The Alcubierre Drive was the first theoretical construction for a warp drive, with all the mathematical underpinnings necessary for something to move from the realm of scientific fiction to theoretical non-fiction. However, despite the mathematical underpinnings of its construction, it was wholly unphysical and was recognised as so by the community pretty quickly. As such, we shall not go into the detail of the proposed warping of the Alcubierre Drive but rather outline its problems. Firstly, the drive assumes the ability to accelerate beyond the speed of light barrier. However, Einstein’s theory of relativity does not allow objects to break the speed of light barrier, doing so would require an infinite amount of positive energy. The second problem is that, to attempt to get around the previous issue, the construction guiltily introduces negative energy. And not just a little, an immense amount of this negative energy is built into the formulation. Negative energy, to the best of our knowledge, does not exist in our universe. So the idea of the warp drive returned to live in the wishful world of science fiction, until earlier this year. 

A paper ‘Introducing Physical Warp Drives’ was released in February 2021, by Alexey Bobrick and Gianni Martire at Applied Physics in New York – what seems a somewhat mysterious yet promising new independent research institute. Let me attempt to explain simply the construction of this warp drive. The warp drive is, in essence, the spaceship itself. The spaceship can be imagined like a bubble, where its walls, referred to as the ‘warp shield’, are made of an incredibly dense material. The inside of the bubble, i.e the ship, is open and constitutes the passenger area. The ship then travels through the external spacetime. In mathematical phrasing, the geometry of the ship is then embedded into the geometry of the external universe. 

The first key idea is that the passengers are in the reference frame of the ship as a whole. A common analogy for reference frames in relativity is being aboard a train here on Earth. When you are sitting on a train and it is moving with a smooth constant speed, you can often feel like you are stationary and it is the world outside the windows that is moving. You are in the reference frame of the train (here, the spaceship). The second key idea is how mass warps spacetime, this is a fundamental pillar of Einstein’s theory of general relativity. Like I have explained in previous posts here at RTU, high densities of mass cause spacetime to bend or warp. For observers residing near these high mass densities, their passage of time slows relative to other observers. This effect is known as time dilation. If Alice travels close to a black hole (an area of extreme mass density), leaving Bob at a far distance, her passage of time will be far slower relative to his. By the time she returns to Bob, 4 days may have passed for her whilst 4 months or even 4 years may have passed for Bob (depending on the mass of the black hole!). This is a pretty huge idea so if you’re coming across it for the first time I’d recommend some extra reading, it won’t help your sanity but over time it might help normalise the phenomena for you.

The construction of Bobrick and Martire’s warp drive is built on the exploitation of this phenomena. The ships high density walls warp the surrounding spacetime, causing time to pass slower for the passengers inside relative to outside, allowing them to perceive a (relatively!) quick journey from A to B. If you are undertaking a warp drive journey, you have to make sure you’re happy with the fact that you don’t plan on seeing the friends that you left behind on Earth again. (By the time you return from your interstellar voyage they will be long gone.)

This physical warp drive does not break the speed of light barrier and does not require negative energy. Although superluminal travel is thrown out, the construct would still be exciting – given how far we have currently travelled as a species is our hop across to the Moon. However, to achieve substantial warping the material of the walls would have to be incredibly dense. “If we take the mass of the whole planet Earth and compress it to a shell with a size of 10 metres, then the correction to the rate of time inside it is still very small, just about an extra hour in the year,” says Bobrick. Obviously we as a species do not currently have the ability to acquire, let alone manipulate such resources but the key difference here is that the construction is not unphysical with respect to what we know about the universe – unlike the Alcubierre Drive. The mathematical underpinnings therefore can continue to be explored, without a feeling that the work is done in total vain. For example things like the geometry of the spaceship can be experimented with, as some configurations will require less massive materials to achieve the same time dilation effects. Bobrick and Martire have showed that a flattened ship, in the direction of travel, would require less energy (i.e. less mass in the warp shield) for the same degree of warping. This makes intuitive sense, making things aerodynamic in classical dynamics seems to echo the same reasoning. I read a quote in Popular Mechanics which I thought summed up the difference between the new construction and the Alcubierre drive very neatly – “this new concept uses floating bubbles of spacetime rather than floating ships in spacetime.”

Now that the warp drive construction has been explained, I’d like to end on one aspect that has always troubled me when discussing the overall topic. Warp drives allow the spaceship’s passengers to travel interstellar distances at sub, yet near light speeds. In the standard visualisations of warp drives you see the millions of stars flying past your view, as you hurtle through the cosmos. What I’ve never understood is how are the passengers always so relaxed during the journey, how can they be sure their trajectory isn’t going to collide with one of the intermediate stars (or planets, or asteroids)? Such a collision would without a doubt result in entire disintegration! I understand the space is incredibly sparse but if you’re travelling these interstellar distances your odds build up… To be confident of plain sailing you’d have to have a map of the entire space between destination A and B before embarking and set your trajectory accordingly. Not feasible if you’re using warp drives to explore new parts of the universe! Furthermore, as I laid out, time is passing slowly for you inside the ship but outside the processes are continuing as usual. Planets are orbiting stars, stars are orbiting the centres of their galaxies and asteroids are whimsically flying around. So not only do you need to map out your trajectory, you need to account for the movements of the celestial bodies over what will be the millions of years that pass for them whilst you are inside your ship. This seems like a very complex calculation indeed requiring huge amounts of galactic data. Maybe by the time we will have acquired the ultra dense resources for the warp drive construction we will have super computers to perform these cosmic calculations for us…

Feature Image Credit: GettyImages

Artificial Intelligence

The first is artificial intelligence (AI). AI has seen huge advancements in recent years, with possible revolutionary developments on the near term horizon. A term used in the field of AI is ‘super-intelligence’, hypothetical cognitive performance possessed by an agent that far surpasses that of the brightest human minds. It is a contentious issue, somewhat even a philosophical debate, as to whether the level of present-day human intelligence could be attainable or even surpassable by AI. Some argue that the lack of human consciousness would prevent AI ever being able to rival a human level of sophistication in their thought. However, others argue that the advantage of perfect recall, a digital knowledge storage base and the ability to multitask gives AI powerful potential to displace human beings. 

Another term in the field of AI is ‘semi-autonomy’ or ‘autonomy’, whereby agents develop the ability to make independent choices, not directly fed as prior inputs from their creators. The line from independent choice to independent values is a fuzzy one. Oxford philosopher Nick Bostrom has written that possible super-intelligent AI would be able to realise any goal they ‘valued’. Therefore, even if such AI were not actively malicious towards humans, should human activity block the realisation of their goals, Bostrom believes they would work towards the removal of such a barrier. A 2008 survey by the Future of Humanity Institute estimated a 5% probability of extinction by superintelligence by 2100. 

Biotechnology

Bioengineered organisms are those whose genetic sequences have been artificially modified in some way. These could be pathogens of humans, livestock or crops on which we depend.  Due to these genetic alternations, such organisms could have the potential to catastrophically disrupt ecosystem functions or be the cause of pandemics. For example a bioengineered pathogen of crops could have the potential to cause a global blight on essential agriculture. Remember the state of Earth in Interstellar? Alternatively, a bioengineered human pathogen could cause a pandemic more infectious or fatal than that yet seen by humanity. With technological developments in genetic modification increasing and laboratories with advanced biological equipment becoming commonplace, there must exist regulations to safeguard biotechnology. 

As Martin Rees, a British cosmologist and astrophysicist said “The global village will have its village idiots, and they’ll have global range”.

Overpopulation and Environmental Disaster

The 20th century has seen an exponential increase in human population. Whether the planet can cope with humanity’s ever increasing demand on its resources is becoming a serious question. The increasing need for energy, food and infrastructure puts an alarming demand on what are finite supplies. Agricultural crises, not due to pathogens but simply over demand, have been speculated to come to the forefront of humanity’s problems shortly after 2050.  You don’t have to have watched many post-apocalyptic movies to then imagine the ensuing wars over remaining scarce resources. David Pimentel, Professor of Ecology at Cornell University published a study which stated that, in order to avert disaster, the world population will have to be reduced by two-thirds…

The increasing demand on the planet from humanity, resulting in massive deforestation, eradication of natural habitats, loss of biodiversity, water and air pollution could be putting Earth on a path to eventual inhabitability. The Lancet Commission has warned that pollution levels are now at the point of exceeding “the envelope on the amount the Earth can carry” and “threaten the continuing survival of human societies”. The subsequent effect of global warming and the increase in frequency and severity of extreme weather events and weather-related disasters paint a dark picture for the future life on our planet, should we not take substantial action.

Warfare and mass destruction

The last of our anthropogenic risk is probably the most dismaying, mutual destruction. Sadly, despite our loneliness in the cosmos, we are not yet a collective species. Much divides humanity, political ideologies, religion, wealth, to name a few. Although a war that results destruction on a global scale is low, some argue it is inevitable in the long run unless we become a truly united species. In 2008, the Future of Humanity Institute estimated a 4% probability of extinction from warfare by 2100, with a 1% chance of extinction from nuclear warfare. 

These anthropogenic existential risks, that now exist due to the state of advancement humanity has reached, could provide a potential explanation to the Fermi Paradox. The paradox as to why, when considering the vastness of the universe that we inhabit, we seem completely alone. That explanation being, that perhaps civilisations reach a level of advancement that results in their own destruction, before they develop the capability to colonise other planets or acquire the sense in enough numbers to do what is necessary to protect their species on whatever planet they call home. This is a rather pessimistic thought, condemning not only our species but any potential species to be its own worst enemy.  I recently read an interesting paper that argued that the Fermi Paradox should in fact not be regarded a paradox at all. It is argued that the calculation that presents the probability that we are surely not alone, is inherently wrong in its formulation. The paper is titled ‘Dissolving the Fermi Paradox’ can be found here. I may revisit the paradox, that I originally wrote about back in 2016, in light of it soon.

As for now, although this post may have filled you with doom and gloom, it need not be so. Discussing existential risk today helps us think about the measures that need to be taken to best safeguard humanity’s tomorrow. Planning for the worst, puts us on the path to realising the best.

Extraterrestrial Arrival

For years we have been sending out signals hoping that someone out there will hear our cries. Humanity’s songs have been played out across the universe’s sky and missions have been sent into the depths of space carrying time capsules intending to communicate a story of our world to extraterrestrials. We boldly shout out into the abyss where we are, what we are and that we are currently (as a planet and species) alone.

Although alien life has to this day eluded us, many prominent scientists such as Carl Sagan have hypothesised that the existence of such life in the vast cosmos is very likely. Quoting Sagan, “the universe is a pretty big place. If it’s just us, seems like an awful waste of space.” There are many then that have heavily cautioned against efforts to actively hail extraterrestrial life to our blue planet. Should the life-form who hears us be advanced enough to have mastered interstellar travel in order to able to reach us, they would of course then be far more advanced than humanity and why should we assume them kind to us? They may not empathise with us but instead regard us equally as we disregard inferior animals species. They may simply raid the planet for resources useful them to them and move on as we simply raid natural habitats here on Earth. Stephen Hawking once said “If aliens visit us, the outcome would be much as when Columbus landed in America, which didn’t turn out well for the Native Americans.” Whether we should be a species that prudently batons down the hatches and focus on our own advancement or be a species that naively and optimistically shouts out into the cosmic jungle, is hotly up for debate.

Cosmic Catastrophe 

A few rather big hitters fall into this category. First up is asteroid impact. Asteroids with around a 1km diameter impact the Earth on average once every 500,000 years; this size is unlikely to wipe out the species but, depending on the impact location, may kill on the scale of billions. The annual probability of asteroid impact sufficient to cause extinction has been calculated as less than 1 in 10^8, though whether these estimates can be said to be truly reliable given the timeframe in which humans have been around to able to perform such calculations, is up for debate. Hawking (ever the vigilant) strongly proposed that an asteroid collision should be considered the biggest threat to the planet. Currently no known weapon system exists to shoot down an asteroid that is about to impact Earth and it is said that NASA would require at least five years of preparation time before such an interception mission could be attempted. 

The second risk is from our neighbours in the solar system stepping out of line. Long-term planetary movement is the change in the trajectories of bodies within a solar system, resulting from factors such as the change in mass of the system’s constituents. There is believed to be a 1% chance that Mercury’s orbit could be disrupted by Jupiter’s gravitational pull sometime during the lifetime of the Sun. One particularly terrifying outcome of this is the subsequent collision of Mercury with Earth, which somewhat eclipses the asteroid scenario.. 

The last risk to mention is down to the Sun itself. A dramatic increase in brightness of the Sun, known as a solar flare, if particularly powerful, could scorch the Earth’s surface. This could result in a large scale wipeout of life though, due to the orientation of the Sun to the Earth, likely not cause total extinction. However at the end of the day, and a very long day it will be, it is the Sun moving into its last stage of stellar life (for more detail see Story of the Stars) that will cause the demise of our planet. The expansion of the Sun will be so great that it will engulf the planet and they’ll be no safe retreat in sight. Such an event however, is 5.4 billion years away, so even a species optimist wouldn’t feel an impending need to prepare for this.

Humanity’s best chance to mitigate other existential risk events from the cosmos is to branch off of this one planet. Hawking was a resounding voice for humans to begin the process of permanently settling other planets, his sentiment echoed by SpaceX’s Elon Musk (see Making Humans Interplanetary). The need to colonise other planets and become an interplanetary species is the clearest way to ensure our survival as a species, keeping all our eggs in basket Earth is ultimately, a vulnerable position indeed. 

Pandemic

This final non-anthropogenic existential risk in today’s discussion is one we may all be sick and tired of hearing of – so I’ll keep it short. In our globalised world, with the speed and scale of human movement, increasing populations and living proximity, natural pandemics pose a serious risk to humanity. A common understanding in virology is that naturally evolving pathogens will, as a result of natural selection, reach a limit to their deadliness. This is simply because killing the host, kills the pathogen itself and even the pathogen wants to live. However, high transmission rates, incubation periods and the time required for natural selection to occur may cause a pandemic that is close to existential in its level of risk. 

Nevertheless our level of advancement in the science of immunisation and infection diseases with regards to its full potential, is relatively far higher than that of space travel. It is far easier to take the necessary steps here on Earth than the first steps on a new planet. As the speed of vaccine creation during this pandemic has shown us, we do have the tools to mitigate, and fight, such an existential risk. I should caveat that the cosmic risks presented today, are risks likely to occur on the scale of hundreds of thousands, if not millions of years. The same cannot be said however for risks originating from causes closer to home..

In the next post of this series we will face up to the anthropogenic risks to humanity’s survival. I will cover artificial intelligence, biotechnology, environmental disasters, overpopulation and mass warfare. I’ll then draw some interesting links to the Fermi Paradox, which may give reason to the silence of the cosmos. 

Feature Image via Getty/AdobeBox

Let me first clarify what I mean by a particular system. I make an extreme understatement when I say the universe is complicated. We can acquire some mental sanity by breaking it down and grouping its components into different systems. For example, you sitting in your living room reading this, could be treated as a system and a mathematical model could be designed to measure the evolution of this system. The model could measure effects such as the fluctuating temperature due to the incoming and outgoing heat flows, or the change in mass as more objects enter or leave the room. We can have much bigger systems, such as the solar system with models that track the dynamics of the planets around the sun. Or, we could have a system describing two black holes about to collide in a far corner of the universe. We state from the off-set what is included in our system and assume influence from no outside objects within our model, mathematically this is done through the inclusion of constraints and boundary conditions. 

The Einstein equation is most often used to describe the evolution of relativistic systems on the cosmological scale. Think black holes, exploding stars and the big bang. The deceptively simple looking equation is actually comprised of ten distinct highly non-linear partial differential equations which describe the behaviour of the system. To write each of the ten equations out in full, in their most general form without any grouping of the terms, would literally take hundreds of pages. Solving it, is therefore an incredibly daunting task.

To be able to find exact solutions to this equation is extremely rare and only occurs for a handful of simple systems in which a large number of these terms fall away to zero. For example, if we are looking at a system with an isolated body of mass sitting in an otherwise empty space-time, the term T in the above equation (the Stress-Energy tensor) disappears, greatly simplifying the equations with now nothing on the right hand side. You may wonder how could this could represent any interesting physical situation in nature, but remember our thinking in systems. An isolated black hole, far away from any other matter can be well represented by this scheme due to the negligible influence from far away bodies and thus their exclusion from the system. Symmetry in a system also provides a big helping hand, if a system has spatial (or far less common temporal) symmetry this will also make the equations much more tractable due to a large cancellation of terms. Think back to the living room example if this isn’t immediately obvious, if the left half of my living room is identical in every way to the right half, my model needs only do half the work to represent the system. 

There then exist systems which are not exact solutions to the Einstein equation, but to which we can find approximate solutions due to certain simplifications. If the gravitational field is weak or the speed of the bodies in the system is substantially slower than the speed of the light, a number of the terms in the equations become very small and can essentially be ignored. Such approximations allow us, to a high a degree of accuracy, to model the dynamics of planets, certain binary neutron stars and particular emissions of gravitational waves. However, the exact and approximately solvable cases only represent a fraction of the systems we’d like to model in the universe and unfortunately, as well as obviously, the most interesting and physically realistic cases are the most complex. 

To examine gravitational waves from colliding black holes or supernovae, to model relativistic phenomena such as active galactic nuclei or to follow spacetime singularities, we work in the regime of strong gravity and require the ability to solve the Einstein equation in its full, almighty form. The Einstein equation must be solved everywhere in the system, tracking the matter at each point, how fast it is moving, the pressures and stresses and the resulting warping of the surrounding spacetime. The changes at one point in the system then affect the spacetime geometry at every other point. All the terms laid out in the hundreds of pages must be inputted into the equation to ensure accurate results. Thankfully for the human brains of all relativists, we now have the technology to pass this less than enviable job onto computers. This is the field of Numerical Relativity, the ability to provide approximate solutions to the Einstein equation for systems using (as the name suggests) numerical methods.

Researchers have developed methods to computationally evolve systems by inputting the data describing the system at an initial moment and then using finite differencing numerical methods to evolve the state forward step by step in time. However, numerical discretisation is a double edged sword. The smaller the taken steps the smaller the introduced error and the smaller the deviation from the true solution. Small steps however come at the cost of runtime. If the problem is discretised up into smaller chunks, there obviously exists a larger number of them for the computer to process, taking a longer time to spit out a complete simulation. A main job of the numerical relativist is to ensure the inputted data describing the system at an initial time was well-posed. This meaning, it will not lead to numerical instabilities when the computer evolves it and will ultimately present an accurate approximation for the system’s behaviour over time. 

This problem is known as the initial value problem and the nature of the theory of general relativity, to which Einstein’s equation belongs, provides a high entry barrier for acceptable initial data due to the theory being gauge invariant. What this means is that the model that describes the behaviour of your system must be independent of the coordinates you choose to do the modelling! Coordinates are after all just a mathematical choice to make certain aspects of your calculation easier, but more on this subtlety another time. This gauge invariance means the data must be subject to certain  mathematical constraints and boundary conditions which ensures criticial information about the physical situation trying to be modelling is appropriately included. Takeaway message, although we give the brute work to computers, we must still work extremely hard to formulate what we feed in before we can kick back and let the algorithm chug on. I hope to do a more detailed post on the formulation of Numerical Relativity soon.

For a beautiful visualisation of a numerical simulation of two merging black-holes, with asymmetric masses and the extra complications of orbital precession (GW190412) see the following video from the Albert Einstein Institute.

Such intricate behaviour, all ultimately encapsulated in the equation given at the top of this post.

Feature Photo Credit: NASA/VICTOR TANGERMANN

Though there has not been any concrete proof of IMBHs so far, some evidence provides strong suggestion. Whilst gravitational waves are the medium with which we can detect black hole mergers, while they live as solitary beasts there are other ways in which we can detect their presence. As black holes consume matter many emit high-energy radiation in the form of X-rays. Observers have previously found strong X-ray emission from nearby galaxies, such as NGC 1313. From the analysis of the X-ray emission, its strength and periodicity, a constraint can be put on the mass of the source. In the case of NGC 1313, this came in at around 1,000 solar masses, firmly putting it in intermediate mass black hole territory. Further evidence that such strong X-ray emitting sources are indeed black holes comes when the radiation clearly does not have with a visible light counterpart, which would be the case should the source instead have been a star or galaxy. The radiation signals often also show periodicity, a phenomenon thought to be due to the consumption pattern of the black hole, whereby every time it rips out matter from encircling nearby stars it emits a strong burst of X-rays. 

As detection of such signals is sporadic and not entirely conclusive, concrete proof of IMBHs will only come when we can detect a merger. This will either take the form of two intermediate black holes colliding, or intermediate mass-ratio inspirals (IMIRIs) when a stellar mass black holes falls into an IMBH or when an IMBH falls into a supermassive black hole. To detect gravitational waves signals from IMRIs requires innovative methods of modelling their gravitational waveform templates, an exciting new field which myself and my supervisors are currently working on. The next generation of gravitational wave detector, the space satellite LISA, will have a frequency detection range well suited to IMRI signals, so the race is on to provide accurate templates before its launch. It is also hoped that Advanced LIGO may be able to tune into the gravitational waves from IMRIs once we know what waveforms it is that we are looking for. The detection of IMBHs would be provide a vital bridge in our understanding of black holes, helping us piece together black hole formation, population and evolution over time. Stay tuned!

The dawn of the universe was flooded with radiation produced by the Big Bang. The popular cosmological picture of the beginning of the universe is that of a swirling soup of such radiation which, as the cosmos expanded, began to clump together to  form matter and subsequently the first stars and planets. In this popular picture it was only millions of years later, once these stars became sufficiently dense that the strength of their own gravity caused them to collapse and form black holes. However, new models suggest that the early universe could have been a breeding ground for other beasts, primordial black holes (PBHs (the cosmic OAPs)). It is believed that black holes could have also been formed from extreme density fluctuations in the early universe, less than one second after the Big Bang. There are many cosmological phenomena that could have produced such density fluctuations such as cosmic inflation, reheating or cosmological phase transitions. From these, fluctuations (sharp points of contrast) in the matter densities, the spacetime would again be in the position to undergo gravitational collapse upon itself, forming a black hole. Such PBHs would then be able to devour the radiation surrounding them, growing as they ate.

Theoretically PBHs could have initial masses ranging from 10^(-8)kg to thousands of solar masses, however those having masses lower than 10^(11)kg would not have survived to the present day due to having evaporated entirely by now (see Glowing and Shrinking) through the process of Hawking radiation. However these limits still allow good theoretical scope for observation of some of such relics today, which in turn would resolve many unanswered cosmic questions.

Shedding light on darkness

Dark matter is a substance thought to account for approximately 85% of the matter in the universe and about a quarter of its total energy density. The fact that the main constituents of our universe remain a mystery is a sorry state of affairs for theoretical physicists. Popular candidates for the elusive constituents of dark matter are WIMPs (see The Dark Side) and MACHOs: massive compact halo objects. MACHOs are large objects that emit little to no radiation, given their nature PBHs are a possible type of such object. Taken into account their formation at the dawn of time, their supreme density and the masking properties of the horizon to direct observation, it is easily believable that PBHs could be the dominant, or even sole, component of dark matter.

A second theory is that even if PBHs are not directly the dark matter constituents, through their evaporation they could emit whatever the true dark matter particles are. The type of particles emitted during the process of Hawking radiation (during the evaporation of a black hole) crucially do not depend on what fell into reach of the black hole during its lifetime. The black hole amalgamates all it ingests and the by-products of its evaporation can take the from of whatever particle exist in nature. Dark matter treated on an equal footing.

Cosmic speed limit

The rate of the expansion of the universe has not yet been pinned down and cosmologists currently have two ways to measure the rate of acceleration. The first involves the measurement of light from supernovae, whilst the second uses the ancient radiation leftover over from the Big Bang (cosmic microwave background radiation). The trouble is, these two measurements are currently in conflict with each other. However if we account for the radiation effects from the ancient relics of PBHs alongside the ancient radiation of the CMB, this would seem equate rate calculated from the two approaches.

The Supermassive

The mass of a black hole increases as it sucks in the matter surrounding it. However if black holes are only able to be born from the fiery deaths of stars, this puts a size limit on the what their mass upper bound should be (due to the restricted time they could have been alive and thus been able to grow). This formation theory for black holes is in direct contradiction with the size of the supermassive black holes (SBHs) we now know exist at the centres of most large galaxies. The gargantuan size of these SBHs is simply impossible based on the current understanding of standard black hole formation. Either there is another process in place by which black holes can grow, perhaps the amalgamation of black holes born from stars is much more frequent than we predict or perhaps PBHs are the answer. If black holes can exist from moments after the Big Bang, seeded instead from cosmic density fluctuations and not have to wait around for stars to form and die, it becomes plausible to reach the supermassive size necessary to agree with current day findings.

Are they out there

LIGO – the Laser Interferometer Gravitational-Wave Observatory has now detected gravitational waves signals from over ten binary black hole mergers (for more on the spectacular details of a black hole merger and what we can learn from them see Inspirational Systems). There are mutterings amongst the LIGO community that some of these detections came from PBHs rather than the standard stellar remnant black holes .

Many of the black holes detected by LIGO did not seem to be spinning fast. If the black holes were formed from resurrected-stars in a binary system, they would tend to have a degree of spin as the stars would have possessed angular moment. PBHs born in isolation in the early universe however, do not tend to have much spin.

PBHs were born from density fluctuations in the early universe and predictions on the nature of such fluctuations can then be extrapolated to tell us what the masses of such PBHs would roughly be today. The average answer is suggested to be about 30 solar masses. Remarkably most of the LIGO observed black holes fall around such a mass range. The majority of the early LIGO measurements coming in at this range is argued by some to support the case.

As the next generation of gravitational wave detectors enter the game, a resolution to the debate over PBHs may come. Whatever the answer may be one thing is for certain, gravitational waves are a revolutionary new medium with which we can explore and understand the universe. For now we continue to wonder whether primordial black holes may hold the answer to such primordial questions.

• Supervised learning
• Unsupervised learning
• Semi-supervised learning
• Reinforcement learning
• Deep learning

All of these can be imagined to be within the bubble of machine learning, a term you’ve probably heard before. The main differences in these methods, and why some can be more desirable than others for certain tasks more will be briefly looked at now.

Supervised learning is called as so because the whole learning process of the program is relatively controlled. When a machine like this learns it is fed training data as the input, and in this case the program is also told the desired answer to each piece of data (the output). This way the program creates a function mapping the input to the desired output, which it can then use to predict future outputs when given new input data. All of these machine learning programs are usually fed validation data after the training data, to confirm the working state of the AI. A basic example of supervised learning in use would be giving a program data that represents the attributes of a house, such as the area of floor space, number of bedrooms, and the location of the house, and then also giving the program the outputs of how much each house sold for. The idea is then to give the program relevant data about new houses to find an accurate value for them.

A somewhat more interesting technique is unsupervised learning. Unsupervised learning can spot similar patterns that the former method would when being used for the same task however, in a more abstract way. The main difference between these two approaches is that in unsupervised learning the program isn’t given any output data to match to the given input data, ultimately leading to the program finding patterns and correlations in the data without being explicitly told what to look for. Because of this, unsupervised learning is more so used when the results wanted are not so obvious to the people working with the data. Since this method of learning has less strict instructions and fewer guidelines, it’s seen to be closer to general intelligence than supervised learning. Unsupervised learning is commonly used in things like online shopping recommendations, where after you have bought something you are targeted with advertisements based off of what other users who bought the same product as you also bought after of before.

Semi-supervised learning is as the name suggests, partly supervised and partly not. The data given in this approach is typically a small amount of labelled data (like in supervised learning) and a large amount of unlabelled data (same as in unsupervised learning). Firstly, this helps with a few things, such as reducing bias and error in the data as not all the data is labelled by someone who could have made mistakes or impacted the data in an inaccurate way. Also, not having to label a large majority of the data helps greatly with timing and cost issues too. Semi-supervised learning can be taken advantage of in certain situations to do with organising things into groups, at less cost than with supervised learning. A program could for instance take unlabelled data of pictures of fruit like apples bananas and oranges, and put them into groups based on things like colour and shape. It cannot however, actually state which one is an orange or an apple or a banana, but with a small amount of labelled data it would then be able to recognise out of all of the pictures it has, which ones correspond to which fruit after examining similar pictures that have a name attached to them.

Reinforcement learning is quite different in how it learns compared to the previous three. It uses a reward-based system, often with punishment involved as well, to incentivise the program to perform a task well. When the program is presented with a task, it has an observable environment and the ability to perform certain actions. For certain actions it is rewarded and for others it is punished, usually through a numbered score system, where a positive action would give +1 and a negative -1, or even larger numbers depending on the severity of the consequence of the action. This approach is pretty similar to training your dog to do tricks by giving it treats when it does it right. But a difference between the two is the vast amounts of ways some problems can be approached and proceeded through. Where a dog rolling over is just one action for the dog to perform, and AI playing chess for instance is faced with a lot of different actions that each lead to a new set of different actions, and so on until the option pathways aren’t really comprehendible for a person due to all the different moves the opponent can make on top of that. Thankfully though these types of chess playing programs can play millions of games in a couple hours during their learning phases, so this kind of brute force computing power means it does not encounter problems when faced with the vast number of possible options. Something that could seem to be a problem however, is if a path of actions that seems bad at first, giving punishment to the AI, eventually turns out to lead to a better or more efficient solution overall. This can lead to some interesting situations though.. DeepMind’s Alpha Zero, a chess program that learnt by just being told the rules and playing games against itself managed to reach the level of play of Stockfish 8 (a chess playing program that is consistently ranked near the top) in just 4 hours of training, and beat it in a 100 game tournament (28 wins, 72 draws) in 9 hours. Normally these chess playing programs would analyse games that had already been played by other people or other programs during it learning phase, Alpha Zero however only played games against itself to learn. Throughout these games Alpha Zero seemed to play different to other AIs; where you might expect, due to the reward system in reinforcement learning, that it would highly value taking pieces and minimising losses to eventually win, it unexpectedly made large sacrifices of valuable pieces to instead gain positional advantages that lead to victory in the long term. Alpha Zero also utilised neural networks to come out on top too, something that is a core aspect of the
next subject.

Deep learning uses neural networks in a way that models the human brain to process data it is given. Deep learning uses supervised, semi-supervised or unsupervised learning, and it can also use reinforcement learning. In a multilayer perceptron model, the artificial neurons in a neural network are connected to each other in layers, with a minimum of three. At the minimum an input and output layer are needed, as well as a hidden layer in the middle, every neuron in the input layer are connected to all of the neurons in the middle layer, which then connect to every neuron in the output layer. Each of these neurons has a weight assigned to it that adjusts the information it has been sent and decides where to send it or if even to send it on at all, these weightings are adjusted throughout the training phase to hone in on the optimal final state. It is this sandwich of hidden neuron layers that holds the model which assigns outputs to inputs. There are other types of ways neural networks can be implemented as well such as convolutional neural networks and recursive neural networks, and needless to say there is a lot of interest in the field of deep learning at the moment. Some of this interest is actually from neuroscientists who are observing how neural networks arrive at the conclusions they do as an insight to how the process might work with biological neurons. Due to the presence of hidden layers in these neural networks though, there are times when an AI can arrive at a result without anyone understanding why it did, or what sort of path it followed to get there, which raises some ethical questions. For instance, if you had an AI judge that sentenced someone as guilty without there being a clear reason how it reached its conclusion, it would far from instil trust and could leave potential for undectectable abuse if someone were able to force it to provide a fake answer. Another situation which may have more relevance at this time is the decision-making process in a self-driving car during an emergency. If the car was faced with its own version of the trolley problem or something similar, involving having to decide between the safety of different people, how could we come to the conclusion that the decision the car had made was fair and reasonable? Along this path there have been AIs developed to try and understand the actions of other AIs, in a bid to try and keep the ethical problems under control. Though this methodology raises obvious questions of circularity. ..

This was a very brief introduction into some of the main types of machine learning. There is a lot more to say about these methods and many others, especially on the subject of neural networks, but these will have to be explored more at a later time. Artificial intelligence as a field will only continue to grow with new and interesting developments being abundant, and with AI creeping its way into many parts of our lives it will be worthwhile to keep up with its evolution, wherever it leads.

Back in 2017, I wrote a post on gravitational waves here at RTU, describing how such waves are generated. I briefly explained that, in order for the waves to be currently detectable, the sources need to be extremely massive i.e. colliding neutron stars or black holes. Just as with any other astronomical observation, to pick out a clear signal, one needs to know what they are looking for in the data. Here’s where the theory comes in; systems such as black hole binaries (two black holes locked in orbit around each other) are complex solutions, but of course solutions nonetheless to Einstein’s equations of motion. The field of numerical relativity uses numerical methods and algorithms to solve Einstein’s equations for such complex, dynamical systems. Solutions of the Einstein Field Equations that we can solve fully by hand represent only trivially simple systems in nature and astrophysical binaries certainly don’t fall into this box. Equipped with computer clusters, we can now computationally model these systems and theoretically compute the templates of the gravitational waves they would emit.

Such computational methodology works well when the two objects in the binary system are roughly the same size – i.e. when their mass ratio is roughly 1. The two objects circle each other a handful number of times before spiralling inward and amalgamating into one fat mass. This process is known as an inspiral. Key point being, the number of orbits undertaken during the inspiral in this case is relatively small and consequently, the evolution of the system can be computationally run in a reasonable amount of time. When the two entities of the binary are of roughly equal mass it is known as a Comparable Mass Ratio Inspiral (CMRI). Our success with numerical relativity in this area has led to the LIGO gravitational wave detector spotting eleven of such events since 2015! Detailed descriptions of such inspirals have been a major computational effort in gravitational research for recent decades. The ability to predict the exact pattern of gravitational waves for such systems, allows for meaningful observation and it can be safely said that gravitational waves have now firmly entered the domain of the observational.

Artists impression of the gravitational waves from a CMRI system

The challenge comes when we move from objects of comparable mass to those of disparate mass. Of particular interest is the set up where the larger object is a factor of 10,000 or more heavier than it’s partner in the system. This type of binary system is called an Extreme Mass Ratio Inspiral (EMRI) and is often embodied in nature by a supermassive black hole at the center of a galaxy, being orbited by a stellar mass black hole. Because the little black hole is so much smaller than its partner, it exhibits between 10^(5)-10^(6) orbits before eventually plunging in. The examination of the gravitational waves from such a system would provide us with a wealth of knowledge. Due to the thousands of orbits, the gravitational wave signal encodes highly detailed mapping of the spacetime geometry surrounding the super massive black hole. You can think of the little black hole as tracing out the structure of spacetime with each encircling and transmitting this information in the form of gravitational waves. 

Artists impression of an EMRI system’s spacetime curvature

Results from such set ups would be extremely accurate tests for the predictions of Einstein’s theory of General Relativity in the regime of strong gravity – a regime which has largely been untestable thus far. Additionally, the data from such an inspiral would give in profound insight into parameters of the components, such as mass and angular momentum. This would hugely help theoretical physicists validate their hypotheses on the types of black holes that exist.

Due to the colossal number of orbits in an EMRI system, modelling the gravitational waveforms with numerical relativity would be highly computationally expensive, if not impossible. However, large mass difference in the EMRI case can be used to our advantage, providing us with a highly accurate approximation scheme to solving the Einstein equations. Approximation schemes, are often used in theoretical physics and center around expanding equations about a small perturbative parameter – in the case of EMRI’s we expand in one over the mass ratio of the two objects. The Einstein equations are perfectly accepting of a perturbative expansion in powers of such a parameter and in the case of EMRI systems the mass ratio can be as small as 10^(-6). At first order of the expansion, the path of the lighter object is simply treated as that of a massive test particle, affected solely by the gravity created by the larger black hole. Then, order by order we add corrections into the equations, to account for the mass of the lighter object and the small effective force it imposes. This force is known as the gravitational self-force. In fact, it has been estimated that reaching the second-order expansion will be sufficient for accuracy in the gravitational waveform templates, allowing for detection of EMRI systems from data gathered by the upcoming gravitational wave detector, LISA. This analysis of EMRI systems is a key area of research of my supervisors to be, Professor Leor Barack and Dr. Adam Pound, and one where they have already had great success.

Artists impression of the LISA space mission

LISA, a space-based observatory to detect gravitational waves, is planned to launch in the early 2030s. The sensitivity of LISA will peak in the mililihertz band, the frequency range at which EMRI systems will emit gravitational waves. However, even if an EMRI system is very close, its signal will still be much weaker than the instrumental noise gathered by LISA. Such is the problem when trying to catch such extraordinarily sensitive signals that are buried in detector noise. To maximise the science return from the multi-billion dollar mission it is vital that the theoretical waveform models are derived accurately, in advance. Then, the data from LISA can be matched up against these theoretical templates, acting as a filter against the noise, allowing us to clear signals. Getting the EMRI waveforms right would unlock a wealth of scientific information. The encoding of the geometry of spacetime in the gravitational waves, would provide profound insight into our understanding of gravity in the strong regime – we just need the wave template cipher. 

To recap, we have the comparable mass binary systems (i.e. two similar size black holes) whose gravitational waves have been detected by LIGO, for which numerical methods have proved fruitful to model. And, the extreme mass binary systems, key LISA targets, for which we are using our perturbative tricks to model. A third system sits between these, the logically named Intermediate Mass Ratio Inspiral (IMRI). IMRI systems are those for which the mass ratio is around 1000. They would be embodied in nature by either an intermediate mass black hole around a supermassive black hole (case 1) or a stellar mass black hole around a intermediate mass black hole (case 2). There is doubt around the existence of such systems however, as intermediate black holes have not yet been proven to exist.

Being the middle sibling in this situation, means neither of our above methods for theoretical waveform modelling can do the trick. The accuracy of the perturbative expansion in the mass ratio method severely deteriorates as the parameter is no longer small, yet the number of orbits remains large. Such a set up thus requires a hybrid approach and this is what my PhD will hope to investigate. But let me end by telling you why this last case is worth cracking. As well as providing the first confirmation of the existence of an intermediate mass black hole, observations of IMRI gravitational waves will allow us to probe the dynamical processes in globular clusters and galactic nuclei. Rich astrophysical insights are up for grabs, along with fundamental knowledge on black hole formation and morphology. In case 1 IMRI’s, since the central object is large, gravitational waves are produced at a low frequencies. Such systems would then be detectable by the capabilities of LISA in the future. In case 2, IMIRI’s the central object is smaller, producing higher frequency gravitational waves which could actually be detectable by the currently running Advanced LIGO instrument. Tantalising prospects, whereby discoveries are theoretically possible as soon as we have the correct gravitational wave templates against which to filter the LIGO data.

Gravitational waves, black holes and all things gravity will return to being a central theme here at RTU. Posts in the near future will also include a more in-depth look at IMRI systems and the workings of the LISA instrument. Lots to discuss in this exciting and relatively new field of theoretical physics.

To understand fuzzballs we must first remind ourselves of the key properties of black holes. Earlier posts in the Black Holes series (#1, #2, #3, #4) at RTU cover these fantastical features in more depth, but in a nutshell they are defined by two key features. Firstly, the event horizon, the barrier from which information cannot escape. Secondly, the singularity, the point at the very centre of the black hole at which, due to an infinity matter density, space and time as we know them breakdown. The problem with the original black hole view is that the nature of these beasts can be described through both the quantum lens and the gravity lens. The two leading theories of the universe have been unable to reconcile their differences and their clash, in the context of black holes, has caused arguably the most troublesome conflict in the subject, the information paradox. This, coupled with the seemingly impossible understanding of a singularity has caused physicists to tear their hair out over the years. Fuzzballs, claim to present solutions to both these problems. To understand these let us take each problem and its supposed resolution in turn.

The information paradox

The Black Hole

In the standard description of a black hole there exists the infamous event horizon – a boundary a distance from the centre of the black hole from which nothing can escape. A point of no return. Hawking realised that in the empty space surrounding this horizon there can enter into existence, particle and anti-particle pairs. If this happens, there is chance that one of these pairs will escape outwards, while the other passes through the event horizon of the black hole, never to be seen again. As a result of the outwardly escaping particle, the black hole is seen to be radiating and with a loss of energy through radiation comes a shrinking of the black hole. For a dedicated explanation of this process see Black Holes: #2 Glowing and Shrinking. As a result of this ongoing phenomena, a black hole will finally cease to exist altogether, having evaporated entirely. In doing so, information of whatever fell into the black hole will be destroyed and this destruction of information is staunchly in opposition to the laws of quantum mechanics. In quantum mechanics, information is never lost. General Relativity also states that a black hole is characterised only by its mass, spin and charge. There is no other information that can be deduced about a black hole from examination of its event horizon. This lack of information and eventual disappearance of it altogether is known as the information paradox.

The Fuzzball 

The fuzzball view claims to resolve this paradox with doing away with the event horizon altogether. The theory instead claims that these extremely dense coagulations of matter are comprised entirely of strings and do have a physical surface, just like a neutron star, ordinary star, or planet does. This surface however, is fuzzy instead of entirely solid. The diagram below may help your visualisation.

By eliminating the event horizon, we eliminate the phenomena of Hawking radiation as information can not longer be lost past a boundary or no return as there is no boundary of no return. Radiation still gets emitted from the fuzzball if one particle falls in and the other escapes but there is no clash with quantum mechanics. The information about the infalling particle can be retrieved. Furthermore because the fuzzball has a surface, there is structure here and information about the past history of the fuzzball can be deduced from it. From analysis of this structure all fuzzballs are seen to be unique and are characterised by a lot more than just their mass, spin and charge. As John Wheeler famously said to sum up the generic nature of black holes, ‘a black has no hair’. Fuzzballs however very much do have hair, and knotty hair at that.

The singularity

The Black Hole

Another troubling feature of the black hole is the point at the very centre where space and time breakdown due to the extreme density of matter. In the standard theory of general relativity the curvature of spacetime tends towards infinity with the mathematics blowing up in our faces, producing seemingly unphysical results.

The Fuzzball

The fuzzball structure, as we have said, is made from strings – as, according to string theory, is everything in our universe as they are the fundamental components of matter. As objects fall into the fuzzball, their strings combine with those on fuzzball’s surface forming larger, more complex string structures. When these strings combine together there is resultant outward pressure from the massless fields at play. At the centre of the fuzzball the density of these strings is at its highest and the strong resultant outward pressure causes a phase transition to a new state of matter which prevents the formation of a singularity. Perhaps a little hard to swallow without examining the maths first hand but i’m giving you the quick and dirty jist of it.

a) the black hole view with singularity in spacetime represented by a jagged line

b) the fuzzball view with the centre of the fuzzball represented by a dense coagulation of strings

Entropy

Another advocate for fuzzballs is entropy. As required by the second law of thermodynamics, black holes have entropy – an inherent measure of their level of disorder or simply put, chaos. All systems have a measure of entropy and this entropy can be quantified by counting the number of microstates of the system. Different microstates are the different ways the components of the system can be arranged whilst preserving the overall macroscopic picture. For example a messy room has a high entropy as the items can be strewn around in many ways, i.e. a large number of microstates, whilst still preserving the overall look of messiness.

In 1973 Bekenstein postulated that the level of this entropy associated to the black hole is proportional area of the black hole’s event horizon. Together with Hawking, the formula for a black hole’s entropy was produced, expressing it as proportional to the area of the horizon with factors of fundamental constants. It is a truly remarkable formula as it includes the fundamental constant of gravity and a fundamental constant of the quantum world, the planck length. Such constants rarely meet in our descriptions of nature, given the long standing incompatibility of quantum mechanics and general relativity. In the original black hole view, the only way we can measure this entropy is from properties of the event horizon since we cannot retrieve any further information from inside.

The fuzzball theory however, allows us to directly count the number of microstates of the system. Within string theory, a black hole’s structure comes in the forms of strings and branes and the ways in which these can be arranged represent the different microstates. Mathur’s calculation of the entropy from analysing these microstates can be found to equal that found by the Bekenstein-Hawking formula! A very promising find.

Fuzzy thoughts

Fuzzballs present a way to reconcile classical and quantum descriptions of black holes, however the jury is still out in the theoretical physics community. Fuzzballs make use of string theory, much to the delight of many who have poured over its formulation as a possible quantum gravity theory. However, string theory is by no means a complete theory and the fuzzballs rely heavily on its claims. Although the framework seemingly resolves problems of singularities and information destruction, it raises new questions in lieu, including the nature of extra dimensions to name one (did I mention, string theory is at minimum 10 dimensional?!) And… as much as the event horizon of a black hole is a wicked feature, physicists have a somewhat twisted affinity for it. Not all are keen to champion its dismissal and instead would rather find a theory which resolves the paradox whilst maintaining its inclusion.

The final fate of the fuzz is still unknown.

The Standard Model of particle physics is the basis of our current best understanding of the sub-atomic realm. The model postulates a conglomeration of different fundamental particles, that together explain the behaviour of the forces and matter that we observe in nature. A recent triumph of the LHC in 2012 (recent as major discoveries in particle physics go) was the discovery of Higgs Boson, the elusive last member of the Standard Model to be observed experimentally. The Higgs is believed to be the particle that explains the existence of the range of masses of different particles and was a crucial missing piece to fully validate the Standard Model.

However, there is still a lot about our universe that we cannot describe with the Standard Model. To be precise, the known constituents make up only 5% of the whole universe. The remaining 95% of the universe is made up of what physicists call dark matter and dark energy. The LHC has provided no insight into the nature of these mysterious entities and it is believed that collisions at a much higher energy are necessary to unlock their secrets. Additionally, the current model cannot unite the forces that govern the quantum world with the force of gravity. Since 1905 there has been an incompatibility in theoretical physics, between quantum mechanics (our best theory of the very small) and general relativity (our best theory of the very large). By seeking to probe physics beyond the Standard Model, the FCC represents a chance for physicists to find a way to break this stalemate.

Such bold ideas come with a very hefty price tag – £9 billion for the least expensive design, rising to £20 billion for the full capabilities that the CERN team are hoping for. Such a cost has sparked serious criticism at a time when issues of environmental sustainability and climate change are at the forefront of many discussions amongst scientific and political communities. A crucial problem lies within the very nature of the quest, a probing of the unknown. There is no guarantee that the energy at which the FCC is built to operate, will be the energy at which currently hidden physics becomes visible. The entire endeavour could function at an energy way off, or just short of that necessary to reveal the currently unseen particles. Some argue this is too large a gamble on resources that could deliver tangible, guaranteed benefits to humanity’s very human problems of the environment and health. Nevertheless, lead scientists at CERN, such as Director-General Professor Fabiola Gioanotti and senior physicist John Womersley, are keen to emphasise the peripheral advancements to technology and benefits to society that the endeavour would bring. Being at the very forefront of science, it is argued the FCC will unearth innovative technologies during its design, construction and operation phases; just as electronics, the internet and superconducting magnets in MRI machines all arose from previous enterprises in fundamental physics.

The FCC has now been proposed to the European Strategy for Particle Physics. A decision is expected in 2020 and if accepted, the initial phases of the collider would be up and running between 2040-2050. CERN scientists firmly believe the creation of this facility is the necessary next step towards uncovering nature’s secrets, but such a gigantic vision will no doubt require global support from both national governments and the public. Although the potential challenges of the FCC are enormous, its potential impact on humanity’s understanding of the universe is arguably much larger. To stop pushing the limits of our exploration, is to stop discovering and this is something CERN physicists are determined not to allow.