Tag Archives: #relativity

Yes to Breaking the Speed-of-Light Barrier (Physics / Quantum)

It could happen if the tunnel is long enough, but the chances are basically zero.

How much time does it take to send a package from New York to Tel Aviv, and how does that compare with sending an email from one side of the Weizmann Institute of Science campus to the other? Now shrink the package down to the size of one of the electrons making up the email and put up an impenetrable barrier over the ocean. The “package” electron could make the crossing faster, even breaking the light “speed limit.”  Prof. Eli Pollak, together with postdoctoral fellow Dr. Tom Rivlin, both of the Weizmann Institute’s Chemical and Biological Physics Department, and Prof. Randall Dumont of McMaster University in Canada, recently provided theoretical support for this idea.

(l-r) Prof. Eli Pollak and Dr. Tom Rivlin © Weizmann Institute of Science

Impenetrable barriers are integral to one of the more fascinating quantum phenomena: tunneling. For around ninety years, researchers have been studying the way that quantum particles are able to pass through such barriers. In the 1960s, Thomas Hartman added a strange twist to tunneling: He showed that tunneling takes a fixed amount of time, no matter what length “tunnel” the particle transverses. That means that a particle could speed up while tunneling, and to make its goal in that fixed amount of time, it might even surpass the speed of light – if the tunnel is long enough or the barrier thick enough. Of course, this idea does not fit with the precepts of relativity – neither special nor general relativity – which are quite strict in insisting that particles cannot exceed the speed of light. Still, most researchers were not overly concerned with the results of this study, since it was already known that quantum mechanics and the physics of relativity do not jibe in many ways.

Therefore, so the thinking has been, this is another apparent anomaly that will work itself out once we figure out how to reconcile relativity with quantum mechanics. Pollak and his colleagues recently developed a new calculation of Hartman’s idea, basing it on equations for quantum behavior first developed by Paul Dirac, which enable one to perform quantum mechanical calculations that are consistent with special relativity.

Their results support the scenario in which a particle is traveling in a tunnel and the timing of the process is a constant, independent of the length of the tunnel (or the thickness of the barrier). Theoretically, if the barrier is very long, the particle may reach the end of the tunnel faster than if it had just flown to the same destination in open space with no barrier in the way. And if the particle normally travels near the speed of light, then a tunneling particle would be able to get there faster than the speed of light.

Back to those emails: Could this finding enable us to send our information faster than the speed of light? The answer, to the likely disappointment of some and relief of others, is no. Prof. Pollak: “The chances of a particular particle tunneling are quite small, and those chances decrease exponentially as the length of the tunnel or thickness of the barrier increases. So the odds of the particle carrying our information making that faster-than-light trip through the tunnel are basically zero. For now, we’ll have to content ourselves with the speeds of the existing options for sending packages and information, even if they do move slower than the speed of light.”

Reference: Randall S Dumont, Tom Rivlin and Eli Pollak, “The relativistic tunneling flight time may be superluminal, but it does not imply superluminal signaling”, New Journal of Physics, Volume 22, September 2020. https://iopscience.iop.org/article/10.1088/1367-2630/abb515/meta

Provided by Weizmann Institute of Science

Not So Fast!: Controlling the Speed of Light Bullets (Physics)

Researchers from Osaka University accurately and arbitrarily control flying velocities of light bullets, offering new opportunities for optical and physical applications.

Though it sounds like something straight out of science fiction, controlling the speed of light has in fact been a long-standing challenge for physicists. In a study recently published in Communications Physics, researchers from Osaka University generated light bullets with highly controllable velocities.

Flying light bullet with variable-velocities (see beam center) © Osaka University

According to Albert Einstein’s principle of relativity, the speed of light is constant and cannot be exceeded; however, it is possible to control the group velocity of optical pulses.

Currently, the spatiotemporal coupling of optical pulses provides an opportunity to control the group velocity of three-dimensional non-diffraction optical wave-packets, known as “light bullets,” in free space.

In their previous study (Scientific Reports, DOI: 10.1038/s41598-020-68478-1), this group found that by deforming the pulse-front of optical pulses and keeping the phase-front unchanged, the velocity and the acceleration of the generated flying Bessel-Gaussian (diffraction- and dispersion-free) light bullets can be controlled.

“However, the problem is that only one determined motion form, for example, superluminal or subluminal for velocity and accelerating or decelerating for acceleration, can be achieved in a single propagation path,” explains corresponding author Zhaoyang Li.

In this newly improved method, by using the combination of a deformable mirror and a spatial light modulator, the pulse-front of optical pulses can be arbitrarily deformed, which results in light bullets with arbitrarily-variable velocities (and accelerations) during a single propagation path; e.g., subluminal followed by superluminal and/or accelerating followed by decelerating.

“This non-diffraction light bullet with nearly-programmable flying velocities may bring new opportunities in a wide range of applications, such as free-space communication, bio-imaging, optical detection and processing, particle acceleration and manipulation, radiation generation, among others,” says Zhaoyang Li.

The article, “Optical wave-packet with nearly-programmable group velocities,” was published in Communications Physics at https://www.nature.com/articles/s42005-020-00481-4 DOI: https://doi.org/10.1038/s42005-020-00481-4.

Provided by Osaka University

About Osaka University

Osaka University was founded in 1931 as one of the seven imperial universities of Japan and is now one of Japan’s leading comprehensive universities with a broad disciplinary spectrum. This strength is coupled with a singular drive for innovation that extends throughout the scientific process, from fundamental research to the creation of applied technology with positive economic impacts. Its commitment to innovation has been recognized in Japan and around the world, being named Japan’s most innovative university in 2015 (Reuters 2015 Top 100) and one of the most innovative institutions in the world in 2017 (Innovative Universities and the Nature Index Innovation 2017). Now, Osaka University is leveraging its role as a Designated National University Corporation selected by the Ministry of Education, Culture, Sports, Science and Technology to contribute to innovation for human welfare, sustainable development of society, and social transformation.

Website: https://resou.osaka-u.ac.jp/en/top

Hubble Observed Rings Of Relativity (Astronomy /Cosmology)

The narrow galaxy elegantly curving around its spherical companion in this image is a fantastic example of a truly strange and very rare phenomenon. This image, taken with the NASA/ESA Hubble Space Telescope, depicts GAL-CLUS-022058s, located in the southern hemisphere constellation of Fornax (The Furnace). GAL-CLUS-022058s is the largest and one of the most complete Einstein rings ever discovered in our Universe. The object has been nicknamed by the Principal Investigator and his team who are studying this Einstein ring as the “Molten Ring”, which alludes to its appearance and host constellation.

GAL-CLUS-022058s Credit:ESA/Hubble & NASA, S. Jha

First theorised to exist by Einstein in his general theory of relativity, this object’s unusual shape can be explained by a process called gravitational lensing, which causes light shining from far away to be bent and pulled by the gravity of an object between its source and the observer. In this case, the light from the background galaxy has been distorted into the curve we see by the gravity of the galaxy cluster sitting in front of it. The near exact alignment of the background galaxy with the central elliptical galaxy of the cluster, seen in the middle of this image, has warped and magnified the image of the background galaxy around itself into an almost perfect ring. The gravity from other galaxies in the cluster is soon to cause additional distortions.

Objects like these are the ideal laboratory in which to research galaxies too faint and distant to otherwise see.

Provided by ESA/Hubble

RUDN University physicist Developed Software Solution To Measure The Black Holes Stability (Astronomy)

Even if a black hole can be described with a mathematical model, it doesn’t mean it exists in reality. Some theoretical models are unstable: though they can be used to run mathematical calculations, from the point of view of physics they make no sense. A physicist from RUDN University developed an approach to finding such instability regions. The work was published in the Physics of the Dark Universe journal.

Even if a black hole can be described with a mathematical model, it doesn’t mean it exists in reality. Some theoretical models are unstable: though they can be used to run mathematical calculations, from the point of view of physics they make no sense. A physicist from RUDN University developed an approach to finding such instability regions. ©RUDN University.

The existence of black holes was first predicted by Einstein’s general theory of relativity. These objects have so strong gravitational pull that nothing, not even light, can escape them. Dense and massive, black holes deform space-time (a physical construct with three spatial and one temporal dimension). Many mathematical models used to describe black holes include corrections to account for such space-time curvatures. The main condition of existence for every black hole model is its stability in cases of minor spatial or temporal changes. Mathematically unstable black holes make no physical sense, as the objects they describe cannot exist in reality. A physicist from RUDN University suggested a method to identify black hole instability parameters in 4D space-time.

“For a model to be considered feasible, a black hole described by it has to remain stable in case of minor space-time fluctuations. One of the most promising approaches to developing alternative gravity theories includes adding corrections to Einstein’s equation, including the fourth-order Gauss-Bonnet correction and the Lovelock correction that provides a higher level of generalization,” said Roman Konoplya, a researcher at the Educational and Research Institute of Gravitation and Cosmology, RUDN University.

The physicist studied stability in the Einstein-Gauss-Bonnet theory in which a black hole is described by Einstein’s equation with a fourth additional component. Previously, he had focused on a different mathematical description of a black hole, the so-called Lovelock theory, that describes a black hole as a sum of an infinite number of components. The instability region turned out to be closely associated with the values of the so-called coupling constants: numerical coefficients by which the corrections to Einstein’s equation are multiplied.

According to the physicist, the Einstein-Gauss-Bonnet model does not provide for the existence of small black holes, because if coupling constants are relatively big compared to other parameters (such as the radius of a black hole), the model almost always turns out to be unstable. The stability region is much bigger if the coupling constant has a negative value. Based on these calculations, he and his team developed a program to calculate black hole stability based on any of its parameters.

“Our approach helps test black hole models for stability. We made the code publicly available so that any of our colleagues could use it to calculate instability regions for models with an unspecified set of parameters,” added Roman Konoplya.

References: R.A.Konoplya, A.Zhidenko et al., “(In)stability of black holes in the 4D Einstein–Gauss–Bonnet and Einstein–Lovelock gravities”, Physics of the Dark Universe, Volume 30, December 2020, 100697 https://doi.org/10.1016/j.dark.2020.100697

Provided by RUDN University

Einstein’s Theory of Relativity, Critical For GPS, Seen In Distant Stars (Astronomy)

What do Albert Einstein, the Global Positioning System (GPS), and a pair of stars 200,000 trillion miles from Earth have in common?

The answer is an effect from Einstein’s General Theory of Relativity called the “gravitational redshift,” where light is shifted to redder colors because of gravity. Using NASA’s Chandra X-ray Observatory, astronomers have discovered the phenomenon in two stars orbiting each other in our galaxy about 29,000 light-years (200,000 trillion miles) away from Earth. While these stars are very distant, gravitational redshifts have tangible impacts on modern life, as scientists and engineers must take them into account to enable accurate positions for GPS.

Image credit: NASA/CXC/M. Weiss

While scientists have found incontrovertible evidence of gravitational redshifts in our solar system, it has been challenging to observe them in more distant objects across space. The new Chandra results provide convincing evidence for gravitational redshift effects at play in a new cosmic setting.

The intriguing system known as 4U 1916-053 contains two stars in a remarkably close orbit. One is the core of a star that has had its outer layers stripped away, leaving a star that is much denser than the Sun. The other is a neutron star, an even denser object created when a massive star collapses in a supernova explosion. The neutron star (grey) is shown in this artist’s impression at the center of a disk of hot gas pulled away from its companion (white star on left).

These two compact stars are only about 215,000 miles apart, roughly the distance between the Earth and the Moon. While the Moon orbits our planet once a month, the dense companion star in 4U 1916-053 whips around the neutron star and completes a full orbit in only 50 minutes. 

In the new work on 4U 1916-053, the team analyzed X-ray spectra — that is, the amounts of X-rays at different wavelengths — from Chandra. They found the characteristic signature of the absorption of X-ray light by iron and silicon in the spectra. In three separate observations with Chandra, the data show a sharp drop in the detected amount of X-rays close to the wavelengths where the iron or silicon atoms are expected to absorb the X-rays. One of the spectra showing absorption by iron is included in the main graphic, and an additional graphic shows a spectrum with absorption by silicon.

However, the wavelengths of these characteristic signatures of iron and silicon were shifted to longer, or redder wavelengths compared to the laboratory values found here on Earth (shown with the dashed line). The researchers found that the shift of the absorption features was the same in each of the three Chandra observations, and that it was too large to be explained by motion away from us. Instead they concluded it was caused by gravitational redshift. 

How does this connect with General Relativity and GPS? As predicted by Einstein’s theory, clocks under the force of gravity run at a slower rate than clocks viewed from a distant region experiencing weaker gravity. This means that clocks on Earth observed from orbiting satellites run at a slower rate. To have the high precision needed for GPS, this effect needs to be taken into account or there will be small differences in time that would add up quickly, calculating inaccurate positions.

All types of light, including X-rays, are also affected by gravity. An analogy is that of a person running up an escalator that is going down. As they do this, the person loses more energy than if the escalator was stationary or going up. The force of gravity has a similar effect on light, where a loss in energy gives a lower frequency. Because light in a vacuum always travels at the same speed, the loss of energy and lower frequency means that the light, including the signatures of iron and silicon, shift to longer wavelengths.

This is the first strong evidence for absorption signatures being shifted to longer wavelengths by gravity in a pair of stars that has either a neutron star or black hole. Strong evidence for gravitational redshifts in absorption has previously been observed from the surface of white dwarfs, with wavelength shifts typically only about 15% of that for 4U 1916-053.

Scientists say it is likely that a gaseous atmosphere blanketing the disk near the neutron star (shown in blue) absorbed the X-rays, producing these results. The size of the shift in the spectra allowed the team to calculate how far this atmosphere is away from the neutron star, using General Relativity and assuming a standard mass for the neutron star. They found that the atmosphere is located 1,500 miles from the neutron star, about half the distance from Los Angeles to New York and equivalent to only 0.7% of the distance from the neutron star to the companion. It likely extends over several hundred miles from the neutron star.

In two of the three spectra there is also evidence for absorption signatures that have been shifted to even redder wavelengths, corresponding to a distance of only 0.04% of the distance from the neutron star to the companion. However, these signatures are detected with less confidence than the ones further away from the neutron star.

Scientists have been awarded further Chandra observation time in the upcoming year to study this system in more detail.

A paper describing these results was published in the August 10th, 2020 issue of The Astrophysical Journal Letter and also appears online. The authors of the paper are Nicolas Trueba and Jon Miller (University of Michigan in Ann Arbor), Andrew Fabian (University of Cambridge, UK), J. Kaastra (Netherlands Institute for Space Research), T. Kallman (NASA Goddard Space Flight Center in Greenbelt, Maryland), A. Lohfink (Montana State University), D. Proga (University of Nevada, Las Vegas), John Raymond (Center for Astrophysics | Harvard & Smithsonian), Christopher Reynolds (University of Cambridge), and M. Reynolds and A. Zoghbi (University of Michigan).

NASA’s Marshall Space Flight Center manages the Chandra program. The Smithsonian Astrophysical Observatory’s CXC controls science and flight operations from Cambridge and Burlington, Massachusetts.

References: Nicolas Trueba, J.M. Miller, A.C. Fabian, J. Kaastra, T. Kallman, A. Lohfink, D. Proga, J. Raymond, C. Reynolds, M. Reynolds, A. Zoghbi, “A Redshifted Inner Disk Atmosphere and Transient Absorbers in the Ultra-Compact Neutron Star X-ray Binary 4U 1916-053”, ArXiv, pp. 1-15, 2020. DOI: 10.3847/2041-8213/aba9de arXiv:2008.01083

Provided by University Of Michigan

Black Hole ‘Family Portrait’ Is Most Detailed To Date (Astronomy)

An international research collaboration including Northwestern University astronomers has produced the most detailed family portrait of black holes to date, offering new clues as to how black holes form. An intense analysis of the most recent gravitational-wave data available led to the rich portrait as well as multiple tests of Einstein’s theory of general relativity. (The theory passed each test.)

A collection of masses for a wide range of compact objects. The graphic shows black holes (blue), neutron stars (orange) and compact objects of uncertain nature (gray) detected through gravitational waves. Each compact binary merger corresponds to three compact objects: the two coalescing objects and the final merger remnant. Credit: Aaron M. Geller, Northwestern University and Frank Elavsky, LIGO-Virgo.

The team of scientists who make up the LIGO Scientific Collaboration (LSC) and the Virgo Collaboration is now sharing the full details of its discoveries. This includes new gravitational-wave detection candidates which held up to scrutiny—a whopping total of 39, representing a variety of black holes and neutron stars—and new discoveries as a result of combining all the observations. The 39 events averaged more than one per week of observing.

The observations could be a key piece in solving the many mysteries of exactly how binary stars interact. A better understanding of how binary stars evolve has consequences across astronomy, from exoplanets to galaxy formation.

Details are reported in a trio of related papers which will be available in pre-print on Oct. 28 at arxiv.org. The studies also are being submitted to peer-reviewed journals.

The gravitational-wave signals on which the studies are based were detected during the first half of the third observing run, called O3a, of the National Science Foundation’s Laser Interferometry Gravitational-wave Observatory (LIGO), a pair of identical, 4-kilometer-long interferometers in the United States, and Virgo, a 3-kilometer-long detector in Italy. The instruments can detect gravitational-wave signals from many sources, including colliding black holes and colliding neutron stars.

“Gravitational-wave astronomy is revolutionary—revealing to us the hidden lives of black holes and neutron stars,” said Christopher Berry, an LSC member and author of the papers. “In just five years we have gone from not knowing that binary black holes exist to having a catalog of over 40. The third observing run has yielded more discoveries than ever before. Combining them with earlier discoveries paints a beautiful picture of the universe’s rich variety of binaries.”

This illustration shows the merger of two black holes and the gravitational waves that ripple outward as the black holes spiral toward each other. Credit: LIGO/T. Pyle.

Berry is the CIERA Board of Visitors Research Professor in Northwestern’s CIERA (Center for Interdisciplinary Exploration and Research in Astrophysics) and a lecturer at the University of Glasgow. Other Northwestern authors include CIERA members Maya Fishbach and Chase Kimball. CIERA is home to a broad group of researchers in theory, simulation and observation who study black holes, neutron stars, white dwarfs and more.

As a member of the collaboration, Northwestern researchers analyzed data from the gravitational-wave detectors to infer the properties of detected black hole and neutron star binaries and to provide an astrophysical interpretation of these discoveries.

The papers are summarized as follows:

The “catalog paper” details the detections of black holes and neutron stars from the first half of O3a, bringing the total number of detection candidates for that period to 39. This number vastly exceeds detections from the first two observing runs. (The first run had three gravitational-wave detections, and the second had eight.) Previously announced detections from O3a include a mystery object in the mass gap (GW190814) and the first-of-its-kind intermediate mass black hole (GW190521).

In the “populations paper,” the researchers reconstructed the distribution of masses and spins of the black hole population and estimated the merger rate for binary neutron stars. The results will help scientists understand the detailed astrophysical processes which shape how these systems form. This improved understanding of the mass distribution of black holes and knowing that black hole spins can be misaligned suggests there could be multiple ways for binary black holes to form.

Using the set of detections reported in the catalog paper, the researchers conducted detailed analysis by combining everything together. In what they call the “testing general relativity paper,” the authors placed constraints on Einstein’s theory of general relativity. The theory passed with flying colors, and they updated their best measurements on potential modifications.

“So far, LIGO and Virgo’s third observing run has yielded many surprises,” said Fishbach, a NASA Einstein Postdoctoral Fellow and LSC member. “After the second observing run, I thought we’d seen the whole spectrum of binary black holes, but the landscape of black holes is much richer and more varied than I imagined. I’m excited to see what future observations will teach us.”

Fishbach coordinated writing of the populations paper which outlines what the collaboration has learned about the properties of the family of merging black holes and neutron stars.

This illustration generated by a computer model shows multiple black holes found within the heart of a dense globular star cluster. Credit: Aaron M. Geller, Northwestern University/CIERA

Berry helped coordinate analysis as part of a global team to infer the properties of the detections, and he served as an LSC Editorial Board reviewer for the catalog and testing general relativity papers.

Graduate student Chase Kimball, an LSC member, contributed calculations of the rates of mergers to the populations paper. Kimball is co-advised by Berry and Vicky Kalogera, the principal investigator of Northwestern’s LSC group, director of CIERA and the Daniel I. Linzer Distinguished University Professor of Physics and Astronomy in the Weinberg College of Arts and Sciences.

The LIGO and Virgo detectors finished their latest observing run this past March. The data analyzed in these three papers were collected from April 1, 2019, to Oct. 1, 2019. Researchers are in the process of analyzing data from the second half of the observing run, O3b.

The detectors are scheduled to resume observing next year after work is done to increase their detection range.

“Merging black hole and neutron star binaries are a unique laboratory,” Berry said. “We can use them to study both gravity—so far Einstein’s general relativity has passed every test —and the astrophysics of how massive stars live their lives. LIGO and Virgo have transformed our ability to observe these binaries, and, as our detectors improve, the rate of discovery is only going to accelerate.”

References: (1) The “populations” paper is titled “Population properties of compact objects from the second LIGO-Virgo Gravitational-Wave Transient Catalog.” (2) The “catalog” paper is titled “GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run.” (3) The “testing general relativity” paper is titled “Tests of General Relativity with Binary Black Holes from the second LIGO-Virgo.”

Provided by Northwestern University

Timekeeping Theory Combines Quantum Clocks And Einstein’s Relativity (Physics)

A phenomenon of quantum mechanics known as superposition can impact timekeeping in high-precision clocks, according to a theoretical study from Dartmouth College, Saint Anselm College and Santa Clara University.

Quantum mechanics allows for a clock to move as if it were simultaneously traveling at two different speeds. New research finds that this leads to a correction in atomic clocks known as “quantum time dilation.” Credit: Petra Korlevic.

Research describing the effect shows that superposition—the ability of an atom to exist in more than one state at the same time—leads to a correction in atomic clocks known as “quantum time dilation.”

The research, published in the journal Nature Communications, takes into account quantum effects beyond Albert Einstein’s theory of relativity to make a new prediction about the nature of time.

“Whenever we have developed better clocks, we’ve learned something new about the world,” said Alexander Smith, an assistant professor of physics at Saint Anselm College and adjunct assistant professor at Dartmouth College, who led the research as a junior fellow in Dartmouth’s Society of Fellows. “Quantum time dilation is a consequence of both quantum mechanics and Einstein’s relativity, and thus offers a new possibility to test fundamental physics at their intersection.”

In the early 1900s, Albert Einstein presented a revolutionary picture of space and time by showing that the time experienced by a clock depends on how fast it is moving—as the speed of a clock increases, the rate at which it ticks decreases. This was a radical departure from Sir Isaac Newton’s absolute notion of time.

Quantum mechanics, the theory of motion governing the atomic realm, allows for a clock to move as if it were simultaneously traveling at two different speeds: a quantum “superposition” of speeds. The research paper takes this possibility into account and provides a probabilistic theory of timekeeping, which led to the prediction of quantum time dilation.

To develop the new theory, the team combined modern techniques from quantum information science with a theory developed in the 1980s that explains how time might emerge out of a quantum theory of gravity.

“Physicists have sought to accommodate the dynamical nature of time in quantum theory for decades,” said Mehdi Ahmadi, a lecturer at Santa Clara University who co-authored the study. “In our work, we predict corrections to relativistic time dilation which stem from the fact that the clocks used to measure this effect are quantum mechanical in nature.”

In the same way that carbon dating relies on decaying atoms to determine the age of organic objects, the lifetime of an excited atom acts as a clock. If such an atom moves in a superposition of different speeds, then its lifetime will either increase or decrease depending on the nature of the superposition relative to an atom moving at a definite speed.

The correction to the atom’s lifetime is so small that it would be impossible to measure in terms that make sense at the human scale. But the ability to account for this effect could enable a test of quantum time dilation using the most advanced atomic clocks.

Just as the utility of quantum mechanics for medical imaging, computing, and microscopy, might have been difficult to predict when that theory was being developed in the early 1900s, it is too early to imagine the full practical implications of quantum time dilation.

References: Smith, A.R.H., Ahmadi, M. Quantum clocks observe classical and quantum time dilation. Nat Commun 11, 5360 (2020). https://doi.org/10.1038/s41467-020-18264-4 link: http://dx.doi.org/10.1038/s41467-020-18264-4

Provided by Dartmouth College

What Will Be The Effect On The Mass Of Neutron Stars On Higher Dimensions?? (Astronomy)

Many theories allow existence of higher dimensions that are non compact. Study of stability and structure of stars in such a framework is interesting and explored by different groups. All these studies have been performed for compact objects like white dwarfs, neutron stars, and black holes; all of which exhibit strong field gravity. These studies were mostly analytical and did not give numerical values of observable properties like the mass, radius, gravitational redshift, etc. for the stars. The reason for this is the fact that we do not know the value of the gravitational constant and properties of matter at higher dimensions. In the present work, M. Bagchi provided values of these observables for a few dimensions and discuss possible observational aspects.

Tolman-Oppenheimer-Volkoff equations, are equations which determines the structure of a spherically symmetric body of isotropic material in equilibrium, in general relativity (GR). It is widely used in the study of properties of compact stars.

In her paper, she expressed

these Tolman-Oppenheimer-Volkoff equations in terms of parameters of 4 dimensional spacetime and solved numerically for 4 (n= 1), 5 (n =2), 6 (n =3), and 7 (n = 4) dimensions using a standard equation of state for the neutron star matter derived for the 4 dimensional spacetime.

Mass-radius plots (solid lines) for APR Equation of state obtained for n = 1, 2, 3, and 4 where n = (D-3). The hatched region in the top-left corner is the region of singularity. The limit of compactness are shown for each n with dashed lines. The lines for gravitational redshift parameter z = 0.05, 0.1, 0.14, 0.2, 0.3, and 0.7 are shown with dotted lines.
Maximum mass and corresponding radius and central density for n = 1, 2, 3, and 4 where n = D-3.

You can see in above table, it has been shown that with the increase of the dimensionality, the maximum value of the mass of the neutron star decreases and the stars become less compact means 7-D neutron star have mass of just 1.35 compared to 4-D neutron star which has 2.19. While the radius and corresponding central density of the neutron star increases with the increase of the dimensionality. Thus, although the compactness limit decreases with increased dimensionality, neutron stars never violate this limit.

However, it still remains an open question whether low mass neutron stars have just low central density, or they belong to higher dimensions. In principle, if one can measure mass, radius, and gravitational redshift for a neutron star i.e. M, R, z – all three at the same time it would be possible to constrain both the equation of state, central density and the dimension of the spacetime inside that object. This will be an extremely challenging task for observational astronomers, but not impossible by combining timing and spectral analysis of binary pulsars. Where timing analysis of binary pulsars would result in measurements of the mass of the star while the spectral analysis would give the radius (using the value of the mass obtained from timing analysis) and gravitational redshift (if any known spectral line is detected).

References: Manjari Bagchi, “A study of neutron stars in D≥4 dimensions”, ArXiv, pp. 1-8, 2020. arXiv:2010.08928 link: https://arxiv.org/abs/2010.08928

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What Is An Arrow Of Time? (Quantum Mechanics)

Time appears to have a direction, to be inherently directional: the past lies behind us and is fixed and immutable, and accessible by memory or written documentation; the future, on the other hand, lies ahead and is not necessarily fixed, and, although we can perhaps predict it to some extent, we have no firm evidence or proof of it. Most of the events we experience are irreversible: for example, it is easy for us to break an egg, and hard, if not impossible, to unbreak an already broken egg. It appears inconceivable to us that that this progression could go in any other direction. This one-way direction or asymmetry of time is often referred to as the arrow of time, and it is what gives us an impression of time passing, of our progressing through different moments. The arrow of time, then, is the uniform and unique direction associated with the apparent inevitable “flow of time” into the future.

The idea of an arrow of time was first explored and developed to any degree by the British astronomer and physicist Sir Arthur Eddington back in 1927, and the origin of the phrase is usually attributed to him. What interested Eddington is that exactly the same arrow of time would apply to an alien race on the other side of the universe as applies to us. It is therefore nothing to do with our biology or psychology, but with the way the universe is. The arrow of time is not the same thing as time itself, but a feature of the universe and its contents and the way it has evolved.

Is the Arrow of Time an Illusion?

In order to know you must have knowledge of Relativity or Relativistic Time. If you a beginner, let me tell you, according to the Theory of Relativity, the reality of the universe can be described by four-dimensional space-time, so that time does not actually “flow”, it just “is”. The perception of an arrow of time that we have in our everyday life therefore appears to be nothing more than an illusion of consciousness in this model of the universe, an emergent quality that we happen to experience due to our particular kind of existence at this particular point in the evolution of the universe.

Perhaps even more interesting and puzzling is the fact that, although events and processes at the macroscopic level – the behaviour of bulk materials that we experience in everyday life – are quite clearly time-asymmetric (i.e. natural processes DO have a natural temporal order, and there is an obvious forward direction of time), physical processes and laws at the microscopic level, whether classical, relativistic or quantum, are either entirely or mostly time-symmetric. If a physical process is physically possible, then generally speaking so is the same process run backwards, so that, if you were to hypothetically watch a movie of a physical process, you would not be able to tell if it is being played forwards or backwards, as both would be equally plausible.

In theory, therefore, most of the laws of physics do not necessarily specify an arrow of time. There is, however, an important exception: the Second Law of Thermodynamics.

Thermodynamic Arrow of Time

Most of the observed temporal asymmetry at the macroscopic level – the reason we see time as having a forward direction – ultimately comes down to thermodynamics, the science of heat and its relation with mechanical energy or work, and more specifically to the Second Law of Thermodynamics. This law states that, as one goes forward in time, the net entropy (degree of disorder) of any isolated or closed system will always increase (or at least stay the same).

The concept of entropy and the decay of ordered systems was explored and clarified by the German physicist Ludwig Boltzmann in the 1870s, building on earlier ideas of Rudolf Clausius, but it remains a difficult and often misunderstood idea. Entropy can be thought of, in most cases, as meaning that things (matter, energy, etc) have a tendency to disperse. Thus, a hot object always dissipates heat to the atmosphere and cools down, and not vice versa; coffee and milk mix together, but do not then separate; a house left unattended will eventually crumble away, but a pile of bricks never spontaneously forms itself into a house; etc. However, as discussed below, it is not quite as simple as that, and a better way of thinking of it may be as a tendency towards randomness.

It should be noted that, in thermodynamic systems that are NOT closed, it is quite possible that entropy can decrease with time (e.g. the formation of certain crystals; many living systems, which may reduce local entropy at the expense of the surrounding environment, resulting in a net overall increase in entropy; the formation of isolated pockets of gas and dust into stars and planets, even though the entropy of the universe as a whole continues to increase; etc). Any localized or temporary instances of order within the universe are therefore in the nature of epiphenomena within the overall picture of a universe progressing inexorably towards disorder.

It is also perhaps counter-intuitive, but nevertheless true, that overall entropy actually increases even as large-scale structure forms in the universe (e.g. galaxies, clusters, filaments, etc), and that dense and compact black holes have incredibly high entropy, and actually account for the overwhelming majority of the entropy in today’s universe. Likewise, the relatively smooth configuration of the very early universe (see the section on Time and the Big Bang) is actually an indication of very low overall entropy (i.e. high entropy does not necessarily imply smoothness: random “lumpiness”, like in our current universe, is actually a characteristic of high entropy).

Most of the processes that appear to us to be irreversible in time are those that start out, for whatever reason, in some very special, highly-ordered state. For example, a new deck of cards are in number order, but as soon as we shuffle them they become disordered; an egg is a much more ordered state than a broken or scrambled egg; etc. There is nothing in the laws of physics that prevents the act of shuffling a deck of cards from producing a perfectly ordered set of cards – there is always a chance of that, it is just a vanishingly small chance. To give another example, there are many more possible disordered arrangements of a jigsaw than the one ordered arrangement that makes a complete picture. So, the apparent asymmetry of time is really just an asymmetry of chance – things evolve from order to disorder not because the reverse is impossible, but because it is highly unlikely. The Second Law of Thermodynamics is therefore more a statistical principle than a fundamental law (this was Boltzmann’s great insight). But the upshot is that, provided the initial condition of a system is one of relatively high order, then the tendency will almost always be towards disorder.

Thermodynamics, then, appears to be one of the only physical processes that is NOT time-symmetric, and so fundamental and ubiquitous is it in our universe that it may be single-handedly responsible for our perception of time as having a direction. Indeed, several of the other arrows of time noted below (arguably) ultimately come back to the asymmetry of thermodynamics. Indeed, so clear is this law that the measurement of entropy has been put forward a way of distinguishing the past from the future, and the thermodynamic arrow of time has even been put forward as the reason we can remember the past but not the future, due to the fact that the entropy or disorder was lower in the past than in the future.

Cosmological Arrow of Time

It has been argued that the arrow of time points in the direction of the universe’s expansion, as the universe continues to grow bigger and bigger since its beginning in the Big Bang. It became apparent towards the beginning of the 20th Century, thanks to the work of Edwin Hubble and others, that space is indeed expanding, and the galaxies are moving ever further apart. Logically, therefore, at a much earlier time, the universe was much smaller, and ultimately concentrated in a single point or singularity, which we call the Big Bang. Thus, the universe does seem to have some intrinsic (outward) directionality. In our everyday lives, however, we are not physically conscious of this movement, and it is difficult to see how we can perceive the expansion of the universe as an arrow of time.

The cosmological arrow of time may be linked to, or even dependent on, the thermodynamic arrow, given that, as the universe continues to expand and heads towards an ultimate “Heat Death” or “Big Chill”, it is also heading in a direction of increasing entropy, ultimately arriving at a position of maximum entropy, where the amount of usable energy becomes negligible or even zero. This accords with the Second Law of Thermodynamics in that the overall direction is from the current semi-ordered state, marked by outcroppings of order and structure, towards a completely disordered state of thermal equilibrium. What remains a major unknown in modern physics, though, is exactly why the universe had a very low entropy at its origin, the Big Bang.

It is also possible – although less likely according to the predictions of current physics – that the present expansion phase of the universe could eventually slow, stop, and then reverse itself under gravity. The universe would then contract back to a mirror image of the Big Bang known as the “Big Crunch” (and possibly a subsequent “Big Bounce” in one of a series of cyclic repetitions). As the universe contracts and collapses, entropy will in theory start to reduce and, presumably, the arrow of time will reverse itself and time will effectively begin to run backwards. In this scenario, then, the arrow of time that we experience is merely a function of our current place in the evolution of the universe and, at some other time, it could conceivably change its direction.

However, there are paradoxes associated with this view because, looked at from a suitably distant and long-term viewpoint, time will continue to progress “forwards” (in some respects at least), even if the universe happens to be in a contraction phase rather than an expansion phase. So, the cosmic asymmetry of time could still continue, even in a “closed” universe of this kind.

Radiative Arrow of Time

Waves, like light, radio waves, sound waves, water waves, etc, are always radiative and expand outwards from their sources. While theoretical equations do allow for the opposite (covergent) waves, this is apparently never seen in nature. This asymmetry is regarded by some as a reason for the asymmetry of time.

It is possible that the radiative arrow may also be linked to the thermodynamic arrow, because radiation suggests increased entropy while convergence suggests increased order. This becomes particularly clear when we consider radiation as having a particle aspect (i.e. as consisting of photons) as quantum mechanics suggests.

Quantum Arrow of Time

The whole mechanism of quantum mechanics (or at least the conventional Copenhagen interpretation of it) is based on Schrödinger’s Equation and the collapse of wave functions, and this appears to be a time-asymmetric phenomenon. For example, the location of a particle is described by a wave function, which essentially gives various probabilities that the particle is in many different possible positions (or superpositions), and the wave function only collapses when the particle is actually observed. At that point, the particle can finally be said to be in one particular position, and all the information from the wave function is then lost and cannot be recreated. In this respect, the process is time-irreversible, and an arrow of time is created.

Some physicists, including the team of Aharonov, Bergmann and Lebowitz in the 1960s, have questioned this finding, though. Their experiments concluded that we only get time-asymmetric answers in quantum mechanics when we ask time-asymmetric questions, and that questions and experiments can be framed in such a way that the results are time-symmetric. Thus, quantum mechanics does not impose time asymmetry on the world; rather, the world imposes time asymmetry on quantum mechanics.

It is not clear how the quantum arrow of time, if indeed it exists at all, is related to the other arrows, but it is possible that it is linked to the thermodynamic arrow, in that nature shows a bias for collapsing wave functions into higher entropy states versus lower ones.

Weak Nuclear Force Arrow of Time

Of the four fundamental forces in physics (gravity, electromagnetism, the strong nuclear force and the weak nuclear force), the weak nuclear force is the only one that does not always manifest complete time symmetry. To some limited extent, therefore, there is a weak force arrow of time, and this is the only arrow of time which appears to be completely unrelated to the thermodynamic arrow.

The weak nuclear force is a very weak interaction in the nucleus of an atom, and is responsible for, among other things, radioactive beta decay and the production of neutrinos. It is perhaps the least understood and strangest of the fundamental forces. In some situations the weak force is time-reversible, e.g. a proton and an electron can smash together to produce a neutron and a neutrino, and a neutron and a neutrino smashed together CAN also produce a proton and an electron (even if the chances of this happening in practice are very small). However, there are examples of the weak interaction that are time-irreversible, for example the case of the oscillation and decay of neutral kaon and anti-kaon particles. Under certain conditions, it has been shown experimentally that kaons and anti-kaons actually decay at different rates, indicating that the weak force is not in fact time-reversible, thereby establishing a kind of arrow of time.

It should be noted, though, that this is not such a strong or fundamental arrow of time as the thermodynamic arrow (the difference is between a process that could go either way but in a slightly different way or at a different rate, and a truly irreversible process – like entropy – that just cannot possibly go both ways). Indeed, it is such a rare occurrence, so small and barely perceivable in its effect, and so divorced from any of the other arrows, that it is usually characterized as an inexplicable anomaly.

Causal Arrow of Time

Although not directly related to physics, causality appears to be intimately bound up with time’s arrow. By definition, a cause precedes its effect. Although it is surprisingly difficulty to satisfactorily define cause and effect, the concept is readily apparent in the events of our everyday lives. If we drop a wineglass on a hard floor, it will subsequently shatter, whereas shattered glass on the floor is very unlikely to subsequently result in an unbroken held wine glass. By causing something to happen, we are to some extent controlling the future, whereas whatever might do we cannot change or control the past.

Once again, though, the underlying principle may well come back to the thermodynamic arrow: while disordered shattered glass can easily be made out of a well-ordered wineglass, the reverse is much more difficult and unlikely.

Psychological Arrow of Time

A variant of the causal arrow is sometimes referred to as the psychological or perceptual arrow of time. We appear to have an innate sense that our perception runs from the known past to the unknown future. We anticipate the unknown, and automatically move forward towards it, and, while we are able to remember the past, we do not normally waste time in trying to change the already known and fixed past.

Stephen Hawking has argued that even the psychological arrow of time is ultimately dependent on the thermodynamic arrow, and that we can only remember past things because they form a relatively small set compared to the potentially infinite number of possible disordered future sets.

Anthropic Principle

Some thinkers, including Stephen Hawking again, have pinned the direction of the arrow of time on what is sometimes called the weak anthropic principle, the idea that the laws of physics are as they are solely because those are the laws that allow the development of sentient, questioning beings like ourselves. It is not that the universe is in some way “designed” to allow human beings, merely that we only find ourselves in such a universe because it is as it is, even though the universe could easily have developed in a quite different way with quite different laws.

Thus, Hawking argues, a strong thermodynamic arrow of time is a necessary condition for intelligent life as we know it to develop. For example, beings like us need to consume food (a relatively ordered form of energy) and convert it into heat (a relatively disordered form of energy), for which a thermodynamic arrow like the one we see around us is necessary. If the universe were any other way, we would not be here to observe it.

This article is republished here from exactly what is time under common creative licenses