All scientific inquiry involves some kind of uncertainty, but the uncertainties in cosmology are particularly daunting. As well as being complex and difficult to describe, the systems cosmologists investigate are almost by definition out of reach. In these conditions of uncertainty, how confident can we be in the models we’ve built? How can we come to know how galaxies form, how the universe began or how much dark matter it contains?

In The Random Universe: How Models and Probability Help us Make Sense of the Cosmos, cosmologist and astrophysicist Andrew Jaffe offers a masterful and refreshing take on these questions. As the director of the Centre for Inference and Cosmology at Imperial College London, UK, and a past co-investigator on ESA’s Planck satellite that provided us with so much new information about the cosmos, Jaffe is well-equipped to walk readers through the tools that allow us to learn about the world despite its uncertainties. Anchoring his insights in beautifully narrated episodes from the history of physics, astrophysics and cosmology, he sheds light on how our theories of the universe evolved into our current best cosmological model – which nonetheless still has limitations.

Jaffe is particularly good at recounting how we refined, revised and even replaced some of our assumptions in light of incoming evidence such as the first measurements of stellar distance; the discovery of galaxies beyond our own; and precise measurements of cosmological parameters. Throughout this journey, he engages thoughtfully with a rich philosophical tradition that runs from David Hume in the 18th century through Willard Van Orman Quine, Imre Lakatos and Paul Feyerabend in the 20th.

Bayes’ theorem is important because it tells us how to update our degree of belief in light of new evidence

The book’s main protagonist, though, is the mathematician Thomas Bayes. For Jaffe, Bayesian probability is key to dealing with uncertainty, and even to solving Hume’s notorious problem of induction: how do we justify inferences from a finite set of observations to generalizations that go beyond them? Bayes’ theorem is important, Jaffe argues, because it tells us how to update our degree of belief in light of new evidence. It shows us why and how, even in an uncertain world, “the more observations we make, the surer we become”.

Of course, before we can use probability to deal with uncertainty, we first need a model. As Jaffe puts it, “Absent a model, I can’t assign a probability, and absent a probability, I can’t quantify my uncertainty about the world.” So, what exactly is a model? I found Jaffe’s answer to be one of the most captivating elements of the book. As the title of a subsection of chapter five puts it, “a model is a story about the world”. Without models, Jaffe tells us, our world would be an unexplained series of unrelated events. Models are also what allow us to take a finite set of data and use it to create something new. Without this leap, Jaffe suggests, we cannot learn anything about the world, because “you can’t make sense of an experimental result unless you have some model to interpret it”.

Of course, if the way we interpret data depends on our model, then different people may well obtain different interpretations depending on which model and which prior probability they choose. This charge of subjectivity is a longstanding accusation against Bayesians, but Jaffe offers at least a partial solution: “If you and I agree on the model, we should assign the same probability.” This, Jaffe argues, is where objectivity emerges, writing that “we come to the same conclusions if we start from the same premises”.

Models allow us to understand the world by bridging subjectivity with objectivity, and the personal with the collective

Many contemporary philosophers are at odds with the idealized view of science as an objective and linear enterprise that produces theories from a God’s-eye view. Instead, they strive to portray it as something that is social and human, but reliable nonetheless. Jaffe’s own views seem to align with this endeavour; as he puts it, “the scientific coupling of models and observations is a living, breathing, subjective endeavour, simultaneously collective and personal”. Through their interplay with data, he argues, models allow us to understand the world by bridging subjectivity with objectivity, and the personal with the collective.

Not everyone will agree with Jaffe that Bayesian probability offers a solution to Hume’s problem of induction. Personally, I (or perhaps the hardcore rationalist in me) was not convinced. Nevertheless, I found the book’s thesis – that uncertainty is not a hindrance to knowledge, but an opportunity to learn (and learn more) about the world – simultaneously liberating, humbling and empowering. I recommend The Random Universe to scientists, philosophers and anyone interested in better understanding the role of probability in science; the philosophical problems with how we handle uncertainty; and how our standard cosmological model came to be. I also hope it will encourage more collaborations between philosophers and scientists. There are many questions we can explore further if we work together.

• 2025 Yale University Press, £25hb, 288pp

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The event horizons of black holes that are far from equilibrium can now be described by the first and second laws of thermodynamics thanks to new work by theoretical physicists at Pennsylvania State University in the US. The result augments the work of the late Stephen Hawking and others who showed in the 1970s that these classical concepts have applications in idealized, static black holes.

Black holes are objects so dense that their gravitational pull prevents anything – even light – from escaping them. The “point of no return” of any object falling into a black hole is called the event horizon, and it represents the black hole’s mathematically defined “edge”.

Although black holes can be described using concepts from quantum mechanics and Einstein’s general theory of relativity, some 50 years ago physicists like Hawking and Jacob Bekenstein showed that the equations governing them are also astonishingly similar to the fundamental laws of thermodynamics. “This seminal observation sparked a rethinking of black holes in thermodynamics terms,” explains Abhay Ashtekar, a physicist at Penn State’s Eberly College who led the new study. In particular, Ashtekar says it meant that black holes could be assigned an entropy that is equal to the area of their event horizon.

The problem, he continues, is that technically, these relationships are only valid for black holes in equilibrium – that is, those that are stable and do not change over time. In contrast, real astrophysical black holes are constantly changing: they form, merge and eventually evaporate because of quantum effects.

“In these dynamical objects, event horizons are ‘teleological’, meaning that we need to know how a black hole will behave for all of eternity to be able to define its entropy today,” Ashtekar explains. “This notion of black hole entropy is therefore physically untenable. Indeed, this limitation was already recognized in the 1990s and it has been the elephant in the room since then.”

Extending the laws of thermodynamics

In their new work, Ashtekar and colleagues sought to overcome this limitation by replacing static event horizons with an alternative concept known as dynamical horizon segments. These segments are characterized by the physical properties of a black hole at a given moment in time, and other researchers have employed them in numerical simulations of black hole mergers and gravitational collapse. Indeed, Ashtekar and various colleagues had previously shown that dynamical horizons were a physically admissible replacement for event horizons.

However, Ashtekar says that these earlier studies had not addressed two central questions. These involved defining intensive parameters – analogues of pressure and temperature in ordinary thermodynamics systems such as gases – and defining the energy of a black hole by itself in a highly curved region of space-time at a given instant.

“Our study now shows that Einstein’s equations imply that these dynamical horizons also satisfy equations very similar to the first and second laws of thermodynamics,” Ashtekar tells Physics World. “What is more, the change in thermodynamical quantities of these horizons at any given moment in time are caused directly by fluxes of energy and changes in the angular momentum of the black hole at that instant.”

The researchers’ new calculations show that even when black holes are very far from equilibrium, their evolution defines specific trajectories in the space of different equilibrium states. “This allows us to transport observables from these states to instantaneous non-equilibrium ones,” explains Ashtekar. “Such a procedure cannot be applied to conventional thermodynamics systems; black holes are very special in this regard.”

Event horizons “entirely absent” when quantum effects are included

According to team member Daniel Paraizo, the new work treats the event horizon as a dynamical horizon segment that forms in a gravitational collapse and then evaporates because of quantum effects. Intriguingly, Paraizo says that within this framework, event horizons vanish entirely when quantum effects are included – a fact which, he says, “removes a great deal of confusion currently surrounding the issue of information loss from a black hole, for example”. This same finding, he notes, also supports an idea that Hawking advocated shortly before his death in 2018: the possibility that a “true” event horizon never actually forms.

The Penn State researchers now plan to build on their present work with theories involving both classical and quantum gravity. Team member Jonathan Shu says that such theories may provide a thermodynamic explanation of several puzzling features that have been observed in numerical simulations of black hole mergers. “We have also already extended our results to theories of gravity beyond general relativity,” he reveals. “For quantum gravity, dynamical horizon segments have been successfully deployed in the so-called semi-classical phase of black hole evaporation and work is underway to address still unanswered questions about the final stages of the process using a theory known as loop quantum gravity.”

The researchers report their work in Physical Review Letters. Ashtekar will also be speaking on this subject at Penrose Fest@95, which is due to be held in Oxford, UK in September.

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A system will generally move towards equilibrium when a change is made to it in a process called relaxation. To predict the state of the system after some period of time, we only need to know its current state and the external conditions. However, some polymers have memory behaviours where the evolution of the system is not only dependent on the current state, but also on previous states. This is known as the Kovacs effect.

In this work, the researchers investigated the Kovacs effect in a system consisting of suspensions of rod-like nanoparticles. By applying an electric field to these nanoparticles they align, therefore the particles change the liquid’s optical anisotropy, which can be measured as birefringence, which is how the liquid changes light polarization. More birefringence means the particles are more aligned. Importantly, there are faster- and slower-relaxing nanoparticles because of their polydispersity and different sizes, meaning they align at different rates. By changing the strength of the electric field, the faster and slower nanoparticles become out of sync with each other. The future behaviour will then depend on the system’s previous history that is overall hidden by the global birefringence measurement; this is the Kovacs effect.

The researchers modelled the orientational dynamics using the Smoluchowski equation, which describes rotational diffusion of particles. They found that relaxation is not determined by a single timescale or relaxation mode. When some of the modes are fast and some are slow, memory effects will occur. The Kovacs effect is important because it shows that a simple strategy of applying a strong electric field before switching to the target field does not necessarily speed up relaxation. Due to memory effects arising from particles relaxing at different rates, the system overshoots the target state, reducing the expected gain in speed.

To overcome this, the researchers designed improved two- and three-step protocols that suppress the slowest relaxation modes rather than simply matching the average birefringence. These protocols reduce the memory effect, produce a smoother approach to equilibrium, and achieve faster relaxation, although the benefit of additional switching steps becomes progressively smaller. This research improves our understanding of memory effects in complex systems and provides a practical strategy for controlling nanoparticle dynamics more quickly and efficiently.

Do you want to learn more about this topic?

Scientific developments of liquid crystal-based optical memory: a review by Jai Prakash, Achu Chandran and Ashok M Biradar (2016)

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Topological materials have been receiving a lot of attention in recent years because of their potential applications in future electronic and quantum technologies.

These are a type of material whose electrons have properties that stay stable even when the material has small defects, impurities, or imperfections. They often have surface or edge behaviour that is very different from the interior, because of the structure of the material’s quantum states.

Researchers use quantities such as Berry curvature and Chern numbers to describe topological materials. Berry curvature measures how an electron’s quantum state changes as its momentum changes. Adding this curvature across the whole band gives a Chern number, a whole-number label that can show whether the material is topological.

A key question in this area is: when a material has topological properties, how much of that behaviour is actually tied to quantum entanglement?

In a new paper published recently, Kazuki Ikeda and Steven Rayan tackled this question using the spinless Haldane model. This is a widely used theoretical model for understanding topological materials. This model describes electrons moving on a honeycomb lattice, which has two different sublattices, called A and B.

Here, the researchers added an extra layer of analysis. Instead of only calculating whether the model is topological, they were able to determine where the topological signal comes from.

By introducing a filter based on quantum entanglement, they tested whether the Berry curvature is associated with electron states that are spread across both A and B sublattices, or with states that mostly sit on one sublattice.

They also focused on what happens when the system moves between different topological phases, giving a more organised way to describe what changes when the energy gap closes and the material switches phase.

These results will provide invaluable insights into understanding and designing topological materials going forward.

What’s also interesting here is that, in order to obtain these results, the authors employed Langlands-inspired mathematics to keep track of what changes when the material switches between topological phases.

The Langlands programme is an ambitious mathematical dictionary that tries to translate problems about numbers into problems about symmetry, geometry and analysis.

Although the link in this work is purely conceptual, it does show that Langlands-style structures can organise real physics problems in topological matter.

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Tissue engineering offers a means to restore, maintain or replace biological tissues. But it is difficult to grow blood vessels using conventional fabrication techniques like 3D printing, as they are typically not precise enough to print fine capillaries and veins. A team of engineers from the Massachusetts Institute of Technology (MIT) has now developed a new approach to do just that, by using mechanical forces. Their blood-vessel-on-a-chip could be the first step in the scalable production of vascular networks that could then be implanted in the body to replace tissue that has been damaged by disease or injury.

The researchers, led by Ritu Raman, made their chip by filling a Petri dish with a gel containing nutrients and cell-growth factors. They then embedded a small magnet into the gel. Finally, they introduced a thin, hollow tube into the gel and coated the inside of the tube with live endothelial cells – the cells that naturally line blood vessels in the body.

Once anchored onto the inner walls of the tube, the endothelial cells began sprouting new, capillary-like vessels in the gel. And when the researchers moved the embedded magnet back and forth in different directions and by varying degrees, they found that the mechanical forces created by the moving magnet could stretch the vessels and increase the number of new capillaries that grew, as well as their length.

‘Steering’ blood vessel growth

“We also showed that blood vessel growth, or angiogenesis, could be directionally patterned using the mechanical forces created by the magnet and that these directions could change dynamically over time,” explains Raman. “This allows us to ‘steer’ blood vessel growth in all three spatial directions (x, y, z) and make complex geometries (like L-shaped branches) that would not be possible to fabricate using conventional methods.”

The researchers had previously demonstrated that biological cells are highly responsive to mechanical forces in the body, but they did not know how different types of forces – for example, stretching in different directions and at different degrees and frequencies – impacted the 3D structure of blood vessels. The main obstacle lay in developing a coupled magnet system to precisely stretch blood vessels in different directions. To achieve this, they designed a method for mechanically stimulating tissues, dubbed “magnetic matrix actuation”.

In their new work, which is detailed in PNAS, they went a step further and developed a method to accurately yet non-invasively stretch 3D blood vessel tissues they had built in the laboratory.

To better understand the effect of mechanical forces on angiogenesis, the MIT team decided to look into the role of a gene known as PIEZO1, which is just one of the many mechanically sensitive genes in the body. They built on the work of molecular biologist Ardem Patapoutian, who received the 2021 Nobel Prize in Physiology or Medicine for discovering that ion channels in cells open and close in response to mechanical pressure. One such ion channel is PIEZO1, which is regulated by the PIEZO1 gene.

By suppressing this PIEZO1 gene in the endothelial cells they studied, the researchers indeed observed that significantly fewer new blood vessels grew in the gel. This, they say, provides evidence that the applied mechanical forces in their experiment may have been opening the PIEZO1 ion channel in the endothelial cells, so triggering the new blood vessel growth.

“My group has always been interested in engineering artificial tissues that can be implanted in the body to repair damage caused by disease or traumatic injury, but such artificial tissues require integrated networks of blood vessels in order to function,” says Raman. “We hope that our method for precisely fabricating complex networks of blood vessels within engineered tissues will enable the development of such implants,” she tells Physics World.

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