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What Are Some Tests for Quantum Gravity and the Theory of Everything?

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

Two Good Theories, But No Middle Ground

Quantum mechanics (QM) and general relativity (GR) are amongst the greatest accomplishments of the 20th century. They have been tested in so many ways and have passed, giving us the confidence in their reliability. But a hidden crisis exists when both are considered for certain situations. Problems like the firewall paradox seem to imply that while both theories work well independently, they don’t mesh well when considered for applicable scenarios. It can be shown in circumstances how GR impacts QM but not so much for the other direction of impact. What can we do to shed light on this? Many feel if gravity would have a quantum component to it that could serve as the bridge to unite the theories, possibly even leading to a theory of everything. How can we test for this?

Time Dilating Effects

QM is often governed by the time-frame I am looking at. In fact, time is officially based on an atomic principle, the realm of QM. But time is also affected by my movement, known as dilating effects according to GR. If we took two superpositioned atoms in different states, we can measure out timeframe as the period of oscillating between the two states based on environmental cues. Now, take one of those atoms and launch it at a high speed, some percentage of the speed of light. This ensures that time dilating effects happen, and so we can get good measurements on how GR and QM are impacting each other. To practically test this out (since superimposing the electron states and achieving near-light-speeds is difficult), one could use the nucleus instead and energize it via X-Rays (and lose energy by expelling X-Rays). If we have a collection of atoms at the ground and above the ground, gravity works on each set differently because of the distance involved. If we get an X-Ray photon to go up and only know something absorbed the photon, then the top atoms are effectively superimposed with the probability of having absorbed the photon. Something then emits an X-Ray photon back to the ground, superimposing and acting like each contributed a piece to the photon. Enter gravity, which will pull on those photons in a different way because of that distance and the time of travel. The angle of the emitted photons will be different because of this and can be measured, possibly giving insights into a quantum gravity model (Lee “Shining”).

Superimposing Space-Times

On the note of using superposition, what exactly happens to space-time when this occurs? After all, GR explains how objects cause curvature to the fabric of space. If our two superimposed states cause this to be curved in different ways, couldn’t we measure that and the sudden affects that would have on space-time? The issue here is scale. Small objects are easy to superimpose but difficult to see the effects of gravity while large-scale objects can be seen to disrupt space-time but cannot be superimposed. This is due to environmental disturbances that cause objects to collapse into a definite state. The more I am dealing with then the more difficult it is to keep everything in check, allowing collapse into a definite state to occur easily. With a single, small object I can isolate that much easier but then don’t have much interacting ability to see its gravity field. Is it impossible to do a macro experiment because gravity causes collapse, therefore making a large scale test impossible to measure? Is this gravitational decoherence a scalable test and so we can measure it based on the size of my object? Improvements in tech are making a possible test more feasible (Wolchover “Physicists Eye”).

Dirk Bouwmeester (University of California, Santa Barbara) has a set-up involving an optomechanical oscillator (fancy talk for a spring-mounted mirror). The oscillator can go back and forth a million times before stopping under the right conditions, and if one could get it to be superimposed between two different vibration modes. If isolated well-enough, then a photon will be all it will take to collapse the oscillator into a single state and thus the changes to space-time can be measured because of the macroscale nature to the oscillator. Another experiment with those oscillators involves the Heisenberg Uncertainty Principle. Because I cannot know both the momentum and position of an object with 100% certainty, the oscillator is macro enough to see if any deviations from the principle exist. If so, then it implies that QM needs modification rather than GR. An experiment by Igor Pikovksi (European Aeronautic Defense and Space Company) would see this with the oscillator as light hits it, transferring momentum and causing a hypothetical uncertainty in position of the phase of the resulting waves of “just 100-million-trillionth the width of a proton.” Yikes (Ibid).

The optomechanical oscillator.

The optomechanical oscillator.

Fluidic Space

One interesting possibility for a theory of everything is spacetime acting as a superfluid according to work done by Luca Maccione (Ludwig-Maximilian University). In this scenario, gravity results from the motions of the fluid rather than the individual pieces endowing spacetime with gravity. The fluid motions happen on the Planck scale, which places us at the smallest lengths possible at about 10-36 meters, gives a quantum nature to gravity, and “flows with virtually zero friction or viscosity.” How could we even tell if this theory is true? One prediction calls for photons having different speeds depending on the fluidic nature of the region the photon is traveling through. Based on known photon measurements, the only candidate for spacetime as a fluid must be in a superfluid state because photon speeds have held up so far. Extending this idea to other space traveling particles like gamma rays, neutrinos, cosmic rays, and so on could yield more results (Choi “Spacetime”).

Black Holes and Censorship

Singularities in space have been a focal point of theoretical physics research, especially because of how GR and QM have to meet at those locations. The how is the big question, and it has led to some fascinating scenarios. Take for example the cosmic censorship hypothesis, where nature will prevent a black hole from existing without an event horizon. We need that as a buffer between us and the black hole to essentially lock away the dynamics of the quantum and the relative from being explained. Sounds like a slight-of-hand, but what if gravity itself supports this no-naked-singularity model. The weak gravity conjecture postulates that gravity must be the weakest force in any Universe. Simulations show that no matter the strength of other forces, gravity seems to always cause a black hole to form an event horizon and prevent a naked singularity from evolving. If this finding holds up, it supports string theory as a potential model for our quantum gravity and therefore our theory of everything, because the tying together of the forces via a vibrational means would correlate with the changes to the singularities seen in the simulations. QM effects would still cause the mass of particles to collapse enough to form a singularity (Wolchover “Where”).

Diamonds Are Our Best Friend

That weakness of gravity is really the inherent problem with finding quantum secrets about it. That is why a potential experiment detailed by Sougato Bose (University College London), Chiara Marletto and Vlatko Vedral (University of Oxford) would look for the effects of quantum gravity by attempting to entangle two microdiamonds via gravitational effects only. If this is true, then quanta of gravity called gravitons must be exchanged between them. In the setup, a microdiamond with a mass roughly 1*10-11 grams, a width of 2*10-6 meters, and a temperature less than 77 Kelvin has one of its central carbon atoms displaced and replaced with a nitrogen atom. Firing a microwave pulse via a laser at this will cause the nitrogen to enter a superposition where it does/doesn’t intake a photon and allows the diamond to hover. Now bring a magnetic field into play and this superposition extended out to the whole diamond. With two different diamonds entering this state of individual superpositons, they are allowed to fall near each other (at about 1*10-4 meters) in a vacuum more perfect than any ever achieved on Earth, mitigating the forces acting on our system, for three seconds. If gravity does have a quantum component, then each time the experiment happens the fall should be different because the quantum effects of the superpositions only allow for a probability of interactions that changes each time I run the set-up. By looking at the nitrogen-atoms after entering another magnetic field, the spin correlation can be determined and so the potential superposition of the two established solely via gravitational effects (Wolchover “Physicists Find,” Choi “A Tabletop”).

Planck Stars

If we want to get really crazy here (and let’s face it, haven’t we already?) there are some hypothetical objects that may help our search. What if a collapsing object in space doesn’t become a black hole but instead may achieve the right quantum matter-energy density (about 1093 grams per cubic centimeter) to balance the gravitational collapse once we get to about 10-12 to 10-16 meters, causing a repulsive force to reverb and form a Planck star of shall we say a small size: about the size of a proton! If we could find these objects, they would give us another chance to study the interplay of QM and GR (Resonance Science Foundation).

The Planck star.

The Planck star.

Lingering Questions

Hopefully these methods will yield some results, even if they are negative. It may just be that the goal of quantum gravity is unachievable. Who is to say at this point? If science has shown us anything, it’s that the real answer is crazier than what we can conceive it to be…

Works Cited

Choi, Charles Q. “A Tabletop Experiment for Quantum Gravity.” Insidescience.org. American Institute of Physics, 06 Nov. 2017. Web. 05 Mar. 2019.

---. “Spacetime May Be a Slippery Fluid.” Insidescience.org. American Institute of Physics, 01 May 2014. Web. 04 Mar. 2019.

Lee, Chris. “Shining an X-Ray torch on quantum gravity.” Arstechnica.com. Conte Nast., 17 May 2015. Web. 21 Feb. 2019.

Resonance Science Foundation Research Team. “Planck Stars: Quantum gravity research ventures beyond the event horizon.” Resonance.is. Resonance Science Foundation. Web. 05 Mar. 2019.

Wolchover, Natalie. “Physicists Eye Quantum-Gravity Interface.” Quantamagazine.com. Quanta, 31 Oct. 2013. Web. 21 Feb. 2019.

---. “Physicists Find a Way to See the ‘Grin’ of Quantum Gravity.” Quantamagazine.com. Quanta, 06 Mar. 2018. Web. 05 Mar. 2019.

---. “Where Gravity is Weak and Naked Singularities Are Verboten.” Quantamagazine.com. Quanta, 20 Jun. 2017. Web. 04 Mar. 2019.

© 2020 Leonard Kelley