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What Is Emergent Gravity and Teleparallel 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.

Dark matter and dark energy remain some of the biggest mysteries in physics. For decades, scientists have attempted and toiled largely in frustration as theory after theory has bitten the dust. This darkness just seems to be beyond current scientific tools. But what if we are looking at the picture wrong? Maybe our idea of missing things out there is just incompleteness in a current theory we don’t have enough knowledge on. Enter the alternate theories, and one of the most intriguing is emergent gravity.

Dark Gravity Physics

Work by Erik Verlinde seems to show that dark energy and dark matter don’t really exist. He took a look at one of the clues for dark matter: gravity. By examining how this weak force operates on larger scales, one can see the theories don’t predict what we see and hence the need for a dark material to fill in the void. Galaxies are too light without it, star movement is all wrong, and the gravitational pulls we see would result from nothing if relativity was solely operating (O’Connell, Maartens).

But Verlinde has a solution to save gravity and eliminate the unnecessary fluff. He postulates that gravity is really a property that arises from the field of statistics – that is, particle interactions or the kinetic energy model for thermodynamics. By examining the entropy associated for a portion of de-Sitter space and how it’s affected when matter is present near it (like with gravity), Verlinde was able to draw parallels between this dark gravity and the dark energy’s accelerated expansion of the Universe. For a given region, we can talk about a holographic layer for a space that conveys the information of the space on its surface. When sufficient matter is present, entropic effects are minimized as entanglements settle out, our layer separating spaces breaks down and so we get Newtonian gravity. But when we have little matter over a large space, our entropic effects are not mitigated and we get dark energy behavior as the region expands. And when this emergent gravity effect interplays with large amounts of matter on a macroscale, we get dark matter behavior. The information isn’t just on the surface in that layer, it’s in the space itself. Verlinde initially developed a gravity model based on this concept in 2010 that accurately predicted Newtonian and Einstein’s gravity, but in 2017 he was able to extend this dark gravity model to large scales and demonstrate that this was sufficient to provide the forces scientists have seen. Dark energy is really just an emergent feature of space-time gravitational effects on a microscopic scale that grow to a macroscopic effect (Lee "Emergent," Kruger, Wolchover, Skibba, O’Connell, Delta, Mosher).

Alexander Peach (Durham University) extended this work to consider what happens with emergent/non-emergent regions of space that are separated by a holographic layer break down. That holographic boundary deals with information of the emergent space as conveyed to the non-emergent (in the form of gravity) with a reduction of a degree a usual consequence of this. If we have a massive particle in proximity to this layer then any changes to its position will correlate to how the layer’s entropy is. It’s essentially an emergent force happening to our separated region, and the work by Peach shows that for a critical radius, the holography collapses and violates our physical laws…unless it’s non-holographic beyond that point, but still separated. We therefore have found the boundary when we transition from holography to non-holographic emergent spaces. Couple this with the changes in entropy and thermodynamics as the region grows and we have a new, bulk-like explanation which accounts for the layer’s collapse. That is, it’s a dark matter explanation from an emergent dark gravity scenario that Verlinde’s work only brushed over and gives a new explanation for the dark matter properties that the emergent dark gravity is attributed to. It should be noted that the most basic formula of Verlinde’s which uses anti-deSitter space (not like our reality) was developed, so it remains to be seen how a more complicated model will hold up but this holographic work does reflect our reality better and is a step in the right direction. It really hits home how the information of gravity isn’t on our layers but in the space itself because that holographic layer collapses. This extension also gives a network approach to mapping out the effects predicted by the theory (Peach, Delta, Mosher).

Testing Emergent Gravity

To see if dark gravity has any merit, we need some evidence for it. Observations by Margot Brouwer (Leiden Observatory) and team were done on gravitational lensing objects to find the mass of 33,613 galaxies, as recorded by GAMA and KiDS arrays. With these in mind, they ran all the necessary parameters into both dark matter and dark gravity models, and wouldn’t you know it: They both gave the same result (O’Connell, Mosher).

What a Twist

Another possible path for the future study of gravity lies in its past. Einstein later in his life expressed dissatisfaction with general relativity, feeling that it was missing something with the structure of space time. Sure, his work showed that it stretches and compresses, but maybe it does it in ways contrary to our expectations…like twist about. Einstein couldn’t get this idea to work and its largely been forgotten. But struggles with cosmology have forced a reexamination of the ideas behind teleparallel gravity (Sutter 47).

Ironically, it was the inherent mysteries of quantum mechanics that got Einstein started on his alternate theory. Quantum indeterminacy plagued him for the rest of his life because he couldn’t accept that probability was at the heart of the theory. Instead, he felt that the chance properties that the theory put to realty was instead hinting at something missing rather than reflecting actual behavior. So he delved into some mathematics to explore his ideas (Ibid).

Bending space can be done in two separate ways. Relativity talks about curving space very well, bending it depending on the behavior at the site. But spacetime can also be twisted, and through this Einstein wanted to try and merge electromagnetic theory with relativity. His new idea was that gravity or EM fields could cause spacetime to twist, with how this action was occurring giving us certain properties of either gravity or EM effects. He published what he could find in 1928 but it really didn’t account for EM well and in fact just gave the same results as standard relativity did (Ibid).

Teleparallel gravity, named for the initial approach of examining effects on parallel lines, didn’t get much attention after this. Yet as the years have passes, quantum mechanics and general relativity do not show any signs of converging into one theory without some kind of reconceptualizing of one, if not both. Recent problems like dark energy and the Hubble tension were found, indicating issues with the expansion of the Universe. Maybe gravity isn’t what we think it is and through some kind of rework could eliminate the need for dark energy (47-8).

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Many efforts have tried to adjust general relativity to take other factors besides mass and energy into account, but gravity waves strike most of them down. The alternatives suggest gravity waves would move at less than the speed of light, but we haven’t seen that. The only option that agrees with relativity’s gravity wave speed? Teleparallel gravity, which in 1976 was shown mathematically to predict curvature the same, just described differently (48).

Testing Teleparallel Gravity

Teleparallel gravity offers the benefit of being easy to adjust for new terms, allowing for tests on how things besides mass and energy can impact gravity. In fact, extreme environments like black holes and supernovas could offer tests to see how teleparallel does in comparison with relativity. 2018 saw a promising development when Rafael Nunes (National Institute for Space Research in Sao Paulo) reexamined the Hubble Tension using one version of the alternate theory. Using the teleparallel theory, the Hubble tension was erased, with the cosmic microwave data ultimately agreeing with supernova measurements. Other versions of teleparallel gravity help fix dark energy, dark matter, and inflation but no one version can account for all (Ibid).

It's all just the start of the journey, so let's see where this takes us...

Works Cited

Delta Institute for Theoretical Physics. “New theory of gravity might explain dark matter.” Science X Network, 08 Nov. 2016. Web. 06 Mar. 2019.

Lee, Chris. "Diving Seep into the World of Emergent Gravity." Kalmbach Publishing Co., 22 May 2017. Web. 10 Nov. 2017.

Kruger, Tyler. "The Case Against Dark Matter. Kalmbach Publishing Co., 07 May 2018. Web. 10 Aug. 2018.

Maartens, Roy. “Dark Energy and Dark Gravity.” Doi:10.1088/1742-6596/68/1/012046.

Mosher, Dave. “Astronomers found evidence for a ‘dark’ gravitational force that might fix Einstein’s most famous theory.” Insider, Inc., 14 Dec. 2016. Web. 06 Mar. 2019.

O’Connell, Cathal. “New theory of ‘dark gravity’ passes first test, but Einstein’s still on top.” Cosmos. Web. 05 Mar. 2019.

Peach, Alexander. “Emergent Dark Gravity from (Non)Holographic Screens.” arXiv:1806.1019v1.

Skibba, Ramin. "Researchers Check Space-Time to see if It's Made of Quantum Bits." Quanta, 21 Jun. 2017. Web. 27 Sept. 2018.

Sutter, Paul M. “Gravity with a twist.” New Scientist 16 Oct. 2021. Print. 47-8.

Wolchover, Natalie. "The Case Against Dark Matter." Quanta, 29 Nov. 2016. Web. 27 Sept. 2018.

© 2020 Leonard Kelley

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