Inhaltsübersicht über die Gesetzesauslegung). The translation is due to the following authors: W.Groeters and Mathias Simon Vol. 1, Karl Müller Vol. 2, Ernst Quack and Th. Bergfried Vol. 3.
I. Ekeland, Le meilleur des mondes possibles. Mathématiques et Destinée. (Editions du Seuil, Paris, 2000).
English Translation: “Men are only numbers for you.” “Sire, give freedom of thought!” These two quotations are taken from different places in Friedrich Schiller’s “Don Carlos” and refer to an image of man, human society and mankind in a historical context.
R. L. Frost, Collected Poems, Prose and Plays. (The Library of America, Library Classics, New York, 1995).
R. R. Ernst, Angewandte Chemie 115, 4572 (2003),
R. R. Ernst, Angew. Chem. Int. Edit. 42, 4434 (2003).
English translation: “ With this I appear before Thy throne”. The history is told in A. Schweitzer Johann Sebastian Bach, (10th edition reprinted, the first edition in German being from 1908, Breitkopf and Härtel, publishers, Wiesbaden 1979), see chapter 12 and the foreword of Charles Marie Widor. Note that the original was written in French by A. Schweitzer. An English translation is not available to me, although it probably exists. It might be noted that it seems that when J. S. Bach wrote this organ choral just before his death (as recorded by one of his sons, from which time the printed version was made) this was only a rewriting of a similar choral written much earlier in Bach’s life.
English translation: “The scientist (philosopher) would rather obtain a single fundamental understanding than become king of the Persians.”
M. Quack and J. Troe, Berichte der Bunsen-Gesellschaft für Physikalische Chemie 78, 240 (1974), This theoretical model has stood the test of time, see . The printed version of 1974 is essentially identical with the handwritten manuscript I left in Lausanne before traveling to the summer school. There existed actually a short earlier manuscript on the topic, which we had previously submitted to Chem. Phys. Letters, but never published, a story best told on another occasion.
M. Quack and J. Troe, Statistical Adiabatic Channel Model in Encyclopedia of Computational Chemistry, edited by P. von Ragué Schleyer, N. Allinger, T. Clark, J. Gasteiger, P. A. Kollman, H. F. I. Schaefer, and P. R. Schreiner (John Wiley & Sons, 1998), Vol. 4, pp. 2708.
D. E. Knuth, The art of computer programming, Second ed. (Addison-Wesley, Reading, Massachusetts etc., (Reprint of the 2nd edition, Reading, Massachusetts , 1973–1981).
M. Hehenberger, H. V. McIntosh, and E. Brändas, Physical Review A 10 (5), 1494 (1974).
J. P. Dahl, Correlation Between Position and Momentum. A Phase-Space View. in Fundamental World of Quantum Chemistry. A Tribute to the Memory ofPer-Olov Löwdin, edited by E. J. Brändas and E. S. Kryachko (Kluwer Academic Publishers, Dordrecht, 2003), Vol. I, pp. 237.
P. O. Löwdin, Reviews of Modern Physics 35 (3), 724 (1963).
P. O. Löwdin, International Journal of Quantum Chemistry 58 (6), 549 (1996).
Per-Olov Löwdin, “Some recent progress in the quantum theory of molecular electronic spectra”, preprint 1996 (probably printed by now). This paper discusses effective hamiltonian operators somewhat related to, although with different properties than those used in our spectroscopic work (Fig. 3 and related discussion in the present paper).
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Quack, M. (2004). Time and Time Reversal Symmetry in Quantum Chemical Kinetics. In: Brändas, E.J., Kryachko, E.S. (eds) Fundamental World of Quantum Chemistry. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0448-9_19
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