Tag Archives: Rotation

Mathematicians Uncover a ‘Reset Button’ to Reverse Rotation

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Can I put the top back on?

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Picture a spinning top coming to a halt. Is it possible to make it spin again and return to its original position, as if no movement had occurred? Surprisingly, mathematicians affirm that there is a universal method to revert the rotation of nearly any object.

It seems that the sole method to reverse a complicated rotation sequence is to meticulously execute the exact reverse motion, one step at a time. However, Jean Pierre Eckmann from the University of Geneva, alongside Tzvi Trusty and a research team from South Korea’s Ulsan Institute of Science and Technology (UNIST), discovered a concealed reset mechanism that modifies the initial rotation by a common scaling factor and applies this process twice.

For a spinning top, if it makes three-quarters of a turn during its first spin, you can apply an eighth scaling to retrace your steps back to the start and repeat that sequence again to achieve another quarter turn. Yet, Eckmann and Trusty have shown that this principle applies to much more intricate scenarios.

“Essentially, this property extends to nearly any rotating object, including spins, qubits, gyroscopes, and robotic arms,” Trusty explains. “You merely need to scale all rotation angles by the same factor and replicate this complex pathway twice, navigating through an intricate trajectory in space before returning to the origin.”

Their mathematical proof stems from a comprehensive catalog of all potential rotations in three-dimensional space, known as SO(3), which follows specific rules. This can be visualized as an abstract mathematical space resembling a ball. Transporting an object through various rotations in physical space translates to moving from one point to another within this ball, akin to a bug tunneling through an apple.

When a piece undergoes a complicated rotation, its corresponding trajectory in SO(3) may initiate at the center of the ball and terminate at different points within, depending on the intricacies of the rotation. The objective of reversing this rotation is akin to discovering a route back to the center, yet given that there is only one center within the ball, randomly accomplishing this is improbable.

Some of the many paths that can be taken through the mathematical space SO(3). Corresponds to rotation sequences in real space.

Tzvi Trusty

Eckmann and Trusty realized that due to the structure of SO(3), halting a rotation midway is analogous to finding a path that ends on any point on the ball’s surface. Because the surface comprises numerous points, Trusty notes that this approach is significantly more straightforward than directly targeting the center. This insight led to a new proof.

Eckmann mentioned that they invested considerable time unraveling mathematical tensions that yielded no results. The breakthrough came from a 19th-century formula that merged the two successive rotations, known as Rodriguez’s formula, along with an 1889 theorem in number theory. Ultimately, the researchers concluded that a scaling factor is nearly always necessary for resetting.

For Eckmann, this latest research exemplifies the richness of mathematics, even in seemingly familiar domains like rotation studies. Trusty pointed out potential practical outcomes, such as in nuclear magnetic resonance (NMR), which underpins magnetic resonance imaging (MRI). Researchers assess material and tissue properties by examining the behavior of internal quantum spins under the influence of external magnetic fields. The new proof could pave the way for strategies to negate unwanted spin rotations that disrupt the imaging process.

The findings could also spur advancements in robotics, says Josie Hughes at the Federal Institute of Technology in Lausanne, Switzerland. For instance, a rolling robot may be developed to navigate a path comprising repetitive segments, featuring a reliable roll-reset-roll motion that could theoretically continue indefinitely. “Visualize a robot that could transition between any solid form and subsequently follow any desired trajectory through shape transformation,” she envisions.

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Source: www.newscientist.com

The Earth’s Rotation is Acting Strangely – The Explanations Revealed

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For the past two decades, the rotation of the Earth has shown unusual behavior. Scientists have now identified a surprising cause for this phenomenon: the loss of water from the land.

A recent study published in Science reveals that significant changes in the Earth’s axis since the early 2000s, resulting in a wobble of about 45 cm, were not due to changes in the core, ice loss, or glacial rebound. Instead, they were caused by underestimated changes in soil moisture across the planet.

Between 2000 and 2002, over 1,600 Gigatonnes of water were lost from the soil worldwide. This water, when discharged into the ocean, impacted the Earth’s balance and influenced its rotation.

According to Professor Clark Wilson, a geophysicist at the University of Texas at Austin and co-author of the study, there was a period in the early 2000s when significant water losses occurred from the continents, aligning with certain climate models’ predictions.

Research led by Professor Ki-Weon Seo from Seoul National University in Korea used satellite radar data and soil moisture models to track changes in Earth’s water reservoirs from the late 20th to early 21st centuries. They discovered a sudden drop in soil moisture between 2000 and 2002, contributing to a yearly rise in the global sea level.

This decrease in soil moisture continued from 2003 to 2016, with an additional loss of 1,000 Gigatonnes of water. By 2021, soil moisture levels had still not recovered, indicating a significant and lasting shift in Earth’s land water storage.

The study emphasizes how changes in terrestrial water, particularly soil moisture, can influence Earth’s axis and rotation, leading to observable effects on the planet’s vital signs. The researchers suggest that this trend of drying soil is likely irreversible and could have far-reaching consequences on global water security, agriculture, ecosystems, and climate patterns.

Experts Involved

Clark Wilson: Professor Emeritus at the University of Texas at Austin, specializing in Earth and Planetary Sciences.

Ki-Weon SEO: Associate Professor at Seoul National University with a focus on ice mass losses and sea level rise.

Jay Famiglietty: Global Futures Professor at ASU’s School of Sustainability, specializing in water innovation and sustainable food systems.

This study highlights the importance of improving climate models to better understand and predict future climate conditions in the face of changing water dynamics on Earth.

Source: www.sciencefocus.com

Physicists develop innovative form of structured light: Optical rotation

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According to a team of Harvard physicists, the structure of the optically rotating animal continues in a logarithmic spiral.

The evolution of light beams carrying the optical decy as a function of propagation distance. Image credits: Dorrah et al. , doi: 10.1126/sciadv.adr9092.

“This is a new behavior of light consisting of optical vortices that propagate space and change in an anomalous way,” says Professor Federico Capaso, a senior author of the study.

“It can potentially help you manipulate small substances.”

With a unique twist, the researchers have discovered that orbital angular momentum-mediated beams of light grow in mathematically recognizable patterns found throughout nature.

Reflecting the Fibonacci number sequence, their optical rotations propagate into logarithmic spirals found in Nautilus shells, sunflower seeds, and tree branches.

“It was one of the unexpected highlights of this study,” says Dr. Ahmed Dora, the first author of the study.

“Hopefully we can help others, who are experts in applied mathematics, to further study these light patterns and gain unique insight into their universal signature.”

This study is based on previous research by the team using thin lenses etched with thin nanostructures to create a light beam with controlled polarization and orbital angular momentum along its propagation path, converting the input of light into other structures that change when it moves.

Now they have introduced another degree of freedom in their light. There, spatial torque can be changed as it propagates.

“We show even more versatility in control and we can do it on a continuous basis,” said Alfonso Palmieri, co-author of the study.

Potential use cases for such exotic rays involve the control of very small particles, such as colloids, in suspension, by introducing new types of forces according to the unusual torque of light.

It also allows for precise optical tweezers for small operations.

Others have demonstrated light that changes torque using high-intensity lasers and bulky setups, but scientists have created theirs with a single liquid crystal display and a low-intensity beam.

By showing that they can create rotary rotary devices in industry-compatible, integrated devices, the barriers to entry for their technology to become a reality are much lower than in previous demos.

“Our research expands the previous literature on structured light, providing new modalities for light and physics, and sensing, suggesting similar effects of condensed material physics and Bose-Einstein condensates,” they concluded.

study Published in the journal Advances in science.

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Ahmed H. Dora et al. 2025. Rotation of light. Advances in science 11 (15); doi:10.1126/sciadv.adr9092

Source: www.sci.news

How are human activities impacting the Earth’s tilt and rotation, and what are the implications for the planet?

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Most of us are aware that our planet is constantly spinning around its own axis as it orbits the sun. However, the Earth actually rotates around a tilted axis of 23.44°, leading to changes in its slope over time due to natural oscillations and cycles.

Human activities, such as global warming and groundwater extraction for irrigation, are causing significant changes in Earth’s tilt. Scientists have found that as polar ice melts and water redistributes, it can affect the planet’s rotation.

Researchers estimate that pumping large amounts of groundwater for irrigation purposes has led to significant changes in Earth’s tilt over recent decades. This redistribution of water mass is impacting the planet’s rotation, with measurable effects on sea levels and pole shifts.

Experts like Professor Seo Ki-won note that even small changes in water mass can affect Earth’s rotation, leading to shifts in its axis. These changes have been observed over the past few decades, indicating the impact of human activities on a global scale.

While these changes may not directly impact the climate, they do have implications for systems that rely on precise measurements and timing, such as GPS and financial markets. As Earth’s rotation slows due to mass redistribution, adjustments will need to be made to prevent system failures.

It is becoming increasingly clear that human activities are influencing not just the climate, but also the fundamental movements of Earth within space. As we continue to alter the planet’s mass distribution, we must be prepared to adapt our technologies and systems to accommodate these changes.

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Source: www.sciencefocus.com

Melting Ice Causing Earth’s Rotation to Slow and Axis to Shift, Research Finds

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A recent study reveals that climate change is fundamentally reshaping the Earth, impacting its core. The melting of polar ice caps and glaciers due to global warming is causing a redistribution of water towards the equator, resulting in a shift in the Earth’s rotation and leading to increased daylight hours. This phenomenon is supported by new evidence suggesting that changes in the Earth’s ice could potentially affect its axis. These alterations create feedback loops within the Earth’s molten core, as highlighted in studies published in Nature Geoscience and the Proceedings of the National Academy of Sciences.

According to Benedict Soja, an assistant professor at ETH Zurich in Switzerland, human activities are significantly influencing the Earth’s rotation. Changes in the planet’s shape and mass distribution, influenced historically by forces like the moon’s gravitational pull and rebounding of crust after ice age glaciers disappeared, are now being accelerated by rapid ice melting caused by climate change. Soja warns that continued carbon emissions could make ice loss a more significant factor in Earth’s rotation than the moon.

In addition to external factors like gravity and ice loss, fluid movements in the Earth’s core also play a role in affecting the planet’s rotation. These movements can speed up or slow down the Earth’s rotation and are currently compensating for the slowdown caused by climate change. The new study suggests that climate change is leading to small variations in polar motion due to changes in mass distribution, estimated to be about one meter per decade.

An iceberg in Antarctica on February 8th.
Şebnem Coşkun / Anadolu via Getty Images File

These changes in rotation are expected to have implications for space missions, navigation, and timekeeping. Understanding how Earth’s rotation and axis are affected by climate change will be crucial for accurate space exploration and maintaining global time standards. The research emphasizes the interconnectedness of surface processes with the Earth’s core, shedding light on the complex relationship between human activities and the planet’s inner workings.

Source: www.nbcnews.com

Quantum entanglement used by physicists to measure Earth’s rotation

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Physicists at the University of Vienna have used a maximally entangled quantum state of light paths in a large interferometer to experimentally measure the speed of the Earth’s rotation.

Silvestri othersThey have demonstrated the largest and most precise quantum-optical Sagnac interferometer to date, sensitive enough to measure the Earth’s rotation rate. Image courtesy of Marco Di Vita.

For over a century, interferometers have been key instruments for experimentally testing fundamental physical questions.

They disproved the ether as a light-transmitting medium, helped establish the theory of special relativity, and made it possible to measure tiny ripples in space-time itself known as gravitational waves.

Recent technological advances allow interferometers to work with a variety of quantum systems, including electrons, neutrons, atoms, superfluids, and Bose-Einstein condensates.

“When two or more particles are entangled, only the overall state is known; the states of the individual particles remain uncertain until they are measured,” said co-first author Dr. Philip Walther and his colleagues.

“Using this allows us to get more information per measurement than we would without it.”

“But the extremely delicate nature of quantum entanglement has prevented the expected leap in sensitivity.”

For their study, the authors built a large fiber-optic Sagnac interferometer that was stable with low noise for several hours.

This allows the detection of entangled photon pairs with a sufficiently high quality to exceed the rotational precision of conventional quantum-optical Sagnac interferometers by a factor of 1000.

“In a Sagnac interferometer, two particles moving in opposite directions on a rotating closed path reach a starting point at different times,” the researchers explained.

“When you have two entangled particles, you get a spooky situation: they behave like a single particle testing both directions simultaneously, accumulating twice the time delay compared to a scenario where no entanglement exists.”

“This unique property is known as super-resolution.”

In the experiment, two entangled photons propagated through a 2 km long optical fiber wound around a giant coil, creating an interferometer with an effective area of ​​more than 700 m2.

The biggest hurdle the team faced was isolating and extracting the Earth’s stable rotation signal.

“The crux of the problem lies in establishing a measurement reference point where light is not affected by the Earth’s rotation,” said Dr Raffaele Silvestri, lead author of the study.

“Since we can’t stop the Earth’s rotation, we devised a workaround: split the optical fiber into two equal-length coils and connect them through an optical switch.”

“By switching it on and off, we were able to effectively cancel the rotation signal, which also increased the stability of larger equipment.”

“We’re basically tricking light into thinking it’s in a non-rotating universe.”

The research team succeeded in observing the effect of the Earth’s rotation on a maximally entangled two-photon state.

This confirms the interplay between rotating reference systems and quantum entanglement, as described in Einstein’s special theory of relativity and quantum mechanics, and represents a thousand-fold improvement in precision compared to previous experiments.

“A century after the first observations of the Earth’s rotation using light, this is an important milestone in that the entanglement of individual quanta of light is finally in the same region of sensitivity,” said co-first author Dr Haokun Yu.

“We believe that our findings and methods lay the foundation for further improving the rotational sensitivity of entanglement-based sensors.”

“This could pave the way for future experiments to test the behaviour of quantum entanglement through curves in space-time,” Dr Walther said.

Team work Published in a journal Scientific advances.

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Raffaele Silvestri others2024. Experimental Observation of Earth’s Rotation through Quantum Entanglement. Science Advances 10(24); doi: 10.1126/sciadv.ado0215

Source: www.sci.news

The Melting of Polar Ice Could Alter Earth’s Rotation and Timekeeping.

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Global warming is causing the Earth’s rotation to slow slightly, which could affect the way we measure time.

A study published Wednesday found that the melting of polar ice, a trend accelerated primarily by anthropogenic climate change, is causing the Earth to spin more slowly than it would otherwise.

Study author Duncan Agnew, a geophysicist at the Scripps Institution of Oceanography at the University of California, San Diego, said melting polar ice changes where the Earth’s mass is concentrated. This change affects the planet’s angular velocity.

Agnew likened the dynamic to a figure skater spinning around on ice. He said, “If a skater starts spinning and lowers his arms or extends his legs, he will slow down.” However, if the skater’s arms are pulled inward, the skater will rotate faster.

So less solid ice at the poles means more mass around the equator, at the Earth’s waist.

“What melting ice does is take water that has solidified in places like Antarctica or Greenland, and when that frozen water melts, it moves that liquid to other parts of the planet. “Thomas Herring said. He was a professor of geophysics at the Massachusetts Institute of Technology but was not involved in the new research. “Water flows toward the equator.”

In other words, this study shows how human influence can successfully manipulate forces that have puzzled scholars, stargazers, and scientists for millennia: forces long thought to be constants beyond human control. It suggests that it has happened.

“It’s kind of impressive, even to me, that we were able to accomplish something that measurably changed the rotational speed of the Earth,” Agnew said. “Something unprecedented is happening.”

His research, published in the journal Nature, suggests that climate change is playing a significant enough role in the Earth’s rotation to delay the possibility of a “negative leap second.” If the polar ice hadn’t melted, clocks around the world might have needed to subtract one second by 2026 to synchronize universal time with the Earth’s rotation, which is influenced by a variety of factors.

Rather, the impact of climate change has delayed that outlook by an estimated three years. If timekeeping organizations ultimately decide to add negative leap seconds, the adjustment could disrupt computer networks.

A view of the Earth captured by a deep space climate observation satellite.NASA

The leap second adjustment is necessary because even without climate change, the Earth’s daily rotation tends to slow down over time, even though it appears constant.

Studies show that about 70 million years ago, days became even shorter, lasting about 23.5 hours. Implications of paleoceanography and paleoclimatology. This means that Cretaceous dinosaurs experienced 372 planetary days a year.

Several important factors influence a planet’s rotation, but they sometimes act in opposition.

Due in part to the moon’s gravitational pull, tidal friction in the oceans slows the Earth’s rotation. Meanwhile, since the last Ice Age, the Earth’s crust has been uplifting in some areas in response to the removal of ice sheet weight. This effect changes the distribution of mass, causing the planet to spin faster. Both of these processes are approximately constant and have predictable rates.

Yet another factor is the movement of fluids within Earth’s liquid inner core, a wild card that can either speed up or slow down Earth’s rotation, Agnew said.

Here, melted polar ice was added to the mix. As climate change intensifies, researchers expect melting ice to have an even more profound effect on the Earth’s rotation.

“As we predict, as melting accelerates over time, its contribution will become even larger,” Herring said. He added that the new study is a thorough and robust analysis that combines research from multiple scientific fields.

The need for timekeepers to adjust universal time to match the Earth’s rotation is not a new phenomenon. But historically, this involved adding leap seconds to the common standard for clocks. This is because astronomical time lags behind atomic time (measured by the vibrations of atoms in atomic clocks) due to the slowing of the Earth’s rotation.

But in recent decades, changes in the Earth’s core have caused the Earth to rotate faster than expected. This has led timekeepers, for the first time since Coordinated Universal Time was officially adopted in the 1960s, to consider whether it makes sense to subtract leap seconds to synchronize universal time with the Earth’s rotation. Ta.

The melting of polar ice counteracted that trend, avoiding any decision points regarding negative leap seconds. According to Agnew’s estimates, if the current rate of Earth’s rotation is maintained, it will likely be delayed by three years from 2026 to 2029.

Adding or subtracting leap seconds is troublesome because it can disrupt satellite, financial, and energy transmission systems that rely on very precise timing. For that purpose, Timekeepers around the world have voted to abolish leap seconds in 2022. By 2035, addition and subtraction will shift universal time from the pace of the Earth’s rotation.

“Since around 2000, there has been a movement to abolish leap seconds,” Agnew said.

Regardless of whether the clocks ultimately change, the idea that melting polar ice is affecting the Earth’s rotation speaks to how important an issue it has become. Studies have already shown that ice loss has significant impacts on coastal communities.

Scientists predict that sea level rise will accelerate as the climate warms, a process that will continue for hundreds of years. Last year, leading polar researchers warned in a report that parts of the major ice sheets could collapse and coastal regions should brace for several feet of sea level rise. If humans allowed global average temperatures to rise by 2 degrees Celsius, Earth could see sea levels rise by more than 40 feet.

Source: www.nbcnews.com