The Infinities of the Universe

The Infinities of the Universe

By Geraint F. Lewis, Professor of Astrophysics, University of Sydney, Australia

Our universe is home to many strange and mysterious things and hidden in the darkness between the fiery stars is perhaps the strangest of them all. Formed during the explosive death of a giant star, when the stellar core was smashed out of existence, a black hole is little more than the gravitational scar of the star’s fleeting existence.

Black holes are amongst the simplest objects in the universe, defined only by their mass and spin. Their intense gravitational field inexorably draws matters in towards its ultimate doom. At the hearts of galaxies, where black holes a billion times more massive than the Sun can exist, this infalling matter is whipped to extraordinary speeds and temperatures, shining brighter than a trillion stars.

Matter eventually passes the point of no return, known as the event horizon, on a journey that will take it to the centre of the black hole. It will be crushed into a point, a point known simply as a singularity. The singularity has no size, with all mass squeezed into a volume of zero. At the heart of every black hole lies an infinity.

Physicists have a love-hate relationship with infinities. When they appear in equations, it usually tells us that something has gone horribly wrong, that we have pushed our theories too far and have somehow divided by zero. But black holes are written in the mathematics of Einstein’s general theory of relativity, a scientific success of the twentieth century, and the equations give no hint of just where we have strayed from the path.

Another singularity lies at the very start of the universe. Our telescopes reveal that we live in an expanding universe, with density dropping every day. In the past, the universal density must have been higher, and, as we wind the clock back almost fourteen billion years, we find that the density at the birth of the universe must have been infinite. As with black holes, the equations of cosmology are drawn from Einstein and his relativity, and again, give no clue to escape this initial singularity at cosmic dawn.

Whilst physicists are perplexed by relativity’s infinities, they are not discouraged. Most think that they mark a path to enlightenment, a path to the holy grail of a theory of everything. They have known for almost a century that the two great pillars of physics, Einstein’s gravity to explain the world of the massive and the quantum world of the microscope are incompatible. Whilst both are highly successful, they are written in different languages that have refused all attempts to unite them. The hunt for the single language, maybe superstrings or branes or quantised spacetime, that encompasses the quantum and gravity has been the focus of fundamental physics for many decades, but a solution still appears frustratingly elusive.

The dream is that this theory of everything will banish gravity’s infinities from the universe. At the centre of black holes, new forces will be revealed, preventing the collapse of matter into a singular point. Instead, the actions of the quantum will support immense, but finite, densities. In a similar vein, instead of an infinite state, the birth of the universe will be revealed to be an extreme yet finite event, possibly linking our cosmos to a wealth of other universes in a multiverse.

But other, more perplexing, infinities exist in our universe. Firstly, there is the infinity in space. In Einstein’s cosmologies, space can be curved, containing either a finite or infinite quantity of space, with the geometry determined by the mix of mass and energy in the universe. Observations of our universe reveal it to be flat, with space extending infinitely in all directions. There appears to be an infinite amount of universe out there.

Then there is the infinity of time. While our universe has existed for around fourteen billion years, the cosmological equations reveal it has an infinite future ahead of it. And what about before our universe? Did that stretch infinitely far into the past?

What are we to make of these infinities? Maybe they just are, and we have to live with the reality that infinities do truly exist. But maybe there is a way that these two can be banished.

Einstein’s general relativity is a geometric theory, it tells us about the geometry of space and time. But geometry is a subset of a larger idea about shapes, that of topology. Think of an American doughnut. An appropriate cut can turn it into a cylinder and with an additional cut from top to bottom, this cylinder can be unrolled and flattened, if somewhat messily, into a sheet. Geometrically, the doughnut and a flat sheet are the same, but whereas a flat sheet has an infinite area, that of the doughnut is finite. Perhaps our universe is suitably contorted topologically, simply appearing to be flat and infinite while space is truly finite.

What about our infinite future? Again, in the simplest picture, there is no escape from the eternal expansion ahead, maybe time is part of this topological dance, folding back on itself like some cosmic ouroboros. Maybe our universe is just the current incarnation of cosmic dawn, day, and dusk. Whilst the singularity at our universal birth currently shrouds our ultimate origins, maybe our infinite future will be lost in this cosmic recycling.

Worries about infinity remain. It might seem that with a theory of everything and topological twisting, we have expelled infinities from our reality, all we have truly done is move them elsewhere. Did time have a beginning? If not, infinities return. If it did, what came before if that question has any meaning? And where does our convoluted universe live? Is it embedded in higher dimensions that themselves extend to infinity, or are they suitably convoluted? And what is beyond them if they are, again, if this question has any meaning?

Advances in physics might eradicate the need for infinities within our cosmos, but maybe some infinities may stubbornly remain. We can, however, take solace in the fact that infinities are going to inhabit our reality, that they are a feature of our entire magnificent universe.

Geraint F. Lewis is a Welsh astrophysicist, who is best known for his work on dark energy, gravitational lensing and galactic cannibalism. Lewis is a Professor of Astrophysics at the Sydney Institute for Astronomy, part of the University of Sydney's School of Physics. He examines the universe through the uniquely accessible lenses of quantum physics and cosmology, tackling questions such as: Where did the universe come from? Do black holes last forever? What is left for humans to discover?

October 6, 2023