The Information Paradox is a problem that has plagued physicists for a while. It stems from what we thought was an absolute law of physics coupled with the existence of black holes, and one possible solution involves another type of hypothetical stellar remnant.

Conservation of Information

Basically, “information” is a property pertaining to the arrangement of atoms and subatomic particles, and it is of paramount importance to modern physics that it is conserved. This is down to two principles in quantum mechanics, quantum determinism and reversibility. Quantum determinism is different from regular determinism, as instead of measuring exactly how particles will behave based on their initial properties (velocity, mass etc.), instead each set of initial properties generates a number of possibilities for how the particle will behave. However, the way the particle behaves is still based on its initial properties. Reversibility is the idea that physical processes are time-reversible, if the dynamics of the process are still well-defined.

These principles combined lead to the idea that information must be conserved, ie. if we have a remnant of something, we should be able to tell what that original progenitor was. A common example is that you burn a piece of paper and painstakingly collect all of the atoms of ash and smoke, analyse them all and be able to construct a picture of exactly what the piece of paper looked like.

The problem with this is, as always, black holes.

The Information Paradox

Black holes, as we know them now, do not allow for conservation of information, because once you throw something into a black hole, you have no way of ever telling what it was you threw in. This is for two reasons, the first having basically already been debunked, which is that stuff doesn’t come back out of black holes. This was solved, of course, by the late Stephen Hawking, when he arrived at the idea of Hawking radiation.

This idea relies on the fact that empty space is not as empty as we used to think it is, but is actually a quantum foam full of virtual particles popping in and out of existence. These particles form in pairs of matter and antimatter, “borrowing” energy from the void to do so. At the event horizon of a black hole though, pairs of these virtual particles can form with one inside the event horizon and one just outside. One is able to escape, and one is trapped inside the black hole. This means that the virtual particles are no longer able to annihilate, and so become real. This means they are no longer able to “pay back” the energy debt to the void, and so that debt is transferred to the black hole, which loses a tiny piece of its energy (which is the same as mass in this instance). Since this process happens constantly, this means that black holes slowly radiate away their mass, i.e., mass slowly “leaks out” of a black hole. This process accelerates as the black hole gets smaller, eventually releasing all of the remaining energy in a sharp burst, as the black hole disappears into nothing. However, information cannot be conserved in a classical black hole, as it has no volume. There is, effectively, no space to store the information. This means that when the black hole finally evaporates, it may give off a lot of energy, but it will not give off any information from objects that fell into the black hole.

Planck Stars

Planck stars are essentially a “replacement” for the traditional idea of a singularity (a point of infinite density and infinitely small volume) in a black hole. Proposed by Carlo Rovelli and Francesca Vidotto et al in 2014, this theory relies on a repulsive quantum force (derived from Heisenberg’s uncertainty theorem, the idea that knowing with complete certainty the momentum of a particle means you no longer have any idea where it is) halting the collapse of the core of a star when it reaches the Planck density, 5.1×10^96 kilograms per meter cubed. For the mass-energy of the star to be denser than the Planck density, it would violate the uncertainty principle for spacetime itself. This is similar to the other degenerative forces I’ve talked about in this column before, such as quark degeneracy pressure, the last force pushing outwards against a star’s total collapse. Unlike quark degeneracy or electron degeneracy though, this force, theoretically, cannot be overcome by any amount of mass, as the Planck density is the absolute density. This gives us the ability to derive a rough formula for the radius of such an object, as mass = density x volume. This is, of course, ignoring relativistic effects and totally ignoring the effect of the fact that such an object would probably be spinning very quickly. The radii I calculated ranged from between 10^-22 to 10^-21, making this object, although very small, comfortably larger than a Planck length (1.6×10^-35). This means that there would, theoretically, be enough room on the surface of such an object for information to be conserved.

The more experienced of my readers may have spotted a problem with this theory already. If there is a solid remnant at the centre of a black hole, why don’t we see the outer layers of the star rebound off it when the star collapses, like we see with other remnants? There is actually a pretty neat solution to this, and it relies on everyone’s favorite sci-fi plot device, time dilation. If you already know what this is, feel free to skip ahead a few sentences, but for everyone else: time dilation is basically the idea that space and time are a) the same thing and b) distorted by objects in the universe. Imagine spacetime as a fabric that we are all embedded in, like beads, and we all create tiny stretches and distortions in it. These distortions, according to Einstein, are the cause of gravity, and while a massive object warps space, it also warps time. The more massive the object, the slower time runs on its surface. Because a Planck star is so massive and distort spacetime so much, time near a Planck star would run very, very slowly. This means that any rebound of the outer layers of the star would take a long, long time. Such a long time, in fact, that it would take longer than the timescale of the universe so far. This means that theoretically, every black hole is currently still going through its supernova, but it is happening so slowly that we can’t notice it. The black hole, to us, appears stable.

As the black hole shrinks due to hawking radiation, the Planck star would eventually explode when the event horizon reaches its core, releasing all the information encoded on its surface. This means that Planck stars, if they existed, would solve the information paradox.

Can we find them?

I will say it again, Planck stars are entirely theoretical at this point, and they rely on the existence of quantum loop gravity, which means that there is every chance they are not real. In science, you cannot build absolute conclusions from other theories. A solid conclusion, like a table, it built from theory and evidence to back it up, like a table being built with a plank of wood and 4 legs. If you build your conclusion out of more theories, you don’t have a table you have a pile of wood. Essentially, this is all somewhat of a scientific conspiracy theory, although a lot more credible, as quantum gravity is looking pretty likely at the moment. What’s more, we can seemingly find Planck stars, if we look for them. They apparently would emit a signal, in the 12-14cm wavelength range, caused by quantum gravity. If we could detect one of those signals, we would be well on our way to confirming not only the existence of Planck stars, but also of quantum gravity itself (although that already has a decent amount of evidence for it).

That concludes this week’s column. It was originally supposed to be published about 2 weeks ago, but unfortunately I am lazy and also have A-levels to study for. Basically, this is a warning that these columns will become more and more intermittent as May approaches, but hopefully more frequent after June. The next column will be on… something. You’ll have to wait a couple of years for me to publish it and then see.