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Bouncing ball in a rotating space station: The objective reality of the ball bouncing off the outer hull is confirmed both by a rotating and by a non-rotating observer, hence the rotation of the space station is an "absolute", objective fact regardless of the chosen frame of reference.

In physics, the concept of absolute rotation—rotation independent of any external reference—is a topic of debate about relativity, cosmology, and the nature of physical laws.

For the concept of absolute rotation to be scientifically meaningful, it must be measurable. In other words, can an observer distinguish between the rotation of an observed object and their own rotation? Newton suggested two experiments to resolve this problem. One is the bucket argument, regarding the effects of centrifugal force upon the shape of the surface of water rotating in a bucket; it is equivalent to the phenomenon of rotational gravity used in proposals for human spaceflight. The second is the effect of centrifugal force upon the tension in a string joining two spheres rotating about their center of mass.

Classical mechanics

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Newton's bucket argument

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Main article: Bucket argument
Further information: Artificial gravity
Figure 1: The interface of two immiscible liquids of different density (a denser colorless liquid and a lighter orange-colored liquid) rotating around a vertical axis is an upward-opening circular paraboloid.

Newton suggested the shape of the surface of the water indicates the presence or absence of absolute rotation relative to absolute space: rotating water has a curved surface, still water has a flat surface. Because rotating water has a concave surface, if the surface you see is concave, and the water does not seem to you to be rotating, then you are rotating with the water.

Centrifugal force is needed to explain the concavity of the water in a co-rotating frame of reference (one that rotates with the water) because the water appears stationary in this frame, and so should have a flat surface. Thus, observers looking at the stationary water need the centrifugal force to explain why the water surface is concave and not flat. The centrifugal force pushes the water toward the sides of the bucket, where it piles up deeper and deeper, Pile-up is arrested when any further climb costs as much work against gravity as is the energy gained from the centrifugal force, which is greater at larger radius.

If you need a centrifugal force to explain what you see, then you are rotating. Newton's conclusion was that rotation is absolute.[1]

Other thinkers suggest that pure logic implies only relative rotation makes sense. For example, Bishop Berkeley and Ernst Mach (among others) suggested that it is relative rotation with respect to the fixed stars that matters, and rotation of the fixed stars relative to an object has the same effect as rotation of the object with respect to the fixed stars.[2] Newton's arguments do not settle this issue; his arguments may be viewed, however, as establishing centrifugal force as a basis for an operational definition of what we actually mean by absolute rotation.[3]

Rotating spheres

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See also: Rotating spheres
Figure 2: Two spheres tied with a string and rotating at an angular rate ω. Because of the rotation, the string tying the spheres together is under tension.

Newton also proposed another experiment to measure one's rate of rotation: using the tension in a cord joining two spheres rotating about their center of mass. Non-zero tension in the string indicates rotation of the spheres, whether or not the observer thinks they are rotating. This experiment is simpler than the bucket experiment in principle, because it need not involve gravity.

Beyond a simple "yes or no" answer to rotation, one may actually calculate one's rotation. To do that, one takes one's measured rate of rotation of the spheres and computes the tension appropriate to this observed rate. This calculated tension then is compared to the measured tension. If the two agree, one is in a stationary (non-rotating) frame. If the two do not agree, to obtain agreement, one must include a centrifugal force in the tension calculation; for example, if the spheres appear to be stationary, but the tension is non-zero, the entire tension is due to centrifugal force. From the necessary centrifugal force, one can determine one's speed of rotation; for example, if the calculated tension is greater than measured, one is rotating in the sense opposite to the spheres, and the larger the discrepancy the faster this rotation.

The tension in the wire is the required centripetal force to sustain the rotation. What is experienced by the physically rotating observer is the centripetal force and the physical effect arising from his own inertia. The effect arising from inertia is referred to as reactive centrifugal force.

Whether or not the effects from inertia are attributed to a fictitious centrifugal force is a matter of choice.

Relativity

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Special relativity

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Main article: Sagnac experiment

French physicist Georges Sagnac in 1913 conducted an experiment that was similar to the Michelson–Morley experiment, which was intended to observe the effects of rotation. Sagnac set up this experiment to prove the existence of the luminiferous aether that Einstein's 1905 theory of special relativity had discarded.

The Sagnac experiment and later similar experiments showed that a stationary object on the surface of the Earth will rotate once every rotation of the Earth when using stars as a stationary reference point. Rotation was thus concluded to be absolute rather than relative.[citation needed]

General relativity

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Further information: Mach's principle and Frame-dragging

Mach's principle is the name given by Einstein to a hypothesis often credited to the physicist and philosopher Ernst Mach.

The idea is that the local motion of a rotating reference frame is determined by the large-scale distribution of matter in the universe. Mach's principle says that there is a physical law that relates the motion of the distant stars to the local inertial frame. If you see all the stars whirling around you, Mach suggests that there is some physical law which would make it so you would feel a centrifugal force. The principle is often stated in vague ways, like "mass out there influences inertia here".

The example considered by Einstein was the rotating elastic sphere. Like a rotating planet bulging at the equator, a rotating sphere deforms into an oblate (squashed) spheroid depending on its rotation.

In classical mechanics, an explanation of this deformation requires external causes in a frame of reference in which the spheroid is not rotating, and these external causes may be taken as "absolute rotation" in classical physics and special relativity.[4] In general relativity, no external causes are invoked. The rotation is relative to the local geodesics, and since the local geodesics eventually channel information from the distant stars, there appears to be absolute rotation relative to these stars.[5]

See also

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Absolute rotation

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Absolute rotation refers to the concept in Newtonian mechanics of rotational motion that is defined with respect to an absolute space, independent of any relative motion to surrounding bodies, and detectable through physical effects such as centrifugal forces. Introduced by in his (1687), this idea posits that true rotation produces observable phenomena, like the concave surface formed by water in a spinning , which cannot be explained solely by the bucket's motion relative to the or nearby objects. In Newtonian physics, absolute rotation underpins the distinction between inertial and non-inertial reference frames, where rotational acceleration is absolute and gives rise to fictitious forces, such as the outward push felt in a rotating system, regardless of external references. Newton illustrated this absoluteness through thought experiments, including the rotating bucket and two connected globes that twist when spun, arguing that these effects reveal motion against an immutable spatial background, essential for the laws of motion and universal gravitation. This framework assumes space as a fixed, infinite , providing a universal standard for measuring , in contrast to translational motion, which Newton viewed as relative. The notion of absolute rotation faced significant challenges in the , particularly from , who critiqued it in The Science of Mechanics (1883) by proposing that rotational effects arise from an object's relation to the entire distribution of matter in the universe, such as distant stars, rather than an abstract absolute space. influenced Albert Einstein's development of general relativity (1915), where rotation remains detectable but is framed within curved influenced by mass-energy, effectively incorporating relational elements while retaining some absolute aspects through boundary conditions like asymptotic flatness. In contemporary physics, absolute rotation continues to inform discussions in and alternative theories, such as shape dynamics, where efforts persist to reconcile Newtonian absolutes with fully relational descriptions of motion. These debates highlight absolute rotation's enduring role in understanding the foundations of , time, and dynamics, bridging classical and modern paradigms.

Historical and Classical Foundations

Newton's Concept of Absolute Space

In his (1687), introduced the concept of absolute space in the Scholium following the definitions, describing it as a fixed and immutable entity that exists independently of any external relations. Absolute space, in its own nature, without relation to anything external, remains always similar and immovable, serving as the unchanging backdrop against which all physical phenomena occur. This contrasts with relative space, which Newton defined as a movable dimension or measure of the absolute spaces, determined by our senses through its position relative to surrounding bodies. Newton extended this framework to motion, positing absolute motion as the translation of a body from one absolute place into another, detectable through its intrinsic effects rather than mere observations of relative positions. Specifically, absolute rotation manifests through forces such as centrifugal effects, which arise independently of the surrounding environment and indicate true motion relative to absolute space, as opposed to relative rotation that depends on observable changes in position among bodies. Thus, while relative motion describes apparent shifts perceptible to observers, absolute motion represents the genuine change in a body's location within the immutable framework of absolute space, essential for explaining dynamical phenomena like inertial forces in rotating systems. This conception arose in the 17th-century context as Newton's direct response to René Descartes' relational view of space and motion, which treated space as merely the arrangement of material bodies without an independent existence. Descartes argued that motion is inherently relative, defined solely by changes in the positions of bodies with respect to one another, denying any absolute reference frame. Newton rejected this relationalism, insisting that absolute space provides the necessary fixed arena to account for the uniformity of natural laws and the observability of true motions, thereby laying the philosophical groundwork for classical mechanics.

The Bucket Argument

In Newton's , known as the , a cylindrical suspended by a long twisted rope is filled with water and then released to rotate about its vertical axis. Initially, as the bucket begins to spin, the water remains at rest relative to the surrounding environment, maintaining a flat surface. Gradually, causes the water to acquire the same as the bucket, at which point the surface becomes concave, with the water level rising at the edges and dipping at the center. This concavity arises due to the acting on the water particles, pushing them outward from the axis of rotation. Newton interpreted this phenomenon as evidence of absolute rotation, arguing that the observed effects occur even when the water and bucket are rotating together with no relative motion between them. If rotation were merely relative to surrounding bodies, the flat surface should persist once the water co-rotates with the bucket, as there would be no differential motion. Instead, the concavity demonstrates that the water is rotating relative to an absolute space, which remains fixed and undetectable directly but manifests through these inertial effects. This distinguishes true circular motion, characterized by forces tending to recede from the axis, from mere relative translation. In Newtonian mechanics, the centrifugal force is a fictitious force appearing in the rotating reference frame of the bucket, but Newton viewed the resulting concavity as proof of genuine absolute rotation against an inertial frame defined by absolute space. To find the equilibrium shape of the water surface, consider the balance between the gravitational potential and the centrifugal potential in the rotating frame. The effective potential energy per unit mass is Φ=gz−12ω2r2\Phi = gz - \frac{1}{2}\omega^2 r^2, where zz is the height, gg is gravitational acceleration, ω\omega is the angular velocity, and rr is the radial distance from the axis. At equilibrium, the surface is an equipotential, so z(r)=z(0)+ω2r22gz(r) = z(0) + \frac{\omega^2 r^2}{2g}, yielding a parabolic profile h(r)=ω2r22gh(r) = \frac{\omega^2 r^2}{2g} relative to the lowest point at the center. This derivation confirms the concavity's dependence on absolute rotation rate ω\omega, independent of relative motion to the bucket walls. The was first published in the Scholium following the Definitions in Book I of Newton's in 1687, where it served as a key defense of absolute space against relational theories of motion, such as those proposed by Descartes. By linking observable physical effects to relative to an absolute frame, it established a foundational criterion for identifying true motion in , influencing subsequent debates on space and .

The Rotating Spheres Experiment

In Newton's second thought experiment on absolute rotation, described in the scholium following the definitions in Philosophiæ Naturalis Principia Mathematica, two identical globes of equal mass are connected by a taut cord and caused to revolve around their common center of gravity in an otherwise empty space devoid of external bodies or influences. If the system is at rest or in uniform rectilinear motion relative to absolute space, the cord remains slack with no tension, as the globes exhibit no tendency to separate. However, upon imparting rotation to the system, the cord becomes tense, indicating an internal force that stretches it, even though the globes maintain a fixed distance from one another and rotate together without relative motion between them. Newton argued that this tension arises solely from the absolute rotation of the globes with respect to absolute space, rather than any relative motion between the globes themselves, since they co-rotate as a without approaching or receding from each other. He posited that the tension reveals the "endeavor" of each globe to recede from the axis of , a manifestation of inertial forces detectable independently of external references, thereby distinguishing true (absolute) from apparent motion. By measuring the tension and applying forces to the faces of the globes, one could further determine the quantity and direction (clockwise or counterclockwise) of this absolute . Mechanically, the tension in the cord counteracts the radial acceleration required for circular motion. Consider two spheres of mass mm connected by a massless cord of total length 2L2L, rotating with angular velocity ω\omega about the midpoint (their common center of gravity). In an inertial frame, each sphere undergoes uniform circular motion at radius LL from the axis, requiring a centripetal acceleration a=ω2La = \omega^2 L directed inward toward the center. The cord provides this centripetal force via tension TT, so for each sphere, Newton's second law gives T=ma=mω2LT = m a = m \omega^2 L. To derive this, start from the tangential velocity v=ωLv = \omega L; the centripetal acceleration is then a=v2/L=(ωL)2/L=ω2La = v^2 / L = (\omega L)^2 / L = \omega^2 L. Thus, the net inward force on each sphere is TT, balancing the tendency to fly outward in the rotating frame (or providing the curvature in the inertial frame). In the absence of rotation (ω=0\omega = 0), T=0T = 0, and the cord slackens. Newton emphasized that even in a void, the tension persists, underscoring its origin in absolute space. This setup parallels the by similarly revealing centrifugal effects through internal stresses, but focuses on rigid-body tension rather than fluid deformation. In the 18th century, contemporaries like refined these ideas in discussions of , exploring how the tension in such rotating systems implies absolute motion in celestial bodies, such as the mutual revolutions of planets and satellites, and integrating it with gravitational theories to explain stable orbits without relying solely on relative positions.

Philosophical Criticisms and Alternatives

Leibniz and Berkeley's Objections

In the correspondence between and from 1715 to 1716, Leibniz articulated a relational view of as an ideal order among coexisting bodies, rejecting Newton's absolute as an unnecessary and unobservable entity. He contended that absolute rotation or motion lacks meaning without reference to other bodies, as differences in absolute states would be indiscernible and violate the principle of sufficient reason, making such motion a mere . For instance, Leibniz argued that if the entire rotated uniformly in absolute , no observable effects would distinguish it from , rendering absolute rotation empirically empty. George Berkeley extended these relationalist critiques in his 1721 treatise De Motu, where he dismissed absolute space and motion as imperceptible and thus irrelevant to natural philosophy. Berkeley specifically addressed rotational phenomena, asserting that effects like the concavity in Newton's rotating bucket arise from the water's relative motion against the surrounding air or container, not any absolute inertial frame. He emphasized that true motion involves changes in situation relative to sensible objects and impressed forces from interactions, eliminating the need for an invisible absolute space. At the core of both philosophers' objections lies relationalism, which posits that space and motion derive solely from relations among bodies, with forces emerging from their interactions rather than an absolute frame. This framework reinterprets Newton's experiments: the bucket's water results from relative motion to the or laboratory, while the tension in rotating spheres stems from adjustments in their mutual attractions due to relative velocities, without invoking absolute rotation. These 18th-century critiques shifted philosophical and scientific debates toward relational explanations, prompting empirical investigations into motion's dependence on distributed throughout the 18th and 19th centuries.

Mach's Principle

Ernst Mach, in his 1883 work The Science of Mechanics, proposed that local inertial frames are defined relative to the distant stars and the overall distribution of in the , rendering the concept of absolute rotation meaningless without such cosmic references. He argued that originates not from an abstract absolute space but from the interactions of a body with all other in the , emphasizing that "motion is completely determined by the entire ." This formulation challenged Newtonian by tying the determination of and inertial effects to the relative configuration of massive bodies, particularly the fixed stars, rather than an independent spatial framework. Mach applied this idea directly to Newton's rotating bucket experiment, suggesting that the concavity of the water's surface arises from its rotation relative to the of the and other celestial bodies, not against an absolute space. He famously questioned the experiment's outcome by positing an alternative: "Try to fix Newton's bucket and rotate the heaven of and then it is easy to see that the water will take the form of a concave surface," implying that the centrifugal effects would reverse if the rotated instead. In this view, the bucket's result demonstrates relational motion against the 's distribution, dismissing Newton's invocation of empty absolute space as an unphysical and arbitrary . Mach's ideas profoundly influenced , who credited them with inspiring key aspects of , including the and the notion that matter curves to define inertial paths. explicitly coined the term "" in a address, viewing it as a guiding for relativizing through the global distribution of . This connection briefly manifests in 's description of geodesic motion, where distant matter influences local frames. Despite its impact, has faced criticisms for lacking a precise mathematical quantification of how distant matter exactly determines local . Modern tests, such as those confirming effects in via satellites like , indicate partial validity by showing that rotating masses influence nearby inertial frames, though the full cosmic dependence of remains unresolved.

Relativistic Perspectives

Special Relativity

Special relativity, formulated by in 1905, revolutionized the classical notion of absolute space by establishing that there is no privileged and eliminating the idea of an absolute . In his foundational paper "On the Electrodynamics of Moving Bodies," Einstein addressed the inconsistencies between Newtonian mechanics and Maxwell's electromagnetism by introducing two postulates: the laws of physics are identical in all inertial frames, and the in vacuum is constant regardless of the source's motion. This framework discarded the , previously invoked as an absolute medium for light propagation, thereby rendering absolute space unnecessary and undetectable. At its core, treats not as an absolute property but as a form of relative to inertial , with no preferred frame to define absolute rotational motion. All inertial observers are equivalent, and uniform is undetectable without external references, but introduces non-inertial effects that can be locally measured. In a rotating frame, fictitious forces such as centrifugal and Coriolis forces emerge due to the frame's , yet these are relational, depending on the choice of inertial frame, and do not indicate an absolute against the . thus affirms the relativity of inertial motion while preserving the detectability of , including , through local experiments. Lorentz transformations, which underpin special relativity, mix spatial and temporal coordinates between inertial frames, ensuring that concepts like simultaneity and length are frame-dependent. For rotational scenarios, these transformations—particularly boosts—affect the measurement of angular velocity, as the relativity of simultaneity prevents a unique, observer-independent definition of angular displacement over time. An observer undergoing a Lorentz boost relative to a rotating system will perceive a different angular velocity due to the non-invariance of rotation rates under such transformations, underscoring that absolute angular velocity cannot exist without specifying the reference frame. In rotating frames, this manifests as the impossibility of globally synchronizing clocks, since Einstein synchronization is non-transitive around a closed loop, further highlighting the local, relative nature of rotation. The implications of these principles extend to thought experiments like the , where path-dependent arises from non-inertial trajectories. In a rotational variant, one twin remains in an inertial frame while the other follows a circular path at relativistic speeds; upon reunion, the rotating twin has aged less due to the integrated effects of velocity changes along the accelerated worldline, demonstrating that rotational motion leads to differential aging relative to inertial paths. This effect, analyzable within for the acceleration phases, reinforces the absence of absolute rotation by tying aging differences to the geometry of paths rather than an intrinsic rotational absolute. The offers a key experimental confirmation, manifesting as a phase shift in light propagating in opposite directions within a rotating apparatus, detectable locally but relative to the inertial frame.

General Relativity

In , the asserts that locally, the effects of a uniform are indistinguishable from those experienced in an accelerated reference frame, including rotational . This principle extends to rotation, where a rotating observer in flat cannot locally differentiate their motion from the influence of a gravitational field, thereby relativizing acceleration and eliminating absolute notions of rotation within small regions of . Frame-dragging, also known as the Lense-Thirring effect, describes how a rotating mass generates a gravitomagnetic field that drags nearby , rendering relative to the distribution of cosmic rather than an absolute frame. In the weak-field approximation, the precession rate Ω\Omega of a or due to this effect is given by Ω=2GIωc2r3,\Omega = \frac{2 G I \omega}{c^2 r^3}, where GG is the , II is the of the rotating body, ω\omega is its , cc is the , and rr is the from the body. This effect demonstrates that inertial frames are influenced by the of distant masses, aligning with the overall geometry of . Geodesic motion in further underscores the absence of absolute rotation, as freely falling particles follow defined by , with locally non-rotating inertial frames determined relative to the distant stars through this rather than a fixed absolute space. Einstein reinterpreted Newton's rotating bucket experiment in this framework, attributing the concave water surface not to motion against absolute space but to the of curved induced by the bucket's and the universe's mass distribution. General relativity incorporates Machian elements by suggesting that inertia arises from interactions with the universe's mass distribution, though it does not fully implement , as can exist independently of matter and absolute rotational solutions persist in certain limits. Einstein viewed this partial alignment as a step toward relativizing , influenced by Mach's ideas during the theory's development.

Modern Experimental Tests

Interferometry and Sagnac Effect

In 1913, Georges Sagnac conducted a pivotal experiment using an interferometer mounted on a rotating turntable to investigate the propagation of light in a rotating frame. A coherent light beam from a source was split by a beam splitter and directed along opposite paths around a closed polygonal loop formed by mirrors, before recombining to produce interference fringes. When the apparatus rotated, the counter-propagating beams experienced different travel times due to the motion of the mirrors, resulting in a observable shift in the interference pattern proportional to the rotation rate. This setup demonstrated a phase difference that Sagnac initially attributed to an "optical whirlwind" in the luminiferous aether dragged by the rotation. The phase shift Δϕ\Delta \phi in the Sagnac interferometer is described by the formula Δϕ=8πAωcλ,\Delta \phi = \frac{8 \pi A \omega}{c \lambda}, where AA is the enclosed area of the loop, ω\omega is the angular rotation rate, cc is the speed of light in vacuum, and λ\lambda is the wavelength of the light. This shift arises from the path length difference ΔL=4Aω/c\Delta L = 4 A \omega / c between the two beams in the rotating frame, leading to a time delay Δt=ΔL/c\Delta t = \Delta L / c and thus Δϕ=2πΔt/(λ/c)\Delta \phi = 2\pi \Delta t / (\lambda / c). The derivation follows from considering the velocity addition in the non-inertial frame, where one beam travels with the rotation while the other opposes it. Sagnac's original measurements on a turntable with an area of approximately 0.08 m² and rotation rates on the order of 2 Hz (approximately 12.6 rad/s) yielded fringe shifts on the order of 0.07 fringes, confirming the predicted dependence on ω\omega and AA. Subsequent replications solidified the effect's reliability. In 1925, Albert Michelson and Henry Gale constructed a massive rectangular interferometer (dimensions 640 m by 320 m) to measure , observing a fringe shift of about 0.23 fringes at a of 41.4°N, consistent with the Sagnac formula using Earth's of 7.29×10−57.29 \times 10^{-5} rad/s relative to distant stars as the inertial reference. This demonstrated the effect's sensitivity to rotation against the cosmic background, interpreted as an inertial frame. Later turntable-based tests, such as those by Dufour and Prunier in 1937, replicated the setup on controlled platforms and confirmed the phase shift's independence from linear translation, as no shift occurred under pure uniform motion but appeared solely with angular rotation. These experiments underscored that the Sagnac effect detects rotation relative to a non-rotating inertial frame, not absolute motion in a Newtonian sense. Modern applications exploit the in fiber-optic gyroscopes (FOGs), which use coiled optical fibers as the interferometer loop to measure rotational velocity for in , ships, and . In a FOG, counter-propagating beams in the fiber experience the phase shift, converted to an electrical signal proportional to ω\omega, enabling drift-free operation without moving parts and accuracies down to 0.001°/h. These devices confirm the effect's robustness in practical settings, such as inertial navigation systems that account for relative to inertial space. However, the measures only relative rotation with respect to distant inertial frames, offering no evidence for an absolute space and aligning with special relativity's treatment of non-inertial frames, where the shift reflects differences rather than a preferred absolute .

Quantum and Superfluid Experiments

In the late 1990s, experiments with superfluid 4^4He demonstrated the potential to detect absolute rotation through the phase coherence of the superfluid state, analogous to a . Researchers constructed a superfluid analog of a superconducting RF , utilizing the circulation of superflow around a multiply connected geometry to sense rotational phase shifts. This device, fabricated from silicon micromachined orifices filled with superfluid 4^4He, achieved detection of Earth's rotation by measuring the phase difference induced by the planet's angular velocity, confirming the superfluid's sensitivity to inertial frame rotation without viscous drag. Building on these foundations, proposals in the and early explored vortex states in rotating superfluid 4^4He as indicators of absolute , where quantized vortices form arrays mimicking solid-body rotation in an inertial frame. The principles of superfluid-helium gyroscopes (SHEGs) involve reorienting a superflow loop relative to the rotation vector to induce detectable phase shifts, offering high sensitivity limited primarily by at millikelvin temperatures. By the 2010s, theoretical work extended this to generated by vortices in rotating superconductors, treated as charged superfluids, where rotation couples to electromagnetic effects, potentially revealing absolute through flux measurements. A 2021 proposal detailed practical designs for detecting using charged objects rotating within superconducting enclosures, generating that could be measured with SQUIDs to distinguish inertial from non-inertial frames. These setups leverage the to confine fields from rotating charges, producing Aharonov-Bohm-like phase shifts in nearby quantum probes, with sensitivity sufficient to resolve Earth's sidereal rate using commercial cryogenic detectors. Analysis indicated that such configurations test in rotating frames and could confirm whether low-frequency electromagnetic propagation shares the inertial frame of matter. More recent theoretical advancements highlighted the vortex magnetic effect (VME) in superfluid 4^4He, where rotating vortices carry detectable magnetic due to coupling between and magnetic in an effective field theory framework. Estimates suggest a flux per vortex of approximately 10−10Φ010^{-10} \Phi_0 (where Φ0\Phi_0 is the flux quantum), large enough for experimental detection using quantum-limited SQUIDs over integration times of days, providing a novel probe of rotational absoluteness in neutral superfluids. In , a table-top quantum experiment employed path-entangled pairs in a large-scale Sagnac-like interferometer to measure , achieving unprecedented sensitivity through quantum correlations. The setup utilized a 715 fiber loop with maximally entangled N00N states generated via , yielding a rotation resolution of 5 μrad/s—three orders of magnitude better than prior classical optical sensors—and confirming the Earth's rate of 7.1(5) × 10^{-5} rad/s from Earth's spin, corresponding to a Sagnac phase shift of 5.5(4) mrad. This doubled sensitivity arises from the Heisenberg-limited scaling of entangled states, demonstrating rotational effects via quantum-enhanced without relying on classical light paths. In November 2025, researchers reported using Sagnac phonon interferometry in rotating fermionic superfluids to measure via Doppler shifts in counter-propagating phonons, confirming quantized circulation at h/2m (where m is the fermion mass) and demonstrating sensitivity to absolute rotation in the BEC-BCS regime. The mission (2004–2011) provided indirect tests of rotational absoluteness through satellite-based gyroscopes, measuring general relativistic to assess by Earth's rotation. Four superconducting gyroscopes, orbiting at 642 km altitude, recorded a geodetic of −6601.8±18.3-6601.8 \pm 18.3 mas/yr (predicted: −6606.1-6606.1 mas/yr) and a of −37.2±7.2-37.2 \pm 7.2 mas/yr (predicted: −39.2-39.2 mas/yr), confirming Einstein's predictions to 0.28% and 19% accuracy, respectively. These results validate that rotation induces local effects detectable in inertial frames, without evidence for a preferred absolute . Collectively, these quantum and superfluid experiments indicate that is relative to inertial frames and detectable through phase coherence, vortex dynamics, or gravitational coupling, but they find no support for Newtonian absolute space, consistent with relativistic principles. Post-2013 advancements, including the 2024 entangled-photon measurement and 2025 fermionic superfluid , fill critical gaps by enhancing sensitivity to rotational signals at quantum limits, enabling tests of foundational physics in controlled laboratory settings.

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