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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.

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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).

The entangled black hole.

The entangled black hole.

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 Routes

Mathematics is often the source of many people's frustrations but sadly even fewer people’s salvation. It's the language we use to formulate physics and find new connections between how the world relates to itself. Yet somehow mathematics seemingly has led us to a contradiction when it comes to unifying quantum mechanics and general relativity. Despite decades of struggle, we only have a few promising routes for a full theory of quantum gravity. Math may save us yet though and show that space-time itself may be an emergent phenomenon. 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.

One route towards a theory of quantum gravity lies in string theory, something often touted as the ultimate answer to any burning physics questions. It’s the simple idea that all of reality boils down to tiny vibrating 1-dimensional strings that can interact in a myriad of ways and from these interactions we get the reality around us. If true, then we would expect to see a graviton, or the force carrier of gravity, but so far no signs of it have popped up. Oh, and the math behind string theory is nuts, making its predictive power low, but not impossible to solve for (Becker 28, Purcell, Hossenfelder)

Loop quantum gravity sounds similar at first, it being about space-time, discrete units of spin networks that connect and interact via nodes and links, building a quantum foam upon which space time is constructed from. However, loop quantum gravity doesn’t scale well to relativistic levels. Relativity predicts length contraction at great speeds, and how this impacts the discrete pieces of quantum foam is unclear (especially with who is observing it in different reference frames) (Becker 28, Purcell, Hossenfelder).

These two theories don’t mesh too well, based on how each interprets reality. String theory needs 10 dimensions to operate, while loop quantum gravity cannot exist in such a space. String theory treats space-time as a fundamental while loop quantum gravity literally constructs it. Loop quantum gravity implies that because of this, space time itself is emergent in behavior. But how can it scale to a large structure like we see in the Universe? (Purcell, Hossenfelder)

AdS/CFT Correspondance

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.

In 1997, Juan Maldacena (Institute for Advanced Study) found a mathematical duality between two seemingly unrelated topics in physics: conformal field theory (CFT) and anti-de-Sitter space (AdS). CFT is dominated by quantum mechanics while AdS is dominated by relativity mechanics. Yet somehow, it turns out that the same mathematical tools can be used to describe both of them, implying a deeper connection between them than first appears. This is formally known as the AdS/CFT correspondence (Becker 29, Hossenfelder, McCormick).

This promising link between quantum mechanics and general relativity seems to have a major problem right away: AdS has an extra dimension that CFT doesn’t contain. Surely this is a game ender, but once again math can come to the rescue thanks to work from Gerard ‘t Hooft (Utrecht University in the Netherlands) and Leonard Susskind (Stanford University. Via the holographic principle, we can map dimensional spaces into lower levels and yet retain the information contained in it. An example of this can be seen in black holes, whose surfaces are thought to encode 3-D information onto a 2-D surface (Becker 29).

With the Ads/CFT correspondence, we can show how the 4-D CFT has the 5-D of AdS encoded onto it. AdS is the hologram and source of gravity, while CFT is the quantum base. It is because of this mapping that certain interactions of the quantum components of AdS become the space time of CFT. And the interactions that generate that space? Quantum entanglement, the classic spooky-action-at-a-distance that seems to violate locality. Somehow, it seems that components can influence each other from vast distances at a great speed exceeding the speed of light. In reality, while the changes do occur at superluminal speeds, the information of this is conveyed at speeds approaching the speed of light (Becker 29, McCormick).

The idea that entanglement itself is what causes space to emerge stems from work by Shinsei Ryu (Princeton University) and Tadashi Takayangi (Kyoto University). While looking at the AdS/CFT correspondence, they noticed that entanglement is key to measuring distances in AdS. This is because the correspondence shows that any close regions of space in AdS corresponds to closely entangled systems in CFT. Therefore, as entanglement increase, the proximity of the regions of space increase too. Entanglement is the glue that holds space together (Barber 29, Moskowitz 36, Cowen 291).

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The AdS/CFT correspondence shows then 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! (Ibid).

If true, this would make finding quantum gravity so much easier to solve for. We would no longer be trying to describe the changes to space-time in a quantum way but instead establish that space itself emerges from quantum properties. We cannot talk about gravity, the changes to space time based on mass and energy, without this. Can we do something similar with time, establish its emergent behavior? We are not sure yet. 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 (Berber 29-31, Moskowitz 36, Cowen 291).

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 (Ibid).

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)

Interesting Perspectives

If space (and maybe time) is a result of entanglement, what is it exactly that is being entangled? How could anything be said to exist anywhere if it’s just a mesh of entanglement? Eleanor Knox, a philosopher of physics, offers the idea that maybe the issue is how we are framing the question. We could be letting our intuitions of how reality operates get in the way. Space time maybe isn't fundamental yet we can still have things in it, we just have to establish a way to emerge from what is considered fundamental at a given moment (Barber 31).

Christian Wuthrich (University of Geneva) offers an excellent view point to understand the ideas here better. Consider the idea of a liquid, being made of many particles. We wouldn’t say that the particles themselves are a liquid, but that collectively they take on the behavior of a liquid state. For space time, we could think of this in the same capacity. We don’t think about the individual pieces itself but instead the collective behavior. Maybe we need to think about emerging from matter and energy, not matter and energy inhabiting the region (Becker 31).

Alyssa Ney (University of California at Davis) wonders if the AdS/CFT correspondence really implies that space and time emerge from quantum principles. What if it is really the other way around, with quantum mechanics being the emergent behavior from the fundamental space time? What if instead both quantum mechanics and space time are emergent from something even more fundamental? (Becker 31)

Then again, maybe all this conjecturing with AdS/CFT is pointless, since the basic geometry of AdS isn’t compatible with our Universe. We certainly know that at least one type of correspondence exists, but can we find one that matches with our version of reality? Here, we have a de Sitter situation, with ever-expanding space. How holography could work here isn’t clear. Plus, we haven’t seen signs of supersymmetric particles that we should be seeing, implying faults with string theory. Obviously, we need to refine our models to account for these issues. But take heart in that mathematics, with all its beauty, does imply that much more is going on here. Something seems to be emerging that will offer new insights into reality…someday (Hossenfelder, Becker 31, McCormick).

Quantum cosmology: a dream or a goal?

Quantum cosmology: a dream or a goal?

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

Becker, Adam. “The Origins of Space and Time.” Scientific American, Feb. 2022. Print. 28-33.

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

Hossenfelder, Sabine. “String Theory Meets Loop Quantum Gravity.” quantamagazine.org. Quanta, 12 Jan. 2016. Web. 14 Mar. 2022.

McCormick, Katie. “Symmetries Reveal Clues About the Holographic Universe.” quantamagazine.org. Quanta, 12 Jan. 2022. Web. 16 Mar. 2022.

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

Purcell, Conor. “Can we craft a theory in which space and time aren’t assumed to exist?” arstechnica.com. Conte Nast., 20 Apr. 2020. Web. 10 Mar. 2022.

© 2018 Leonard Kelley

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