Localization and the interface between quantum mechanics, quantum field theory and quantum gravity II: The search of the interface between QFT and QG

The main topics of this second part of a two-part essay are some consequences of the phenomenon of vacuum polarization as the most important physical manifestation of modular localization. Besides philosophically unexpected consequences, it has led to a new constructive “outside-inwards approach” in which the pointlike fields and the compactly localized operator algebras which they generate only appear from intersecting much simpler algebras localized in noncompact wedge regions whose generators have extremely mild almost free field behavior.Another consequence of vacuum polarization presented in this essay is the localization entropy near a causal horizon which follows a logarithmically modified area law in which a dimensionless area (the area divided by the square of dR where dR is the thickness of a light-sheet) appears. There are arguments that this logarithmically modified area law corresponds to the volume law of the standard heat bath thermal behavior. We also explain the symmetry enhancing effect of holographic projections onto the causal horizon of a region and show that the resulting infinite dimensional symmetry groups contain the Bondi–Metzner–Sachs group. This essay is the second part of a partitioned longer paper.     

Holism and structuralism in U(1) gauge theory

After decades of neglect philosophers of physics have discovered gauge theories—arguably the paradigm of modern field physics—as a genuine topic for foundational and philosophical research. Incidentally, in the last couple of years interest from the philosophy of physics in structural realism—in the eyes of its proponents the best suited realist position towards modern physics—has also raised. This paper tries to connect both topics and aims to show that structural realism gains further credence from an ontological analysis of gauge theories—in particular U(1) gauge theory. In the first part of the paper the framework of fiber bundle gauge theories is briefly presented and the interpretation of local gauge symmetry will be examined. In the second part, an ontological underdetermination of gauge theories is carved out by considering the various kinds of non-locality involved in such typical effects as the Aharonov–Bohm effect. The analysis shows that the peculiar form of non-separability figuring in gauge theories is a variant of spatiotemporal holism and can be distinguished from quantum theoretic holism. In the last part of the paper the arguments for a gauge theoretic support of structural realism are laid out and discussed.     

Did Einstein prove E=mc2?

Although Einstein's name is closely linked with the celebrated relation E=mc² between mass and energy, a critical examination of the more than half dozen “proofs” of this relation that Einstein produced over a span of forty years reveals that all these proofs suffer from mistakes. Einstein introduced unjustified assumptions, committed fatal errors in logic, or adopted low-speed, restrictive approximations. He never succeeded in producing a valid general proof applicable to a realistic system with arbitrarily large internal speeds. The first such general proof was produced by Max Laue in 1911 (for “closed” systems with a time-independent energy–momentum tensor) and it was generalized by Felix Klein in 1918 (for arbitrary time-dependent “closed” systems).     

Sur les interactions entre l'axe embryonnaire normal et les formations secondaires produites par la centrifugation de la blastula et de la gastrula chez les Amphibiens

Summary The complexes of organs induced by centrifugation of Amphibia blastulas or gastrulas interfere with the primary axis of the embryo: (a) explantates of centrifugated ectoblast are always poorer in differentiation than the same ectoblast leftin situ; (b) the complexes arising in the ventral part of the embryo have the tendency to elongate parallel to the main axis of the embryo and become connected with the head of the primary embryo; (c) grafts made on Axolotl eggs show that, when the reaction is poor, it cannot express itself except in cases of close contact with the normal organizer; (d) reciprocally, implants of strongly reacting centrifugated ectoblast placed on the ventral part of a normal gastrula of Pleurodeles induce modifications of the primary organs, viz. the transformation of the first somites into chorda.These facts lead to the conclusion that quantitative factors—and not qualitative—are effective in the differentiation of the embryo.     

Empirical adequacy: A partial structures approach

Based on da Costa's and French's notions of partial structures and pragmatic truth, this paper examines two possible characterizations of the concept of empirical adequacy, one depending on the notion of partial isomorphism, the other on the hierarchy of partial models of phenomena, and both compatible with an empiricist view. These formulations can then be employed to illuminate certain aspects of scientific practice.An empirical theory must single out a specific part of the world, establish reference to that part, and say—by way of contingent, substantial claim about the world—that its models fit that. Now, how exactly can this be done? Bas C. van Fraassen (1993, p. 9)     

On Minkowskian branching structures

In Belnap's [Branching space-time. Synthese, 92, 385–434. ‘Postprint’ archived at http://philsci-archive.pitt.edu/archive/00001003] theory of branching space-times (BST) Our World's possible histories are thought of as space-times, yet the theory has models in which histories do not resemble relativistic space-times or any other physical space-times. The aim of this paper is to define a certain class of BST models, called ‘Minkowskian Branching Structures’ (MBSs), in which histories are isomorphic to Minkowski space-time. By focusing on these models rather than on general BST models, we hope that one may be able to improve on earlier BST analyses of physical phenomena. Also, introducing MBSs sets the stage for recent discussions about whether or not branching is physically feasible.     

Legend naturalism and scientific progress: An essay on Philip Kitcher's : The advancement of science

Philip Kitcher's The Advancement of Science sets out, programmatically, a new naturalistic view of science as a process of building consensus practices. Detailed historical case studies—centrally, the Darwinian revolutio—are intended to support this view. I argue that Kitcher's expositions in fact support a more conservative view, that I dub ‘Legend Naturalism’. Using four historical examples which increasingly challenge Kitcher's discussions, I show that neither Legend Naturalism, nor the less conservative programmatic view, gives an adequate account of scientific progress. I argue for a naturalism that is more informed by psychology and a normative account that is both more social and less realist than the views articulated in The Advancement of Science.     

Gamma aminobutyric acid induced changes in the spontaneous firing rates of insect neurons

Zusammenfassung -Aminobuttersäure (GABA) vermindert die Impulsfrequenz der spontan-aktiven Nervenzellen beim Insekt. Wirksame Konzentrationen betragen 0,1–25 · 10^–4 M. Ein unerwartetes Ergebnis war die Beobachtung, dass nach Applikation von GABA eine Erhöhung der Impulsfrequenz vor der Verminderung stattfindet.

---

---

This investigation was supported in part by the NSF College Teacher Research Participation Program, Grant No. GY-682, and by NSF Undergraduate Research Participation Program, Grant No. GY-151. — We thank Mr.A. McAfee, our undergraduate participant, for his assistance in this investigation.     

On the chemical nature of the heat-stable exotoxin ofBacillus thuringiensis

Zusammenfassung Das hitzestabile Exotoxin vonBacillusthuringiensis — auf Insekten spezifisch toxisch wirkend — wurde aus dem Kulturmedium angereichert und stark gereinigt. Sämtliche toxischen Fraktionen zeigen ein Absorptionsmaximum bei 258–260 nm, ein Absorptionsminimum bei 232–234 nm und eine positive Aldopentosereaktion. Bei der toxischen Substanz scheint es sich um ein Nucleosid oder Nucleotid des Adenins oder Uracils zu handeln.     

Zur Polymorphie eines Chromosoms innerhalb von Populationen des LaufkäfersCarabus auronitens Fabr

Summary C. auronitens has 26 autosomes (2n), from which one pair — calledA-chromosomes — is relatively long.A-chromosomes consist of an euchromatic and a heterochromatic arm. In 63% of the individuals, theA-chromosomes are intraindividually anisomorph with regard to the length of their heterochromatic arm. According to its length, this arm shows 0–3 secondary constrictions. Hence there are at least 4 different forms of theA-chromosome.     

Detection and substitution-pattern determination of guanidines

Summary The guanidine function can be detected and its substitution pattern determined taking into account the¹H-NMR signals of the N–H and N–C–H groups. Satisfactory results were obtained with mono-to penta-substituted guanidines (as picrate salts).Part XX ofStudies on Plants; preceding part,R. A. Corral, O. O. Orazi andI. A. Benages, Tetrahedron29, 205 (1973).     

Catalysis and inhibition of the oxidative degradation of deoxyribonucleic acid by catalase showing maximum catalytic effect in pico-molar concentrations

Zusammenfassung Es wird gezeigt, dass eine 2·10^–12 molare Katalase-Lösung den durch Luftsauerstoff sowie durch ein Wasserstoffperoxid-lieferndes Cytostaticum bewirkten — nicht aber den durch zugesetztes Wasserstoff-peroxid verursachten — Abbau von Desoxyribonucleinsäure (DNS) wesentlich verstärkt. Mitsteigender Katalase-Konzentration wird dieser Effekt immer kleiner und verschwindet schliesslich. Im Falle des Cytostaticums wird der DNS-Abbau durch Katalase-Konzentrationen über 10^–11 M/1 inhibitiert. Dieser Übergang von Katalyse zu Inhibition wird auf die Fähigkeit der Katalase zu peroxydatischer bzw. häminkatalytischer Wirkung einerseits und zu katalatischer Wirkung andererseits zurückgeführt, wobei mit steigender Katalase-Konzentration eine Verschiebung zugunsten der katalatischen Reaktion erfolgt.     

Cold tolerance of two Antarctic terrestrial arthropods

Summary Two Antarctic arthropods,Alaskozetes antarcticus (Acari) andCryptopygus antarcticus (Collembola) possess the ability to supercool to –30°C, but the realisation of this potential is dependent on starvation. The mite contains glycerol in a concentration of about 1% fresh weight.Acknowledgments. We thank the British Antarctic Survey, Cambridge and the Zoological Institute. University of Oslo for support and reasearch facilities, and the Natural Environment Research Council for a research grant (GR. 3/2797). We are grateful to Ms I. Tambs-Lyche for technical assistance.     

Vegetation structure and primary production in acidified lakes in southwestern Sweden

Summary Research during the last two decades has clearly pointed out that dramatic ecosystem changes have occured in lakes due to deposition of acid substances and decreased pH. Today a large number of lakes and running waters in Scandinavia are suffering biological damage with disappearing fish populations, overgrowth of the bottom by mosses and filamentous algae, reduced invertebrate fauna, increased transparency etc.—Of all documented biological changes the effect on macrophyte succession, in particular that ofSphagnum, is the most striking effect. Along with the growth of filamentous algae, these changes have brought about major shifts in the composition of the primary producers. The biomass in one lake was estimated to be 6.5 t (dry wt) corresponding to about 24 g m^–2, the relevant proportions being 52% forSphagnum, 34% forLobelia and 15% forIsoetes. Percentage production in the whole lake is 54% forSphagnum, 29% forLobelia and 17% forIsoetes, which gives an estimated production of 2.9 t yr^–1 or 9 g m^–2 yr^–1.Sphagnum is a recent flora element and its occurrence is related to the acidification of the lakes. The investigations also show that the growth ofLobelia is reduced in acid lakes compared to other oligotrophic lakes due to shading by the benthic mat of filamentous algae, detritus andSphagnum debris.—One can conclude that there are several quantitative and qualitative changes in the macrophyte community which are related to acidification. One can also conclude that liming of lakes cause elimination ofSphagnum and some increase in the production ofIsoetids.     

The autonomy of models and explanation: anomalous molecular rearrangements in early twentieth-century physical organic chemistry

During the 1930s and 1940s, American physical organic chemists employed electronic theories of reaction mechanisms to construct models offering explanations of organic reactions. But two molecular rearrangements presented enormous challenges to model construction. The Claisen and Cope rearrangements were predominantly inaccessible to experimental investigation and they confounded explanation in theoretical terms. Drawing on the idea that models can be autonomous agents in the production of scientific knowledge, I argue that one group of models in particular were functionally autonomous from the Hughes–Ingold theory. Cope and Hardy’s models of the Claisen and Cope rearrangements were resources for the exploration of the Hughes–Ingold theory that otherwise lacked explanatory power. By generating ‘how-possibly’ explanations, these models explained how these rearrangements could happen rather than why they did happen. Furthermore, although these models were apparently closely connected to theory in terms of their construction, I argue that partial autonomy issued in extra-logical factors concerning the attitudes of American chemists to the Hughes–Ingold theory. And in the absence of a complete theoretical hegemony, a degree of consensus was reached concerning modelling the Claisen rearrangement mechanism.     

Decision theory and information propagation in quantum physics

In recent papers, Zurek [(2005). Probabilities from entanglement, Born's rule p_k=|ψ_k|² from entanglement. Physical Review A, 71, 052105] has objected to the decision-theoretic approach of Deutsch [(1999) Quantum theory of probability and decisions. Proceedings of the Royal Society of London A, 455, 3129–3137] and Wallace [(2003). Everettian rationality: defending Deutsch's approach to probability in the Everett interpretation. Studies in History and Philosophy of Modern Physics, 34, 415–438] to deriving the Born rule for quantum probabilities on the grounds that it courts circularity. Deutsch and Wallace assume that the many worlds theory is true and that decoherence gives rise to a preferred basis. However, decoherence arguments use the reduced density matrix, which relies upon the partial trace and hence upon the Born rule for its validity. Using the Heisenberg picture and quantum Darwinism—the notion that classical information is quantum information that can proliferate in the environment pioneered in Ollivier et al. [(2004). Objective properties from subjective quantum states: Environment as a witness. Physical Review Letters, 93, 220401 and (2005). Environment as a witness: Selective proliferation of information and emergence of objectivity in a quantum universe. Physical Review A, 72, 042113]—I show that measurement interactions between two systems only create correlations between a specific set of commuting observables of system 1 and a specific set of commuting observables of system 2. This argument picks out a unique basis in which information flows in the correlations between those sets of commuting observables. I then derive the Born rule for both pure and mixed states and answer some other criticisms of the decision theoretic approach to quantum probability.     

Behavioral phenomenology of sleep (somatic and vegetative)

Conclusions The foregoing analysis of behavioral sleep phenomenology shows that the most significant factual and theoretical aspects of sleep can be logically organized only according to several criteria, it being impossible to choose a singli one as truly paradigmatic. For this reason an ordinal classification of sleep phases was preferred. This fact does not detract from the usefulness of classifications based consistently on 1 criterion at a time (e.g.: synchronized-desynchronized; quiet-active; orthodoxical-paradoxical; NREM-REM; homeostatic-poikilostatic; spindle wave-slow wave-fast wave; external appetitive-internal appetitive-internal consummatory; and so on). In this respect, the bioelectrical classification is surely the best as it allows an analytical subdivision of the evolution of sleep with high resolving power^137–139. In particular, the electroencephalographic activity of late phase II (stage 4 in man¹³⁹ and slow wave¹¹ or deep slow wave¹⁴⁰ sleep in the cat) appears to be related to the triggering mechanisms and to the quantitative regulation of the circadian amount of phase III^3,5,11,140. However, in extending the field of functional implications of sleep phenomenology other criteria may be more significant. In fact, the somatic and vegetative events of sleep also lend themselves to an analysis according to the behavioral model of ethology^6,141–144 and the theory of homeostasis^{3–5, 145}, respectively. As an example, a number of classifying criteria are indicated in the table, where others, particularly neurochemical ones^146,147, could be added. At any rate, the difficulty of organizing sleep events into a satisfactory operational scheme is due to the fact that sleep is still an open problem as far as its mechanisms and functional significance are concerned.     

Growth ofNostoc muscorum mutants in the presence of diuron (DCMU) and L-methionine-DL-sulfoximine

Summary Diuron (DCMU) is inhibitory to the photoautotrophic and photoheterotrophic growth of the N₂-fixing blue-green algaNostoc muscorum at concentrations of 1.0×10^–5 M and 2.0×10^–5 M, respectively. A mutant of this organism resistant to 5.0×10^–5 M DCMU under its photoheterotrophic growth conditions, with the ability to utilize DCMU as a carbon and nitrogen source for growth, and complete inability to grow photoautotrophically has been isolated. With the apparent defect in its photosynthetic ability, it is suggested that theDCMU ^r mutant lacks the step inhibited by 1.0×10^–5 M DCMU, and metabolizes DCMU by an existing enzyme system in the absence of such inhibition. That this enzyme may be glutamine synthetase (GS) is explained with the help of a L-methionine-DL-sulfoximine (MSO)-resistant mutant ofN. muscorum which is able to grow faster with 2.0×10^–5 DCMU and is known to contain an altered GS.Thanks are due to the Council of Scientific and Industrial Research, CSIR Complex, Govt. of India, New Delhi-110012, for appointing the author to the Scientists' Pool for undertaking researches on the physiological and genetic controls of nitrogen metabolism in blue-green algae, a part of which is presented in this literature.     

Das Parallelenproblem im Corpus Aristotelicum

Summary In the Corpus Aristotelicum are numerous items suggesting that the assertion of the fifth postulate in Euclid's Elements had been preceded by attempts to demonstrate this postulate itself, or some equivalent fundamental proposition, within the rigorous frame of Absolute Geometry in Bolyai's sense. Thus geometers contemporary with Aristotle tried to solve the problem which became known commonly in later centuries as the Problem of Parallels.Probably these geometers first attempted a direct solution. Only one text at our disposal supports this hypothesis: (1) Anal. Prior. 65 a 4–7. My analysis below in Chapter I shows that a mathematical meaning can be read from this somewhat obscure text only if it is interpreted as an allusion by Aristotle to those geometers who believe they are demonstrating, obviously in an absolute way, the proposition Elem. I 29, equivalent to the fifth postulate, but do not realize that in the process they are using lemmas which result themselves from the proposition to be demonstrated. Such a lemma would assert the uniqueness of the parallels, existence of which was shown in an absolute way in Elem. I 27. My conjecture and reconstruction afford a natural explanation for an inconsequence singular for Book I of the Elements, namely, the presence of the proposition Elem. I 31 in the purely Euclidean part of the book, in spite of the fact that the assertion merely repeats the absolute proposition Elem. I 27 without explicitly containing any Euclidean element.It is probable that the failure of these direct attempts led to an indirect approach to the problem through reductio ad absurdum of some hypothesis contrary to what was to become Postulate V or to some equivalent proposition. Numerous texts survive from which it is clear that geometers contemporary with Aristotle followed fairly far the consequences of an hypothesis contrary to the fifth postulate, obtaining important results which are partly identical with some theorems of Saccheri. Some of these texts attest first of all that what Saccheri called the Hypothesis of the Obtuse Angle had been stated in an independent and explicit way and that the fundamental result, identical with Prop. 14 of Saccheri's Euclides ab omni naevo vindicatus (1733), had been obtained, namely, that within Bolyai's Absolute Geometry this hypothesis leads to the remarkable formal contradiction that parallels intersect. This conclusion followed from two different formulations of the Obtuse Angle Hypothesis: (2) Anal. Prior. 66a 11–14, if the exterior angle (formed by a secant which intersects two parallel straight lines) is smaller than the interior angle (opposite and situated on the same side of the secant), and (3) 66a 14–15, if the sum of the angles in a triangle is greater than 2R. Finally, an item in (4) Ethica ad Eudemum 1222b 35–36 shows us that by investigating the Obtuse Angle Hypothesis, the Greek geometers also discovered the quadrilateral in which the sum of the angles is equal to 8R; this quadrilateral, which does not appear even in Saccheri's book, is the maximal quadrilateral of the Riemann geometry, a quadrilateral degenerated into a straight line closed upon itself (Chapter IV 20).Nowhere in the Corpus does the Hypothesis of the Acute Angle appear in an independent formulation. Nevertheless in (5) Anal. Poster. 90a 33–34 this Hypothesis is mentioned along with the other two: namely, Aristotle states that the essence of the triangle consists in the sum of its angles' being equal to, greater than or less than 2R (Chapter V 27). The formulation of the fifth postulate in the Elements allows greater probability to the conjecture of independent existence of the Acute Angle Hypothesis as well. Indeed, in its original formulation the fifth postulate is redundant, since it unnecessarily specifies in which of the half-planes (bounded by the secant) the intersection of the two straight lines occurs; this specification is itself a theorem. The Acute Angle Hypothesis must have been formulated not only symmetrically to (3) Anal. Prior. 66 a 14–15, that is, the sum of the angles of the triangle is less than 2R, as results from (5) Anal. Poster. 90 a 33–34, but also symmetrically to (2) Anal. Prior. 66 a 11–14. In the latter case the following final conclusion should have been reached in order to reduce to absurdity the Acute Angle Hypothesis: Two straight lines cut by a secant are incident if the sum of the interior angles (on the same side of the secant) is smaller than 2R, and the incidence occurs on that side of the secant where the sum of the angles is less than 2R. In the frame of the Acute Angle Hypothesis, this end conclusion is relevant only if this final specification (concerning the half-plane where the incidence occurs) is explicitly emphasised. According to my conjecture, it was precisely the practical impossibility of reaching this conclusion as a theorem of Absolute Geometry that later determined Euclid to transpose this decisive end conclusion from the Acute Angle Hypothesis, without changing its wording, and to include it among the postulates (Chapter II 13).A queer passage of Proklos (In primum Euclidis Elementorum, ed. Friedlein p. 368, 26–369, 1) in which the Acute Angle Hypothesis is presented in the form of a Zenonian paradox reinforces the conjecture that this hypothesis was studied independently by the ancient geometers (Chapter VI 33). Thus failure to solve the Problem of Parallels preceded not only the later Non-Euclidean geometry but also Euclidean geometry itself.The general undifferentiated Contra-Euclidean Hypothesis appears in the following form in all the other texts examined: The sum of the angles in the triangle is not equal to 2R. This hypothesis is nowhere qualified by Aristotle as being absurd or impossible: On the contrary, he takes it always as being just as much justified a priori as is the Euclidean theorem Elem. I 32 which contradicts it. For instance in (6) Anal. Poster. 93 a 33–35 Aristotle puts the problematical alternative: Which of the two propositions is right (or, which of the two constitutes the Logos, the raison d'être of the triangle), the one that states that the sum of the angles in the triangle is equal to 2R, or on the contrary, the one that states that the sum of the angles in the triangle is not equal to 2R (Chapter V 28)?In a number of texts the theorem Elem. I 32 itself and the general Contra-Euclidean Hypothesis are treated as being a sort of principle, and stress is laid on the idea that the logical consequences of each of these items invariantly preserve its specific (Euclidean or non-Euclidean) geometrical content [(7) 1187 a 35–38 (Chapter IV 18); (8) 1222 b 23–26 (Chapter IV 19); (9) 1187 b 1–2 (Chapter IV 18); (10) 1222 b 41–42 Chapter IV 21); (11) 1187 b 2–4 (Chapter IV 18)]; (12) Physica 200 a 29–30: If the sum of the angles in the triangle is not equal to 2R, then the principles of geometry cannot remain the same (Chapter V 25); (13) Metaph. 1052 a 6–7: It is impossible that the sum of the angles in the triangle be sometimes equal to 2R and sometimes not equal to 2R (Chapter V 24). Finally, the most important item of this sort is to be found in (14) De Caelo 281 b 5–7: If we accept as a starting hypothesis that it is impossible for the sum of the angles in the triangle to be equal to 2R, then the diagonal of the square is commensurable with its side (Chapter III).Another group of texts reveal Aristotle's attitude as regard these Contra-Euclidean theorems: (15) 1222 b 38–39 (Chapter IV 20); (16) 200 a 16–19 (Chapter VI 30); (17) 402 b 18–21 (Chapter VI 31); (18) 171 a 12–16 (Chapter VI 32); (19) 77 b 22–26 (Chapter V 26); (20) 101 a 15–17 (Chapter VI 31); (21) 76 b 39–77 a 3 (Chapter VI 31). These passages reveal Aristotle's conviction that these paradoxical Contra-Euclidean propositions (which cannot be annihilated by reductio ad absurdum) are nevertheless inacceptable as bad, probably because their graphical construction requires curved lines for representing the concept of straight lines.Finally, another group of texts show that Aristotle sensed in a way the necessity of adding to the foundations of Geometry a new postulate, from which the proposition Elem. I 32 should follow rigorously.

---

---

Aram Frenkian zum Gedächtnis

---

Vorgelegt von J. E. Hofmann     

Age and evolution of bacteria

Summary Age and evolution of bacteria can be estimated, including facts and hypotheses belonging to morphology, biochemistry, paleontology, ecology and pathogenicity. The corresponding dates are summarized in the following.About 3.5×10⁹ years: Origin of heterotrophic eobiontes.—About 3.0×10⁹ years: The increasing lack of prebiogenic substances is due to the evolution of the respiratory pathway, that is due to the evolution of the photoautotrophy and now released O₂ is due to the evolution of strictly aerobic cells. There is, simultaneously, a transition of spheres to long forms, development of an amoebalike motility, the evolution of spirochetes and the substitution of cholesterol for cardiolipin in the more evolved cells (i.e. strictly aerobic cells etc.).—About 2.0×1.0×10⁹ years: Evolution of the eucyte by symbiosis of a great, primitive, anaerobic, cholesterol-containing cell with a little, strictly aerobic, cardiolipin-containing cell, with a spirochete and in some extent also with photoautotrophic cell.—About 1.0×10⁹ years (maximum: 1.8–1.5×10⁹ years, minimum: 7×10⁸ years): Evolution of metazoa and begin of cell differentiation.—About 2.0–1.0×10⁹ years: Evolution of the bacterial murein sacculus and then development of flagella mediated motility.—About 6×10⁸ years (maximum:1.0×10⁹ years, minimum: 4.5×10⁸ years): Evolution of the gram-negative cell wall.—About 4.0×10⁸ years: Evolution of the gram-positive cell wall.—About 5.0×10⁸ years: Gram-negative, strictly anaerobic bacteria become the first enteric bacteria in coelenterates. About 4.0×10⁸ years: gram-negative, microaerophilic bacteria become Enterobacteriaceae in vertebrates in addition to the strictly anaerobic organisms.—About 3.0–2.0×10⁸ years: Consolidation of the Salmonella in reptiles.—About 2.0–1.5×10⁸ years: Consolidation of Escherichia and other coliform species in mammals.—About 10⁶ years: Evolution of typically human pathogenic organisms, transmitted in homogeneous-homonomous infection ways, i.e. N. gonorrhoeae, S. typhi, T. pallidum, etc.Dedicated to Prof. H. Habs, Bonn, to his 75th anniversary on 11 September 1977.Acknowledgment. I thank Prof. F. Müller, Hamburg, and Prof. P. Sitte, Freiburg i. Br., for stimulating discussions.