For the better part of a century, quantum physics and the general theory of relativity have been a marriage on the rocks. Each perfect in their own way, the two just can't stand each other when in the same room.

Now a mathematical proof on the quantum nature of black holes just might show us how the two can reconcile, at least enough to produce a grand new theory on how the Universe works on cosmic and microcosmic scales.

A team of physicists has mathematically demonstrated a weird quirk concerning how these mind-bendingly dense objects might exist in a state of quantum superposition, simultaneously occupying a spectrum of possible characteristics.

Their calculations showed the superpositions of mass in a theoretical type of black hole called the BTZ black hole occupy surprisingly different bands of masses simultaneously.

Ordinarily, any garden-variety particle can exist in a superposition of states, with characteristics such as spin or momentum only determined once they've become part of an observation.

Where some qualities, like charge, only come in discrete units, mass isn't typically quantized, meaning the mass of an unobserved particle can sit anywhere within a range of maybes.

Yet as this research shows, the superposition of masses held by a black hole tends to favour some measures over others in a pattern that could be useful for modelling mass in a quantized fashion. This could give us a new framework for probing the quantum-gravitational effects of black holes in superposition in order to ease the tension between general relativity and quantum theory.

"Until now, we haven't deeply investigated whether black holes display some of the weird and wonderful behaviors of quantum physics," explains theoretical physicist Joshua Foo of the University of Queensland in Australia.

"One such behavior is superposition, where particles on a quantum scale can exist in multiple states at the same time. This is most commonly illustrated by Schrödinger's cat, which can be both dead and alive simultaneously."

"But, for black holes, we wanted to see whether they could have wildly different masses at the same time, and it turns out they do. Imagine you're both broad and tall, as well as short and skinny at the same time – it's a situation which is intuitively confusing since we're anchored in the world of traditional physics. But this is reality for quantum black holes."

The extreme gravity surrounding black holes makes an excellent laboratory for probing quantum gravity – the rolling continuum of spacetime according to general theory of relativity wedded to quantum mechanical theory, which describes the physical Universe in terms of discrete quantities, such as particles.

Models based on certain types of black hole just might lead to a single theory could explain particles and gravity. Some of the effects observed around a black hole can't be described under general relativity, for instance. For this, we need quantum gravity – a unified theory that incorporates both sets of rules and somehow gets them to play nice.

So, Foo and his colleagues developed a mathematical framework that effectively allows physicists to observe a particle placed outside a black hole that's in a state of quantum superposition.

Mass was the main property they probed, since mass is one of the only properties of black holes that we can measure.

"Our work shows that the very early theories of Jacob Bekenstein – an American and Israeli theoretical physicist who made fundamental contributions to the foundation of black hole thermodynamics – were on the money," says quantum physicist Magdalena Zych of the University of Queensland.

"[Bekenstein] postulated that black holes can only have masses that are of certain values, that is, they must fall within certain bands or ratios – this is how energy levels of an atom works, for example. Our modeling showed that these superposed masses were, in fact, in certain determined bands or ratios – as predicted by Bekenstein.

"We didn't assume any such pattern going in, so the fact we found this evidence was quite surprising."

The results, the researchers say, provide a path for future investigation of quantum gravity concepts, such as quantum black holes and superposed space-time. In order to develop a complete description of quantum gravity, inclusion of these concepts is crucial.

Their research also allows for more detailed investigation into that superposed spacetime, and the effects it has on particles within it.

"The Universe is revealing to us that it's always more strange, mysterious and fascinating than most of us could have ever imagined," Zych says.

The research has been published in Physical Review Letters.