Sabine Hossenfelder and Steve Mould on Gravitation

An accelerometer of the kind she refers to works by measuring the variable capacitance of a micro-mechanical spring as it is "stretched by the acceleration applied to it by the thing from which it is suspended," See for example https://www.siliconsensing.com/technology/mems-accelerometers/:

All accelerometers work on the principle of a mass on a spring, when the thing they are attached to accelerates then the mass wants to remain stationary due to its inertia and therefore the spring is stretched or compressed, creating a force which is detected and corresponds to the applied acceleration.

They also seem a bit confused however:

MEMS accelerometers are used wherever there is a need to measure linear motion, either movement, shock or vibration but without a fixed reference.  They measure the linear acceleration of whatever they are attached to. Acceleration is measured in m/s-2, but the convention for accelerometers is in ‘g’, or units of gravity, 1g being 9.81m/s-2.

I am not an electronics engineer, but I suspect that the way the capacitance is measured is by finding the resonant frequency of an RC or LC filter of some kind, of which the capacitance of the micro-mechanical element is a part. In order to measure the acceleration accurately one would presumably require to measure the frequency of the oscillations and perhaps take into account non-linear effects of the measuring currents upon the mechanical element. The measurement of the frequency would then be under an assumption of the time-constant actually being constant.

The equivalence principle has a long and distinguished history: Equivalence principle.

See also David Hestenes - Tutorial on Geometric Calculus, in particular the reference (16:10) to Lasenby, Doran & Gull (1998[2004]) Gravity, Gauge Theories and Geometric Algebra.

A new gauge theory of gravity is presented. The theory is constructed in a flat background spacetime and employs gauge fields to ensure that all relations between physical quantities are independent of the positions and orientations of the matter fields. In this manner all properties of the background spacetime are removed from physics, and what remains are a set of `intrinsic' relations between physical fields. The properties of the gravitational gauge fields are derived from both classical and quantum viewpoints. Field equations are then derived from an action principle, and consistency with the minimal coupling procedure selects an action that is unique up to the possible inclusion of a cosmological constant. This in turn singles out a unique form of spin-torsion interaction. A new method for solving the field equations is outlined and applied to the case of a time-dependent, spherically-symmetric perfect fluid. A gauge is found which reduces the physics to a set of essentially Newtonian equations. These equations are then applied to the study of cosmology, and to the formation and properties of black holes. The existence of global solutions enables one to discuss the properties of field lines inside the horizon due to a point charge held outside it. The Dirac equation is studied in a black hole background and provides a quick derivation of the Hawking temperature.

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Here's Steve Mould's recent video on Gravitation:

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