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# What is the Black Hole Firewall Paradox?

Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly improve it.

Though they can be hard to imagine, black holes are not a simple matter. In fact, they continue to offer new mysteries, especially when we least expect them. Once of these quirks was uncovered in 2012 and is known as the Firewall Paradox (FP). Before we can talk about it though, we need to go over a few concepts from Quantum Mechanics and General Relativity, the two big theories that thus far have eluded unification. Perhaps with the solution to the FP we will finally have an answer.

## The Event Horizon

All black holes have an event horizon (EH), which is the point of no return (gravitationally speaking). Once you pass the EH, you cannot escape the pull of the black hole and as you get nearer and nearer the black hole you will be stretched out in a process called “spaghettification.” Even though this sounds unusual, scientists call all of this the “No Drama” solution to black holes, because nothing terribly special happens once you pass the EH, i.e. that different physics suddenly come into play upon passing by the EH (Ouellette). Note that this solution does not mean that once you pass the EH that you begin to undergo “spaghettification,” for that happens as you approach the actual singularity. In fact, if the next concept is true, you will not notice anything as you pass the EH.

## The Equivalence Principle

A key feature of Einstein’s Relativity, the equivalence principle (EP) states that an object in free fall is in the same reference frame as an inertial frame. Put another way, it means that an object experiencing gravity can be thought of as an object resisting a change in its motion, or something with inertia. So as you pass the EH, you will not notice any changes because we have made the transition in reference frames, from outside the EH (inertia) to the inside (gravitational). I would not perceive any difference in my reference frame once I pass the EH. In fact, it would only be in my attempt to escape the black hole that I would notice my inability to do so (Ouellette).

## Quantum Mechanics

A couple of concepts from Quantum Mechanics are also going to be key in our discussion of the FP and will be mentioned here in board strokes. It is worth reading the ideas behind all of these in length. The first is the concept of entanglement. In this situation, two particles which interact with each other can pass information about one another based solely on the actions done to one of them. For example, if two electrons become entangled, by changing the spin (a fundamental property of an electron) to up, the other electron will respond accordingly, even at great distances. The main point is that they are not physically touching after entanglement but are still connected and can influence each other.

It is also important to know that in Quantum Mechanics, only “monogamous quantum entanglement” can occur. This means that only two particles can be entangled with the strongest bond and that any subsequent bonding with other particles will result in a lesser entanglement (Oulellette).

This information, and any information (or state of an object) cannot be lost, according to unitarity (Ouellette). No matter what you do to a particle, information about it will be preserved, whether that be though its interaction with other particles and by extension entanglement.

## Hawking Radiation

This one is another grand idea that contributes heavily to the FP. In the 1970’s, Stephen Hawking found an intriguing property of black holes: they evaporate. Over time, the mass of the black hole is emitted in a form of radiation and eventually will disappear. This emission of particles, called Hawking radiation (HR) arises from the concept of virtual particles. These arise in the near- vacuum of space as quantum fluctuations in space-time cause the particles to sprout out from vacuum energy, but they usually end up colliding and producing energy. We usually never see them, but in the vicinity of the EH one encounters uncertainty in space-time and virtual particles appear. One of the virtual particles in a pair that forms can cross over the EH and leave behind its partner. To ensure that energy is conserved, the black hole must lose some of its mass in exchange for that other virtual particle leaving the vicinity, and hence the HR (Ouellette, Powell 68, Polchinski 38, Hossenfelder, Fulvio 107-10).

## The Firewall Paradox

And now, let’s put all that to use. When Hawking first developed his theory of HR, he felt that information had to be lost as the black hole evaporated. One of those virtual particles would be lost past the EH and we would have no way to know anything about it, a violation of unitarity. This is known as the information paradox. But in the 1990’s it was shown that the particle which enters the black hole actually becomes entangled with the EH, so information is preserved (for by knowing state of EH, I can determine the state of the trapped particle) (Ouellette, Polchinski 41, Hossenfelder).

But a deeper problem seemingly rose from this solution, for Hawking radiation also implies a motion of particles and therefore a transference of heat, giving a black hole another property besides the main three that should describe it (mass, spin, and electrical charge) according to the no hair theorem. If such internal bits of a black hole exist, it would lead to black hole entropy around the event horizon courtesy of quantum mechanics, something that general relativity hates. We call this the entropy problem (Polchinski 38, 40).

Seemingly unrelated, Joseph Polchinski and his team looked into some string theory possibilities in 1995 to address the information paradox that had arisen, with some results. When examining D-branes, which exist on many dimensions higher than ours, in a black hole it led to some layering and small pockets of space time. With this result, Andrew Strominger and Cumrun Vaya found a year later that this layering happened to partially resolve the entropy problem, for the heat would become trapped and thus not a property describing the black hole, The but though it that the solution worked only for symmetrical black holes (Polchinski 40).

To address the information paradox, Juan Maldacena developed the Maldacena Duality, which was able to show through extension how quantum gravity could be described using specialized quantum mechanics. For black holes, he was able to extend the math of hot nuclear physics and describe some of the quantum mechanics of a black hole. This helped the information paradox because now that gravity has a quantum nature it allows information an escape route through uncertainty. While it is not known if the Duality works, it actually doesn't describe how the information is saved, only that it will be because of quantum gravity (Polchinski 40).

In a separate attempt to resolve the information paradox, Leonard Susskind and Gerard Hooft develop the Black Hole Complementarity theory. In this scenario, once you are past the EH you can see the trapped information but if you are outside then no dice because its trapped. If two people were placed so that one was past the EH and the other outside, they would not be able to communicate with each other but the information would be confirmed, hence why information laws are maintained. But as it turns out, when you try to develop the full mechanics, you run into a brand new problem. Seeing a troubling trend here? (Polchinksi 41).

You see, Polchinski and his team took all this information and realized a new problem, and it is subtle but important: what if someone outside of the EH tried to tell someone in the inside of the EH what they observed about the HR? They could certainly do that by one-way transmission. The information about that particle state would be doubled (quantumly) for the insider would have the HR particle state and the transmission particle state as well and thus the entanglement. But now the inside particle is entangled with the HR and the outside particle, a violation of “monogamous quantum entanglement." (Ouellette, Parfeni, Powell 70, Polchinski 40, Hossenfelder).

It seems that some combination of the EP, HR, and entanglement can work but not all three. One of them has to go, and no matter which one scientists choose problems arise. If entanglement is dropped, then that means that HR will no longer be linked to the particle that has passed EH and information will be lost, a violation of unitarity. To preserve that information, both virtual particles would have to be destroyed (to know what happened to both of them), creating a “firewall” which will kill you once you pass EH, a violation of the EP. If HR is dropped, the conservation of energy will be violated as a bit of reality is lost. The best case is dropping EP, but after so many tests have shown it to hold true it may mean that General Relativity would have to be altered (Ouellette, Parfeni, Powell 68, Moyer, Polchinksi 41).

## Possible Solutions

The scientific community has not given up on any of the fundamental principles mentioned above. The first effort, over 50 physists working in a two-day period, yielded nothing (Ouellette). A few select teams have presented possible solutions, however.

Juan Maldacena and Leonard Susskind looked into using wormholes. These are essentially tunnels that connect two points in space-time, but they are highly unstable and collapse frequently. They are a direct result of General Relativity but Juan and Leonard have shown that wormholes can be a result of Quantum Mechanics also. Two black holes can actually become entangled and through that create a wormhole (Aron).

Juan and Leonard applied this idea to the HR leaving the black hole and came up with each HR particle as an entrance to a wormhole, all leading to the black hole. Now that HR is no longer entangled with the outside but is instead tied to the black hole in a monogamous entanglement. This means the bonds are preserved and do not release energy, preventing a firewall from developing. That does not mean that the FP cannot still happen, for Juan and Leonard noted that is someone sent a shockwave through the wormhole, a chain reaction could create a firewall. Since this is an optional feature and is not a mandatory set-up of the wormhole solution, they feel confident in its ability to solve the paradox (Aron).

Or course Mr. Hawking has a possible solution. He thinks that we should reimagine black holes as more like grey holes, where there is an apparent horizon along with a possible EH. This apparent horizon, which would be outside of the EH, directly changes with quantum fluctuations inside the black hole and causes information to be mixed around. This preserves general relativity by having the EP maintained (for no firewall exists) and it also saves QM by ensuring that unitarity is also obeyed (for information is not destroyed, just mixed up as it leaves the grey hole). However, a subtle implication of this theory is that the apparent horizon can evaporate based on a similar principle to Hawking radiation. Once this happens, then anything could leave a black hole potentially. Also, the work implies that the singularity may not be needed with an apparent horizon at play but a chaotic mass of information (O'Neill "No Black Holes," Powell 70, Merall, Choi. Moyer).

Another possible solution is the concept of a LASER, or “Light Amplification by Simulated Emission of Radiation.” Specifically, it is when a photon hits a material which will emit a photon just like it and cause a runaway effect of light production. Chris Adami applied this to black holes and the EH, saying that the information is copied and emitted in a “simulated emission” (which is distinct from HR). He knows about the “no-cloning” theorem which says that information cannot be exactly copied, so he showed how the HR prevents this from occurring and allows for the simulated emission to occur. This solution also allows for entanglement because the HR will no longer be tied to the outside particle, thus preventing the FP. The laser solution does not address what happens past the EH nor does it give a way to find this simulated emissions, but further work looks promising (O’Neill "Lasers").

Or course, black holes may just be fuzzy. Work in string theory and quantum mechanics points to a different version of black holes than we expect. In it, the black hole has a very small (not zero) volume and the surface is a conflicting mess of strings that makes the object fuzzy in terms of surface details. That is how holograms can be made that copy and transform objects into a lower-dimensional copy, with the Hawking radiation as a consequence of the copy. No longer does a firewall destroy you but instead you are preserved on a black hole. The main catch is that such a principle requires a perfect black hole, of which there are none. Instead, people are looking into a "near-perfect" solution (Reid, Taylor).

The hardest solution may be that black holes don't exist. Laura Mersini-Houghton, from the University of North Carolina, has work which shows that the energy and pressure generated by a supernova pushes outward and not inward as it is widely believed. Stars implode rather than explode once they reach a certain radius, thus not generating the conditions needed for a black hole to form. She goes on further though, saying that even if a black hole scenario were possible that one could never fully form because of the distortions to space time. We would see a star surface approaching the event horizon forever. Not surprisingly, scientists are not warm to this idea because ,mounds of evidence points to black holes being real. Houghton's work is just one piece of counter-evidence and isn't enough to overturn what science has found thus far (Powell 72, Freeman).

## Works Cited

Aron, Jacob. "Wormhole Entanglement Solves Black Hole Paradox." - Space. Newscientist, 20 June 2013. Web. 21 May 2014.

Choi, Charles Q. "No Black Holes Exist, Says Stephen Hawking—At Least Not Like We Think." NationalGeographic.com. National Geographic Society, 27 Jan. 2014. Web. 24 Aug. 2015.

Freeman, David. "This Physicist Says She Has Proof Black Holes Simply Don't Exist." HuffingtonPost.com. Huffington Post, 01 Oct. 2014. Web. 25 Oct. 2017.

Fulvio, Melia. The Black Hole at the Center of Our Galaxy. New Jersey: Princeton Press. 2003. Print. 107-10.

Hossenfelder, Sabine. “Head Trip.” Scientific American Sept. 2015: 48-9. Print.

Merall, Zeeya. "Stephen Hawking: Black Holes May Not Have 'Event Horizons' After All." HuffingtonPost.com. Huffington Post, 24 Jan. 2014. Web. 24 Aug. 2015.

Moyer, Michael. "The New Black Hole Battle." Scientific American Apr. 2015: 16. Print.

O’Neill, Ian. “Lasers to Solve the Black Hole Information Paradox?” Discovery News. Discovery, 25 March 2014. Web. 21 May 2014.

- - - . "No Black Holes? More Like Grey Holes, Says Hawking." Discovery News. Discovery, 24 Jan. 2014. Web. 14 Jun. 2015.

Ouellette, Jennifer, and Quanta Magazine. "Black Hole Firewalls Confound Theoretical Physicists." Scientific American Global RSS. Scientific American, 21 Dec. 2012. Web. 19 May 2014.

Parfeni, Lucian. "Black Holes and the Firewall Paradox That Has Baffled Physicists." Softpedia. Softnews, 6 Mar. 2013. Web. 18 May 2014.

Polchinski, Joseph. "Burning Rings of Fire." Scientific American Apr. 2015: 38, 40-1. Print.

Powell, Corey S. "No Such Thing as a Black Hole?" Discover Apr. 2015: 68, 70, 72. Print.

Reid, Caroline. "Scientist Proposes That Black Holes are Harmless Holograms." iflscience.com. IFL Science, 18 Jun. 2015. Web. 23 Oct. 2017.

Taylor, Marika. "Falling into a Black Hole May Convert You into a Hologram." arstechnica.com. Kalmbach Publishing Co., 28 Jun. 2015. Web. 23 Oct. 2017.

© 2014 Leonard Kelley

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