In a 5D universe there may be no black hole information paradox
Because there are no black holes as we know them
The black hole information paradox is pretty easy to understand if you think about it. You have a black hole. Nothing can escape its event horizon. Therefore, if I throw anything into it, it becomes lost inside.
Then you have quantum theory which predicts that information is always retrievable and never lost. What that means is that, even if you took something like a harddrive and pulverized it to subatomic particles, theoretically, all of those particles could be guided to reassemble back into the harddrive. While that may be as unlikely as a Firefly reboot, it’s still physically possible.
The reason why is because all laws of physics, all particle trajectories, are time reversible. Even all quantum processes such as the decay of particles are reversible. Thus, even if the atoms in your harddrive were destroyed and turned into muons or photons, they could still theoretically reassemble.
This universal reality breaks down with black holes because nothing can escape them; therefore any quantum particle that falls in cannot be time reversed back out. It is stuck behind the event horizon.
Part of the reason for this is because time and space switch places when a particle crosses the horizon. Therefore, time reversing as a concept breaks down since time doesn’t remain consistently any particular direction. Inside a black hole the singularity represents all possible futures.
The only way to time reverse a trajectory, therefore, would be to carry the particle through the singularity and back out into the universe. Yet the singularity appears to block that path in classical physics. (This is really easy to see in a type of diagram called a conformal or Penrose diagram, invented by Sir Roger Penrose.) This might not be an issue if all singularities are actually passages to other places or universes but that is highly hypothetical.
The key principles in quantum mechanics that create the paradox are (1) determinism, that quantum wavefunctions evolve deterministically from one time to the next, and (2) unitary evolution, which means that quantum wavefunctions maintain their complete state in their evolution.
Some researchers such as Nobel laureate Sir Roger Penrose object to the second idea, saying that quantum measurements collapse the wavefunction, meaning that the evolution of the wavefunction is not unitary. We lose information all the time. Thus, information paradox is no paradox at all.
Not all physicists including yours truly believe unitarity is ever violated and have proposed a myriad of interpretations that preserve it, so integral is it to how we understand quantum theory. Therefore, we press on to other resolutions that are more technical.
The reason why we want to solve it is because quantum theory fundamentally needs information to be conserved or its very foundation on principles such as the conservation of energy would be violated.
While general relativity has a complicated relationship with time-dependent ideas like energy and information (after all time isn’t even well defined in GR), it seems as though information should be preserved in some way at least from the perspective of an observer in a more or less flat spacetime, not near the black hole but observing matter fall into it. We can all agree on time from at least one point of view there.
A number of other solutions have been proposed to the problem, e.g., the event horizon (false horizon really) contains the information or that Hawking radiation encodes it somehow, which is dubious.
Hawking radiation is, of course, the radiation that black holes produce from just beyond their event horizons that causes them to evaporate.
Side note: Hawking famously made up an explanation for it in order to present it to the public. He suggested little pairs of particles were being created in the vacuum by quantum fluctuations all the time. These pairs normally annihilate one another but sometimes interact with the event horizon. One falls in and the other escapes. I even have the illustrated version of A Brief History of Time with a computer image of the particles separating. The explanation is ludicrous for a number of reasons, but this complete fabrication on Hawking’s part has become so ubiquitous that even highly regarded physicists have made the mistake of quoting it. (I won’t name names here.) The real explanation is that the vacuum of curved spacetime has more thermal energy than the vacuum of less curved spacetime and so naturally radiates that energy away causing its curvature to shrink. It is not a property of black holes but rather a property of gravity itself. Gravity is always trying to smooth spacetime out flat. It just happens to be stronger near black holes.
One of the most prominent solutions is called the “remnant” theory that as black holes evaporate, they eventually expose all their information to the universe in a remnant. While classical general relativity doesn’t admit a remnant, quantum gravity might. Considering how much mass has to be carried away for this to happen, however, it is unclear the remnant could contain the amount of information contained in the original star.
Another option however is to suggest that there is no information paradox because quantum fields exist in a higher dimension. This is the Space-Time-Matter theory that proposes the universe has a 5th dimension and that all matter is really ripples (waves) in the fabric of the 5th dimension.
Indeed, we have known for at least a century that Einstein’s equations can generate matter purely from the geometry of an empty 5D universe. This theory, known as non-compactified Kaluza-Klein theory, has a handful of proponents and a long body of work associated with it.
If all matter really is geometry, then that means that black holes are actually formed out of empty spacetime and so is everything else. This does not necessarily mean that the geometry that forms matter can escape the black hole since it is still subject to the geodesic equation that governs particle trajectories in 4D relativity.
The quantum field theory interpretation of the 5D STM theory, however, provides some insight on the problem. In this interpretation, quantum fields are classical waves in 5D that appear as quantum states in 4D. Since all matter can be represented with quantum fields, we can ask how that implies unitary evolution of the wavefunction even in a black hole.
In the 5D theory, unitary evolution is a result of the stochastic (i.e., random) evolution of the quantum history of the particle. This means that the path a particle takes, even falling into a black hole, is randomly changing in a 5th dimension. The unitary aspect of the evolution has to do with the probability distribution of particle paths over the 5th dimension. Thus, it is a probability distribution that is selected from randomly one path at a time rather than a mysterious entity that exists all at once as in standard quantum theory. The two interpretations are equivalent.
From that perspective, a particle can stochastically evolve its history from falling into a black hole to not falling into it because the entire history evolves at once. Even after it has “fallen in” its history continues to evolve, remaining unitary. Because the particle must evolve over all possible paths, it must eventually escape the black hole in the 5th dimension bringing the information it contains out as well.
Is this a solution to the information paradox? No, because although the quantum history as a whole evolves and escapes the black hole, the trajectories that do fall into the black hole carry a measurable proportion of the particle’s total state, which includes all histories. This means that some proportion of the information is unaccounted for (non-unitary). Indeed, all we have done is restate the original problem in the context of 5D theory without offering any solution.
In reality, the problem from a 5D perspective is the idea of black holes as singularities of matter, with zero size, surrounded by an event horizon. In 4D they are unique, standard solutions, but in 5D they are anomalous, extremal solutions of a class of objects frequently called solitons (but also sometimes referred to as magnetic monopoles or even as “black holes”).
Solitons are basically clouds of ultra-relativistic matter (meaning matter moving near the speed of light or radiation). They are naked singularities, meaning that they have no event horizon shielding them from view. (Mathematically, their event horizons shrink to a point.) They contain holes in the spacetime manifold of non-zero size, meaning that they are genuine singularities but spheres rather than points. The matter they contain surrounds the spheres and there is nothing inside the spheres, not even space.
Solitons are related to black holes in that black holes are an extreme form of soliton where the matter is so compressed that a true event horizon forms. This suggests that as a black hole evaporates and its event horizon shrinks and it loses matter it may lose its extremal state of compression and revert to a soliton, a naked singularity. In this case, the information paradox is resolved because a naked singularity, as the name implies, reveals all. This is like the remnant theory on steroids since it is hardly a remnant but a collapse of the event horizon itself.
It is questionable, however, whether black holes that Stephen Hawking and others have published the information paradox about even exist, since they are so extreme. Despite the images that have been taken of supposed black holes and the detection of others with gravitational waves, might not these actually be solitons? Solitons are not bright like stars, even though they are naked singularities. (For this and other reasons, they have been suggested as a dark matter candidate.) They hug their radiation close to themselves, maintaining their state as “dark” stars. Indeed, their density falls off as the fourth power of the distance from their surfaces. Nevertheless, information about them can be extracted since there is no event horizon, i.e., unlike black holes and the Hotel California, you can leave.
Andersen, Timothy D. “A Dynamic Histories Interpretation of Quantum Theory.” arXiv preprint arXiv:2009.04244 (2020).
Sajko, W. N., and P. S. Wesson. “The Energy of 5D Solitons.” Modern Physics Letters A 16.10 (2001): 627–632.
Wesson, Paul S., and J. Ponce de Leon. “The physical properties of Kaluza — Klein solitons.” Classical and Quantum Gravity 11.5 (1994): 1341.
Wesson, Paul S. “A new dark matter candidate: Kaluza-Klein solitons.” The Astrophysical Journal 420 (1994): L49-L52.