When you hear quantum gravity, you probably think, “what is that?”. If you’re like me, you might think about subatomic forces pulling everything inwards. Or perhaps you’re a Marvel fan, and you think about the “quantum realm” in Ant-Man. Either way, quantum gravity is seen as something of a buzzword outside (and sometimes even inside) the scientific community. We usually think we need to use hand-waving physics or baseless speculations to even begin to understand it, and even then it seems  like “unprovable science fiction” [1]. Our current understanding of physics defines quantum gravity as a theory that defines physical gravity in the field of quantum mechanics [1]. However, much of this definition is based on luck and guesswork, much like most mathematical phenomena.

The “lucky guess” we credit for somewhat understanding quantum gravity was first presented as an expression called the DOZZ formula. DOZZ laid the foundation for better understanding how quantum mechanics could be visualized through d point alternative matrix models [2] and served to help find a “fixed smooth ‘reference’ [matrix]” that best fit a Riemann sphere [image 1], or any multidimensional sphere. We can think of d point alt matrices as our version of a Sling Ring to access the quantum “realm”. Mathematicians Dorn, Otto, and the Zamolodchikov brothers created a formula that broke apart the Liouville Field Theory (LFT) which was essentially a proof of the DOZZ formula [3]. This allowed for greater understanding of how physical states of quantum gravity in 2D, and later 3D, could be modeled [7]. By proving LFT using DOZZ, physicists could create Gaussian models of 2D gravity and find the area of the models using Gaussian free form integrals [image 2]. Using these models they could begin to diagram the gravitational fields in a quantum space [2].

Dorn, Otto, and the Zamolodchikovs showed particular interest in the central charge of matter, or conformal field theory, which states that any given configuration of spacetime (visual representations of states of space over time) can be warped such that its angles are preserved [image 3]. Since quantum mechanics often deals with particulate matter, mathematicians often use space as a reference. Dorn and his team specifically looked at cases where the theory exceeds 1 (c > 1) which is when spacetime is warped multiple times. This theory suggests that quantum matter could also be warped in a similar way [4]. We can imagine this as Scott Lang having to travel through multiple stages of the Quantum Realm to reach Janet Van Dyne. In his 1997 paper, Maldacena demonstrated that in bootstrap configurations —or piecewise evaluations of a theory —of c > 1, “spacetime shifts [image 3] essentially pops out of the system like a hologram” [5]. Though we don’t know exactly how spacetime pops out, we can speculate that it’s due to an immense pull of gravity or a similar rapidly accelerating force. While revisiting these papers, physicists were shocked to find something they recognized – these instances guarantee the existence of paradoxically dense objects like black holes that are capable of warping gravity so nothing can escape [4]. Black holes also cause spacetime to project like a hologram since nothing, including light, actually exits the system. Perhaps the gravity around black holes could be a representation of quantum gravity?

Unfortunately, it’s still hard to tell since we know very little about how quantum anything looks, let alone behaves [1]. To actually be able to visualize the 2D model for quantum gravity, we must look at traditional gravity: if gravity is the acceleration of an object in spacetime, quantum gravity should reasonably be when spin-2 particles couple together to accelerate in quantum spacetime [6]. Note, spin-2 particles are really interesting and complex, but for the sake of this article all you need to know is that they involve a set of particles with a combined angular momentum equal to 2. This is a bit like how different variants of Loki could be existing in different realities while still having to follow a specific narrative for how they must live their lives. However, in order for spin-2 particles to accelerate beyond 2, we must create a paradox, for how can something be equal to and more than 2 at once [6]? The coupling particles will either come to a complete halt or have an increased acceleration due to the inelastic collision. Thus we have created Schrödinger’s spin-2 particle, or Loki [7]. However, in the quantum “realm,” since particles no longer oscillate between states when being observed, this probability collapses as soon as particles interact with the environment.

But then we’re plagued with a fundamental question: what is quantum spacetime? If we operate under the assumption that Schrödinger’s particles (and cat) are multiple things at once, then how can we question Marvel for suggesting the existence of the multiverse and several variants of Loki? Quantum spacetime, as per our current understanding of the subject, differs from Einstein’s version of spacetime in that time is essentially at an everlasting standstill and is not influenced by external factors [8-9]. Well, the number one thing about the quantum realm in Ant Man was that it was a place where “all concepts of time and space become irrelevant.” [10]. Seems pretty similar to me.

Regardless, this mystery is what makes quantum theory so exhilarating. Each piece leads to new discoveries in understanding the jigsaw puzzle that is physics. For instance, LFT has been integral in finding black hole mergers via gravitational waves. Gravitons are theorized to create waves in the gravitational field like photons do in the electromagnetic [11]. Quantum gravity holds so much potential to revolutionize the way we interact with particle and mechanical physics, and it may even be the link between sci-fi and reality. Best of all, it could be our quantum bridge to becoming like the Avengers.

References:

1. Wood, C. (2021, June 17). Mathematicians Prove 2D Version of Quantum Gravity Really Works. Quanta Magazine. www.quantamagazine.org/mathematicians-prove-2d-version-of-quantum-gravity-really-works-20210617/.
2. David, F., Kupiainen, A., Rhodes, R., & Vargas, V. (2016). Liouville Quantum Gravity on the Riemann Sphere. Communications in Mathematical Physics, 342(3), 869–907. https://doi.org/10.1007/s00220-016-2572-4.
3. Zamolodchikov, A., and Al. Zamolodchikov. (1996). Conformal Bootstrap in Liouville Field Theory. Nuclear Physics B, 477(2), 577–605. https://doi.org/10.1016/0550-3213(96)00351-3.
4. Wolchover, Natalie. (2017, Feb. 23). Using the Bootstrap Physicists Uncover Geometry of Theory Space. Quanta Magazine, www.quantamagazine.org/using-the-bootstrap-physicists-uncover-geometry-of-theory-space-20170223/.
5. Maldacena, Juan. (1999). The Large N Limit of Superconformal Field Theories and Supergravity. International Journal of Theoretical Physics, 38(4), 1113–1133. https://doi.org/10.1023/a:1026654312961.
6. Bonifacio, James, et al. (2018). Massive and Massless Spin-2 Scattering and Asymptotic Superluminality. Journal of High Energy Physics, 2018(6). https://doi.org/10.1007/jhep06(2018)075.
7. Wolchover, Natalie. (2013, Nov. 5). Physicists Eye Quantum-Gravity Interface. Scientific American. www.scientificamerican.com/article/physicists-eye-quantum-gravity-interface/.
8. Page, D. N., & Wootters, W. K. (1983, June 15). Evolution without evolution: Dynamics described by stationary observables. Physical Review D. https://journals.aps.org/prd/abstract/10.1103/PhysRevD.27.2885.
9. Siegfried, Tom. (2019, May 3). A Quantum Origin for Spacetime. Knowable Magazine. https://knowablemagazine.org/article/physical-world/2019/quantum-origin-spacetime.
10. Reed, P., Wright, E., Cornish, J., McKay, A., Rudd, P., Feige, K., Lilly, E., ... Buena Vista Home Entertainment (Firm),. (2015). Ant-Man.
11. Lewton, Thomas. (2020, July 23). How the Bits of Quantum Gravity Can Buzz. Quanta Magazine. https://www.quantamagazine.org/gravitons-revealed-in-the-noise-of-gravitational-waves-20200723/.

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