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A general theory of inertia tends to be circular because momentum and therefore inertia are taken as assumptions in quantum field theories. In this paper we explore instead using position uncertainty to infer inertia with mediation by quasi-measurement interactions. This method avoids attachment to the reference frame of the source masses and is thus completely relativistic, overcoming a conflict between historical theories of inertia and relativity. We investigate what laws of motion result, and whether natural explanations for equivalence and dark energy emerge.
or clock paradox has been a subject of lively discussion and occasional disagreement
among both relativists and the public for over 100 years, and continues to attract
physicists who write papers giving new analyses or defending old ones, even though
many physicists now consider the matter only of educational interest. This paper
investigates the number of papers, which is increasing, and trends in explanations,
some of which are now targeted at professional physicists and other of which are
targeted at optical or radar visualization rather than problem solving. Observations
of students indicate that the latest techniques help but only somewhat. An analysis
is made of 21 previous treatments appearing in the education related American Journal
of Physics, Einstein’s discussions and several other pedagogical papers. A new memory
aid for simultaneity transformation is given that puts it on a par with “time dilation”
and “length contraction” for quick and easy problem visualization. The point of
view of a trailing twin is introduced to show how simultaneity changes account for
missing time in the turnaround. Length contraction is treated on equal footing with
time dilation, and Swann’s insight into clocks is extended to lengths. Treatments
using the conventionality of simultaneity are seen as equivalent to choice of co-moving
frames. Responses to difficult questions are suggested which avoid being dismissive,
and engage students’ critical thinking.
In this paper, we derive an explicit form in terms of
end-point data in space-time for the classical action, i.e. integration of the Lagrangian
along an extremal, for the nonlinear quartic oscillator evaluated on extremals.
The problem analytically investigated is that a thin free plate of mild-steel struck at normal incidence by a flat ended rigid rod moving at high velocity. As in quasi-static deformation by extended slip, the strain-rate tensor is solenoidal and under dynamic loading conditions the Tresca yield criterion is modified so that the solenoidal property replaces the hypothesis of a viscoplastic overstress. Overstress then arises from inertial body forces and the high magnitudes found, in the following, for these forces are due to the influence of the propagating boundary. Two new theorems are proven. These theorems show that the deflection in the plate is entirely transverse, even in the case of indefinitely large punch deflections, and that the lines of equal transverse deflection in the plate are also principal lines of stress and strain-rate, as are the lines of steepest descent. A formula is obtained giving the inertial force opposing the punch as a function of the time and the theoretical deflection profile on a plate deformed by a flat-ended punch of circular section is presented. The stresses in the plate are then analyzed and it is shown that the stress inside the boundary in the direction of propagation, equals ρc2where ρ is the mass density of the plate material and the boundary wave propagates at speed c which, it is shown, is equal to one-half of the velocity of elastic waves of rotation in the solid concerned.