One important role of science fiction is to provide an arena for thought-experiments, letting writers explore concepts and ideas that cannot be placed in a real-world setting. One area of particular interest which has received such attention is what I’ll call thought-experiment worlds: universes or regions of our own Universe in which the laws of physics operate differently to those we encounter in everyday life.

Some of the earliest such thought-experiment worlds were deliberate efforts to communicate complex scientific or mathematical ideas, written by scholars and intended to intrigue a popular audience. Amongst the first and best known of these was Flatland, published pseudonymously by mathematician and schoolmaster Edwin A. Abbott in 1884. This novella, which is accompanied by rigorous technical diagrams, introduces a character Mr A. Square, who exists in a two-dimensional universe (or manifold, in modern terminology). When he is visited by a sphere-being who can perceive and move through higher dimensions, Square can only see them as a circle, whose size varies as the sphere moves in the unseen third dimension.

As Abbott points out, we could be equally ignorant of a fourth spatial dimension, and just as likely to misinterpret its manifestations as the Square was the sphere. This observation was not unique to Flatland, but the effective imagery and pedagogy brought the book back to popular attention after the formulation of modern relativistic physics in the early 1900s highlighted the possibilities of higher dimensional spaces. As a result, Flatland and its successors and imitators have had a large impact on both popular culture and science fiction. Just to give one interesting example of the latter we can consider E E “Doc” Smith’s Lensman series. Here the natives of Palain VII and other cold worlds exist in four dimensions (a trait described as necessary for low temperature metabolism), and are perceived by humans as constantly changing in shape and size as they move, sometimes disappearing entirely and then reappearing elsewhere as they travel through unseen dimensions. An example appears where a Palainian tries to demonstrate the activity of dexitroboping to First Lensman Virgil Samms:

"to Samms the Palainian's movements were pointless indeed. The peculiarly flowing subtly changing thing darted back and forth, rose and fell, appeared and disappeared; undergoing the whole cyclic changes in shape and form and size, in aspect and texture. It was now spiny, now tentacular, now scaly, now covered with peculiarly repellant feather-like fronds, each oozing a crimson slime. But it apparently did not do anything whatsoever. The net result of all its activity was, apparently, zero" (First Lensman, Panther edition, 1977, pg 123)

Another scientist to use fiction this way was physicist George Gamow. He published four popular science books following the adventures of Mr C. G. H. Tompkins through a series of experiences that elucidated various advanced physics principles. In the first, Mr Tompkins in Wonderland (1939), the title character experiences a world in which the speed of light is just 10 miles per hour (rather than 300,000,000 km per second). As a result, relativistic effects such as length contraction and time dilation are observed in everyday life (as the image here shows). This and the subsequent stories (including others which change physical constants) were explicitly written as science communication for a general audience. In his preface to the second edition, Gamow described how his initial effort found a home in the popular science magazine Discovery, published by Cambridge University Press, who then commissioned further stories. Again, Tompkins was a forerunner of other popular science books in which the characters experience physics thought experiments, memorably including the Uncle Albert children’s books (in which a young girl called “Gedanken” - German for “thought” - is sent by her Einsteinian uncle on exciting adventures involving rockets) written by particle physicist and science populariser Russell Stannard. 

However the occurrence of thought experiment worlds is by no means confined to the realm of deliberate science communication. Such worlds have formed the primary setting for a number of more mainstream science fiction texts.

The novel Inverted World by Christopher Priest won a BSFA award and a Hugo nomination on its publication in 1974, recognising its striking world-building and narrative. The novel begins with a clue that time and space are going to be entwined within it. The opening line reads: “I had reached the age of six hundred and fifty miles.”

As gradually becomes apparent, the protagonists live on a city-sized vehicle for which track must be constantly laid ahead and taken up behind. The city is forced to remain in constant slow but steady motion because the world behind it distorts, with time and space both stretching and an ever increasing effort required from expeditions who fall behind to communicate with outsiders or to catch up with their home. Their culture is thus enclosed and highly restrictive. Both the sun and the world ahead is also distorted, with the city sitting on a sweet spot in which time appears to progress at a normal rate.

Priest’s world is, in fact, inverted in the mathematical sense. In our familiar world, speed relates time and space linearly i.e. constant speed leads to a progression in both time and space in proportion to one another (distance travelled = speed x time, so a vehicle travelling at fifty miles an hour for two hours has travelled 100 miles). Instead the relation in Priest's novel is inverted (distance=speed/time), so that it’s only at one particular, ever moving point where the two progress in the familiar proportion to one another - the point where the two dashed lines are parallel in the diagram here and which is known in the novel as "the Optimum".

This is a very effective evocation of a universe which functions by different rules. However the focus in Inverted World is on the characters’ perceptions of their world, rather than its physical reality, and the ending of the novel reflects that focus, leaving a number of questions about the mechanism and underlying physics unanswered.

While Priest’s attempt to explain his world is in Clarke’s Third Law territory [1], one phenomenon actually known to distort both time and space, stretching them in different directions, is gravity. In his short story “Mountain” (2006), Cixin Liu gives physicality to not one but two worlds that differ from our own. In the framing narrative, an alien planetoid-based ship approaches Earth, its gravity distorting the ocean into a kilometres-high mountain. A man climbs that mountain, first in a paddle boat and then simply swimming. Here we see the surface of the Earth being distorted into something approaching the hyperboloid of Priest’s Inverted World, although the isolation of the main character and the ocean setting deprives us of any evidence for time distortions or spatial distortions beyond the surface. Given the relatively minor consequences of this huge gravitational distortion (e.g. the lack of civilisation-ending megastorms and continent-ripping earthquakes), it’s hard to take the physics here entirely seriously, but the characters ever changing perception of whether the alien ship and his own home vessel are behind, above or level with him twists the readers' view of reality.

That shift in perception is, however, merely a framing device for a narrative related by the aliens regarding their own cosmos. This involves their evolution inside an air bubble in the planetoid. Rather than standing on the surface of a finite solid sphere with emptiness all around (as on Earth), they stand on the inner surface of a solid and apparently infinite universe which engulfs a finite and rather small region of emptiness. This idea is implicit in a wide variety of Hollow Earth stories in western tradition [1a], but serves as an effective way to focus the mind of readers on the political and philosophical structures of Liu’s alien world, the paradigm shift necessary when the aliens realise their world-view of an infinite solid is wrong, and the problem of conserving limited resources (visualised in this case as the loss of irreplaceable space caused by any attempt to tunnel out of their bubble).

Returning to a more human viewpoint, and to harder scientific science fiction, Raft (novel, Stephen Baxter, 1991) appears to open with a young boy on a normal, if run down and dangerous, space station. However we soon learn that this too is a universe with very different rules. Baxter’s protagonists are the descendants of an exploration ship which finds itself displaced into a manifold in which the force of gravity is billions of times stronger than our own. As a result, stars form at just a mile in size, and live and die rapidly before falling towards the heart of a cluster where a singularity is forming. The humans survive essentially in a free-fall environment by cannibalising their own ship and mining the cooled stellar remnants, but the relentless pace of evolution in the higher gravity leads to a decay in their environment. The gravitational forces are strong enough to distort matter and the local horizon, and to allow the gravitational pull of physical presence to be used still more effectively as a tool of intimidation. Memorably, the novel also includes a scene in which dancers use one another’s gravity to turn a conventional spin into a graceful orbit.

"Their centres of mass, located somewhere around their waists, traced out hyperbolic orbits in the varying gravity fields of the Raft, the stage and the dancers themselves, so that each time the dancers launched themselves from their trampoline the paths of their centres were more or less determined.... But the dancers adorned the paths with movements of their slim bodies so deceptively that it seemed that the two of them were flying through the air at will, independent of gravity. How paradoxical, Rees thought, that the billion-gee environment of this universe should afford humans such freedom" (SF Masterworks edition, 2018, pg 77)

This is a well-thought out world. The balance between gravitational collapse and fusion-powered internal pressure sets the burning rate of stars, and this would indeed be higher (with consequent shorter lifetimes) if gravity were stronger. They would also be smaller, as Baxter speculates, both because collapse to a black hole sets an upper limit and because bodies with smaller masses than in our universe could ignite hydrogen fusion at the temperatures and pressures found in their cores. Baxter also uses the properties of this higher gravity universe to his characters’ advantage in the climactic final sequence of the novel.

While this novel stands alone, it is also the first in Baxter’s Xeelee sequence - in all of which concepts drawn from theoretical physics and cosmology underpin much of the worldbuilding and narrative, either through adjustments to the universe humans inhabit (as in Raft) or in the nature and perspectives of the alien Xeelee themselves.

The speed of light and the strength of gravity aren’t the only physical constants to be adjusted in science fiction. Gamow’s Mr Tompkins books also consider the effects of changing the Planck’s Constant (h) to adjust the influence of quantum effects from the sub-microscopic to human scales.

Also considering quantum physics, Isaac Asimov explored the consequences of changing the strong nuclear force in The Gods Themselves (novel, 1972) [2]. In the first part of this novel, humanity is first puzzled by and then grateful for the appearance of an impossible isotope of plutonium which appears in place of tungsten (which has the same atomic weight but different ratio of protons to neutrons) and rapidly begins to emit radiation. Further offerings of tungsten are also exchanged. In our own universe, the relative effects of strong nuclear attraction and electromagnetic repulsion means that large groups of protons (such as are found in heavy elements) can only be held together by even larger groups of neutrons. In a parallel universe however, with a stronger nuclear force, fewer neutrons are needed and in fact the heavy elements of our own domain are unstable. So parallel-universe material brought to ours becomes unstable and releases radiation, and once it has decayed, the same material transferred in the other direction is equally unstable. By moving material back and forth in a cycle, through cooperation between sentients on both sides, energy can be collected in both universes, with a net exchange between universes of twenty electrons per atom processed.

As is the case in Raft, the most obvious effect of this change in constants is a tendency for stars and planets to be much smaller, in this case because fusion is relatively easy. The second part of the novel is an interesting realisation of an alien life cycle and viewpoint in the para-universe, while the third returns to our own manifold, and a lunar colony, as the non-zero consequences of and problems with inter-universe pumping become apparent.

While constituting one of the five fundamental forces in our universe, the strong nuclear force is rather obscure to most non-physicists. Perhaps more familiar to most is the constant pi (𝞹) - a number which begins 3.14159265359 and continues for an infinite string of digits without repeating. This number is fundamental to the structure of the universe, appearing in both the geometry of curved surfaces and the behaviour of electromagnetic waves.

However its irrational nature (i.e. lack of a simple form) has struck more than a few people over the years as unfortunate and it’s perhaps unsurprising that science fiction authors have considered the possible consequences if 𝞹 were in fact a rational fraction or simply 3.00. This was notably done by accident in the Discworld series of fantasy books by an architect character known as Bloody Stupid Johnson, warping the fabric of reality to achieve it. The same feat was also famously attempted by an early legislative body in defiance of the laws of our own universe. Science fiction examples include Greg Bear’s The Way series of novels (beginning with Eon in 1985). The eponymous space-time tunnel distorts reality in a number of ways, notably including shifts in the value of 𝞹 and the relationship between mass and inertia [3].

Perhaps one of the more ambitious attempts to redefine the physical laws of the universe can be found in the novelet (i.e. longish short story) “The New Reality” by Charles R Harkness (Thrilling Wonder Stories, Dec 1950). This story features a secretive government department. It exists to police ontology - the theory of reality - and was established after a small group of scientists realise that the world’s physical properties change to align with the theoretical laws describing them: “what most of us call reality is simply an integrated synthesis of incoming sensoria. As such it is nothing more than a working hypothesis in the minds of all of us, forever in a process of revision.”

Hence the characters in this narrative conclude that the value of pi was not just estimated to be three exactly in the past, but actually was three until a natural philosopher concluded it must be otherwise. A corollary is that if a scientist can force the breaking of an apparent physical law, the universe must change to negate that law. And if a photon can be stopped in its progress, the relationship between space and time itself will break down, essentially recreating the world in that moment, and destroying all the minds that can’t cope with the change. The ending all gets a bit philosophical and theological, deviating from modern physics as we understand it, but addresses the eternal science-fictional question of what will happen if Man plays at being god.

Since the development of mathematical physics then, and even before modern physics was fully formulated, people have been trying to visualise worlds which operate to laws other than our own. Science fiction has provided a context for such imagining. Novels (and increasingly now, virtual realities and computer visualisations including video games such as Mass Effect and cinematic special effects such as those employed to bend reality in Inception (film, 2010, dir. Nolan)) present an alternative arena for these speculations. At the same time, modern physics posits increasingly complex and interesting alternative realities for such science fiction thought experiments to explore in the future, feeding science fiction, as SF in turn feeds the imagination of many physicists.