The findings add to growing evidence that consistently getting enough sleep may play an important role in preventing weight gain and lowering the risk of obesity related diseases.

“Our study shows that getting adequate sleep may help reduce the risk of weight gain and obesity-related conditions like heart disease and diabetes,” says Marie-Pierre St-Onge, a professor of nutritional medicine in Columbia’s Department of Medicine and Institute for Human Nutrition and study leader. “People tend to gain weight over the course of their adulthood, and obesity is a major risk factor for heart disease. But focusing on eating a healthier diet and getting more physical activity to offset weight gain is simplistic and can be difficult to maintain.”

Looking Beyond Extreme Sleep Deprivation

Much of the previous research connecting poor sleep with obesity has focused on severe sleep deprivation, often limiting people to only four hours of sleep. Those studies have shown that extreme sleep loss can increase appetite and overeating, factors that contribute to weight gain.

However, such severe sleep restriction is difficult for most people to tolerate for more than a few days.

“These studies only show us what happens under the most extreme conditions and don’t tell us if mildly sleep-deprived people, like a lot of Americans who get 5 or 6 hours of sleep a night, will gain weight,” St-Onge says.

To better reflect real life, the researchers examined the effects of chronic, mild sleep loss, a pattern experienced by roughly 30% of adults.

Six Weeks of Less Sleep Led to Measurable Changes

The study included 95 adults who normally slept between 7 and 8 hours each night. During one six week study period, participants delayed their usual bedtime by 90 minutes. During another six week period, they followed their normal sleep schedule.

Throughout both phases, participants wore wrist monitors that tracked sleep and physical activity. Researchers also measured body weight, waist circumference, body composition, and fasting levels of several hormones involved in appetite regulation.

“While the one-pound weight gain observed with modest sleep curtailment is not overwhelming, it is important to remember this is occurring over just six weeks,” says Faris Zuraikat, assistant professor of nutritional medicine in Columbia’s Department of Medicine and Institute for Human Nutrition and first author of the study. “Our study was designed to mimic sleep patterns that most adults experience chronically. When extrapolated to a full year, we would expect that losing less than an hour and a half of sleep per night could result in clinically meaningful weight gain.”

Less Sleep Also Meant More Sitting

The researchers found that participants became less active during the sleep restriction phase. On average, sedentary time increased by 17 minutes per day. Among men and postmenopausal women, inactivity rose by nearly 30 minutes each day.

“Even when we accounted for the fact that they were awake longer when sleep was shortened, participants spent more time being inactive than when they got adequate sleep,” Zuraikat says. “This is notable, as people who are more sedentary have elevated risk for chronic diseases.”

Earlier Research Suggests Broader Health Effects

The same group of participants has also been examined in related studies. In one previous investigation, women with increased cardiometabolic risk who reduced their sleep by about 80 minutes each night for six weeks developed greater insulin resistance, an important risk factor for type 2 diabetes. The effect was especially pronounced in postmenopausal women.

Another study found that men and women with elevated heart disease risk developed an influx of inflammatory cells in the heart after experiencing mild sleep restriction.

“Though more research is needed to further understand how sleep restriction leads to weight gain, all of our findings suggest that insufficient sleep increases the risk of obesity-related conditions like type 2 diabetes and heart disease,” St-Onge says.

“Now we need to understand the health effects of improving sleep in those who fail to get adequate sleep on a regular basis.”

The study, titled “Skimping on Sleep and Its Impact on Body Weight and Composition: A Pooled Analysis of Randomized Trials,” was published on July 6 in Annals of Internal Medicine.

The authors are Faris Zuraikat, Samantha Scaccia, Justin Cochran, Bin Cheng, Keith Diaz, Seth Creasy (University of Colorado), Brooke Aggarwal, Sanja Jelic, and Marie-Pierre St-Onge.

The authors report no conflicts of interest.

The research was supported by the American Heart Association (16SFRN27950012) and the National Institutes of Health (R01 HL128226, UL1 TR001873, P30 DK026687, R01 HL173190, R01 HL155190, R01 HL153642, K01 HL145023, R01 HL169991, R01 HL106041, R35 HL155670, R01 AG071032, R56 DK136601, P30 DK048520, and R01 DK128154).

Black holes are among the most extreme objects in the known universe. They squeeze enormous amounts of mass into an incredibly small region, creating gravity so intense that not even light can escape. To understand these cosmic objects, physicists rely on Einstein’s theory of general relativity and quantum mechanics.

In the early 1970s, Stephen Hawking and other researchers discovered surprising connections between the laws of thermodynamics, which describe familiar processes such as heating water on a stove, and the behavior of black holes.

“Hawking’s laws of black hole mechanics provided a satisfying connecting between extreme and ordinary physics and have been the paradigm for 50 years, but they have a serious limitation,” said Abhay Ashtekar, Atherton University Professor and Evan Pugh Professor of Physics Emeritus in the Eberly College of Science at Penn State and the leader of the research team. “They were formulated for black holes at equilibrium, or unchanging over time, but black holes are constantly changing, they form, merge and eventually evaporate. We wanted to find a way to overcome this limitation and extend the laws to black holes that are out of equilibrium.”

Ashtekar and his colleagues have now proposed a new method for determining a black hole’s entropy, a quantity that measures disorder and, according to the second law of thermodynamics, can never decrease. Their findings, published in Physical Review Letters and selected as an Editor’s Suggestion, introduce an entropy measure that is more closely connected to a black hole’s spin and energy. The researchers say this could improve scientists’ understanding of dynamic events such as black hole mergers and evaporation.

Why Hawking’s Framework Needed an Update

“The laws of black hole mechanics came directly from Einstein’s equations,” said Daniel E. Paraizo, a graduate student in physics at Penn State and an author of the paper. “Because you cannot see into a black hole, it seemed that there could be an infinite number of ways to make a black hole making their entropy infinite as well. They were also thought to only absorb energy and never radiate, so their temperature was zero.”

At first, those ideas made black holes appear incompatible with the familiar laws of thermodynamics because they seemed to have infinite entropy and no temperature. Hawking later changed that picture by using quantum mechanics to demonstrate that black holes can emit particles and energy.

“This changed the thinking about the thermodynamic properties black holes from a sort of mathematical concept described by equations, to being more of a physical reality,” Paraizo said. “This opened the door to finding analogies in black holes of entropy and temperature used in thermodynamics.”

Hawking proposed that the size of a black hole’s event horizon, the boundary beyond which even light cannot escape, is proportional to its entropy. He also showed that a black hole’s temperature depends on a combination of its mass and spin.

A Better Measure for Dynamic Black Holes

According to the researchers, the problem is that Hawking’s approach works only when a black hole is in equilibrium.

“There is a problem, though,” said Jonathan Shu, a graduate student in physics at Penn State and an author of the paper. “These analogies only really work for a black hole that is at equilibrium. In dynamic situations, event horizons can form and grow in what we call flat regions of space-time, where nothing is happening. This makes them teleological — their properties cannot be determined just by the local physics of the black hole but instead rely on prediction of events that may or may not happen in the future. Therefore, the area of event horizons cannot be a measure of the physical entropy of dynamical black holes. If we want to understand black holes that are growing, evaporating, and merging, we need a viable alternative.”

The team’s solution replaces the traditional event horizon with what physicists call a “dynamical horizon,” a concept that is already widely used in computer simulations of black holes. Unlike an event horizon, a dynamical horizon is defined by the black hole’s properties at a specific moment in time, avoiding the complications created by relying on future events.

“This allows us to extend the first and second laws of thermodynamics to black holes that are not at equilibrium, thereby overcoming the limitations of the paradigm that has been used for over half a century,” Ashtekar said. “We can apply these generalized laws to better understand evaporating black holes in quantum theory and black hole mergers, like those detected by the LIGO-Virgo-KAGRA collaboration using gravitational waves.”

The research was supported by the Penn State Atherton Professorship Program and the Penn State Eberly College of Science.

The theory accurately describes a wide range of microscopic phenomena. These include the famous double slit experiment, in which particles also display wave like behavior, and quantum tunneling, where particles have a probability of passing through a barrier even when they do not have enough energy to overcome it in the classical sense. Other key quantum effects, such as entanglement and coherence, now form the foundation of emerging technologies including quantum computing and quantum communication.

Are Complex Numbers Really Essential?

For decades, quantum mechanics has relied on complex numbers, which combine a real component with an imaginary component. In the mathematical description of a quantum state, the real part represents the amplitude, while the imaginary part represents the phase. This framework has long been considered essential for describing many quantum processes.

Even so, physicists have continued to debate whether complex numbers are truly a fundamental part of nature or simply a convenient mathematical tool. That question naturally leads to another: Could quantum mechanics be formulated using only real numbers?

Revisiting a Key Quantum Assumption

A 2021 study concluded that complex numbers are indispensable under the standard postulates of quantum mechanics (Renou et al., Nature 600, 625 (2021)). Experimental results also supported that conclusion.

Researchers from Heinrich Heine University Düsseldorf (HHU) and the German Aerospace Center (DLR), led by Professor Dr Dagmar Bruß and doctoral researcher Pedro Barrios Hita, decided to take another look at the assumptions behind that earlier work.

In a new study published in Physical Review Letters, they found that one of the postulates used in the 2021 analysis was more restrictive than necessary. By replacing it with a different, physically motivated approach for describing how quantum systems combine, they identified a family of theories that can be expressed entirely with real numbers while remaining experimentally indistinguishable from conventional quantum mechanics.

Professor Bruß said: “This means that both frameworks yield identical predictions for any conceivable experiment. Within this framework, imaginary numbers are thus not fundamentally necessary in quantum mechanics and can in principle be replaced by alternative formulations using real numbers.”

The research found that tiny sinking particles known as marine snow release dissolved carbon and nitrogen as they descend into the deep sea. Those leaked nutrients become an immediate food source for microbes living in the surrounding seawater.

Deep ocean pressure unlocks hidden nutrients

Marine snow is made up of tiny clumps of dead algae, microbes, and other organic material drifting through the ocean. According to the study, once these particles reach depths of about 2 to 6 kilometers, the enormous hydrostatic pressure begins forcing dissolved organic matter out of them.

“The pressure acts almost like a giant juicer,” says first author of the study, biologist and Associate Professor Peter Stief from research centers Nordcee and Danish Center for Hadal Research, “It squeezes dissolved organic compounds out of the particles, and microbes can use them immediately.”

The findings were published in Science Advances in the paper, “Hydrostatic pressure induces strong leakage of dissolved organic matter from ‘marine snow’ particles.”

The researchers estimate that sinking marine snow can lose as much as 50% of its original carbon and between 58% and 63% of its original nitrogen during its descent through the deep ocean.

Discovery could reshape understanding of the carbon cycle

The results also have important implications for Earth’s carbon cycle.

Scientists have long assumed that much of the carbon carried by marine snow eventually becomes buried in deep ocean sediments. However, if large amounts of carbon leak out before the particles reach the seafloor, less carbon may be permanently stored in sediments than previously believed.

Instead, much of that dissolved carbon remains suspended in deep ocean waters, where it can stay for hundreds or even thousands of years before gradually returning to the surface ocean and eventually the atmosphere. Carbon that does become buried in seafloor sediments, by contrast, can remain locked away for millions of years, accumulating over vast stretches of time. Much of the oil and natural gas extracted today formed through this long-term burial process.

“This process affects how much carbon the ocean can store and for how long,” says Peter Stief, “It’s relevant for understanding climate processes and for improving future models.”

Simulating marine snow under extreme pressure

To investigate the process, the researchers recreated marine snow in the laboratory using diatoms, microscopic algae that naturally clump together as they sink through the ocean.

The team placed these artificial particles inside specially designed rotating pressure tanks that kept the marine snow suspended instead of allowing it to settle. This setup allowed the researchers to measure how much carbon and nitrogen escaped under conditions similar to those found in the deep ocean.

Their experiments showed that up to half of a particle’s carbon content leaked out while sinking. Most of the released material consisted of proteins and carbohydrates that free-living deep ocean microbes can readily consume.

Microbes respond almost immediately

The leaked nutrients quickly fueled microbial growth.

Within just two days, bacterial abundance increased 30-fold, while respiration rates rose dramatically. These results indicate that dissolved organic matter released from marine snow provides a rapid and valuable energy source for microbes living at great depths.

The researchers also observed the same leakage pattern across multiple species of diatoms, suggesting that this mechanism is likely widespread throughout the world’s oceans.

Next stop: The Arctic Ocean

The next phase of the research will move from the laboratory to the open ocean.

The team plans to search for molecular fingerprints of this process in both surface and deep waters during a future expedition to the Arctic aboard the German research vessel Polarstern. Detecting those signatures in nature would help confirm that the pressure driven leakage observed in the laboratory is occurring throughout the deep ocean.

The study, “Hydrostatic pressure induces strong leakage of dissolved organic matter from “marine snow” particles,” was authored by Peter Stief, Jutta Niggemann, Margot Bligh, Hagen Buck-Wiese, Urban Wünsch, Michael Steinke, Jan-Hendrik Hehemann, and Ronnie N. Glud.

The research was supported by the Danish National Research Foundation, the European Union’s Horizon 2020 Research and Innovation program, and the Independent Research Fund Denmark.