Strong Field General Relativity Fits The Data

All strong gravitational field observations are indistinguishable from general relativity. 

The troublesome cases are in weak gravitational fields in very large systems like galaxies that are usually modeled with simple Newtonian gravity because the math necessary to calculate their behavior in full GR is too hard and is assumed by good arguments, but without actual calculations that could capture non-perturbative effects, to be insignificant.

The signals from the LIGO-Virgo-KAGRA network of gravitational-wave (GW) detectors allow us to perform sensitive tests of general relativity (GR) in the dynamical and strong-field regime of gravity. 

We present the results of seven tests of GR using the observed binary signals in the fifth GW Transient Catalog (GWTC-5.0), i.e., up to and including the second part of the fourth observing run (O4b). We restrict our analysis to the confident signals, henceforth called events, observed by at least two detectors that have estimated false alarm rates ≤ 10^−3 yr^−1. These include 72 events from O4b and five events from the first part of the fourth observing run that are now analyzed due to their increased significance from updated search results, bringing the total number of events for tests of GR in the cumulative GWTC to 168. 

After subtracting the best-fit waveforms, we find the residuals are consistent with detector noise for all events considered. We also find no strong evidence for additional polarizations beyond those predicted by GR. 

We perform tests of GW generation, improving the constraints on deviations from the GR post-Newtonian coefficients by factors of 1.2-2.6. 

Finally, we find overall consistency of the remnants with GR using both time- and frequency-domain methods. For GW240621_195059, postmerger data are consistent with the dominant quadrupolar (ℓ = |m| = 2) mode of a Kerr black hole and its first overtone, with spurious high-frequency content preventing a spectroscopic constraint of GR. In the frequency-domain ringdown analysis, the GR prediction lies in the tails of the combined results, possibly due to the limited catalog size. 

However, the combined results indicate improved consistency with GR over GWTC-4.0, owing to the contribution of GW250114 with a network matched-filter signal-to-noise ratio of 76.9. Overall, we find no evidence for physics beyond GR.

The LIGO Scientific Collaboration, the Virgo Collaboration, the KAGRA Collaboration, "GWTC-5.0: Tests of General Relativity" arXiv:2607.19293 (report number LIGO-P2500781) (July 21, 2026).

Neutrinos Are Very Likely Very Light

Adopting the cosmological bounds on the sum of the neutrino masses and making some other unambitious assumptions, this paper argues that the lightest of the three neutrino masses is less than 2.3 meV and considers a possible phenomenological relations between the three neutrino masses. Direct measurements of the electron neutrino mass at the Katrin experiment bound it at less than 450 meV with good prospects of reducing the bound to 200 meV, but that is still at least two orders of magnitude less than the likely true value.

By way of comparison, the mass of an electron is about 511,000,000 meV, and the first generation quarks are in the low single digit billions of meVs. 

Determining the absolute neutrino mass scale remains one of the most compelling challenges in particle physics. To constrain theoretical models, establishing precise relations among neutrino masses is essential. We propose a simple integral representation of the neutrino mass-squared differences Δm(ij)^2 that provides a complementary perspective on these oscillation parameters. We then demonstrate its utility through several examples. 

Specifically, assuming stringent cosmological bounds that confine the sum of neutrino masses near the normal ordering floor, we derive an analytical condition for the lightest neutrino mass, m(1) < √(61Δm(21)^2)/30. Using recent data from the JUNO experiment, this yields a competitive upper limit of m(1) < 0.0023 eV (95% C.L.). 

We also formulate practical analytical bounds for m(2) and m(3) adaptable to future data, and translate the results into allowed ranges for the effective electron and Majorana neutrino masses m(νe) and m (ββ). Finally, we show that neutrino mass relations of the Gatto-Sartori-Tonin type emerge directly from the proposed integral representation.

I. Alikhanov, "Integral representation of the neutrino mass-squared differences" arXiv:2607.19340 (July 21, 2026).

Medieval DNA From Russia

Medieval ancient DNA from Eastern Europe is consistent with the historical and linguistic narrative of the peoples who make up the Russian state.

The foundation of the first ancient Rus’ state occurred as a result of the consolidation of diverse communities inhabiting Eastern Europe during the second half of the first millennium CE. Historical sources imply that these communities mostly include East Slavs, whose settlement across a vast territory led to the emergence of the East Slavic/Rus’ culture within the Rus’ state. 

We generated genomic data for 200 medieval individuals from different locations to elucidate the origin and genetic structure of the Rus’ population during the early stages of the state formation. Our findings reveal a genetic continuum predominantly shaped by two key genetic groups: a broad Slavic-related continuity of different genetic subclusters of Rus’ occupying the enormous European Plain area, and a Fenno-Ugrian (Uralic)-related component in the Northern Rus’ region. Importantly, both groups have a shared genetic substrate inherited from preceding ancient Baltic region populations. 

To scale Scandinavian ("Viking") heritage, we traced minor Scandinavian genetic lineages that did not make up the dominating genetic stratum of the early Rus’ state. 

Our study presents the first comprehensive genomic image of the medieval Rus’, highlighting the intricate cultural and genetic interactions between Slavic, Fenno-Ugrian, and other groups that formed the first Rus’ state affecting Europe’s history.

Andreeva et al., Genetic history of Rus’, bioRxiv (December 30, 2025), doi: https://doi.org/10.64898/2025.12.30.695215 (Hat tip to Davidski at Eurogenes).

The Widest Galaxy

The galaxy with the greatest diameter ever observed (IC1101) has a diameter of 520 kiloparsecs (1.7 million light years), and it is still growing. By comparison, our Milky Way galaxy has a diameter of about 100,000 light years (about 31 kiloparsecs).

More On Wide Binaries

A paper claims to see MOND in a reanalysis of wide-binary star data. I'm still on the fence.

Wide binary stars provide natural laboratories for directly probing gravity in the low-acceleration regime, as dark matter inferred from any viable gravity has negligible effects on their internal dynamics. Various recent studies including Bayesian 3D analyses have shown that wide binaries with separations greater than several thousand astronomical units experience MOND-type gravity with a boost factor of γ≈1.3−1.6. However, results claiming preference for, or no deviation from, standard gravity have also been published during the same period, particularly highlighting the roles of data quality control and realistic modeling of multiple-star (i.e., triple and higher-order) systems that host hidden companion stars. 

Here we carefully reexamine the issues of data quality control and modeling multiple-star systems in statistical gravity tests based on sky-projected 2D velocities of wide binary stars. Through extensive tests including the acceleration-plane test, the ṽ -distribution test, and the median-ṽ -profile test (where ṽ is the sky-plane 2D relative velocity normalized by the Newtonian circular velocity between the two stars), we show that proper data quality control or reasonable variation in multiple-star modeling cannot remove the low-acceleration gravitational anomaly but confirms the MOND-type gravitational anomaly, particularly consistent with recent realistic MOND solutions of wide binary orbits. 

We find that studies claiming no evidence for the low-acceleration gravitational anomaly are consequences of bypassed calibration of the fraction of multiple-star systems using the Newtonian-regime data, bias-introduction in data quality control that is not taken into account in gravity tests, or insufficient statistics in the low-acceleration regime.

Kyu-Hyun Chae, Youngsub Yoon, "Revisiting Data Quality Control and Multiple-star Modeling in Wide Binary Gravity Tests: Confirmation of MOND-type Gravitational Anomaly at Low Acceleration" arXiv:2607.14450 (July 16, 2026) (submitted to the AAS journals).

The Latest Global Electroweak Fits Of Standard Model Physical Constants

A global electroweak fit combines experimentally measured values of Standard Model physical constants with the theoretical relationships between those constants in the electroweak sector of the Standard Model to determine where, within the range of uncertainties in the experimental measurements the true value of those physical constants is most likely to be. Basically, it uses theory to eke out a bit more precision in our determination of these constants than the measurements make possible in isolation.

The fact that it is possible with experimentally measured value of Standard Model physical constants without serious tensions (which it is) also provides a global test of the consistency of the Standard Model with reality.

The latest paper using up to date experimental data to make a global electroweak fit of Standard Model physical constants can be found here. The discussion of how the input values are chosen (basically, an educated best summary of the data to date) in the paper is also noteworthy.

The global fit of the Z boson mass is 91.1882 ± 0.0019 GeV and the global fit of the Z boson width is 2.4945 ± 0.0006 GeV.

The global fit of the W boson mass is 80.3584 ± 0.0048 GeV and the global fit of the W boson width is 2.090 ± 0.001 GeV.

The Higgs boson mass is 125.13 ± 0.11 GeV. The Standard Model expectation for the Higgs boson width is 4.10 ± 0.06 MeV; a complete global electroweak fit of the data produces 3.78 + 0.30 − 0.27 MeV, which is consistent with the Standard Model expectation. The couplings of the Higgs boson in an electroweak global fit are within roughly 1% ± 1% of the Standard Model expectation. 

The global fit of the charm quark pole mass (in the MS scheme) is 1.273 ± 0.003 GeV.

The global fit of the bottom quark pole mass (in the MS scheme) is 4.183 ± 0.004 GeV.

The global fit of the top quark pole mass is 172.67 ± 0.56 GeV.

The global fit of the strong force coupling constant at the Z boson squared energy scale is 0.1179 ± 0.0009.

The global fit of the effective leptonic weak mixing angle is sin^2(theta) = 0.23149 ± 0.00005.

Can We Measure The External Field Effect On Earth?

Color me skeptical. 

The External Field Effect can be understood as basically a swamping of a second order MOND effect by first order Newtonian effects, so I'm very doubtful that it could be measured experimentally in the solar system anywhere near Earth. Also, a 0.1 fm precision measurement, i.e. a fraction of the size of a proton or neutron, starts to run into definitional issues about what the object your measuring even is due to quantum mechanics and the parton makeup of hadrons. And, the uncertainty regarding the functional form of a MOND interpolating function further muddies the waters and makes any measurement model dependent.

Despite compelling evidence, the absence of a confirmed dark matter particle has sustained interest in modified gravity as an alternative explanation for the observed phenomenology. One prominent example is Modified Newtonian Dynamics (MOND), which predicts that the internal dynamics of a system depends on the external gravitational field in which it is embedded. This so-called External Field Effect violates the strong equivalence principle (SEP) and is absent in canonical mechanics, making it a promising avenue for experimental tests of modified gravity. 

Motivated by this, we investigate the dynamics of two spherical masses arranged such that their symmetry axis is either parallel or orthogonal to the local gravitational field. We derive solutions describing the internal dynamics of such systems in both strong uniform and radial external fields. In particular, for a radial external field, if the non-relativistic gravitational field is free to have non-vanishing curl, we find that the mutual attraction of the masses in the perpendicular configuration is not strictly aligned with their symmetry axis. It acquires a small transverse component, even when the external gravitational field is everywhere balanced by non-gravitational forces. 

Using these solutions, we determine the spatial and temporal sensitivities required to distinguish the two configurations and systematically assess experimentally relevant effects, including air drag, object size, and surface interactions. As an example, detecting the prediction of the simple MOND interpolating function requires a spatial sensitivity of order 0.1 fm for sub-millimeter masses evolving over approximately 30 minutes. Such times may be achievable with levitated particles or in space-based environments. Experiments operating at lower resolutions are also interesting as independent tests of SEP and place constraints on modified-gravity theories.

Ankit Kumar, et al., "Probing the Strong Equivalence Principle through the External Field Effect. How Do Two Masses Fall?" arXiv:2607.10247 (July 11, 2026).

A Central Black Hole's Rotation Direction Doesn't Determine A Galaxy's Rotation Direction

While I didn't have strong expectations one way or the other, this paper's conclusion is potentially important to understanding galaxy formation, and tends to disfavor a purely accretion hypothesis. 

In contrast, the fairly strong correlation between central black hole size and galaxy size tends to argue for a very important role of central black holes in the galaxy formation process, because black holes only make up ca. 1% of a galaxy's mass.

The paper also makes notable observations about other aspects of spiral galaxy geometry.

We compare the apparent directions of rotation in the plane of the sky of active galactic nuclei (AGNs) and their host galaxies. The direction of rotation of the galaxy was inferred from the direction of the spiral arms, while the direction of rotation of the AGN was inferred from spectropolarimetry, where the change in relative polarization position angle (PA) across broad lines is believed to be caused by equatorial scattering. The numbers of co-rotating and counter-rotating AGNs are equal. 

Studies of the relative position angles of radio jets have implied that there is a "zone of avoidance" where jets avoid being in the plane of disk galaxies. We point out that bi-conical narrow-line-region outflows also avoid the plane of the host galaxy. 

The equal numbers of co-rotating and counter-rotating AGNs exclude the hypothesis that the "zone of avoidance" is due to a lack of large tilts of the black hole rotating axis relative to the host galaxy rotation axis. Our results imply that the relative orientations of spin axes are random, at least for the black hole mass range we consider. 

We propose that changes in the broad-line polarization PA with wavelength that do not closely follow the predictions of the simple equatorial scattering model are a consequence of the scattering dust being clumpy. We note a couple of cases of possible changes in PA over several years, which, if real, could be due to motions of the dust clumps or changing anisotropy of the continuum emission.

Loren Gigi, C. Martin Gaskell, "The direction of rotation of supermassive black holes is unrelated to the direction of rotation of the host galaxy" arXiv:2607.06902 (July 8, 2026).

Red River

Red River (Japanese: 天は赤い河のほとり, Hepburn: Sora wa Akai Kawa no Hotori; lit. 'The Sky Is on the Banks of the Red River'), also known as Anatolia Story, is a Japanese manga series written and illustrated by Chie Shinohara. The series was published by Shōgakukan in their Sho-Comi magazine from January 1995 to June 2002 and was collected in 28 tankōbon volumes. It is published in English in North America by Viz Media. An anime television series adaptation produced by Tatsunoko Production is set to premiere in July 2026. 

As of March 2019, the manga had over 20 million copies in circulation, making it one of the best-selling manga series. In 2001, Red River won the Shogakukan Manga Award for the shōjo category.

From Wikipedia.

The river after which the series was named, the "Kızılırmak (Turkish pronunciation: [kɯˈzɯɫɯɾmak], Turkish for "Red River"), historically known as the Halys River (Ancient Greek: Ἅλυς), is the longest river flowing entirely within Turkey.

I read this manga series when my children were in middle school, basically in the early twenty-tens, not long after I began this blog, as one of the first really epic manga series that I'd read. American comics and graphic novels have almost no sub-genre that approximates this series. 

It is back on my radar screen because the first episode of an anime based upon this manga series was released today, and so far, so good. It is a pretty faithful and successful adaptation so far.

Why am I writing about it here?

Because this manga series was instrumental in spurring my interest in prehistory, anthropology, and historical linguistics, in a story that brought the late Bronze Age Hittite Empire to life and contributed a lot to me caring about all of these fields. Some of my own writing on the Hittites can be found here.

And honestly, while it has fictional and magical elements, much like Bronze Age legendary history works actually written at or within a few centuries of that time period, by and large, this series has stood the test of time and is broadly consistent with what archaeologists, anthropologists, ancient historians, and historical linguistics scholars still believe now.

What all of those disciplines lack, however, that historical fiction like this can provide, is synthesis, relatability, and meaning. Academic scholars tend to focus in on tiny details and cower from providing a larger narrative or connecting the dots for fear of being wrong. But doing so takes away the joy and allure of that once captivated the people who are doing the work and keeps them motivated enough to continue to do so. Historical fiction can give the dry piecemeal reconstructions life and a "vibe" allowing you to feel some sense of what life was like back then.

The fictional account does so in ways big and small. For example, while the dialog is in Japanese (and translated into English in the versions I consume), this series retains enough of the historically accurate Hittite proper names to make those names relatable and not so intimidating, when you encounter them as you study the actual history of the Hittite people, a culture the remains the source of pivotal and important open questions in the broader picture of the Bronze Age and Indo-European linguistics.

Even the magical and supernatural and religious aspects of the story, while not actually things that happened in the past, are largely consistent with the religious and metaphysical worldviews of the people who lived in that era in Anatolia.

The Age Of The Universe

The Big Bang was about 13.6 billion years ago, although the uncertainty in that estimate is considerable since it is model dependent. This is consistent with both the age of the oldest stars inferred from their metal content, and the LambdaCDM model with a constant cosmological constant determined based upon cosmic background radiation. 

But if the Hubble constant had its low redshift value (which calls for a faster expansion of the Universe), the age of the Universe would be much shorter than that of the oldest stars in the Milky Way. 

Thus, you can't solve the Hubble tension by tweaking the model dependent cosmic background radiation based estimate of its value in a way that works. Either the Hubble constant isn't really constant, or there is something wrong with the low redshift estimates of its value which affect all of the methodologies for estimating the Hubble constant at low redshift even though they are independent of each other in their methodology (e.g. the Universe is not as homogeneous as we think and we are in an atypical part of it).

We estimate the age of the Universe using the Xiang & Rix sample of 247,103 Milky Way stars with high-resolution spectroscopy from LAMOST DR7 and Gaia eDR3 parallaxes. Stellar ages were estimated using YY isochrones up to 20 Gyr. To remove stars with unusually high and precise ages, we require old stars to be metal-poor and α-enriched. We also require consistency between YY ages and those obtained with FLAME based only on Gaia data. Our final sample of 155,600 stars within 5 kpc provides consistent cosmic age estimates using several techniques of increasing rigour. Our main results use an MCMC reconstruction of the latent age distribution, though our iterative reconstruction is very similar. 

Applying an innovative approach to our MCMC reconstruction and its uncertainties, we find that the oldest star has an age of A⋆ = 13.73 +0.18 −0.15 Gyr. Varying the quality cuts can at most reduce this to A⋆ = 13.31 +0.21 −0.18 Gyr or raise it to 14.02 +0.18 −0.15 Gyr using a much lower or higher age-dependent metallicity ceiling, respectively. Our inferred A⋆ is consistent with the 13.6 Gyr expected in CMB-calibrated ΛCDM, assuming the first long-lived stars formed when the Universe was 0.2 Gyr old. 

This agreement casts doubt on solutions to the Hubble tension solely through new physics prior to recombination, which generally imply a cosmic age of 12.9 ±0.2 Gyr to match low redshift probes. It is difficult for stellar modelling uncertainties to reconcile such a low age with our result given the low metallicities of the oldest stars in our sample and independent asteroseismic constraints.

Indranil Banik, Thenujaya Kudakolawa Kaluarachchige, Stephen Cookson, Harry Desmond, "The age of the Universe from a large sample of the oldest Galactic stars" arXiv:2607.00764 (July 1 2026) (Submitted to the Monthly Notices of the Royal Astronomical Society).