Image description: Foucault's Pendulum, Panthéon, Paris, France. The Panthéon is a neoclassical monument located in Paris on the Montagne Sainte-Geneviève. It is where notable figures who have marked the history of France are honored.
Foucault's pendulum, named after the French physicist Léon Foucault (1819-1868), is an experimental device designed to demonstrate the Earth's rotation. The first educational demonstrations titled "Come See the Earth Rotate" were conducted at the Panthéon during 1851.
Today, Foucault's pendulum is a 28 kg lead and brass ball suspended from the dome of the Panthéon (Paris) by a 67 m long cable. A magnetic mechanism maintains its inertial motion, which, due to air resistance, would only oscillate for 6 hours. Its swinging allows one to see the terrestrial landmarks (floor, walls, dome of the Panthéon, etc.) move. In other words, one can see the Earth rotate without even looking at celestial objects (Sun, Moon, stars). The observer rotates with the Earth and remains fixed relative to the ground. To them, it is the plane of oscillation of the pendulum that is rotating.
This simple, ordinary object compels us to accept several extraordinary concepts as true.
- Once released, the Foucault pendulum oscillates along an axis that will indefinitely maintain the same direction. This plane of oscillation remains invariant in space over time, regardless of the direction in which it was launched.
- In Paris, the pendulum's plane does not return to its starting point in 24 hours as one might think. With each 16.42-second oscillation, it shifts by 5.4 mm clockwise (opposite to the Earth's rotation) and returns to its starting point in 31 hours 48 minutes. It is not the pendulum's plane that rotates but the Earth.
- The pendulum's plane completes a full rotation in 23 hours 56 minutes (sidereal day) only when placed at the geographical poles (North or South), because at the geographical poles, the pendulum's vertical is parallel to the Earth's rotation axis.
- The closer the latitude is to the Earth's equator, the longer it takes for the pendulums to return to their initial axis.
- At the equator, the pendulum eventually oscillates in a seemingly fixed plane that does not allow the Earth's rotation to be seen. This time, the pendulum's vertical is perpendicular to the Earth's rotation axis. Thus, unlike what happens at the poles, the ground does not rotate around the pendulum's axis but moves the axis with it. To an observer, it is as if the pendulum were transported in a train and swung in the direction of the train's movement. The pendulum's plane is fixed, and the Earth no longer rotates around it. Its period of revolution tends towards infinity.
- At southern latitudes, the pendulum will again show the Earth's rotation, and its plane will rotate counterclockwise.
- It is extremely difficult to imagine the oscillation of a pendulum outside the poles.
All these concepts are explained by a lengthy mathematical development outlining the pendulum's motion equations.
The oscillation period of the Panthéon’s Foucault pendulum is 16.42 seconds because the length of the string is 67 meters. The mass of the pendulum does not matter; the string length alone is sufficient to calculate the oscillation period T.
T = 2π√l/g where l = string length, g = acceleration due to gravity 9.81 m/s²
At a given latitude θ and an angular rotation speed of the Earth Ω, the rotation period is inversely proportional to the sine of this latitude, i.e., 2 π/Ωsin(θ). Since the sine of 30° is 1/2, a Foucault pendulum placed at a latitude of 30° will complete a full rotation in 48 hours. It is the Coriolis force, perpendicular to the motion and proportional to the pendulum's speed, that causes the pendulum to deviate from its initial plane of oscillation.
In Foucault's time, there was an absolute space relative to which all movements were defined. This immutable space was thus a natural frame of reference for the pendulum's oscillation.
But today, space, or rather Einstein's spacetime, is a dynamic entity, and the theory of relativity postulates that no privileged frame of reference exists. In the universe, absolute motion does not exist; it is always relative to another reference point, which is also in motion. Yet, we observe that Foucault's pendulum favors a specific reference frame since its plane indicates a direction. But then, relative to what is the pendulum's plane fixed?
This unresolved enigma remains subject to controversy.
At the North Pole, a Foucault pendulum suspended 67 m high and launched in any direction oscillates every 16.42 seconds. With each oscillation, its plane deviates by 7 mm. If the pendulum is launched toward the Sun, it seems not to deviate relative to the Sun. But after a few hours, a deviation in the pendulum's plane is observed because the Earth/Sun direction is not fixed. Indeed, the Earth orbits the Sun in 365 days, so the 7 mm deviation, 365 times smaller, eventually appears.
If it is not relative to the Sun, then relative to what is the pendulum's plane fixed?
If the pendulum is launched toward any star in our Galaxy, it seems not to deviate relative to the star. Distant stars appear to be the reference frame relative to which the pendulum's oscillation plane seems fixed. But after a few thousand years, a deviation in the pendulum's plane would be observed because the Sun/Star direction is not fixed.
Indeed, the Sun orbits the Galaxy in 250 million years, but the star also orbits the Galaxy, and the two rotations are not synchronous. Thus, the deviation of the oscillation plane relative to the star will eventually appear.
If it is not relative to the stars, then relative to what is the pendulum's plane fixed?
The same would apply if the plane were oriented toward a very distant galaxy. The drift time increases with the distance of the reference object. All reference points will eventually exit the pendulum's plane, but then which reference point would remain in the pendulum's plane?
At 13.77 billion years, the drift seems to stop, and the pendulum's plane remains fixed relative to objects close to the Big Bang. The direction of Foucault's Pendulum once launched is not linked to the movement of our planet, our Sun, our galaxy, or distant galaxy clusters but to the movement of the entire observable universe.
The pendulum's axis then immutably fixes itself on this reference point!!!
Is the pendulum sensitive to all of spacetime?
Is the pendulum sensitive to all objects in the universe?
170 years after its invention, the motion of Foucault's pendulum remains mysterious and unexplained. This seemingly insignificant mechanical object astonishingly transports us to the far reaches of the observable universe.
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