PSR 1913 +16 Research Articles

PINT: Maximum-likelihood Estimation of Pulsar Timing Noise Parameters

PINT is a pure-Python framework for high-precision pulsar timing developed on top of widely used and well-tested Python libraries, supporting both interactive and programmatic data analysis workflows. We present a new frequentist framework within PINT to characterize the single-pulsar noise processes present in pulsar timing data sets. This framework enables parameter estimation for both uncorrelated and correlated noise processes, as well as model comparison between different timing and noise models in a computationally inexpensive way. We demonstrate the efficacy of the new framework by applying it to simulated data sets as well as a real data set of PSR B1855+09. We also describe the new features implemented in PINT since it was first described in the literature.

Einstein's relativity falsified: I. The factor γ can take values larger than √2, which requires a speed of light < c in moving inertial frames

Considering that an Einstein clock can travel at a speed no greater than c, from the principle of relativity, a kinematic time dilation factor can be derived whose value cannot be greater than <mml:math display="inline"> <mml:msqrt> <mml:mn>2</mml:mn> </mml:msqrt> </mml:math> . In fact, however, the kinematic time dilation factor γ can approach an infinite value. This discrepancy demonstrates that the derivation of the kinematic time dilation factor γ in Einstein's special relativity (SR) cannot be physically justified by the principle of relativity, and that it is not physically possible that the speed of light is constant in any frame of reference. The mathematical method of Einstein's SR, which I refer to as the “mathematical method of relativity,” allows the calculation of constant physical values from different quantities of any physical unit and is thus scientifically worthless. Accordingly, it is not surprising that it is possible to predict so-called general relativistic phenomena, e.g., the phenomena observed at the binary pulsar PSR B1913 + 16, just by applying Kepler's second law and simple quantum physical considerations [R. G. Ziefle, Phys. Essays 33, 99 (2020)]. A careful interpretation of interferometer experiments on Earth clearly shows that there is in fact no need for artificial time acceleration by length contraction. However, today's physicists seem to be lost in mathematics. The aim of this paper is to contribute to a physical theory of relativity that does not require mathematical tricks, such as time acceleration (length contraction), space-time curvature, and other mathematical tricks that follow from Einstein's mathematical methods and uphold the illusion that the belief in a constant speed of light c in any frame of reference is physically justified.

Stringent pulsar timing bounds on light scalar couplings to matter

Pulsar Timing constraints on scalar-tensor theories with conformal and disformal couplings to matter are discussed. Reducing the dynamics to the motion in the centre of mass frame and using the mean anomaly parametrisation, we find the first post-Newtonian corrections induced by the conformal and disformal interactions in the form of a generalized quasi-Keplerian solution. We also derive the radiation reaction force due to scalar radiation and the corresponding Post-Keplerian Parameters (PKP). We use different pulsar time of arrival (TOA) data sets to probe the scalar corrections to the PKP. In particular, we focus on systems with large orbital frequencies as the contributions to the PKP terms induced by the disformal coupling are sensitive to higher frequencies. We find that the most constraining { {pulsar timings}} are PSR B1913+16 and the double pulsar PSR J0737-3039A/B, being {{of the order of}} the Cassini bound on the conformal coupling obtained from the Shapiro effect in the solar system. { {The combined constraints using other pulsar timings give an upper bound on the conformal coupling $\beta^2 < 2.33 \cdot 10^{-5}$ and a lower bound on the disformal coupling scale of $\Lambda \geq 1.12 \ {\rm MeV}$ which is comparable to the Cassini bound and to the GW-170817 constraints respectively}}. Future measurements for pulsar timing with black hole companions are also discussed.

Gravitational radiation from binary systems in f(R) gravity: A semi-classical approach

The rate of energy loss and orbital period decay of quasi- stable compact binary systems are derived in f(R) theory of gravity using the method of a single vertex graviton emission process from a classical source. After linearising the f(R) action written in an equivalent scalar-tensor format in the Einstein frame, we identify the appropriate interaction terms between the massless spin-2 tensor mode, massive scalar mode, and the energy momentum tensor. The definition of the scalar field is related to the f(R) models. Then using the interaction vertex we compute the rate of energy loss due to spin-2 quadrupole radiation, which comes out to be the same as the Peter-Mathews formula with a multiplication factor, and also the energy loss due to the scalar dipole radiation. The total energy loss is the sum of these two contributions. Our derivation is most general as it is applicable for both arbitrary eccentricity of the binary orbits and arbitrary mass of the scalar field. Using the derived theoretical formula for the period decay of the binary systems, we compare the predictions of f(R) gravity and general relativity for the observations of four binary systems, i.e. Hulse-Taylor Binary, PSR J1141-6545, PSR J1738+0333, and PSR J0348+0432. Thus we put bound on three well-known f(R) dark energy models, namely the Hu-Sawicki, the Starobinsky, and the Tsujikawa model. We get the best constraint on f'(R 0)-1 (where R 0 is the scalar curvature of the Universe at the present epoch) from the Tsujikawa model, i.e |f'(R 0)-1| < 2.09 × 10-4. This bound is stronger than those from most of the astrophysical observations and even some cosmological observations.

Absurd: Einstein’s special relativity (SR) causes an inconstant speed of light, claiming to explain the consequences of a constant speed c

Einstein was led astray by a physically incorrect calculation by Michelson and Morley in the context of the Michelson‐Morley experiment. For the light beam in the horizontal light path, their calculation yields the claim that [(1 − v/c) × c] + [(1 + v/c) × c] = 2[(1 − v2/c2) × c]. This is incorrect and mathematically increases the horizontal light path 2d 0 by the factor [(1 + v2/c2)], which Einstein’s theory of special relativity corrects by introducing the time dilation factor γ and the length contraction factor 1/γ. When we calculate correctly, the mathematical increase in the length of horizontal light path no longer happens and Einstein’s mathematical corrections of the horizontal light path imply an inconstancy of the speed of light. This means that Einstein’s special relativity is just a mathematical correction of a physical calculation error, not a true physical theory, and it was thus pure chance that Einstein found the physically real kinematic time dilation factor γ. The null result of the Michelson‐Morley experiment, along with the kinematic and gravitational time dilation, must instead be explained by a constant value for the speed c of light with respect to the gravitational potentials of predominant gravitational fields, resulting from the principles of minimum energy and energy conservation. On this basis, it becomes possible to predict so-called general relativistic phenomena, e.g., the precession of Mercury’s perihelion or the phenomena observed in the binary pulsar PSR B1913 + 16, just by applying Kepler’s second law and simple quantum physical considerations. [R. G. Ziefle, Phys. Essays 33, 99 (2020)].

Four hints and test candidates of the local cosmic expansion

The expansion of the universe on short distance scales is a new frontier to investigate the dark energy. The excess orbital decay in binary pulsars may be related to acceleration by the local cosmic expansion, called the cosmic drag. Modern observations of two independent binaries (PSR B1534+12 and PSR B1913+16) support this interpretation and result in a scale-independent expansion with viscous uniformity, in which binary systems have a smaller expansion rate than the Hubble constant. This paper shows additional evidential binaries (PSR J1012-5307 and PSR J1906+0746), supporting the cosmic drag picture. The total anomaly of the conventional model is about $3.6\,\sigma$ including two evidential binaries reported before. In addition, an observable range of the cosmic drag has been calculated for typical models of both NS-NS binary and NS-WD binary. In this region, six test candidates are listed with predictions of the excess orbital decay.

Out-of-plane equilibrium points of extra-solar planets in the central binaries PSR B1620-26 and Kepler-16 with clusters of material points and variable masses

In this paper, the existence and stability of the out-of-plane equilibrium points of extra-solar planets using the model of the restricted three-body problem, when the central binaries are surrounded by a clusters of material points and their motion is described by the Gylden-Mestschersky problem, is investigated. The masses of the central binaries and the clusters of material points are assumed to vary with time at the same rate in accordance with the unified Mestschersky law. The governing non-autonomous equations of motion of the model is obtained and for a complete transformation to the autonomized systems to be obtainable, we assume that the mass of the clusters of materials varies at the same rate as the masses of the central binaries while the radius and the parameters which determines the density profile of the clusters vary at the same rate as the distances. Thus, we introduce a transformation which defines the mass variation of the clusters with the help of the unified Mestschersky law and the Mestschersky transformation and obtain the autonomized system with constant coefficients. Next, the coordinates of the out-of-plane points are found using perturbation method, the Newton-Raphson's method and analytical approximations in the form of power series in the cluster's mass coefficient. The existence of these points depends solely on the mass variation parameter κ, although the points are however affected by the total mass of the clusters of material points Md and the mass parameter υ. Two pairs of out-of-plane equilibrium points are found; the first pair of equilibrium points L6,7 exists for κ>1 while the second pair L8,9 exists for κ>1 and ξ<υ(κ−1), where ξ is the abscissa of the out-of-plane equilibrium points. Further, for our numerical evidence, we compute the out-of-plane equilibrium points of two extra-solar planets PSR B1620-26b and Kepler-16b, in the binary systems PSR B1620-26 and Kepler-16, respectively. Our numerical results shows that the equilibrium points for PSR B1620-26b, exist when the mass variation parameter and the mass of the clusters lie in the intervals 1<κ≤4 and 0≤Md≤0.04, respectively, while for Kepler-16b, the points exist for 1<κ≤4.1 and 0≤Md≤0.04. Also, it is seen that in the absence of the clusters more out-of-plane equilibrium points evolve and are located far away from the line joining the binaries, while in the presence of the clusters, less out-of-plane equilibrium points evolve, but the evolved points are located closest to the line joining the binaries. Finally, we analyze the stability of the equilibrium points of the autonomized and non-autonomous systems, and both were found to be unstable equilibrium points.

Contradiction in Einstein’s subjective explanation of the gravitational and kinematic time dilation

Einstein’s special and general relativity are relics from before quantum physics. If forces are transmitted by quanta, this must also apply to gravity. As light consist of quanta, it is only logical that gravitational quanta interact with light. In my article “Cognitive bias in physics with respect to Einstein’s relativity, demonstrated by the famous experiment of Pound and Rebka (1960), which in reality refutes Einstein’s general relativity” [R. G. Ziefle, Phys. Essays 35, 91 (2022)], I could demonstrate that Einstein’s “proper time” t 0 does not refer to reference frames but to gravitational potentials. That is why “Newtonian quantum gravity” [R. G. Ziefle, Phys. Essays 33, 99 (2020)] can predict the correct curvature of a light beam at the surface of the Sun. Also, the phenomena observed at the binary pulsar PSR B1913 + 16 can precisely be predicted by merely applying Kepler’s second law. If gravitational quanta move away from masses with the constant speed c of light, this coincides with Einstein’s postulate of a constant speed c of light with respect to reference frames, as a mass, such as a star or a planet, can also be defined as a reference frame. Therefore, Einstein’s found by chance an artificial and complicated method to calculate changes in space-time caused by motion, which are in reality additional gravitational effects caused by the relative velocity between gravitational quanta emitted by masses and other masses or photons.

Anisotropic relativistic fluid spheres with a linear equation of state

In this work, we present a class of relativistic and well-behaved solution to the Einstein’s field equations for anisotropic matter distribution. We perform our analysis by using the Buchdahl ansatz for the metric function grr. Three different classes of new exact solution are found for anisotropy factor Δ. We have analyzed our model with various physical aspects such as pressure (radial as well as transverse), energy density, anisotropy factor, mass, compactness parameter, adiabatic index γ and surface redshift. A graphical analysis of energy conditions, TOV equation and causality condition indicates the model is well behaved. The physical acceptability of the model has been verified by considering compact objects with similar mass and radii, such as 4U 1820-30, Vela X-1, PSR J1614-2230, LMC X-4, SMC X-1, 4U 1538-52, Her X-1, Cyg X-2, PSR B1913+16 and PSR J1903+327.

A search for planetary companions around 800 pulsars from the Jodrell Bank pulsar timing programme

ABSTRACT We have searched for planetary companions around 800 pulsars monitored at the Jodrell Bank Observatory, with both circular and eccentric orbits of periods between 20 d and 17 yr and inclination-dependent planetary masses from 10−4 to $100\, \mathrm{M}_{\oplus }$. Using a Bayesian framework, we simultaneously model pulsar timing parameters and a stationary noise process with a power-law power spectral density. We put limits on the projected masses of any planetary companions, which reach as low as 1/100th of the mass of the Moon ($\sim 10^{-4}\, \mathrm{M}_{\oplus }$). We find that two-thirds of our pulsars are highly unlikely to host any companions above $2-8\, \mathrm{M}_{\oplus }$. Our results imply that fewer than $0.5{{\ \rm per\ cent}}$ of pulsars could host terrestrial planets as large as those known to orbit PSR B1257+12 ($\sim 4\, \mathrm{M}_{\oplus }$); however, the smaller planet in this system ($\sim 0.02\, \mathrm{M}_{\oplus }$) would be undetectable in $95{{\ \rm per\ cent}}$ of our sample, hidden by both instrumental and intrinsic noise processes, although it is not clear whether such tiny planets could exist in isolation. We detect significant periodicities in 15 pulsars; however, we find that intrinsic quasi-periodic magnetospheric effects can mimic the influence of a planet, and for the majority of these cases we believe this to be the origin of the detected periodicity. Notably, we find that the highly periodic oscillations in PSR B0144+59 are correlated with changes in the pulse profile and therefore can be attributed to magnetospheric effects. We believe the most plausible candidate for planetary companions in our sample is PSR J2007+3120.

The Orbital-decay Test of General Relativity to the 2% Level with 6 yr VLBA Astrometry of the Double Neutron Star PSR J1537+1155

Abstract PSR J1537+1155, also known as PSR B1534+12, is the second discovered double neutron star (DNS) binary. More than 20 yr of timing observations of PSR J1537+1155 have offered some of the most precise tests of general relativity (GR) in the strong-field regime. As one of these tests, the gravitational-wave emission predicted by GR has been probed with the significant orbital decay ( P ̇ b ) of PSR J1537+1155. However, compared to most GR tests provided with the post-Keplerian parameters, the orbital-decay test was lagging behind in terms of both precision and consistency with GR, limited by the uncertain distance of PSR J1537+1155. With an astrometric campaign spanning 6 yr using the Very Long Baseline Array, we measured an annual geometric parallax of 1.063 ± 0.075 mas for PSR J1537+1155, corresponding to a distance of 0.94 − 0.06 + 0.07 kpc. This is the most tightly constrained model-independent distance achieved for a DNS to date. After obtaining P ̇ b Gal (i.e., the orbital decay caused by Galactic gravitational potential) with a combination of four Galactic mass distribution models, we updated the ratio of the observed intrinsic orbital decay to the GR prediction to 0.977 ± 0.020, three times more precise than the previous orbital-decay test (0.91 ± 0.06) made with PSR J1537+1155.

Sensitive searches for wormholes

The realm of strong classical gravity and perhaps even quantum gravity are waiting to be explored. In this letter we consider the recently detected triple system composed of two stars and a non-accreting black hole. Using published observations of this system we conduct the most sensitive test to date for whether the black hole is actually a wormhole by looking for orbital perturbations due to an object on the other side of the wormhole. The mass limit obtained on the perturber is $\sim4$ orders of magnitude better than for observations of S2 orbiting the supermassive black hole at Sgr A*. We also consider how observations of a pulsar could test for whether the black hole in a pulsar-black hole binary is a wormhole. A pulsar in a similar orbit to S2 would be $\sim10$ orders of magnitude more sensitive than observations of S2. For a nominal pulsar-black hole binary of stellar masses, with orbital size similar to that of the Hulse-Taylor binary pulsar, one year of observations could set a mass limit on a perturber that is $\sim6$ orders of magnitude better than observations of a pulsar around Sgr~A*. A range of limits between the pulsar-Sgr~A* and Hulse-Taylor cases could be obtained for a possible population of pulsar-black hole binaries that may exist near the galactic center.

State-switching Mechanism of Intermittent Pulsars

Abstract The emission feature of intermittent pulsars is significant for understanding the pulsar emission mechanism. Using the observational evidence of radio emissions turning on and off and the corresponding spin-down rates in these two states of an intermittent pulsar, we will examine the polar-cap potential drop, gap height, and curvature radii of a few intermittent pulsars within the regime of the pulsar polar-cap emission theory by applying the current loss and energy flux of particle flow to pulsar braking, which are generally associated with radio emission from the polar cap. It is seen that the polar-cap parameters of the intermittent pulsars are almost equal to their maximum values, which is the main prediction of the pulsar polar-cap theory with respect to the breaking of the radio emission. It is also noticed that the intermittent pulsars are distributed near the dipole death line in the diagram, which is consistent with their emission features and the calculated polar-cap parameters. To further confirm the state switching of the intermittent pulsar, the relationships among spin-down rate, gap height, potential drop, and activity duty cycles of PSR B1931+24 are discussed. It is found that the gap height has an anticorrelation with the activity duty cycle, which indicates that the intermittency of the radio emission has a close connection to the gap height, as indicated by the pulsar polar-cap emission theory.

Newtonian quantum gravity and the derivation of the gravitational constant G and its fluctuations

The theory of gravity “Newtonian quantum gravity” (NQG) is an ingeniously simple theory, because it precisely predicts so-called “general relativistic phenomena,” as, for example, that observed at the binary pulsar PSR B1913 + 16, by just applying Kepler’s second law on quantized gravitational fields. It is an irony of fate that the unsuspecting relativistic physicists still have to effort with the tensor calculations of an imaginary four-dimensional space-time. Everybody can understand that a mass that moves through space must meet more “gravitational quanta” emitted by a certain mass, if it moves faster than if it moves slower or rests against a certain mass, which must cause additional gravitational effects that must be added to the results of Newton's theory of gravity. However, today's physicists cannot recognize this because they are caught in Einstein's relativistic thinking and as general relativity can coincidentally also predict these quantum effects by a mathematically defined four-dimensional curvature of space-time. Advanced NQG is also able to derive the gravitational constant G and explains why G must fluctuate. The “string theory” tries to unify quantum physics with general relativity, but as the so-called “general relativistic” phenomena are quantum physical effects, it cannot be a realistic theory. The “energy wave theory” is lead to absurdity by the author.

The expansion of the universe in binary star systems

Abstract Can all binary star systems merge in infinite time by emitting gravitational waves? The answer is no. The orbital radius shrinks from the gravitational wave emission; simultaneously, the universe is expanding if the Hubble–Lemaitre law is universal on all distance scales. Inside the gravitational bound state, the cosmic expansion becomes visible near the critical radius given by the equilibrium between the orbital decay and expansion. The equilibrium condition gives a different deceleration parameter ( q = − 3 ) from the cosmological observations ( q 0 ≈ − 1 ∕ 2 ), which indicates binary systems could have a smaller expansion rate ( H 0 ∕ 6 ). This model can explain a deviation from general relativity (the excess P b ) in the binary pulsar PSR B1534+12. It is also supported by PSR B1913+16. This means that the expansion of the universe is characterized by viscous uniformity, which has a constant of a ∕ a . By applying this relation to PSR B1534+12, H 0 = 66 ± 37 km s − 1 Mpc − 1 is obtained.

The Two Emission States of PSR B1534+12

Abstract We have observed PSR B1534+12 (J1537+1155), a pulsar with a neutron star companion, using the Five-hundred-meter Aperture Spherical radio Telescope. We found that this pulsar shows two distinct emission states: a weak state with a wide pulse profile and a burst state with a narrow pulse profile. The weak state is always present. We cannot, with our current data, determine whether the pulse energy of the weak state follows a normal or a log-normal distribution. The burst state energy distribution follows a power law. The amplitude of the single-pulse emission in the burst state varies significantly; the peak flux intensity of the brightest pulse is 334 times stronger than that of the average pulse. We also examined the timing precision achievable using only bright pulses, which showed no demonstrable improvement because of pulse jitter and therefore quantified the jitter noise level for this pulsar.

Tests of Conservation Laws in Post-Newtonian Gravity with Binary Pulsars

Abstract General relativity is a fully conservative theory, but there exist other possible metric theories of gravity. We consider nonconservative ones with a parameterized post-Newtonian parameter, ζ 2. A nonzero ζ 2 induces a self-acceleration for the center of mass of an eccentric binary pulsar system, which contributes to the second time derivative of the pulsar spin frequency, . In our work, using Will’s method, we provide an improved analysis with four well-timed, carefully chosen binary pulsars. In addition, we extend Will’s method and derive the effect of on the third time derivative of the spin frequency, . For PSR B1913+16, the constraint from is even tighter than that from . We combine multiple pulsars with Bayesian inference, and obtain the upper limit, at the 95% confidence level, assuming a flat prior in . It improves the existing bound by a factor of 3. Moreover, we propose an analytical timing formalism for . Our simulated times of arrival with simplified assumptions show the capability of binary pulsars in limiting ζ 2, and useful clues are extracted for real-data analysis in future. In particular, we discover that for PSRs B1913+16 and J0737−3039A, can yield more constraining limits than .

Constraints on ultralight axions from compact binary systems

Ultra light particles $(m_a \sim 10^{-21}eV-10^{-22}eV)$ with axion-like couplings to other particles can be candidates for fuzzy dark matter (FDM) if the axion decay constant $f_a\sim 10^{17}GeV$. If a compact star is immersed in such a low mass axionic potential it develops a long range field outside the star. This axionic field is radiated away when the star is in a binary orbit. The orbital period of a compact binary decays mainly due to the gravitational wave radiation, which was confirmed first in the Hulse-Taylor binary pulsar. The orbital period can also decay by radiation of other light particles like axions and axion like particles(ALPs). For axionic radiation to take place, the orbital frequency of the periodic motion of the binary system should be greater than the mass of the scalar particle which can be radiated. This implies that, for most of the observed binaries, particles with mass $m_a< 10^{-19}eV$ can be radiated, which includes FDM particles. In this paper, we consider four compact binary systems: PSR J0348+0432, PSR J0737-3039, PSR J1738+0333, and PSR B1913+16 (Hulse Taylor Binary) and show that the observations of the decay in orbital period put the bound on axion decay constant, $f_a\lesssim \mathcal{O}(10^{11}GeV)$. This implies that Fuzzy Dark Matter cannot couple to gluons.

Newtonian quantum gravity

Newtonian Quantum Gravity (NQG) unifies quantum physics with Newton's theory of gravity and calculates the so-called “general relativistic” phenomena more precisely and in a much simpler way than General Relativity, whose complicated theoretical construct is no longer needed. Newton's theory of gravity is less accurate than Albert Einstein's theory of general relativity. Famous examples are the precise predictions of General Relativity at binary pulsars. This is the reason why relativistic physicists claim that there can be no doubt that Einstein's theory of relativity correctly describes our physical reality. With the example of the famous “Hulse-Taylor binary” (also known as PSR 1913 + 16 or PSR B1913 + 16), the author proves that the so-called “general relativistic phenomena” observed at this binary solar system can be calculated without having any knowledge on relativistic physics. According to philosophical and epistemological criteria, this should not be possible, if Einstein's theory of relativity indeed described our physical reality. Einstein obviously merely developed an alternative method to calculate these phenomena without quantum physics. The reason was that in those days quantum physics was not yet generally taken into account. It is not the first time that a lack of knowledge of the underlying physical phenomena has to be compensated by complicated mathematics. Einstein's theory of general relativity indirectly already includes additional quantum physical effects of gravitation. This is the reason why it cannot be possible to unite Einstein's theory of general relativity with quantum physics, unless one uses “mathematical tricks” that make the additional quantum physical effects disappear again in the end.

Vainshtein regime in scalar-tensor gravity: Constraints on degenerate higher-order scalar-tensor theories

We study the screening mechanism in the most general scalar-tensor theories that leave gravitational waves unaffected and are thus compatible with recent LIGO/Virgo observations. Using the effective field theory of dark energy approach, we consider the general action for perturbations beyond linear order, focussing on the quasi-static limit. When restricting to the subclass of theories that satisfy the gravitational wave constraints, the fully nonlinear effective Lagrangian contains only three independent parameters. One of these, $\beta_1$, is uniquely present in degenerate higher-order theories. We compute the two gravitational potentials for a spherically symmetric matter source and we find that for $\beta_1 \ge 0$ they decrease as the inverse of the distance, as in standard gravity, while the case $\beta_1 < 0$ is ruled out. For $\beta_1 > 0$, the two potentials differ and their gravitational constants are not the same on the inside and outside of the body. Generically, the bound on anomalous light bending in the Solar System constrains $\beta_1 \lesssim 10^{-5}$. Standard gravity can be recovered outside the body by tuning the parameters of the model, in which case $\beta_1 \lesssim 10^{-2}$ from the Hulse-Taylor pulsar.