By Res Jost

Dieses "Märchen" und die anderen hier gesammelten Vorträge richten sich bewußt an ein breites Publikum im Umkreis des "Elfenbeinernen Turmes": Studierende, Dozenten, Physiker, Mathematiker, Wissenschaftshistoriker, aber auch Bildungspolitiker. Personifiziert durch große Gestalten, wie Faraday, Gauss, Boltzmann, Planck und Einstein, werden entscheidende Einflüsse in der Geschichte und Gegenwart der modernen Naturwissenschaft dargestellt. Mit historischen, kulturellen und ethischen Aspekten seiner Wissenschaft hat sich der theoretische Physiker Res Jost (1918-1990) in den letzten zwei Jahrzehnten seines Wirkens an der ETH Zürich ebenso intensiv auseinandergesetzt wie vorher etwa mit den mathematischen Grundlagen der Quantenfeldtheorie.

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This will be shown more rigorously, but will be understood in a simpler manner as follows. 40 The prototype Brans–Dicke model Consider a point mass. 5) where τ is a proper time. The inertial mass m appears only as an overall coeﬃcient, so it does not aﬀect the trajectory in space-time. This implies universal free-fall , a major expression of the WEP. 5) through the presence of the “source” on the righthand side. Generally speaking, the equation of motion will contain m beyond the extent to which it is simply factored out, hence violating the WEP.

Note also that the separated ﬁfth dimension has no curvature. We then ﬁnd s 1 1 MP2 = dy e−2|y|/ = 1 − e−2s/ . 47) ∼ 8πG 8πG5 0 16πG5 This means that MP depends weakly on the distance s, as long as 1. To show how the hierarchy problem is resolved, we consider e−s/ a fundamental Higgs ﬁeld conﬁned in the visible brane with negative tension. 48) vis denotes the four-dimensional components of the ﬁvewhere gµν vis = e−2s/ g . e. 49) 20 Introduction where veﬀ = e−s/ v0 gives the physical symmetry-breaking energy scale, which could be much smaller than the original energy scale v0 .

Since all of the experiments performed to conﬁrm Newtonian gravity have been carried out above the 1-mm scale, the laws of gravity might be diﬀerent only below this scale. We re-emphasize that the extra-dimensional space was a tiny internal space of matter ﬁelds in the KK approach, but is now a larger space wherein only gravity resides. Suppose that the fundamental theory of gravity is given by the Einstein– Hilbert term in D (= 4 + n) dimensions and the entire space-time is compactiﬁed into four-dimensional space-time times n extra dimensions.