Science › Black holes & quantum gravity
Singularities: where physics breaks
1965· Open question
Open questionNobody knows the answer.
Points where general relativity predicts infinite density and curvature, meaning the theory itself stops giving answers.
See it on the Science map →How it works
When relativity is run to its limit, inside a black hole or back at the Big Bang, quantities like density and curvature blow up to infinity. Physicists read that not as a real infinite object but as a sign the theory has been pushed past where it works. Penrose (1965) and Hawking showed singularities are not a quirk of idealized math: under general conditions they must appear. What actually replaces them is unknown.
Why it matters
Singularities mark the exact edge of our best theory of gravity and point to the need for quantum gravity.
Think of it like
Like a spreadsheet cell returning a divide-by-zero error: the building is fine, the formula has hit its limit.
How we know
The singularity theorems are mathematical proofs, accepted since the 1960s–70s. No singularity can be observed directly; those in black holes are hidden behind horizons.
Still a mystery
Is there a real infinity, a smallest grain of space, a bounce, or something else? Only a working theory of quantum gravity can say.
Connections (7)
▸Singularities: where physics breaks sits at the start of (in relativity) The Big BangOpen question
The relationship
Run cosmic expansion backward and everything gets closer and denser. Relativity, applied without limit, says density reaches infinity at a single starting moment: a singularity, like a black hole's center run in reverse. The Hawking–Penrose theorems showed this is unavoidable given relativity and ordinary matter. So in pure relativity, the Big Bang begins with a singularity.
How the link was found
Hawking, building on Penrose, proved the cosmological singularity theorems in 1965–1970, ending hopes that the Big Bang singularity was an artifact of oversimplified models.
Is it proven?
The theorems are mathematical proofs. But they assume relativity holds all the way back, which almost no physicist believes; quantum effects near the Planck time should change the picture.
Open questions and mysteries
Did the universe begin at a true singularity, a bounce, a quantum fuzz, or a period of inflation that blurs the start? Unknown.
▸Black holes hide at their center Singularities: where physics breaksOpen question
The relationship
Inside the horizon, relativity says all matter keeps falling inward with no force able to stop it. The result is a point (or, for spinning black holes, a ring) of infinite density. Because it is hidden behind the horizon, it cannot affect the outside world. Most physicists read it as the place where relativity stops working, not as a real infinite thing.
How the link was found
Present in Schwarzschild's 1916 solution; Penrose proved in 1965 that it is unavoidable, not a product of perfect symmetry. Penrose also proposed (1969) that singularities are always hidden.
Is it proven?
The prediction is a proven feature of relativity. Whether it describes reality is untested, since nothing inside a horizon can be observed.
Open questions and mysteries
What actually replaces the singularity: a dense core, a bounce into a new region, or something only quantum gravity can describe?
▸Roger Penrose proved the inevitability of Singularities: where physics breaksProven
The relationship
Before 1965 many assumed singularities appeared only because models were perfectly symmetric, and real lumpy collapse would avoid them. Penrose defined a "trapped surface," where even outward-aimed light is pulled inward, and proved that once such a surface forms, relativity with ordinary positive energy guarantees a singularity. No symmetry is needed. This made singularities a general prediction.
How the link was found
Roger Penrose, "Gravitational collapse and space-time singularities," Physical Review Letters, January 1965, using new global geometric methods.
Why it's proven
It is a mathematical theorem, checked and extended by many. The Nobel committee in 2020 cited it as the discovery that black hole formation is a robust prediction of relativity.
Open questions and mysteries
The theorem says relativity breaks, not what replaces it. Quantum effects may evade its energy assumptions.
▸Stephen Hawking with Penrose, proved theorems on Singularities: where physics breaksProven
The relationship
Hawking realized Penrose's argument could be run backward in time. An expanding universe is like a collapsing star played in reverse, so the same reasoning implies our universe began from a singularity. Together in 1970 they proved a general theorem covering both black holes and cosmology, under assumptions about gravity and ordinary matter.
How the link was found
Hawking's 1966 PhD thesis and papers from 1965–67, then the joint Hawking–Penrose theorem published in 1970.
Why it's proven
These are accepted mathematical proofs within general relativity. Their conditions are believed to hold for ordinary matter; quantum effects and inflation can bend them.
Open questions and mysteries
Hawking later argued, with the no-boundary proposal, that quantum effects remove the initial singularity. That is unconfirmed.
▸Singularities: where physics breaks demands Quantum gravity: the missing linkOpen question
The relationship
Relativity predicts infinite density at singularities, which signals that the theory has been pushed past its limits. At such extreme compression, quantum effects must dominate, so a description that includes both is needed. Physicists expect quantum gravity to replace the infinity with something finite, much as quantum mechanics explained why electrons do not spiral into atomic nuclei.
How the link was found
The need became sharp after the Penrose (1965) and Hawking–Penrose (1970) theorems showed singularities are unavoidable in classical relativity.
Is it proven?
That relativity fails there is mathematically clear. That quantum gravity fixes the problem is a widely held expectation, not yet demonstrated.
Open questions and mysteries
Will singularities be smoothed into a bounce, a smallest grain, or reveal that space and time are not fundamental?
▸The Big Bounce replaces Singularities: where physics breaksSpeculative
The relationship
The singularity theorems of general relativity assume gravity always attracts. Near the Planck density, bounce models' quantum corrections break that assumption, so the theorems no longer apply. Instead of infinite density and curvature at t = 0, the universe reaches a large but finite maximum. If so, the infinity was the theory failing, as many suspected, not a physical object.
How the link was found
Hawking and Penrose noted from the start that their theorems rely on classical gravity. Loop quantum cosmologists (2001–2006) and other bounce theorists showed specific ways quantum effects remove the singularity.
Is it proven?
Accepted as possible in principle, but shown only in model calculations. Without a confirmed theory of quantum gravity, which replacement is right is unknown.
Open questions and mysteries
Could the same mechanism stop collapse inside black holes too, and what would that mean for what falls in?
▸Singularities: where physics breaks marks where relativity fails, in Planck epoch: the first 10⁻⁴³ secondOpen question
The relationship
Run general relativity backward and density and curvature grow without limit, reaching infinity at t = 0. But long before that, by about 10⁻⁴³ second, curvature is so extreme that quantum effects on spacetime should dominate, and relativity's predictions stop being trustworthy. So the infinite start is probably not a real event in the timeline; it lies inside the zone, the Planck epoch, where the theory has run out.
How the link was found
Hawking and Penrose's singularity theorems (1965–1970) proved relativity must break down there. John Wheeler and others argued from the 1950s that quantum effects take over near the Planck scale.
Is it proven?
That relativity alone predicts a singularity is proven mathematics. That quantum effects intervene first is a near-universal expectation, not tested.
Open questions and mysteries
Does quantum gravity remove the singularity, replacing it with a bounce, a smallest size or a rounded-off start? Does 't = 0' have any meaning at all?