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The principle of relativity; original papers

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Einstein's Theory of Gravitation

Our modern understanding of gravity comes from Albert Einstein’s theory of general relativity, which stands as one of the best-tested theories in science. General relativity predicted many phenomena years before they were observed, including black holes , gravitational waves , gravitational lensing , the expansion of the universe , and the different rates clocks run in a gravitational field. Today, researchers continue to test the theory’s predictions for a better understanding of how gravity works.

Center for Astrophysics | Harvard & Smithsonian astrophysicists research the predictions of general relativity in many ways:

Capturing the first image of a supermassive black hole using the Event Horizon Telescope (EHT). This image of the black hole at the center of the nearby galaxy M87 reveals how gravitation affects the matter in orbit and the light that material emits, providing a novel test of general relativity in a regime where gravity is very strong. CfA Plays Central Role In Capturing Landmark Black Hole Image

Using gravitational lensing to search for the earliest galaxies in the universe. While they’re too faint to be seen directly, closer-by galaxies and clusters sometimes magnify their light, allowing us to learn about the ancestors of the Milky Way and other modern galaxies. Discovering Distant Radio Galaxies via Gravitational Lensing

Reconstructing the location of most of the mass in the universe using gravitational lensing. Next-generation observatories like the Large Synoptic Survey Telescope (LSST) will provide a census of millions of galaxies from their gravitational distortions. Mapping Dark Matter

Performing follow-up observations of gravitational wave events, to confirm the nature of the source. Collisions between neutron stars produce a lot of light in the form of short duration gamma ray bursts in addition to gravitational waves. Astronomers observed such a collision in 2017 using Dark Energy Camera on the Blanco Telescope in Chile, providing complementary data to the observation from LIGO. Astronomers See Light Show Associated With Gravitational Waves

Studying gravitational wave sources that aren’t visible to LIGO, but will be to future gravitational observatories. Using visible light telescopes, astronomers have observed that white dwarf binaries are relatively common in the galaxy, and some of them are in sufficiently tight orbits to be emitters of gravitational waves. One pair in particular orbits every 12.75 minutes, which will make it the strongest source for the future Laser Interferometer Space Antenna (LISA). Space-Warping White Dwarfs Produce Gravitational Waves

Determining whether black holes are actually what GR predicts. While GR is very clear that black holes exist, alternative theories propose different objects that behave in different ways. The challenge is that black holes appear very small in our telescopes, so it’s hard to observe their behavior. However, researchers have ruled out a number of alternative explanations, based on many observations of black holes. Do Stars Fall Quietly into Black Holes, or Crash into Something Utterly Unknown?

Testing general relativity’s prediction about the shape of a black hole. The Event Horizon Telescope is designed to take a picture of the “shadow” of the Milky Way’s supermassive black hole, which is the dark region through which no light passes. The shape of this shadow is predicted by GR, so the EHT will provide the first precision measurement of a fundamental property of a black hole. Event Horizon Telescope Reveals Magnetic Fields at Milky Way's Central Black Hole

A Century of Relativity

Albert Einstein published his full theory of general relativity in 1915, followed by a flurry of research papers by Einstein and others exploring the predictions of the theory. In general relativity (GR), concentrations of mass and energy curve the structure of spacetime, affecting the motion of anything passing near — including light. The theory explained the anomalous orbit of Mercury, but the first major triumph came in 1919 when Arthur Eddington and his colleagues measured the influence of the Sun’s gravity on light from stars during a total solar eclipse.

Physicists made many exotic predictions using general relativity. The bending of light around the Sun is small, but researchers realized the effect would be much larger for galaxies, to the point where gravity would form images of more distant objects — the phenomenon now called gravitational lensing. GR also predicted the existence of black holes: objects with gravity so intense that nothing getting too close can escape again, not even light.

General relativity showed that gravitation has a speed, which is the same as the speed of light. Catastrophic events like collisions between black holes or neutron stars produce gravitational waves. Researchers finally detected these waves in 2015 using the Laser Interferometer Gravitational Observatory (LIGO), a sensitive laboratory that took decades to develop.

For many aspects of astronomy — the motion of planets around stars, the structure of galaxies, etc. — researchers don’t need to use general relativity. However, in places where gravity is strong, and to describe the structure of the universe itself, GR is necessary. For that reason, researchers continue to use GR and probe its limits.

Black holes are extremely common in the universe. Stellar-mass black holes, the remnants of massive stars that exploded, are sometimes the source of powerful X-ray emissions when they are in binary systems with stars. In addition, nearly every galaxy harbors a supermassive black hole at its center, some of which produce powerful jets of matter visible from across the universe. GR is essential to understanding how these objects become so bright, as well as studying how black holes form and grow. The Event Horizon Telescope (EHT) is a world-spanning array of observatories that captured the first image of a supermassive black hole, providing a new arena for testing GR’s predictions.

Gravitational waves are a new branch of astronomy, providing a complementary way to study astrophysical systems to the standard light-based observations. Researchers use GR to provide “templates” of many possible gravitational wave signals, which is how they identify the source and its properties. Gravitational wave astronomy combines with light-based astronomy to characterize some of the most extreme events in the cosmos: collisions of black holes and neutron stars .

Astronomers use gravitational lensing to locate some of the earliest galaxies in the universe, which are too faint to be seen without the magnification provided by gravity. In addition, the distortion created by lensing allows researchers to study dark matter , and map the structure of the universe on the largest scales.

Not long after Einstein published GR, researchers realized the theory predicts that the universe changes in time. Observations in the 1920s found that prediction was true: the universe is expanding, with galaxies moving away from each other. Using GR, cosmologists found the cosmos had a beginning, and was once hotter and denser than it is today. GR provides the mathematical framework for describing the structure and evolution of the universe from its beginnings 13.8 billion years ago, and into the future.

This artist’s illustration depicts two merging neutron stars and the gravitational waves they emit. As the LIGO and Virgo gravitational wave observatories have confirmed, collisions of black holes and neutron stars emit enough gravitational waves to be seen billions of light-years away.

• Why do we need an extremely large telescope like the Giant Magellan Telescope?
• What happens to space time when cosmic objects collide?
• Black Holes
• Gravitational Lensing
• Gravitational Waves
• Very Long Baseline Interferometry
• High Energy Astrophysics
• Optical and Infrared Astronomy
• Theoretical Astrophysics

Related News

M87* one year later: proof of a persistent black hole shadow, unveiling black hole spins using polarized radio glasses, the giant magellan telescope’s final mirror fabrication begins, new horizons in physics breakthrough prize awarded to cfa astrophysicist, cfa selects contractor for next generation event horizon telescope antennas, sheperd doeleman awarded the 2023 georges lemaître international prize, 'the dawn of a new era in astronomy', astronomers reveal first image of the black hole at the heart of our galaxy, bringing black holes to light, connecting the dots: from black hole theory to actual images, physics of the primordial universe, sensing the dynamic universe, castles survey, telescopes and instruments, event horizon telescope (eht), giant magellan telescope, the greenland telescope.

The Collected Papers of Albert Einstein

The Collected Papers of Albert Einstein presents the first complete picture of a massive written legacy that ranges from Einstein's first work on the special and general theories of relativity and the origins of quantum theory, to his active involvement with international collaboration and cooperation, human rights, education, and disarmament.

The large-format published volumes draw upon Einstein's personal papers held at the Albert Einstein Archives and more than 40,000 additional Einstein and Einstein-related documents discovered by our researchers since the 1980s.

When completed, the printed series will contain over 14,000 scientific and non-scientific documents and will fill close to 30 volumes.

We work closely with the Einstein Archives. To learn more about the history of Einstein's personal papers click here .

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• Published: 07 February 2022

The Einstein effect provides global evidence for scientific source credibility effects and the influence of religiosity

• Suzanne Hoogeveen   ORCID: orcid.org/0000-0002-1304-8615 1 ,
• Julia M. Haaf 1 ,
• Joseph A. Bulbulia 2 ,
• Robert M. Ross   ORCID: orcid.org/0000-0001-8711-1675 3 ,
• Ryan McKay   ORCID: orcid.org/0000-0001-7781-1539 4 ,
• Sacha Altay 5 ,
• Theiss Bendixen   ORCID: orcid.org/0000-0001-5729-1281 6 ,
• Renatas Berniūnas 7 ,
• Arik Cheshin   ORCID: orcid.org/0000-0002-0921-0675 8 ,
• Claudio Gentili   ORCID: orcid.org/0000-0002-2579-8755 9 ,
• Raluca Georgescu   ORCID: orcid.org/0000-0001-8329-0063 10 ,
• Will M. Gervais 11 ,
• Kristin Hagel 12 ,
• Christopher Kavanagh 13 , 14 ,
• Neil Levy   ORCID: orcid.org/0000-0002-5679-1986 3 , 15 ,
• Alejandra Neely   ORCID: orcid.org/0000-0002-5565-9676 16 ,
• Lin Qiu 17 ,
• André Rabelo   ORCID: orcid.org/0000-0001-5236-7574 18 ,
• Jonathan E. Ramsay 19 ,
• Bastiaan T. Rutjens   ORCID: orcid.org/0000-0003-3163-4156 1 ,
• Hugh Turpin 13 ,
• Filip Uzarevic 20 ,
• Robin Wuyts 1 ,
• Dimitris Xygalatas   ORCID: orcid.org/0000-0003-1561-9327 21 &
• Michiel van Elk 22  

Nature Human Behaviour volume  6 ,  pages 523–535 ( 2022 ) Cite this article

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People tend to evaluate information from reliable sources more favourably, but it is unclear exactly how perceivers’ worldviews interact with this source credibility effect. In a large and diverse cross-cultural sample ( N  = 10,195 from 24 countries), we presented participants with obscure, meaningless statements attributed to either a spiritual guru or a scientist. We found a robust global source credibility effect for scientific authorities, which we dub ‘the Einstein effect’: across all 24 countries and all levels of religiosity, scientists held greater authority than spiritual gurus. In addition, individual religiosity predicted a weaker relative preference for the statement from the scientist compared with the spiritual guru, and was more strongly associated with credibility judgements for the guru than the scientist. Independent data on explicit trust ratings across 143 countries mirrored our experimental findings. These findings suggest that irrespective of one’s religious worldview, across cultures science is a powerful and universal heuristic that signals the reliability of information.

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Intermediate levels of scientific knowledge are associated with overconfidence and negative attitudes towards science

The intentions of information sources can affect what information people think qualifies as true

Accuracy and social motivations shape judgements of (mis)information

In a heated debate about the proximity of COVID-19 herd immunity, White House health advisor Dr Scott Atlas proclaimed ‘You’re supposed to believe the science, and I’m telling you the science’ 1 . A group of infectious disease experts and former colleagues from Stanford, however, publicly criticized Dr Atlas, who is a radiologist, for spreading ‘falsehoods and misrepresentation of science’ through his statements about face masks, social distancing and the safety of community transmission 2 . In the 2020 pandemic crisis, all eyes turned to scientific experts to provide advice, guidelines and remedies; from COVID-19 alarmists to sceptics, appeal to scientific authority appeared a prevalent strategy on both sides of the political spectrum. Please see the Supplementary Information for a short commentary on how the current work might relate to the COVID-19 situation.

A large body of research has shown that the credibility of a statement is heavily influenced by the perceived credibility of its source 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 . Children and adults are sensitive to the past track record of informants 11 , 12 , 13 , 14 , 15 , 16 , evidence of their benevolence toward the recipient of testimony 17 , 18 , 19 , as well as how credible the information is at face value 20 , 21 . From an evolutionary perspective, deference to credible authorities such as teachers, doctors and scientists is an adaptive strategy that enables effective cultural learning and knowledge transmission 22 , 23 , 24 , 25 , 26 , 27 , 28 . Indeed, if the source is considered a trusted expert, people are willing to believe claims from that source without fully understanding them. We dub this ‘the Einstein effect’; people simply accept that E  =  m c 2 and that antibiotics can help cure pneumonia because credible authorities such as Einstein and their doctor say so, without actually understanding what these statements truly entail.

Knowing that a statement originates from an epistemic authority may thus increase the likelihood of opaque messages being interpreted as meaningful and profound. According to Sperber 29 , in some cases, incomprehensible statements from credible sources may be appreciated not just in spite of, but by virtue of their incomprehensibility, as exemplified by the speech of spiritual or intellectual gurus (the ‘Guru effect’). Here, we investigate to what extent different epistemic authorities affect the perceived value of nonsensical information. To this end, we contrasted judgements of gobbledegook spoken by a spiritual leader with gobbledegook spoken by a scientist. In addition, we assessed whether the source effect is predicted by individual religiosity and varies cross-culturally, as a proxy for how scientists and spiritual authorities function as ‘gurus’ for different individuals and within different cultural contexts.

Although source credibility effects have typically been investigated for persuasion in marketing and communication, both science and spirituality may present particularly suitable contexts for inducing strong source effects. Scientists are generally considered competent and benevolent sources 30 , 31 and scientific information is often difficult and counterintuitive 32 , 33 , 34 . The combination of a credible authority and intangible information can increase the probability of obscure scientific information being accepted, by enhancing perceivers’ reliance on the source 9 , 10 , 35 . Even indirect context cues, such as those emphasizing the scientific nature of a piece of information can increase the probability that (dubious) information is believed 36 . Some experimental evidence, for instance, suggests that irrelevant neuroscience information 37 , 38 , 39 or nonsense mathematical equations 40 can boost the perceived quality of presented claims, though note that replication studies suggest that mere brain images may not suffice 41 , 42 . Notably, these effects were present only among non-experts (that is, people with little formal neuroscientific or mathematical training). This distinction suggests that the appeal of ‘sciencey’ information may be particularly strong when analytical assessment fails and one can only rely on secondary credibility cues.

Similar to the anticipated complexity of scientific information, previous beliefs about religious or spiritual texts instigate expectations that the information presented will be obscure. Supernatural explanations often appeal to phenomena that operate outside the natural world and to experiences deemed ineffable, mysterious and exempt from empirical validation 43 , 44 , 45 , 46 , 47 , 48 . Some scholars have argued that incomprehensible theological language and irrational beliefs may serve as a costly signal towards the religious ingroup, signalling quality by hard-to-fake moral commitment, intellectual capacity and epistemological investment 49 , 50 . However, irrespective of content biases, the evaluation of spiritual or theological obscurity critically depends on one’s personal beliefs about the credibility of spiritual gurus or religious authorities.

Various lines of evidence suggest that perceived credibility of both content and source depends on individual difference factors such as the perceiver’s (political) ideology and worldview 51 , 52 , 53 , 54 . In the absence of the means to rationally evaluate a claim and reliable source information, people probably infer credibility based on beliefs about the group to which the source belongs (for example, ‘conservatives’, ‘scientists’). In this process, similarities between one’s own worldview and that of the source’s group may serve as a proxy for being a benevolent and reliable source 23 , 55 . In a religious context, Christians were found to be more affected by an intercessory prayer when supposedly performed by a (charismatic) Christian than a non-Christian 56 and to require less evidence for religious claims (for example, efficacy of prayer to cure illness) than for scientific claims (for example, efficacy of medication 57 , 58 ). These differences were not present among secular individuals. Furthermore, evangelical Christians were more likely to accept statements opposing their personal views when attributed to an ingroup religious leader versus an outgroup religious leader 59 . This effect was moderated by the amount of contact participants had with the specific group to which the religious leader belonged, highlighting the importance of the person–source fit for message acceptance.

To account for these effects, alongside traditional dual-process models of persuasion 9 , 10 , 60 , 61 , various authors have recently proposed a Bayesian framework in which subjective beliefs about the source (for example, trustworthiness) and one’s worldviews contribute to belief updating in response to new information following Bayesian principles 6 , 62 , 63 , 64 . By including background beliefs, these Bayesian networks describe how a differential weighing of evidence and even divergent updating (belief polarization) can be considered rational and normative. This may explain, for instance, how strong religious believers can become more convinced of their beliefs in the face of disconfirmatory evidence, especially when their faith is being challenged 63 , 65 . Similarly, strong conservatives who distrust science may become less convinced of human-caused global warming when presented with scientific consensus information 62 . In other words, laypeople may apply their own ‘power priors’ 66 to calibrate evidence from different sources, whose trustworthiness is subjectively determined, partly by their broader worldview.

In sum, whereas previous studies have established source credibility effects in a wide array of domains, as-of-yet little is known about whether and to what extent people’s worldview is predictive of the relative credibility evaluation of information from scientific and spiritual sources. In the current study, we presented participants ( N  = 10,195, from 24 countries) with meaningless verbiage (henceforth, ‘gobbledegook’; also referred to in the literature as ‘pseudo-profound bullshit’ 67 ) randomly credited to either a spiritual authority or a scientific authority. We assessed: (1) whether trusting scientific experts over spiritual leaders is a general heuristic (that is, the Einstein effect); and (2) to what extent perceivers’ religiosity predicts relative confidence in the truth of the gobbledegook statements from both sources. Note that we chose a ‘spiritual guru’ authority frame, instead of ‘religious leader,’ because we wanted to avoid selecting an authority specific to any particular religion, to keep the study consistent across countries. Whereas religiosity and spirituality are overlapping but not interchangeable constructs 68 , 69 , self-reported religiosity has been positively associated with belief in spiritual phenomena such as fate, spiritual energy and a connected universe 70 , 71 , 72 (though not unequivocally 73 ). Consequently, we expected religiosity to be associated with increased receptivity to gobbledegook from a spiritual authority.

All confirmatory hypotheses and included measures were preregistered on the Open Science Framework ( osf.io/faj2z/ ; the link contains the original preregistration file). The registered component (including additional subprojects) can be found at osf.io/xg8y5/files . In addition, for exploratory purposes, we included response time measures and a memory test to obtain insight into the cognitive processes underlying the source credibility effect (these measures were anticipated in the preregistration, but no concrete hypotheses were formulated). To further validate the findings from our experimental paradigm, we also analysed a large dataset from 117,191 individuals across 143 countries (including the same countries included in our study) that contains explicit trust ratings of scientists and traditional healers, as well as participant religiosity 74 .

The two dependent variables that were measured (that is, importance of the message and credibility of the message) were highly correlated for both the scientific source (Spearman’s ρ  = 0.772, 95% credible interval (95% CI) (0.764, 0.779)) and for the spiritual source (Spearman’s ρ  = 0.827, 95% CI (0.822, 0.833); Supplementary Fig. 7 ) 75 . Because the pattern of results was equal across the dependent variables, we decided to describe only the findings for credibility in detail (see Table 2 for the results for importance).

Effect of source on credibility

First, we assessed the extent to which the perceived credibility of a gobbledegook statement is affected by its source (that is, a scientist versus a spiritual guru). Note, our initial hypothesis was that there would be no main effect of source, that is, we expected evidence for the null model. However, based on visual inspection of the data (Fig. 1 ), a main effect of source seems evident. To quantify the evidence for the effect of source, we compared between the null model without an effect of condition (that is, the scientist and spiritual guru are judged equally credible), the model with a common positive effect of condition across countries (that is, the scientist is judged more credible than the guru, to an equal degree in every country), the model with a varying positive effect of source (that is, the scientist is judged more credible than the guru, but to varying degrees across countries), and the unconstrained model that allows the source effect to be varying from both positive to negative (that is, in some countries, the scientist is considered more credible than the guru, in other countries, the guru is considered more credible than the scientist).

Countries are ordered by size of the source-by-religiosity interaction (from left to right, top to bottom). Red lines and circles denote ratings for the spiritual guru and grey lines and circles denote ratings for the scientist. Circles reflect individual observations and are jittered to enhance visibility. Credibility was measured on a seven-point Likert scale.

The Bayes factor model comparison summarized in Table 1 shows that the data provide most evidence for the positive effects model, which assumes a varying but consistently positive effect across countries. The source effect is favoured 1.1 × 10 210 -to-1 over the null model, which indicates strong evidence that the meaningless statement from the scientist is considered more credible than the meaningless statement from the guru. The positive effects model strongly outperforms the common effect model (BF +1 = 8.9 × 10 17 ; explained variance (Bayesian R 2 ) is 17.9%, 95% CI (17.0%, 18.7%)). The mean (95% CI) of the unstandardized size of the source effect in the full model is 0.70 (0.60, 0.79) on a seven-point Likert scale and the s.d. between countries is 0.16. Also note that as shown in Fig. 1 , the within-country individual differences in credibility ratings are large, indicating that most of the variance is located at the lower level (that is, the individual level). The intraclass correlation coefficients quantifying the proportion of variance explained by the country clustering, as well as the total explained variance by the included effects for all models (Bayesian R 2 ) are reported in the Supplementary Information . There, we also report MCMC diagnostics to verify the adequacy of the Bayesian models, as well as the estimates for the intercepts, source effect and the source-by-religiosity interaction effect for each country.

Interaction between source and religiosity on credibility

The source-by-religiosity interaction effect assesses to what extent the effect of source depends on raters’ own religious background (religiosity was globally standardized). Our hypothesis states that for individuals with low religiosity, credibility ratings should be higher for gobbledegook from a scientific source than for gobbledegook from a spiritual guru. For highly religious individuals, the reverse effect is expected, that is, higher credibility ratings for gobbledegook ascribed to a guru than for gobbledegook ascribed to a scientist. The interaction term was therefore constrained to be negative, in the sense that the coefficient of the source effect becomes smaller (or negative) with increased religiosity. Note that although the interaction term was constrained to have a negative sign, for consistency, we still refer to the model as the positive effects model.

For hypothesis 2, the model comparison summarized in Table 1 shows that the data provide most evidence for the common source-by-religiosity interaction model, which assumes a consistent interaction effect across countries, BF 10  = 0.99 × 10 15 ( R 2  = 18.1%, 95% CI (17.2%, 19.0%)). The data are uninformative for distinguishing between the common interaction and the varying positive interaction model (BF 1 p  = 1.28), indicating that both are equally plausible. Although we cannot conclude whether the size of the interaction effect differs substantially between countries, both models provide strong evidence for a source-by-religiosity effect across all countries. The mean of the unstandardized source-by-religiosity interaction effect is −0.21 (−0.29, −0.14) and the s.d. between countries is 0.09 on the seven-point Likert scale. As evident from Fig. 2d , the interaction entails that the relative preference in credibility for statements from the scientist versus the spiritual guru decreases with higher religiosity. This effect is further unpacked in Fig. 2c , which shows that in every country, except for Croatia, religiosity is more predictive of credibility ratings for statements from the guru than for statements from the scientist.

a , b , It is apparent that there is substantial variation across the 24 countries in ( a ) overall credibility judgements (that is, intercept) and ( b ) the effect of scientific versus spiritual source. c , Individual religiosity has a stronger effect on credibility judgements for the spiritual guru (red circles) than for the scientist (grey circles). The estimates are ordered from largest to smallest, and the open circles denote negatively valued effects. The error bars give the 95% CI for each country. The vertical lines denote the overall estimated effect with the 95% CI in the shaded bands. The dashed lines indicates zero. d , Predicted credibility as a function of source and individual religiosity, showing that the difference in credibility ratings for the scientist (grey lines) versus the guru (red lines) is less pronounced for high-religiosity individuals than low-religiosity individuals. The shaded bands reflects the 95% CI, crosses reflect the observed values for two randomly sampled participants per country, and circles reflect the corresponding estimated values. Crosses and circles are jittered to enhance visibility.

Exploratory analyses

In an exploratory fashion, we assessed to what extent the source manipulation influenced the effort participants put into processing the statements. To this end, we looked at: (1) response time for the evaluation of each statement as a proxy for processing time of the message, and (2) memory performance of words presented in the statements as a proxy for encoding quality. For these exploratory models, we assessed only evidence for a common effect, because visual inspection of the data suggested no or only very small and homogeneous effects (Fig. 3 ).

a , b , The source effect on ( a ) (log-transformed) processing time and ( b ) memory performance (range 0–1). The estimates are ordered from largest to smallest, and the open circles denote negatively valued effects. The error bars give the 95% CI for each country. The vertical lines denote the overall estimated effect with the 95% CI in the shaded bands. The dashed lines indicate zero.

Processing time

For processing time, the data indicate a common effect of source: participants spent more time processing the statement of the scientist (median response time = 28.30 s) than that of the guru (median response time = 27.0 s; BF 10 = 8,050.48). Processing times were log-transformed for the analysis, to account for the positive skew that is typically observed in response time data. However, the standardized effect size is very small: 0.058 (0.023, 0.087). There was strong evidence against an interaction between source and religiosity ratings on processing time: religiosity is not predictive of the difference in processing time for the scientist versus the guru (BF 10 = 0.03, BF 01 = 30.78).

Memory performance

After the rating question, participants were presented with a recall item that required them to indicate which words they recognized from the statement. The list consisted of five target words (included in the statement) and five distractor words (not in the statement) for each source. An F 1 score was calculated per person per source, which gives the harmonic mean of the precision (proportion true positives of all selected words) and recall (proportion true positives of all presented target words). F 1 ranges between 0 and 1, with 1 being perfect performance.

The analysis indicated anecdotal evidence against a common effect of source on memory performance: participants did not perform better on recognizing words from the statement by the scientist than the statement by the guru (BF 10  = 0.53; BF 01  = 1.90; standardized estimate = 0.014 (0.001, 0.035)). Finally, there was moderate evidence against an interaction, BF 10  = 0.31, BF 01  = 3.27.

As a sanity check, we showed that there is an extremely strong effect of processing time on memory performance; participants who spent more time processing the statement, also performed better on the memory task (BF 10  =  ∞ ).

Validation using previously collected trust ratings

In addition to the experimental data collected in this study, we also examined an existing dataset that includes surveyed trust ratings for scientists and traditional healers for 117,191 participants across 143 countries. Note that the analysis on this dataset was not preregistered. Analysis of these data corroborated the results from our experimental manipulations; on average, scientists are considered more trustworthy than traditional healers, standardized estimate = 0.30 (0.06, 0.58) (for comparison, the standardized estimate for the experimental source effect on credibility is 0.41 (0.22, 0.49)). Although the positive effects model strongly outperforms both the null model and the common effect model (BF +0 , BF +1  > 10 308 ; R 2 for the positive effects model = 28.1% (27.8%, 28.3%)), the analysis indicates most evidence for the unconstrained model \({{{{\mathcal{M}}}}}_{u}\) , which indicates that scientists are not explicitly trusted more than traditional healers in all of the 143 countries (BF u +  = 320.76). Nonetheless, as displayed in Fig. 4a , only in 3 of the 143 countries is the mean of the estimated source effect negative, whereas the overall effect is clearly positive.

a , The source effect on trust ratings for each of the 143 countries, showing that in all but three countries, scientists are trusted more than traditional healers. The estimates are ordered from largest to smallest, and open circles denote negatively valued effects. The error bars give the 95% CI for each country. The vertical lines denote the overall estimated effect with the 95% CI in the shaded bands. The dashed lines indicates zero. b , The predicted trust rating as a function of source and individual religiosity, showing that religious individuals trust scientists slightly less and traditional healers more compared with non-religious individuals. The shaded bands reflect the 95% CI, crosses reflect the observed values for two randomly sampled participants per country, and circles reflect the estimated values per condition. The crosses are jittered to enhance visibility.

We also investigated the fit effect in this dataset, by including an interaction term between authority (scientists versus traditional healers) and religiosity (religious versus not religious). Because in 41 countries all of the participants indicated that they were religious, we could not reliably estimate varying effects for the authority-by-religiosity interaction. There was, however, strong evidence for an overall interaction between authority and religiosity, BF 10  = 6.3 × 10 14 , R 2  = 28.1% (27.8%, 28.4%) standardized estimate = −0.09 (−0.14, −0.02); for comparison, the standardized estimate for the experimental source-by-religiosity effect on credibility is −0.12 (−0.16, −0.08)). The pattern of the interaction is the same as for the experimental credibility data: the relative difference between trust in scientists versus traditional healers is smaller for religious individuals than for non-religious individuals. Interestingly, whereas the experimental study found that religiosity was associated with increased credibility ratings for both sources, albeit to a smaller extent for the scientist (Fig. 2c ), the trust data show a positive effect of religiosity on trust for traditional healers (standardized estimate = 0.03 (0.02, 0.04)), yet a negative effect of religiosity on trust for scientists (standardized estimate = −0.01 (−0.02, −0.01)). See the Supplementary Information for an additional exploratory analysis on the country-level correlation in the source effect between the primary experimental dataset and secondary validation dataset on trust.

Robustness and additional checks

We conducted eight additional analyses that the results should be robust against, including all specifications mentioned in the preregistration:

Excluding observations for which participants did not correctly recall the source of the statement ( n obs  = 1616 (7.95%))

Excluding data from Lithuania because n  < 300 (as preregistered)

Using a different, less-informed prior setting for r scale; \(r=\frac{\sqrt{2}}{2}\approx 0.707\) , corresponding to a ‘wide’ prior scale provided in the BayesFactor package 76

Using the importance rating instead of the credibility rating as the outcome variable

Applying a between-subjects design by taking only the first observation per participant

Including all participants, including those who failed the attention check

Running the analyses without adding any predictors as covariates

Running the analyses including all covariates that might affect either the independent variable (religiosity) or the dependent variable (credibility ratings): statement version (A or B), presentation order (guru–scientist or scientist–guru), participant age (in decades), participant gender, level of education and perceived socio-economic status.

The results of these robustness analyses are given in Table 2 and corroborate the conclusions from the main analyses: the data indicate (1) a source effect that varies between countries but is consistently positive (scientist > guru), and (2) a positive source-by-religiosity interaction effect (either a common or varying effect).

In the current cross-cultural study, we used a straightforward manipulation and measurement of source credibility effects at the individual level. We found a robust source effect on credibility judgements of meaningless statements ascribed to different authority figures; across all 24 countries and all levels of religiosity, gobbledegook from a scientist was considered more credible than the same gobbledegook from a spiritual guru. In addition to this robust overall Einstein effect, participants’ background beliefs predicted the credibility evaluations; individuals scoring low on religiosity considered the statement from the guru less credible than that from the scientist, whereas this difference was less pronounced for highly religious individuals. These patterns were consistent with explicit trust data collected for over 100,000 individuals from 143 countries: across 140 of 143 of these countries, people indicated greater trust in scientists than in traditional healers, with a larger difference for non-religious compared with religious individuals. Robustness analyses for the experimental study indicated that the effects were robust against different data inclusion criteria (for example, attention checks) and analytic choices (for example, selection of covariates, dependent variable, prior settings). Moreover, the effects also emerged compellingly when analysed as a between-subjects design (Table 2 ), suggesting that they are not simply explained by social desirability or participants responding in line with their guess of the research hypothesis (also note that recent empirical work indicates that online survey experiments are generally robust to experimenter demand effects 77 ). Results of exploratory response time analyses suggest that in addition to giving more positive evaluations, people may actually put more effort into processing information from credible sources (although they did not recall it better). In particular, participants spent more time and may have tried relatively harder to decipher the gobbledegook from the scientist, whereas previous scepticism may have steered some to immediately dismiss the information from the guru as nonsense.

The pattern of results suggests that variability in the source effect between individuals and countries is more strongly driven by differences in the credibility of the spiritual authority than the scientific authority. Based on the literature one could consider various plausible hypotheses explaining cross-cultural variation in the source effects, for instance in terms of cultural religiosity, vertically versus horizontally structured societies, general trust in authorities and specific trust patterns toward religious and secular authorities 78 , 79 , 80 , 81 , 82 , 83 . However, although our analysis indicated quantitative differences in the size of the source effect between countries (that is, varying positive effects), we did not find qualitative differences (that is, changes in the direction or presence of the effect). Descriptively, the weakest source effects (that is, smallest difference between the scientific and the spiritual source) are observed in Asian countries (Japan, China, India), possibly because the spiritual guru as presented in the survey more closely fits Eastern belief systems than Abrahamic faith traditions. However, this explanation remains speculative and we are hesitant to overinterpret the cross-national variability both in the overall credibility judgements and the effect of source. Although we included main effects of age, gender, level of education and socio-economic status in the analyses, the different sampling strategies that were applied between countries also calls for caution in making inferences based on direct comparisons.

Our findings could reflect a universal gullibility with regard to gobbledegook statements: only a small minority of participants, regardless of their national or religious background, displayed candid scepticism towards the nonsense statements, and 76% of participants rated the scientist’s gobbledegook at or above the midpoint of the credibility scale (compared with 55% for the guru). However, the notion of a general gullibility underlying the observed effects is not entirely supported by the data. The median response was the midpoint of the credibility scale. Participants may have primarily used the midpoint of the scale to indicate that they were uncertain about whether or not the claim was credible, that is, to refrain from passing judgement at all 84 , 85 , 86 . This response might appear as a lack in motivation to critically reflect on the information that was presented; at the same time, saving one’s cognitive resources can also be considered ‘strategic’. First, as with most psychology experiments, our study was a zero-stakes task with no incentive for accuracy, which may have lowered effort and biased responses toward the midpoint. Second, when analytical reasoning about the plausibility of a presented claim does not yield any conclusion, the most rational thing to do may be either suspending judgement (selecting the neutral midpoint of the rating scale) or calibrating judgement to previous beliefs about the source of the claim. If one considers the group to which the source belongs generally competent and benevolent, it makes sense to give a positive judgement of their difficult-to-evaluate claim. After all, credible experts often acquired credentials based on their reputation of discovering phenomena that seem implausible at first glance 55 . For instance, the premises of using vaccines (‘inserting a virus prevents disease’) or facts about climate change (‘humans are changing the weather’) are intuitively dubious, yet reputable scientists have convinced many laypeople of their truth.

In this study, we intentionally selected authorities that are generally considered benevolent 30 , 31 and we generated statements that are nearly impossible to (in)validate and that bear no relation to controversial or politicized scientific topics about which people may have strong previous attitudes (efficacy of vaccinations, climate change, etc.). By using ambiguous claims without any specific ideological content, we tried to isolate the worldview effect regarding the source from any worldview effect related to the content of the claims. At the same time, we aimed to maximize the efficacy of our manipulation, by varying the names, photographs and visual contexts (chalkboard versus stars) in addition to the authority’s profession. This approach makes it more difficult to single out which specific factor contributes to the source effect (for example, the observed effects might be partly driven by the authority’s appearance rather than their domain of expertise). Relatedly, some participants might have recognized the depicted men (Enrico Fermi and José Argüelles), although we consider it unlikely that many did. Because we did not ask whether participants recognized any of the depicted sources, we tried to indirectly and retrospectively assess recognition by scanning the open text items at the end of the survey (comments and awareness item) for any mentioning of either ‘Enrico’, ‘Fermi’, ‘José’ or ‘Argüelles’ (ignoring capitalization or diacritical marks). Only one (Spanish) participant mentioned recognizing both of the sources. Although this obviously does not prove that no other participants might have known the depicted sources, it seems unlikely that this was the case for a large proportion of participants. On the other hand, the multifaceted nature of the manipulation also increases its ecological validity; our stimuli resemble popular internet memes and real-life instances of source credibility also involve a combination of different features (for example, authorities typically look the part in public and appear in congruous contexts). Furthermore, a recent study showed that the mere mentioning of a famous source such as Aristotle or the Dalai Lama enhanced profundity ratings for pseudo-profound nonsense relative to unauthored versions, suggesting that even the mere name of an authority may suffice to induce source effects 87 .

The effects observed in our experimental data and the associations identified in the existing trust data were highly comparable, suggesting that by using our source credibility manipulation we tapped into participants’ attitudes about scientific and religious authorities. A noteworthy divergence, however, is that whereas our data showed a small positive relation between religiosity and credibility ratings for gobbledegook from the scientist, the trust data demonstrated a small but negative association between religiosity and trust in scientists. The finding that religious people are generally less trusting towards science has often been reported in the literature 53 , 88 , 89 , 90 . However, recent studies suggest that the negative relation between religiosity and trust in science might be US-specific and be weak or absent in other countries 91 , 92 , 93 , 94 . In addition, although trust is probably closely linked to credibility, explicit trust assessments and credibility ratings of specific statements may diverge, perhaps particularly for the kind of obscure statements used in the current study. That is, the gobbledegook statements may still have resonated better with religious individuals than non-religious individuals, resulting in the main effect of religiosity on credibility ratings. This main effect may be driven by a tendency for intuitive reasoning, which has been related to religiosity 78 , 95 , 96 and receptivity of pseudo-profound and pseudo-scientific nonsense 36 , 67 . It could thus be that mistrust in science only partially dampens the allure of well-sounding science-related gobbledegook for intuitive reasoners 36 .

Notably, our study showed that across 24 countries even those who are highly religious are prone to a scientific source credibility bias, what we have deemed the Einstein effect. Looking ahead, there are at least six compelling horizons for future research to address the generalizability and underlying causes of the Einstein effect. First, whether scientific education diminishes the appeal of scientific authority outside its immediate domain remains unclear. Although those who place faith in science are prone to Einstein effects 38 , 40 , 97 , 98 , strong scepticism is normative within the practice of science—as anyone who has experienced peer review will attest. Although it is 150 years since Charles Peirce famously argued for fixing beliefs from the ‘method of science’ in favour the ‘method of authority’, the role of appeals to scientific authority among scientists remains unclear 99 . Second, future researchers might investigate whether political partisanship predicts differences in scientific source credibility. Although political commitments may share common psychological features with religious commitments 100 , 101 , 102 , 103 , the rise of anti-science populist ideologies might diminish or reverse Einstein effects among political partisans. By contrast, individual differences in deference to science 104 may predict enhanced Einstein effects, although a recent study failed to find this pattern for faith in science (van der Miesen et al., in preparation). Third, the historical origins of scientific source credibility across different cultures remain unclear. If we were to wind back the clock a century to Einstein’s era, would we also observe preferential source credibility for scientific authority over spiritual authority? Fourth, the proximate and sustaining social and technological causes of scientific source credibility are not addressed in our study, and remain ripe for investigations. Is scientific source credibility an artefact of global information networks, country-wide science education or the sequestering of religious authority to the private domain? Fifth, although our study covers 24 countries worldwide, we cannot claim universality for our findings. Indeed, investigating source credibility in cultures where spiritual authority dominates may help to clarify the mechanistic questions that our study raises but does not address. Sixth, future work may extend the current work and investigate how the Einstein effect is affected by content cues (for example, the use of jargon, argument coherence, disclosure of uncertainty 105 ) and personal attitudes towards the topic 106 , 107 , 108 .

In conclusion, our results strongly suggest that scientific authority is generally considered a reliable source for truth, more so than spiritual authority. Indeed, there are ample examples demonstrating that science serves as an important cue for credibility; the cover of Donald Trump’s niece’s family history book is adorned by ‘Mary L. Trump, PhD’; advertisements for cosmetic products often claim to be ‘clinically proven’ and ‘recommended by dermatologists’, and even the tobacco industry used to appeal to science (for example, ‘more doctors smoke Camels than any other cigarette’). By systematically quantifying the difference between acceptance of statements by a scientific and spiritual authority in a global sample, this work addresses the fundamental question of how people trust what others say about the world.

Participants

In total, 10,535 participants completed the online experiment. Of these, 340 participants (3.23%) were excluded because they failed the attention check (but see Table 2 for equivalent results when data all participants are included), leaving an analytical sample of N  = 10,195 participants from 24 countries (see Table 3 for descriptive statistics per country). Participants were recruited from university student samples, from personal networks and from representative samples accessed by panel agencies and online platforms (MTurk, Kieskompas, Sojump, TurkPrime, Lancers, Qualtrics panels, Crowdpanel and Prolific). Participants were compensated for participation by a financial remuneration, the possibility of a reward through a raffle, course credits or no compensation. There were no a priori exclusion criteria; everyone over 18 years old could participate. Participants were forced to answer all multiple choice questions, hence there was no missing data (except for 36 people who did not provide a valid age). The countries were convenience sampled (that is, through personal networks), but were selected to cover six continents and include different ethnic majorities and religious majorities (Christian, Muslim, Hindu, Jewish, Eastern religions, as well as highly secular societies). Table 3 displays the method of recruitment and compensation per country.

The study was approved by the local ethics committee at the Psychology Department of the University of Amsterdam (Project #2018-SP-9713). Additional approval was obtained from local IRBs at the Adolfo Ibáñez University (Chile), the Babes-Bolyai University (Romania), the James Cook University (Singapore), Royal Holloway, University of London (UK) and the University of Connecticut (USA).

Sampling plan

We preregistered a target sample size of n  = 400 per country and 20–25 target countries. The preregistered sample size and composition allowed us to look at overall effects, effects within countries and between countries. Because we applied a Bayesian statistical framework, we needed a minimum of 20 countries to have sufficient data for accurate estimation in cross-country comparisons 109 . However, our main interest were overall effects, rather than effects for individual countries. With approximately 8,800 participants, we would have sufficient data to reliably estimate overall effects, especially as the source effect is within-subjects. Data collection was terminated by 30 November 2019. The data from ten participants who completed the survey after this termination date were retained in the dataset.

The study was part of a larger project on cross-cultural effects related to religiosity (see Supplementary Information for details about the project). The full translated survey for each included country can be found at osf.io/kywjs/ . The relevant variables for the current study were individual religiosity, the manipulated source of authority and the ratings of the statements.

Participant religiosity was measured using established items taken from the World Values Survey 80 , covering religious behaviours (institutionalized such as church attendance and private such as prayer/mediation), beliefs, identification, values and denomination (see Supplementary Table 5 for the exact items). Besides having high face-validity, these measures have been applied cross-culturally in other studies 79 , 110 , 111 . A Bayesian reliability analysis using the Bayesrel package 112 indicated good internal consistency of the religiosity measure, McDonald omega = 0.930 (0.927, 0.931). The religious membership item was removed from the scale, as this item was only moderately correlated with the other items (item-rest correlation = 0.608, all others >0.706) and dropping it improved the reliability to omega = 0.939 (0.938, 0.941). The remaining seven individual religiosity items were transformed on a 0–1 scale (to make each item contribute equally to the scale), tallied to create a religiosity score per participant, and grand mean standardized for the analyses.

The experimental stimuli consisted of two gobbledegook statements that were attributed to a spiritual guru and to a scientific authority (within-subjects). We created two versions of the statement, manipulating (1) the background of the frame: an opaque new age purple galaxy background versus an opaque dark green chalkboard with physics equations; (2) the accompanying grey-scale photo of the alleged source: a man in robes (photo of José Argüelles) versus a man in an old-fashioned suit (photo of Enrico Fermi); and (3) the reported profession: spiritual leader versus scientist. In addition, in the introductory text, the source was further announced as ‘Saul J. Adrian—a spiritual authority in world religions’ versus ‘Edward K. Leal—a scientific authority in the field of particle physics’, names counterbalanced. The names were fictitious and the photos were taken from Wikipedia with re-use permission. The two versions of the text were three-sentence, 37/38-word statements. We generated the statements using the New Age Bullshit Generator ( http://sebpearce.com/bullshit/ ), that combines new age buzzwords in a syntactically correct structure resulting in meaningless, but pseudo-profound sounding texts 67 . The two versions of the text were counterbalanced between sources. Participants were randomly assigned to the scientific–spiritual or the spiritual–scientific ordered condition. The stimuli in each language are provided at osf.io/qsyvw/ .

The main outcome variable pertained to judgements of the importance and credibility of gobbledegook, measured on a seven-point Likert scale from not at all important/not at all credible to extremely important/extremely credible, respectively. A multiple choice recognition item for the source that expressed the statement was included as a manipulation check. In our preregistration, we did not specify that we would exclude participants based on incorrect recall of the source of the statement. We therefore kept all observations in the dataset for the main analyses and additionally ran the models without the observations for which the source was not recalled correctly. The results of this robustness check are provided in Table 2 . For exploratory purposes, we also measured reading and processing time for the statement, as well as depth of processing. The latter was operationalized as the number of items correctly identified as having appeared in the statement. Participants were presented with a list of ten words, including five targets and five distractors, and were asked to select the words that they recognized from the statement.

Participants received a link to the Qualtrics survey, either by email, social media or through an online platform. After reading the instructions and providing informed consent, they first completed items for a separate study about religiosity and trustworthiness. Next, they were presented with the first statement and source stimulus, rated its importance and credibility, completed the manipulation check to validate that they registered the source, and completed the word recall item. These elements were then repeated for the second statement. After that, participants completed items about body–mind dualism. Finally, they provided demographics, a quality of life scale, the religiosity items and were given the opportunity to provide comments. It took about 10 minutes to complete the entire survey (median completion time was 11.4 minutes).

Data analysis

We used the R package BayesFactor 76 to estimate and test the multilevel Bayesian regression models 113 , 114 . The multilevel Bayesian modelling approach allows us to systematically evaluate the evidence in the data under different models: (1) across all countries the effect is truly null; (2) all countries share a common non-zero effect; (3) countries differ, but all effects are in the same (predicted) direction; and (4) in some countries the effect is positive, whereas in others the effect is negative. The models differ in the extent to which they constrain their predictions, from the most constrained (1) to completely unconstrained (4). We refer to these models as the null model, the common effect model, the positive effects model and the unconstrained model, respectively. Note that although the predictions from model (3) are less constrained than those from model (2), it is more difficult to obtain evidence for small effects under the latter model because it assumes that the effect is present in every country, rather than only in the aggregate sample. When applied to our hypothesis for the source effect, evidence for (1) would indicate that people from these 24 countries do not differentially evaluate credibility of claims from a guru or a scientist, evidence for (2) would indicate that on average people from these 24 countries consider claims from a scientist more credible than from a guru (or vice versa) with little between-country variability in the size of the effect, evidence for (3) would indicate that in all of the 24 countries, people consider claims from a scientist more credible than from a guru (or vice versa), but there is cultural variation in the size of this effect, and evidence for (4) would indicate that in some countries people consider claims from a scientist more credible than from a guru, and in other countries people consider claims from a guru more credible than from a scientist, indicating cultural variation in the direction (and size) of the effect. We used the interpretation categories for Bayes factors proposed by Lee and Wagenmakers 115 , based on the original labels specified by Jeffreys 116 .

For the main effect of source ( \({{{{\mathcal{H}}}}}_{1}\) ), we specified the following unconstrained model. Let Y i j k be the credibility rating for the i th participant, i  = 1,…,  N , in the j th country, j  = 1,…, 24, for the k th condition, k  = 1, 2. Then Y i j k  ~  N ( μ  +  α j  +  v i β  +  r i δ j  +  x k γ j ,  σ 2 ). Here, the term μ + α j serves as the baseline credibility intercepts with μ being the grand mean and α j the j th country’s deviation from the grand mean. The β term reflects the fixed effect of the level of education covariate. δ j is the j th country’s main effect of religiosity on credibility ratings. The crucial parameter here is γ j which is the source effect for the j th country. In the common effects model, we will replace γ i with γ . The variable x k  = −0.5, 0.5 if k  = 1, 2, respectively, where k  = 1 indicates the scientist condition and the k  = 2 indicates the guru condition. The variable v i is the standardized participant-level education covariate. The variable r i is the standardized religiosity score for each participant. Finally, σ 2 is the variance in credibility ratings across participants.

To test the source-by-religiosity interaction for hypothesis 2, the model from (1) is extended by including an interaction term: Y i j k  ~  N ( μ  +  α j  +  v i β  +  r i δ j  +  x k γ j  +  r i x k θ j ,  σ 2 ), where θ j is the parameter of interest, the religiosity × source interaction effect, with r i x k as the product of the experimental condition and the standardized individual religiosity score. The parameter estimates as reported in the results section are based on the full model from (2).

To systematically investigate which third variables should and should not be included in the statistical model, we used directed acyclic graphs 117 to visually represent the causal relations between the variables in our data 118 , 119 , 120 . In short, this method entails specifying directed relations (arrows) between different constructs and measures (nodes) in a given design that allow one to intuitively reflect causal structures and determine which third variables should be accounted for and which should be ignored in the statistical model. Based on directed acyclic graphs created in the R package ggdag 121 , both country and level of education were identified as potential confounding factors that warranted inclusion, because they may affect both religiosity 122 , 123 and overall credibility assessments (for example, due to scepticism). Country was therefore added as a clustering factor, while level of education was added as a fixed covariate in all models. We also ran the models while including all participant-level variables related to the primary measures, that is, gender 124 , age 125 , socio-economic status 126 , 127 , statement version (A or B) and presentation order (guru–scientist or scientist–guru). Note that including these covariates improved the model fit, but the qualitative results remain the same regardless of the (set of) covariates. See Supplementary Figs. 4 – 6 for details on the causal graphs and Table 2 for the primary results without any and with all covariates.

Prior settings

The BayesFactor package applies the default priors for ANOVA and regression designs 128 , 129 , in which the researcher can determine the scale settings for each individual predictor in the model. We used the settings for the critical priors in the multilevel models as proposed by Rouder et al. 114 , concerning the scale settings on μ γ , μ θ and \({\sigma }_{\gamma }^{2},{\sigma }_{\theta }^{2}\) . The scale on μ γ , μ θ reflects the expected size of the overall source effect and source-by-religiosity effect, respectively, and is set to 0.4 (small–medium effect). The scale of \({\sigma }_{\gamma }^{2},{\sigma }_{\theta }^{2}\) reflects the expected amount of variability in these effects across countries. This scale is set to 60% of the overall effect, resulting in a value of 0.24. The prior scale for the overall between-countries variance was set to 1. We used 31,000 iterations for the Markov chain Monte Carlo sampling and discarded the first 1,000 iterations (‘burn-in’).

Deviations from preregistration

We deviated from the preregistration in the following ways. First, in our preregistration, we formulated a hypothesis about the interaction between source and perceived cultural norms of religiosity in one’s country. However, in retrospect, we realized this hypothesis lacked theoretical justification and the proposed analysis was methodologically suboptimal (see Supplementary Information for details on this analysis).

Second, as a stopping rule, we preregistered that data collection would be terminated (1) when the target of n  = 400 per country was reached, or (2) by 30 September 2019. However, due to unforeseen delays in construction of the materials and recruitment, this deadline was extended to 30 November 2019. We did not download or inspect the data until after 30 November.

Third, we preregistered to only include countries where usable data from at least 300 participants was collected (that is, complete data from attentive participants). However, we decided to keep the n  = 291 participants from Lithuania in the final sample, because the hierarchical models account for uncertainty in estimates from countries with smaller samples and removing these data will actually reduce the overall precision of the estimates. Moreover, it would simply be unfortunate to remove all data from a highly understudied country.

Fourth, we preregistered that we would use the R package brms 130 to analyse the data and estimate model parameters. However, we ended up using the BayesFactor package 76 . This method is arguably more suitable for model comparison and calculating Bayes factors in particular. However, we also ran the models as preregistered and report these results in the Supplementary Information .

Fifth, we added level of education as a participant-level covariate to the models, which improved the model fits. Note that adjustments 3–5 did not qualitatively change any of the results (Table 2 and the Supplementary Information ).

Reporting Summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Data availability

All data collected as part of the experimental study, as well as preprocessed secondary data on explicit trust are provided at https://doi.org/10.17605/osf.io/qsyvw ( https://osf.io/qsyvw/ ). Raw data on the explicit trust ratings are available at https://wellcome.org/reports/wellcome-global-monitor/2018 .

Code availability

Analysis code for all main results and supplementary analyses is available at https://osf.io/qsyvw/ .

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Acknowledgements

This work was supported by funds from the Templeton Foundation (grant number 60663) to M.v.E., the Cogito Foundation (grant number R10917) to R.Mc.K., the Australian Research Council (grant number DP180102384) to N.L. and R.M.R., Templeton Religion Trust (reference TRT0196) to J.A.B., and the French Agence Nationale de la Recherche (reference 17-EURE-0017 FrontCog and 10-IDEX-0001-02 PSL) to S.A. The analysis was carried out on the Dutch national e-infrastructure with the support of SURF Cooperative.

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M.v.E. and S.H. conceptualized the idea, designed the study and formulated the hypotheses. S.A., T.B., R.B., A.C., C.G., R.G., K.H., C.K., R.Mc.K., A.N., L.Q., A.R., J.E.R., R.M.R., H.T., F.U., R.W., D.X. and S.H. provided cultural knowledge (including translations) for adjusting the materials to the national context and collected the data. S.H. analysed the data with input from J.A.B. and J.M.H. S.H. wrote the first draft of the manuscript, with major critical input from J.M.H., J.A.B., R.M.R., R.Mc.K. and M.v.E. and additional suggestions from S.A., T.B., R.B., A.C., C.G., R.G., W.M.G., K.H., C.K., N.L., A.N., L.Q., A.R., J.E.R., B.T.R., H.T., F.U., R.W. and D.X.

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Hoogeveen, S., Haaf, J.M., Bulbulia, J.A. et al. The Einstein effect provides global evidence for scientific source credibility effects and the influence of religiosity. Nat Hum Behav 6 , 523–535 (2022). https://doi.org/10.1038/s41562-021-01273-8

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Right again, Einstein! Scientists find where matter 'waterfalls' into black holes

"Think of it like a river turning into a waterfall — hitherto, we have been looking at the river. This is our first sight of the waterfall."

Scientists have confirmed, for the first time, that the very fabric of spacetime takes a "final plunge" at the edge of a black hole. 

The observation of this plunging region around black holes was made by astrophysicists at Oxford University Physics, and helps validate a key prediction of Albert Einstein's 1915 theory of gravity: general relativity. 

The Oxford team made the discovery while focusing on regions surrounding stellar-mass black holes in binaries with companion stars located relatively close to Earth. The researchers utilized X-ray data collected from a range of space telescopes, including NASA's Nuclear Spectroscopic Telescope Array (NuSTAR) and the International Space Station's mounted Neutron Star Interior Composition Explorer (NICER). 

This data allowed them to determine the fate of hot ionized gas and plasma, stripped from a companion star, taking a final plunge at the very edge of its associated black hole . The findings demonstrated that these so-called plunging regions around a black hole are the locations of some of the strongest spots of gravitational influence ever seen in our Milky Way galaxy .

Related: Does a cosmic 'glitch' in gravity challenge Albert Einstein's greatest theory?

"This is the first look at how plasma, peeled from the outer edge of a star, undergoes its final fall into the center of a black hole, a process happening in a system around 10,000 light years away," team leader and Oxford University Physics scientist Andrew Mummery said in a statement. "Einstein's theory predicted that this final plunge would exist, but this is the first time we’ve been able to demonstrate it happening.

"Think of it like a river turning into a waterfall – hitherto, we have been looking at the river. This is our first sight of the waterfall."

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Where does the black hole plunge come from?

Einstein's theory of general relativity suggests that objects with mass cause the very fabric of space and time, united as a single four-dimensional entity called "spacetime," to warp. Gravity arises from the resulting curvature.

Though general relativity operates in 4D, it can be vaguely illustrated through a rough 2D analogy. Imagine placing spheres of increasing masses onto a stretched rubber sheet. A golf ball would cause a tiny, almost imperceptible dent; a cricket ball would lead to a larger dent; and a bowling ball a massive dent. That's analogous to moons, planets and stars "denting" 4D spacetime. As an object's mass increases, so does the curvature they cause, and thus, their gravitational influence increases. A black hole would be like a cannonball on that analogous rubber sheet. 

With masses equivalent to tens, or even hundreds, of suns compressed into a width around that of Earth, the curvature of spacetime and the gravitational influence of stellar-mass black holes can become quite extreme. Supermassive black holes, on the other hand, are a whole other story. They're hugely massive, with masses equivalent to millions or even billions of suns, dwarfing even their stellar-mass counterparts. 

Returning to general relativity, Einstein suggested this curvature of spacetime leads to other interesting physics. For instance, he said, there must be a point just outside the boundary of the black hole at which particles would be incapable of following a circular or stable orbit. Instead, matter that enters this region would plunge toward the black hole at near-light speeds.

Understanding the physics of matter in this hypothetical plunging region of a black hole has been a goal of astrophysicists for some time. To address this, the Oxford team looked at what happens when black holes exist in a binary system with an "ordinary" star.

If the two are close enough, or if this star is slightly puffed out, the gravitational influence of the black hole can pull away stellar material. Because this plasma comes with angular momentum, it can't fall straight to the black hole — so, instead, it forms a flattened spinning cloud around the black hole called an accretion disk.

From that accretion disk, matter is gradually fed to the black hole. According to models of feeding black holes, there should be a point called the innermost stable circular orbit (ISCO) — the last point at which matter can stay stably rotating in an accretion disk.  Any matter beyond this is in the "plunging region," and it begins its unavoidable descent to the maw of the black hole. The debate about whether this plunging region could ever be detected was settled when the Oxford team found emissions from just beyond the ISCO of accretion disks around a Milky Way black hole binary called MAXI J1820+070.

Located around 10,000 light-years from Earth with a mass of around eight suns, the black hole component of MAXI J1820+070 is pulling material from its stellar companion while blasting out twin jets at around 80% the speed of light ; it's also producing strong X-ray emissions.

The team found that the X-ray spectrum of MAXI J1820+070 in a "soft-state" outburst, which represents emission from an accretion disk surrounding a rotating, or "Kerr," black hole — a full accretion disk, including the plunging region.

The researchers say this scenario represents the first robust detection of emission from a plunging region at the interior edge of a black hole accretion disk; they term such signals as "intra-ISCO emissions." These intra-ISCO emissions confirm the accuracy of general relativity in describing the regions immediately around black holes.

— Black hole-like 'gravastars' could be stacked like Russian tea dolls

— 2nd image of 1st black hole ever pictured confirms Einstein's general relativity (photo)

— Our neighboring galaxy's supermassive black hole would probably be a polite dinner guest

To follow up on this research, a separate team from Oxford's Department of Physics is collaborating with a European initiative to build the Africa Millimeter Telescope. This telescope should enhance scientists' ability to capture direct images of black holes and allow the plunging regions of more distant black holes to be probed.

"What is really exciting is that there are many black holes in the galaxy, and we now have a powerful new technique for using them to study the strongest known gravitational fields," Mummery concluded. 

The team's research is published in the journal Monthly Notices of the Royal Astronomical Society .

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Robert Lea is a science journalist in the U.K. whose articles have been published in Physics World, New Scientist, Astronomy Magazine, All About Space, Newsweek and ZME Science. He also writes about science communication for Elsevier and the European Journal of Physics. Rob holds a bachelor of science degree in physics and astronomy from the U.K.’s Open University. Follow him on Twitter @sciencef1rst.

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• Rod Mack While there might be evidence of a rapidly accelerating energy, due to the immense gravity in these regions, it's difficult to determine the fate of the energy involved. Whether it gets compressed to a near standstill around the object, forming a kind of energetic layer, or somehow gets incorporated remains a mystery. Each has a different set of implications. Reply
• billslugg When someone falls into a Black Hole, they don't know when they pass the event horizon. All they see is a dot of light straight ahead, darkness to the side and behind. They must deal with tidal forces. When an outside observer sees someone fall into a Black Hole, they see the person slowing down, becoming red shifted, disappearing into black. Reply
• Questioner The standard stretched rubber sheet is mind pollution at its worst. For light speed to remain consistent from all frames of reference, slowed/dilated time must be paired with reduced space. The use of the term 'curvature' implies bending, lengthening into an additional dimension, as does the stretched rubber sheet 'ILLustration'. That would increase space in a mass field which is fundamentally wrong in its implications. A mass field is a geometric transition from external fully 3 dimensional space to less than fully 3 dimensional space. To make the shorter path through a mass field requires a straighter line not a curved longer one. It only appears curved to the external viewer. Reply
• Questioner Easier crib notes, A mass field has reduced time flow, So a traversing EM photon makes less phase changes from entry to exit. For that photon to be traveling at the speed of light (phase oscillations per distance) that means it has to have crossed less space in/through the mass field. Seems elementary to me.... Reply
• billslugg A mass field has reduced time flow only to an external observer, the traversing photon sees nothing out of the usual. To an external observer the photon's clock runs slow and the photon is Lorentz contracted and the two exactly cancel out. Reply
• Questioner And to make it to the far side of the mass field with its (the photon's) lower number of phase oscillations it can only have traveled a shorter distance of contracted space to be traveling at its speed of light. And to the external viewer the photon also traveled at their speed of light because from entry point A to exit point B it took their faster expected travel time. The only inconsistencies are the age of the photon and its seeming redirection/'curve'. Reply
• billslugg The photon never changes the number of waves. The photon goes slower, the waves are closer together, the number of waves never changes for a given photon. If you want to change the number of waves you must absorb and then re-emit the photon. Time dilation and Lorentz contraction exactly compensate for each other. Everyone sees the speed of light to be the same. Reply
• Questioner "...the waves are closer together,..." In space? In time? If one takes a velocity measuring device that is launched at one foot per second from the outer edge of a mass field and counts how many seconds it takes to arrive at the far edge of the mass field because time is relatively slower in a mass field we know it will measure less feet than expected from externally calculated Euclidean geometry. If we take a long enough tape measure its measure will concur with that measure. So is the tape measure stretching or is there just less space in a mass field? Reply
• Questioner A given frequency of light has a fixed number of oscillations per distance. Reply
• Questioner If light slows down in a mass field and space is Euclidean normal in the mass field it will take longer for light to travel through that mass field than expected to the external viewer. That light speed would be inconsistent depending on one's POV. Reply
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