Einstein’s theory of general relativity describes the inevitability of singularities, which are obscured by black holes according to Penrose’s cosmic censorship conjecture.
Recent studies indicate that quantum mechanics might reinforce this idea, proposing a quantum Penrose inequality that relates entropy to space-time metrics in the vicinity of black holes.
General Relativity and Singularities
Albert Einstein’s theory of gravity, known as general relativity, is incomplete. Physics Nobel laureate Roger Penrose, showed that when matter collapses under its own gravity, it forms a “singularity” – a point where density and space-time curvature become infinite.
At a singularity, space, time, and matter are compressed to the point of nonexistence, causing the known laws of physics to break down entirely. If singularities were observable, scientists would lose the ability to predict future events based on past conditions. In other words, science would become an impossibility.
Black Holes and Cosmic Censorship
Penrose also realized nature may hold a remedy for this fate – black holes. A defining feature of a black hole is its event horizon, a one-way membrane in space-time. Objects – including light – that cross the event horizon can never leave due to the black hole’s incredibly strong gravitational pull.
In all the known mathematical descriptions of black holes, singularities are present in their core. Penrose postulated that all the singularities of gravitational collapse are “clothed” by the event horizons of black holes – meaning we could never observe one. With the singularity inside the event horizon, physics in the rest of the universe is business as usual.
This conjecture of Penrose, that there are no “naked” singularities, is called cosmic censorship. After half a century, it remains unproven and one of the most important open problems in mathematical physics. At the same time, finding examples of instances where the conjecture doesn’t hold up has proven equally difficult.
Quantum Mechanics and Black Holes
In recent work, published in Physical Review Letters, we showed that quantum mechanics, which rules the microcosmos of particles and atoms, supports cosmic censorship.
Black holes are influenced by quantum mechanics to some extent, but such influence is normally ignored by physicists. For example, Penrose excluded these effects in his work, as did the theory that enabled scientists to measure ripples in space-time called gravitational waves from black holes.
When they are included, scientists call the black holes “quantum black holes”. These have long provided a further mystery, as we don’t know how Penrose’s conjecture works in the quantum realm.
A model where both matter and space-time obey quantum mechanics is often considered the fundamental description of nature. This could be a “theory of everything” or a theory of “quantum gravity”. Despite tremendous effort, an experimentally verified theory of quantum gravity remains elusive.
Challenges and Advances in Quantum Cosmic Censorship
It is widely expected that any viable theory of quantum gravity should resolve the singularities present in the classical theory – potentially showing they are simply an artifact of an incomplete description. So it’s reasonable to expect quantum effects should not make the problem of whether we could ever observe a singularity worse.
That’s because Penrose’s singularity theorem makes certain assumptions about the nature of matter, namely that the matter in the universe always has positive energy. However, such assumptions can be violated quantum mechanically – we know that negative energy can exist in the quantum realm in small amounts (called the Casimir effect).
Without a fully fledged theory of quantum gravity, it is difficult to address these questions. But progress can be made by considering “semi-classical” or “partially-quantum” gravity, where space-time obeys general relativity but matter is described with quantum mechanics.
Though the defining equations of semi-classical gravity are known, solving them is another story entirely. Compared to the classical case, our understanding of quantum black holes is much less complete.
From what we do know of quantum black holes, they also develop singularities. But we expect a suitable generalization of classical cosmic censorship, namely, quantum cosmic censorship, should exist in semi-classical gravity.
Developing Quantum Cosmic Censorship
So far, there is not an established formulation of quantum cosmic censorship, though there are some clues. In some cases, a naked singularity can become modified by quantum effects to shroud the singularities; they become quantum dressed. That’s because quantum mechanics plays a role in the event horizon.
The first such example was presented by physicists Roberto Emparan, Alessandro Fabbri and Nemanja Kaloper in 2002. Now, all known constructions of quantum black holes share this feature, suggesting a more rigorous formulation of quantum cosmic censorship exists.
Intimately linked to cosmic censorship is the Penrose inequality. This is a mathematical relationship that, assuming cosmic censorship, says the mass or energy of of space-time is related to the area of black hole horizons contained within it. Consequently, a violation of the Penrose inequality would strongly suggest a violation of cosmic censorship.
A quantum Penrose inequality could therefore be used to rigorously formulate quantum cosmic censorship. One team of researchers proposed such an inequality in 2019. While promising, their proposal is very difficult to test for quantum black holes in regimes where quantum effects are strong.
In our work, we discovered a quantum Penrose inequality that applies to all known examples of quantum black holes, even in the presence of strong quantum effects.
The quantum Penrose inequality limits the energy of space-time in terms of the total entropy – a statistical measure of a system’s disorder – of the black holes and quantum matter contained within it. This addition of quantum matter entropy ensures the quantum inequality is true even when the classical version breaks down (on quantum scales).
That the total energy of this system cannot be lower than the total entropy is also natural from the standpoint of thermodynamics. To prevent a violation of the second law of thermodynamics – that the total entropy never decreases.
When quantum matter is introduced, its entropy is added to the black hole’s, obeying a generalised second law. In other words, Penrose inequality can also be understood as bounds on entropy – exceed this bound, and the space-time develops naked singularities.
On logical grounds, it was not obvious that all known quantum black holes would satisfy the same, universal inequality, but we showed they do.
Our result is not a proof of a quantum Penrose inequality. But that such a result holds in the quantum domain as well as the classical one strengthens it. While space and time may end at singularities, quantum mechanics screen this fate from us.
Written by:
- Andrew Svesko, Research Associate of Theoretical Physics, King’s College London
- Antonia Micol Frassino, Research fellow, Scuola Internazionale Superiore di Studi Avanzati (SISSA)
- Juan F. Pedraza, Research Fellow at Instituto Fisica Teorica UAM/CSIC, Universidad Autónoma de Madrid
- Robie Hennigar, Willmore Fellow of Mathematical Physics, Durham University
Adapted from an article originally published in The Conversation.
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31 Comments
“If singularities were observable, scientists would lose the ability to predict future events based on past conditions.”
Darn, fingers crossed, because those are the best kinds of predictions.
Anyway, Einstein apparently avoided any possibility of dark matter messing with Mercury’s precession by cleverly not mentioning past measurements, possibly obtained from the other pole.
Besides “knowing” of the existence of “dark matter,” journalists also “know” that gravitational waves are yet another one of Einstein’s incredible “predictions.”
Miraculously Einstein managed to overlook that massive natural gravitational wave detector known as “sea level” for his unbelievable gravitational wave “prediction.”
Journalists will also tell you that Einstein’s “prediction” of gravitational waves also means he realized there have to be quantum particles (cleverly named as “gravitons”) to go with his supposed quantum gravity waves.
Too bad that Einstein’s gravitational waves are not quantum waves but classical waves expressing a continuum of oscillation rates.
Regrettably, pointing out shameless mainstream science propaganda with a comment that for some reason hasn’t been ruthlessly censored away is how to get the trustworthy AI experts at google to derate the comment-bearing article.
A “classical wave” is a wave that spreads out over time.
A quantum wave is not expected under normal circumstances to spread out over time but hold together, like a photon.
Field quanta are bosons, field quanta are spin waves.
“A ‘classical wave’ is a wave that spreads out over time.”
Einstein’s gravitational waves are classical waves because they spread out over time. Nonetheless, a tribal trainable like Harvard’s Avi Loeb wants to suggest Einstein’s gravitational waves are quantum waves. Not my problem.
A classical wave spreads out over time because due to being composed of a large number of substantially independent particles.
“A classical wave spreads out over time … due to being composed of a large number of substantially independent quanta.”
The extent of the classical wave changes over time in that way, weakening in intensity as the inverse square of the distance traveled. Spreading out over time is why gravity waves are not quantum waves but classical waves. Overlooking that makes Einstein look about as elite as his cargo cult fandom.
A point source can produce classical waves that must spread out, plus quantum waves that may (also in some cases may partially not) spread out. If you ask Google’s AI whether classical waves spread out, the answer that it gives is strangely limited to diffractive phenomena, but it does admit Einstein’s gravitational waves are classical wave and that classical waves do not have anything close to a simple Heisenberg-like relationship to their constituent particles. Also, no one expects gravitational refraction to be observed any time soon.
“quantum waves … may … spread out.”
Sorry, that’s too vague. Meant to say that a group of quantum particles/waves may or may not spread out.
What existed before the Big Bang?
Was it not a singularity?
That singularity which existed before Big Bang, can also be called a spiritual being Allah or God
You can call it anything you like, but such an entity is outside our space-time and cannot affect us in any way. It cannot be the Allah that your holy book promises.
That depends on how you define “big bang” – in the current concordance cosmology it was an inflation era before the hot big bang era.
“Surprise: the Big Bang isn’t the beginning of the universe anymore
We used to think the Big Bang meant the universe began from a singularity. Nearly 100 years later, we’re not so sure”
“Lastly, and perhaps most importantly, we can no longer speak with any sort of knowledge or confidence as to how — or even whether — the universe itself began. By the very nature of inflation, it wipes out any information that came before the final few moments: where it ended and gave rise to our hot Big Bang. Inflation could have gone on for an eternity, it could have been preceded by some other nonsingular phase, or it could have been preceded by a phase that did emerge from a singularity.”
[Ethan Siegel, Big Think]
We know robustly and beyond reasonable doubt since 2016 that space expansion, which produces the universe, is a completely natural process, Therefore any significant magic, as proposed by organized superstition along the lines you mention, cannot exist.
Very imaginative: “quantum mathematics?” As a senior lay American male with particular personal “insights” into cosmology since 1978 and gravity in particular since 2009, who’s had at least one low-budget at-home gravity demonstration video online since 2012 with no one proving it wrong yet, I prefer science fiction for entertainment to science fiction for education. As to the end of space and time, how about an immeasurably brief state in-between with Allah/God and universe being mutually exclusive; evolution ruling for eons in accordance with a hierarchy of natural laws?
Quantum mathematics models quantum state logic.
If you expect your “gravity demonstration” video to be “proven” wrong, maybe you shouldn’t declare it gravitation – no one has tested general relativity wrong yet.
And as noted above any significant magic, as proposed by organized superstition along the lines you mention, cannot exist.
The problem with people is they think they are the point of it all, the most important idea – and differentiated like the ‘things’ they imagine.
Seems every year has unofficially become “Drain the proverbial blood from the scientific aspirations of most youth through the exceptional brilliance of made-up things about Einstein by the usual relatives because the rainbow is not enuf” year.
“Penrose’s singularity theorem makes certain assumptions about the nature of matter, namely that the matter in the universe always has positive energy. However, such assumptions can be violated quantum mechanically – we know that negative energy can exist in the quantum realm in small amounts (called the Casimir effect).”
Sub-Planck realm also supports further freedom in negative energy impact. A spin-1 sub-Planck-scale quasi-particle (dipole) or spin-2 quasiparticle (bi-pole) could be massless by being half negative energy and half positive energy.
Negative energy in free space would equate to sub-Planck scale regions of “true vacuum” being effectively n-pairable (“n-pairs” being enabled simply enough through their presumed functional ubiquity) with matching positive energy regions.
Quantum gravity experts apparently believe they can talk practically forever about extra degrees of freedom in quantum gravity without suggesting one of those degrees involves replacing dark matter ripples with conservation of ultra-low angular moments in a coherent massless graviton flow. Figures.
ALMA seems to be starting to pick a gravity ripple effect up but for some reason the picture has been severely size-limited, to the extent that it’s not clear whether the reconstruction process shows aliasing or added information in an unexpectedly sparse information content environment.
To sum up the claims in all your comments: No.
So, what’s in it for the individual or individuals who show it to be otherwise? They can’t be expected to do these equations without some sort of reward; although, to be honest, the equations already exist, as we just recently witnessed with the solution to the accelerating expansion of the universe; an optical illusion caused by very weak gravitational fields. There’s this relationship that we all know about between gravitational fields and the velocity of time, but is it really gravity that effects time; or is it time that that creates the illusion of gravity? I know it sounds childish, but these 5 equations that describe black holes and the velocity of light in time varying medium, only need to be rearranged, to be able to learn how to manipulate gravity in much the same way as we do magnetism, and; wouldn’t that bring us a thousand years into the future, in just a few years? Let me know somebody; I’m an extremely poor person, solve it yourself for glory and fame or get in touch, please.
Scientists generally do it because they are curious and because they want to educate people about nature.
Space expansion is not an “optical illusion”, that is the find by the general relativity the article mention. See e.g. “Big Bang”, Wikipedia.
What about if it was from a higher dimension?
Bingo.
That’s not our universe though, is it?
Presumably, pre the Big Bang there existed the ultimate singularity, the universe in a nutshell, or a nuts’ hell. Why did it decide to stop being a singularity and become a universe?
Boredom.
According to current observation of slow roll inflation, the field fluctuated into end roll whether or not it was actually rolling (or standing still, we don’t know yet).
Inflation caused the following observation:
“Surprise: the Big Bang isn’t the beginning of the universe anymore
We used to think the Big Bang meant the universe began from a singularity. Nearly 100 years later, we’re not so sure.”
– Ethan Siegel, cosmologist
Blackholes SUCK
Negative and positive electric magnetism warped together in a ball circulating extremely fast like distant partners being compress toward the center of a dance floor creating a black hole which is constantly being compressed from all angles simultaneously on the outside by a single pressure wave bubble the Ether which is non-magnetized but the beginning and the end of all angles of any existence. A negative and positive magnetism drive is dark energy. Negative and positive magnetism are the first form of energy .
Read the article: we know it is gravity, not electromagnetism.
I suspect that that’s the way it is with everything, the complicity will be the end of this species, but we keep what we sow. So, obviously, we deserve it.
Relevance?
It seems to be incorrect to claim that “in all the known mathematical descriptions of black holes, singularities are present in their core.” Gravastar solutions are a direct counterexample and reviews of black hole models have about 1/3 of them without singularities.
Kerr himself recently published a paper where he points out that we have to assume unphysical singularities since there is a gap in such models. He then goes on to claim that his own example offers a counterexample: arXiv:2312.00841: “Do Black Holes have Singularities? R. P. Kerr There is no proof that black holes contain singularities when they are generated by real physical bodies. Roger Penrose claimed sixty years ago that trapped surfaces inevitably lead to light rays of finite affine length (FALL’s). Penrose and Stephen Hawking then asserted that these must end in actual singularities. When they could not prove this they decreed it to be self evident. It is shown that there are counterexamples through every point in the Kerr metric. These are asymptotic to at least one event horizon and do not end in singularities.”
Meanwhile, it seems the new research fails to cover “all known quantum black holes”. “The researchers successfully extended the classical Penrose and reverse isoperimetric inequalities to account for quantum effects. Their proposed version holds for all known black holes in three-dimensional AdS space, even with any order of quantum backreaction.” [Tejasri Gururaj, Phys.org] I browsed the paper and I think Gururaj’s assessment is correct – these black holes are not the ones existing in our universe.