Foucault Pendulum

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At approximately 2:32 in the above video, the professor discusses what rotation the Foucault pendulum is sensitive to, and brings up a conjecture by Ernst Mach, stating "The Foucault pendulum is measuring rotation relative to the universe as a whole." I was wondering if there have been any recent developments/discoveries with regards to the Foucault pendulum that would substantiate this conjecture, or if this is a purely metaphysical conjecture?

Cleonis

First, it's a misattribution; Ernst Mach did not make any statement in such a direction, he was against doing so.

What Ernst Mach did was argue that science should limit itself to description of Nature. According to Mach physics should not assume anything. According to Mach the only task was do find the most economic representation that reproduces the observation.

To illustrate how extreme Mach's philosophy of physics was: by the time most scientists were convinced of the existence of atoms Mach argued that there was no hard evidence for the existence of atoms, and therefore science ought to be uncommitted as to whether atoms exist. That is, all of Mach's contemporaries decided that the available circumstantial evidence for the existence of atoms was sufficient, but Mach argued that only hard evidence was enough, and circumstantial evidence required some level of assumption.


In the case of newtonian mechanics Mach argued as follows:
We observe that if we describe all motion as motion with respect to the fixed stars then the laws of motion take a simple form. (By contrast: if you were to use, say, a geocentric model for the motion of celestial bodies then you end up with desperately complicated laws of motion.)

Ernst Mach prescribed as follows:
The reason to use the fixed stars as reference for all motion is that then the laws of motion have the simplest form possible. We should not speculate why the laws of motion take their simplest form in that case; such speculation is beyond the scope of proper science. (As I said, Mach's philosophy of science was extreme, and he hasn't been followed.)


The observation is that the plane of swing of a pendulum remains pointing in the same direction. I noticed a video made by some Airbus engineers with a pendulum swinging inside an airplane in midflight. As the airplane turns the pendulum swing keeps pointing in the same direction

The pendulum plane of swing is unaffected by the bulk of the airplane. The philosophical question is: is the pendulum bob in some sense guided to keep its orientation with respect to the fixed stars? If so, is that guidance supplied locally, or is there some physical connection with the Universe as a whole? As I said, Mach argued that such speculation is not science.

Physicists do like to speculate about that and the framework for doing so is General Relativity.

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I don't understand what with respect to the fixed stars means, or how this infers the simplest form of the laws of motion. Is motion with respect to the fixed stars analogous to motion with respect to an absolute frame of reference?

Why does the pendulum have to be guided to maintain its orientation? Why can't it maintain its plane of swing in space simply because of the inertia of the system?

Cleonis

Confirmed.
If the existence of an absolute frame of reference is assumed then it is assumed that the fixed stars are stationary with respect to that absolute frame of reference.

Cleonis

Ultimately, the phenomenon inertia must be seen as acting as guidance for motion.

I mean, if inertia would be non-existent then all motion would be entirely erratic. What we observe is that motion is not erratic, one of the properties of motion is that when no force acts objects travel in straight lines. We attribute that property to the existence of inertia.

As seen from this point of view inertia is not a property of individual objects. As seen from this point of view inertia is a property of the very fabric of the universe. I don't use the expression 'inertia of the system'. I refer to the momentum of the system if I want to talk about the motion of a particular system.

When I talk about inertia then I am referring to an always and everywhere property of the universe.


It may be that in your mind no such thing as "fabric of the Universe" exists. In other words, it may be that we interpret motion entirely differently.