** As a neuroscience major,** I hold the (completely unbiased) view that the brain is the single most remarkable object in the universe. Its structure is the culmination of 4 billion years of unlikely development, beginning with simple biomolecules and exploding into a dynamic, hyperconnected network whose complexity we’re still trying to decipher today. And this product is not only physically complex, but is crucially and inexplicably linked to something beyond its material constitution: *the mind*. This — the age-old paradox of the mind-body problem — elevates the brain from the level inert matter into something that demands more mystery and wonder.

** But if the universe** held a talent show, I’ll admit that a particular submission from the world of cosmology might beat my favorite pick. These are black holes and wormholes: those most favored plot devices of sci-fi. Spoiler alert here — but who can forget when the protagonist of *Interstellar *interacts with the past by entering a black hole, or when the cyber-prisoners of the Black Mirror episode *USS Calister *escape through a software update disguised as a wormhole? Our public imagination is fascinated by such examples.

** What these popular** conceptions have in common is that they portray these mysterious cosmological objects as fundamental breaks from our reality. Sure, neutron stars and quasars are fascinating; but for all their magnificence, they still fit comfortably in our intuitive conceptions of space, time, and causality. By contrast, there’s a special class of astrophysical concepts that simply *go beyond* these categories. This is intriguing from a metaphysical perspective, since we consider these categories as fundamentally constitutive of reality.

** How can we** convey this metaphysical side of cosmology? The story begins with one of Einstein’s favorite subjects: the nature of gravity.

#### Gravity: force or curvature?

** As most of us** learned in high school physics, gravity is an attractive force between all objects in the universe which is proportional to the product of their masses and inversely proportional to the distance separating them. Given two particles m1 and m2 and their distance r, the gravitational force between them can be given by the equation F=Gm1m2/r^{2}. Here, G represents the gravitational constant, an experimentally-derived number which keeps the dimensions of the equation consistent.

** Thus, according to** Isaac Newton’s famous epiphany, the fall of an apple and the orbit of the moon have a shared cause: the gravitational force exerted by the Earth. This was a significant statement at the time, since the mechanics of celestial bodies was still being attributed to some mysterious ‘aether’, also called quintessence, whose physics was considered separate to that of Earth. With Newton, however, the entire cosmos seemed to bow in one sweep under the predictive capabilities of mankind.

** But Newton’s** equation has a problem: it simply gives you the wrong answer. The error margin associated with Newton’s equation for gravity is imperceptible for most applications here on Earth, but not elsewhere. In the late 19th century physicists were already aware that the expected orbit of Mercury given Newton’s equations deviated slightly — but significantly — from observation. At the time, this was considered a temporary problem whose solution would be some error in measurement. It was difficult to critique a concept that had such a lasting impact on European science and philosophy.

** But this anomaly,** far from being a minor one, foreshadowed one of the most groundbreaking intellectual achievements of the 20th century: Einstein’s theory of relativity. In 1915, Einstein developed a set of 10 field equations which described his new theory of general relativity. Plugging mass into these equations allows for a calculation of gravity which models Mercury’s orbit in perfect agreement with measurements. Einstein’s equations also predicated that light, a massless particle, should be curved by gravity, an idea which was totally antithetical to Newton’s conception. But this prediction, along with literally hundreds of others, was later confirmed by experiments. Einstein’s theory has stood the test of time: GPS relies on his equations in order function properly.

** The difference,** however, between Einstein’s theory of relativity and Newton’s conception of gravity is more than one of numerical accuracy and predictive power. There is a fundamental conceptual antagonism between the two, rooted in a disagreement on the philosophical categories of space and time themselves.

#### Spacetime as the fabric of reality

** The assumptions** of Newtonian physics align nicely with our intuitive conception of reality. There appears to be a static, absolute ‘grid’ of space, along with an extra coordinate of time ticking steadily in the background. Gravity, in that sense, is simply a force that pulls objects along *out there *in the space-and-time arena of the world. If we wanted to describe the path a cannonball takes while traveling in the air, it’s enough to just draw a Cartesian grid labelling space and time, and treat gravity like a force that moves objects along the coordinate system.

** According to Einstein,** however, gravity is not a force exerting its effects on objects in absolute space and time. Instead, gravity *itself* is a warping of space and time, whose effects on objects we mistake as a force. But crucially, space and time are not ‘warped’ separately, but on a single manifold known as spacetime: the equations which describe it treat space and time as a single continuum. What causes this perturbation in spacetime is the presence of mass. Thus, instead of a force, an object’s acceleration due to gravity is simply its straight-line path (or *geodesic*) in a patch of spacetime that is *curved* by the presence of some mass.

** So, what is spacetime?** That’s a tricky question, but one thing is true: it *cannot be* a category of absolute space or time as Newton conceived of them. In spacetime, for example, events that I observe to happen at the same time can happen at different times in another person’s perspective. This apparent paradox, known as the relativity of simultaneity, is not allowed by our intuitive understanding of space and time. In additions, clocks tick slower when they are closer to a massive body due to the influence of gravitational time dilation. These kinds of examples, many of which have been demonstrated experimentally, illustrate that Newton’s philosophical understanding of space and time, intuitive as they are, must be invalid.

** We can now** understand, by the way, why Einstein’s conception of gravity predicts the bending of light rays while Newton’s does not. Photons are massless particles, so classical physics wouldn’t predict that gravity interacts with them. However, if gravity is understood as curvature, then even light should be ‘bent’ by the presence of a massive object since it too has a path in spacetime. This finding is called gravitational lensing, and has been demonstrated by observing a a number of cosmological oddities. One of these is Einstein’s cross, a quasar that is quadrupuled by the presence of another galaxy. The kite-shaped lights are actually a singe source that is that is bending around the central mass before reaching our telescopes.

** Even besides** gravitational lensing, the universe becomes a much weirder place once we start to think of gravity — and reality itself — as relativity demands. To demonstrate this, we have to understand that Einstein’s equations for gravity can be used to model the entire universe.

#### Modeling the universe reveals black holes

** On the largest** of scales, the universe can be modeled as a distribution of massive galaxy clusters with certain position and momentum values. Because gravity is the predominant force guiding the interaction of these clusters, Einstein’s field equations can be used to model the evolution of the universe over time. All physicists need to do is use data collected by telescopes and ‘plug in’ the corresponding values of mass to simulate the past and future conditions of our universe.

** This application** of the Einstein field equations can be used to demonstrate the Big Bang theory. Edwin Hubble provided experimental evidence that the universe is expanding by observing the radiation emitted from distant galaxies. This fact can be modeled into the Einstein field equations, resulting in an expanding spacetime manifold. Reversing time in this system leads us to a singular point of infinite density and temperature, called the singularity. All events which occur in our universe necessarily come after this point, leading to its conceptualization as the ‘origin’ of our universe.

** In the early 1920s,** physicists started to realize that a certain solution of Einstein’s field equations was rather bizarre. When a massive body’s volume is restricted to a certain radius, called the Schwarzschild radius, something strange happens. The ‘orientation’ of spacetime in this region would be such that any light entering a certain region, called the event horizon, can never exit it again. To be more precise, the fabric of spacetime is contorted in such a way that the spatial direction *into* the black hole becomes the temporal direction of the *future*. This shuttles whatever enters the black hole into a necessary future, ‘located’ at a central part called a singularity, which is the end-point of the future-radial path.

** Let’s try to** understand the popular phrase: “nothing can escape from a black hole, not even light”. Within a certain region of space demarcated by the event horizon, not only objects or light, but *events themselves* are forever shut-off from us. Another way to put it is this: all world-lines which cross the event horizon must terminate at the singularity and can never again interact with the rest of the universe. This is what causes black holes to appear black to us. It isn’t because light is slowly ‘sucked in’ by some invincible force: it’s because light particles, like everything else that crosses the event horizon, become *causally bound *to the singularity. This is the kind of thinking one has to grapple with when speaking about a single spacetime manifold.

** When physicists first** came to know of black holes, where was doubt whether such cosmological structures could exist. This is a question of mathematical realism. If the Einstein field equations can be used to model our universe with stunning accuracy, then does everything the equation produce need to have a correlate in our reality? As many of us remember, quadratic equations can be used to model the path of a projectile. But solving these equations also gives us a negative value for the horizontal displacement, -x. Even weirder, this would involve a negative time value. Does this mean that somewhere out there, our object — say a cannonball — goes backwards in time? It’s clear in this example that we shouldn’t take our math too seriously. Physicists were in a similar position: did the black hole solutions to Einstein’s field equations necessarily describe a real feature of our universe, or were they merely mathematical objects?

** It took the** 1964 detection of a massive X-ray burst to put the speculation to rest. It was eventually determined that the source of this burst, dubbed Cygnus X1, was a supergiant star which is slowly giving up mass to a neighboring black hole. The resulting structure is called an accretion disk: a mass of gas and plasma that becomes brighter and more energetic as it circles around the event horizon. The electromagnetic radiation emitted by this disc eventually reached an X-ray detector here on Earth, and analyzing the data revealed the central object’s mass density to be consistent with that of a black hole. This explanation was enough for big-daddy of cosmology Stephen Hawking to concede a bet to a colleague about the existence of black holes in 1990. Today, they’re one of the most well-known objects in astronomy.

** A quick side note:** the Einstein field equations give us another peculiar structure. One solution yields an eternal black hole, and when this system is time-reversed, we get a structure which can be considered its precise functional opposite. Objects are always pushed out of a single point, so we can see nothing but light emanate from it; from the inside of the event horizon, the only future is radially *outward*. These objects are appropriately named white holes. The question of whether white holes exist or are just mathematical oddities hasn’t quite been settled. The gamma ray burst GRB 060614 is considered a white hole candidate by some, owing to its rule-breaking properties.

** How does spacetime** come to be so bizarrely curved? As I mentioned earlier, it’s all a matter of mass density. The Schwartzschild radius of a massive object gives the minimum space it needs to occupy to become a black hole. For example, if the Sun’s mass was compressed into a sphere with a radius of 3.0 kilometers, its density would cause it to collapse into a singularity, and all the ‘space’ within the resulting event horizon would fall outside of our causal universe. However, there’s nothing particularly ‘special’ about the way that black holes effect the universe outside of their event horizon. If the Sun were to collapse into a black hole, our gravitational orbit around the singularity would be essentially unchanged.

** Once an object** enters the event horizon, it can never again be present in any outside events. In fact, the only trace that its existence leaves are to contribute its charge to the black hole and to contribute its mass to the black hole, which in turn expands the event horizon. In this way, stars and nebulae are effectively physically erased from our universe. However, this presents a contradiction with quantum physics, whose equations require that information can never be destroyed. This problem, called the black hole information paradox, suggests that a new theory must be used to combine the worlds of general relativity and quantum mechanics.

#### Wormholes

** Compared to** black holes, worm holes have an advantage in the world of fiction: they’re generally helpful, not harmful, to the average protagonist. Along with the infamous warp-drive, traversing a wormhole is among the most common methods for intergalactic travel. As the story goes, wormholes connect two points of spacetime in such a way that physically traveling between them becomes unnecessary. Thus, one can ‘jump’ to a certain point in the universe without being hindered by that cosmic limit, the speed of light.

** Once again,** wormholes were first discovered as valid solutions to Einstein’s field equations. Recall that white holes are time-reversed black holes whose mathematical description emerges from Schwartzschild’s eternal black hole solution. Because of this, when the black hole is modeled, the white hole appears to be spitting out its contents into ‘another universe’ which is causally separated from the first. This means that, mathematically speaking, the black hole and white hole pair represent a kind of ‘gateway’ between distinct universes. The details of this structure were published in 1935, and came to be known as Einstein-Rosen bridges after the authors of the paper.

** However,** Einstein-Rosen bridges differ greatly from the depiction of wormholes in popular culture. First and foremost, they are *inter*-universe wormholes, not *intra*-universe wormhole. If we wanted to benefit from traveling in our own local universe, we could not rely on the black hole / white hole pair of an Einstein-Rosen bridge. Secondly, they are now known to be untraversable. Einstein himself developed these structures in an ill-fated attempt to combine his theory of general relativity with electrodynamics. For that reason, the ‘throat’ of the bridge was initially only big enough to carry an electron. Then, in 1964, physicist John Archibald Wheeler proved that these types of wormholes are unstable and would collapse before a single photon would be able to traverse it. This came as a relief to some physicists, as the idea of faster-than-light travel may cause problems with our ideas of causality.

** Physicists have tried** to keep the dream of superluminal travel alive, though. Kip Thorne has argued that an exotic kind of matter, one with a negative energy density, would be sufficient to keep the wormhole open for a courageous enough traveler. These are known as traversable wormholes, and once they are created, the two ends would begin in the same place and would have to be physically separated. This is not such a grave limitation, however, since we could keep sending new wormholes through the distance created by the previous set. In this way, our universe may someday be riddled with these gateways, emanating like spokes from their central origin here in the solar system.

** Where might we** find such exotic matter? Interestingly, the vacuum of space itself seems to be a good candidate. In a finding called the Casimir effect, two plates held a microscopic distance apart can either attract or repel slightly, depending on their orientation. But this is not due to gravitational force, or any other kind of standard force for that matter: rather, it is due to the intrinsic qualities of empty space. The quantum mechanics underlying the Casimir effect is complicated, but it demonstrates that the type of negative energy necessary for propping upon a wormhole may already exist naturally.

** Geometrically, wormholes** can be roughly described as a region of spacetime that is continuous, but where a loop would not be able to be contracted to a single point. Topologically, this corresponds to a ‘handle’ that connects two regions of spacetime. This accounts for their popular depiction as a bridge between the two sides of a folded paper. This isn’t as inaccurate a description as we might think, as long as we wrap our heads around the idea that what’s folding is not a physical surface, but spacetime itself. In other words, what’s folding is a field that* gives us* space and time coordinates when we measure them; we really can’t say much about the *actual* ontology of spacetime.

** So, what are** wormholes? Intriguing but imaginary mathematical solutions to the Einstein field equations, or potential sources of travel which will someday be as common and banal to future generations as a car? The course of scientific progress and development will gives us the answer, but it’s probably not discernible within our lifetimes.

#### Further reading

PBS Spacetime has a great series on black holes and general relativity that was immensely helpful for me. You can find their channel here: https://www.youtube.com/channel/UC7_gcs09iThXybpVgjHZ_7g

The following video is a great way to (begin to) grapple with the weirdness of spacetime: https://www.youtube.com/watch?v=sryrZwYguRQ