The Principles of General Relativity

This chapter considers what the theory actually achieved and specifically reexamines the meaning of the relativity principle. The question of its meaning was raised by critical observers whose comments led to a partial reinterpretation of general relativity. The German physicist Erich J. Kretschmann argued that the principle of general covariance has no physical content and only constitutes a mathematical requirement. This contention generated an exchange of letters in which Einstein conceded Kretschmann's criticism, but Einstein does not mention Kretschmann's remarks explicitly in his book. The chapter discusses these developments and correlates them with his correspondence with colleagues and with other texts he published during the formative years.

A Method for Classifying Co-contraction of Lumbar Muscle Activity

Concurrent activation of muscles on opposite sides of joints is a common phenomenon. In simple planar mechanical systems, it is easy to identify such an electromyographic pattern as co-contraction of agonist and antagonist muscles. In complex 3-D systems such as the lumbar spine, it is more difficult to precisely identify whether EMG recordings represent co-contraction. Qualitative definitions of antagonist muscles emphasize that their actions wholly oppose the action of the prime movers. The qualitative definition of antagonist muscles was used to formulate a mathematical requirement for there to be co-contraction of agonists and antagonists. It was shown that the definition of co-contraction implies muscle activity beyond what is required to maintain equilibrium. The method was illustrated by classifying EMG recordings made of the lumbar region musculature during tasks involving combined torso extension and axial twisting loads. The method, which identified muscle activity in excess of that required to maintain static equilibrium, could be used to identify conditions in which muscle activation is required for something other than merely maintaining moment equilibrium.

An analytical study of a two‐layer transient thermal conduction problem as applied to soil temperature surveys

The soil temperature survey is an inexpensive exploration method in groundwater and geothermal resource investigations. In its simplest form, temperatures measured in shallow holes are analyzed to deduce variations in material properties. Typical interpretation schemes are based on simple, one‐layer solutions to the Fourier conduction equation using the annual solar cycle as a surface heat source. We present a solution to the more complicated two‐layer problem that can be computed using inexpensive personal computers and spreadsheet software. The most demanding mathematical requirement is the ability to manipulate a [Formula: see text] matrix. Testing the solution over a range of thermal diffusivity values expected in common soils and rocks reveals that the solution is very sensitive to variations in the thermal diffusivity of the surface layer and to the depth of the interface with the lower layer. When the boundary to the lower layer is less than about 10 m deep, a soil temperature survey is expected to be sensitive to the diffusivity variations in the lower layer. Because variations in shallow thermal properties often can be significant, this two‐layer method should be useful in areas with distinct shallow layering, (e.g., where there is a shallow water table or a thin soil layer).

Force Budget: I. Theory and Numerical Methods

A practical method is developed for calculating stresses and velocities at depth using field measurements of the geometry and surface velocity of glaciers. To do this, it is convenient to partition full stresses into lithostatic and resistive components. The horizontal gradient in vertically integrated lithostatic stress is the driving stress and it describes the horizontal action of gravity. The horizontal resistive stress gradients describe the reactions. Resistive stresses are simply related to deviatoric stresses and hence to strain-rates through a constitutive relation.A numerical scheme can be used to calculate stresses and velocities from surface velocities and slope, and from ice thickness. There is no mathematical requirement that the variations in these quantities be small.

The Reconstruction of the Mathematical Requirement

The following statement contains no material that has been decided upon by the Committee on the Curriculum in Algebra. I must assume personal responsibility for any mistakes of judgment.