# Does Quantum Entanglement Explain Spacetime and How Does It Relate Back to Quantum Gravity?

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

Finding the bridge between relativity and quantum mechanics is considered one of the holy grails of physics. One describes the macro world well, the other the micro but together they just can’t seem to get along. But one phenomenon that operates on both levels well is gravity, and so it is here that science has focused on trying to tie the two theories. But other arenas of quantum mechanics are potentially pointing to different paths of success. New findings are showing that quantum ties to relativity are leading to surprising conclusions that may shake our understanding of reality to the core.

## Qubits

Some research is showing that qubits, tiny particles that carry quantum information, may be entangled in such a way as to generate spacetime as a result of the spooky action between particles. What that information is remains uncertain but most are just concerned with the interactions between the qubits that cause spacetime to exist. The theory comes from a 2006 paper by Shinsei Ryu (University of Illinois at Urbana Champaign) and Tadashi Takayunagi (Kyoto University), where the scientists noted that parallels exist between the geometry of spacetime and the entanglement pathways scientists project on the macro level. Maybe, possibly, this is more than a coincidence (Moskowitz 35).

## Black Holes

Juan Maldacena and Leonard Susskind, both giants in the black hole field, decided to build upon this in 2013 when they extended the work to…black hole. It is well known from previous findings that if 2 black holes become entangled, they form a wormhole between them. Now, we can describe this entanglement in the “classical” way quantum mechanics traditionally does: Only a single characteristic is entangled. Once you know the state of one of the pair, the other will fall into a corresponding state based on the remaining quantum state left. This happens rather quickly in what Einstein called “spooky action.” Juan and Leonard showed that through entanglement, a quantum property possible leads to a macro result (Ibid).

## Quantum Gravity

All of this hopefully will build to quantum gravity, the holy grail for many scientists. But much groundwork is yet to be laid in the hunt for it.

The holographic principle may be of assistance. It is used to describe a projection of a dimension space on a lower dimensional space that still conveys the same information. One of the best uses of the principle to date is the anti-de Sitter/conformed field theory (AdS/CFT) correspondence, which showed how the surface of a black hole communicates all the information of a black hole on it, so a 2D space contains 3D information. Scientists took this correspondence and applied it to gravity…by removing it. You see, what if we took entanglement and let it project 3D information onto 2D surfaces? This would form spacetime and explain how gravity works as a result of spooky action via quantum states, all being projections onto different surfaces! A simulator using techniques developed by Ryu and led by Van Raamsdonk showed that as entanglement went to zero, spacetime itself stretched out until it broke apart. Yes, it is a lot to take in and seems to be a load of nonsense but the implications are huge (Moskowitz 36, Cowen 291).

With that being said, some issues do remain. Why does this even happen? Quantum information theory, which deals with how quantum information is sent and the size of them, could be a crucial part of AdS/CFT correspondence. By describing how the quantum information is conveyed, entangled, and how this relates to spacetime geometry, a full holographic explanation of spacetime and therefore gravity should be possible. The current trend is analyzing the error correcting component of quantum theory, which showed that the possible information contained in a quantum system is less than that between two entangled particles. What is interesting here is that much of the math we find in error-reducing codes has parallels to the AdS/CFT correspondence, especially when examining the entanglement of multiple bits (Moskowitz 36, Cowen 291).

Could this be at play with black holes? Could the surfaces of them have all these aspects at play? It’s hard to tell, for AdS/CFT is a *very* simplified view of the Universe. We need more work to determine what’s really happening (Moskowitz 36)

## Quantum Cosmology

Cosmology has a big (see what I did there?) problem: it requires initial boundary conditions to be assumed if anything is to have occurred. And according to work done by Roger Penrose and Stephen Hawking, relativity implies that a singularity had to be in the past of the universe. But field equations break down at such a location yet work fine afterward. How can this be so? We need to figure out what physics was doing there, for it should work the same everywhere. We need to look at the path integral over nonsingular metrics (that being a path in spacetime) and how they compare to Euclidean metrics used with black holes (Hawking 75-6).

But we need to also scrutinize some underlying assumptions from earlier. So, what were those boundary conditions that scientists wanted to examine? Well, we got “asymptotically Euclidean metrics” (AEM) and those are compact and “without boundary.” Those AEM are great for scattering situations, like particle collisions. The paths the particles take is very reminiscent of hyperbolas, with the entry and exists being the asymptotic nature of the path they take. By taking the path integral of all the possible paths our infinite region of AEM’s could have been produced from, we can find our possible futures as well, for the quantum flux is less as our region grows. Simple, no? But what if we have a finite region aka our reality? Two new possibilities would have to be considered in our probabilities of certain measurements of the region. We could have a connected AEM where our region of interaction is in the spacetime we occupy or we could have a disconnected AEM where it is a “compact spacetime containing the region of measurements and a separate AEM.” This doesn’t seem like reality, so we can ignore this right? (77-8)

Turns out, they can be a thing if one has connecting metrics to them. These would be in the form of thin tubes or wormholes that connect different regions back to spacetime and in a great twist may be the crazy connection between particles driving entanglement While these disconnected regions don’t affect our scattering calculations (because they are not connected to any infinities we may reach before or after the collision) they still might impact our finite region in other ways. When we look at the metrics behind the disconnected AEM and the connected AEM, we find that the former terms from power series analysis are larger than the latter. Therefore, PI for all AEM is about the same as the PI for disconnected AEM, which have no boundary conditions (Hawking 79, Cowen 292).

Simple, it is not. But a start towards enlightenment…possibly.

## Works Cited

Cowen, Ron. “Space. Time. Entanglement.” Nature Nov. 2015. Print. 291-2.

Hawking, Stephen and Roger Penrose. The Nature of Space and Time. New Jersey: Princeton Press, 1996. Print. 75-9

Moskawitz, Clara. “Tangled Up in Spacetime.” Scientific American Jan. 2017: 35-6. Print.

**© 2018 Leonard Kelley**