A uniformly rotating frame is defined as the rest frame of a particle revolving with constant velocityω in a circle about theZ-axis of an inertial frame Σ0. Under the conditionz=Z,r=R, theoretical constraints are established for the solution of the transformation problem Σ0→Σω
r,Σω
r being the cylindrical subframe of Σω. The unique solution of the problem in cylindrical coordinates is isomorphic to the special Lorentz transformationL
x, withβ=v/c replaced byβ
r=ωr/c. Hence the intrinsic geometry on the surface of a rotating cylinder is Euclidean. Though there exists no complete intrinsic geometry on the surface of a rotating disk, the geodesics on it are straight lines while the circumference of a concentric circle isK
r2πr as predicted by Einstein.

Rotating frames in special relativity

In the history of modern physics the name of Ernst Mach has left two distinct marks, known as Mach number and Mach PrincipleA The former refers to Mach as an experimentalist, the second as a philosopher of science and critic of Newton's Principia. It is the second aspect that interests us in this paper. There is no need today to deal with Mach's epistemological doctrine which once was the focus of controversy when Mach's philosophy of science was under discussion. 2 Today, we realize that the doctrine of the 'neutral elements' as expounded in the Analyse der Empfindungen is but a miscarried by-product of Mach's endeavour to create, on the basis of historical, methodological and psychological studies, a unifying philosophy of science that would also solve the psycho-physical problem. The centre of interest in Mach's philosophy of science lies not with epistemology or logic of science but with the historical development of science as a human activity a fact that has been implicitly acknowledged by Mach himself 3, but apparently 'forgotten' by most of his followers. Oddly enough, it was Mach's comment on Newton's mechanics and not the pertinent ideas of Riemann that was seized upon by Einstein as one of his guides to a new theory of gravitation. No wonder that it came as a shock to Einstein when it turned out that his 'Mach Principle' was not satisfied by the new theory. As a consequence the latter was generally held by the experts to have no logical connection at all with Mach's analysis. In the last 10 years more sophisticated interpretations of Mach's ideas have been given and shown to be satisfied by certain cosmological models with closed finite spaceA This has reopened the question as to the logical relation between Mach's ideas and Einstein's theory. In the following this question will be commented on within the frame of a wider discussion. Our primary object is to clarify the relations be-

Einstein's theories and the critics of Newton

In the history of modern physics the name of Ernst Mach has left two distinct marks, known as Mach number and Mach Principle.1 The former refers to Mach as an experimentalist, the second — as a philosopher of science and critic of Newton’s Principia. It is the second aspect that interests us in this paper.

Einstein’s Theories and the Critics of Newton — Intertheory Relations II

An exhaustive treatment of this theme is impossible in this discussion. I shall therefore confine myself to some remarks of philosophical relevance.

Space-Times and State Spaces

I shall talk about two basic concepts of physics which — though of very different nature — are not entirely disconnected even though the connection is different in different theories. The two concepts are ‘inertial frame’ and ‘mass’. The theories we are going to consider are Newtonian mechanics, c-mechanics (mechanics of Special Relativity), Einstein’s theory of gravitation, and the theory of fundamental particles (which is still in the making); h-mechanics (quantum mechanics) and h-c-theory (quantum field theory) will not be considered until the end. c-theory will play a particularly important role: all too often Newtonian mechanics and Einstein’s theory of gravitation are directly contrasted with one another; this obscures the fact that c-mechanics is intermediate between the two, not only historically but also mathematically and logically.

On the Logic of ‘Inertial Frame’ and ‘Mass’

The 60th anniversary of Einstein’s Special Theory seems to be an appropriate occasion to ask ourselves the question: how do we look upon this theory today, in particular, do we still believe in 

(i)

the truth of the two principles used by Einstein to establish the Lorentz group (LG), and




(ii)

the necessity of using them for this purpose.

M. Strauss

Papers

The Lorentz Group: Axiomatics — Generalizations — Alternatives