An interview with Erik Verlinde, who argues that dark matter is an illusion caused by an incomplete understanding of gravity.

### What is wrong with the theory of gravity we have?

The current description of gravity in terms of general relativity has various shortcomings. Perhaps the most important is that we cannot simply apply Einstein’s laws at a subatomic level without generating notorious infinities. There are also conceptual puzzles related to the physics of black holes that indicate that general relativity is not the final answer to gravity, and important lessons learnt from string theory suggesting gravity is emergent. Besides these theoretical issues, there is also a strong experimental motivation to rethink our understanding of gravity. The first is the observation that our universe is experiencing accelerated expansion, suggesting it contains an enormous amount of additional energy. The second is dark matter: additional gravitating but non-luminous mass that explains anomalous galaxy dynamics. Together these entities account for 95 per cent of all the energy in the universe.

### Isn’t the evidence for dark matter overwhelming?

It depends who you ask. There is a lot of evidence that general relativity works very well at length scales that are long compared to the Planck scale, but when we apply general relativity at galactic and cosmological scales we see deviations. Most physicists regard this as evidence that there exists an additional form of invisible matter that gravitates in the same way as normal matter, but this assumes that gravity itself is still described by general relativity. Furthermore, although the most direct evidence for the existence of dark matter comes from the study of galaxies and clusters, not all astronomers are convinced that what they observe is due to particle dark matter – for example, there appears to be a strong correlation between the amount of ordinary baryonic matter and galactic rotation velocities that is hard to explain with particle dark matter. On the other hand, the physicists who are carrying out numerical work on particle dark matter are trying to explain these correlations by including complicated baryonic feedback mechanisms and tweaking the parameters that go into their models. Finally, there is a large community of experimental physicists who simply take the evidence for dark matter as a given.

### Is your theory a modification of general relativity, or a rewrite?

The aim of emergent gravity is to derive the equations that govern gravity from a microscopic quantum, while using ingredients from quantum-information theory. One of the main ideas is that different parts of space–time are glued together via quantum entanglement. This is due to van Raamsdonk and has been extended and popularised by Maldacena and Susskind with the slogan “EPR = ER”, where EPR is a reference to Einstein–Podolsky–Rosen and ER refers to the Einstein–Rosen bridge: a “wormhole” that connects the two parts of the black-hole geometry on opposite sides of the horizon. These ideas are being developed by many theorists, in particular in the context of the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. The goal is then to derive the Einstein equations from this microscopic-quantum perspective. The first step in this programme was already made before my work, but until now most results were derived for AdS space, which describes a universe with a negative cosmological constant and therefore differs from our own. In my recent paper [arXiv:1611.02269] I extended these ideas to de Sitter space, which contains a positive dark energy and has a cosmological horizon. My insight has been that, due to the presence of positive dark energy, the derivation of the Einstein equations breaks down precisely in the circumstances where we observe the effects of “dark matter”.

### How did the idea emerge?

The idea of emergent gravity from thermodynamics has been lingering around since the discovery by Hawking and Bekenstein of black-hole entropy and the laws of black-hole thermodynamics in the 1970s. Ted Jacobson made an important step in 1996 by deriving the Einstein equations from assuming the Bekenstein–Hawking formula, which expresses the microscopic entropy in terms of the area of the horizon measured in Planck units. In my 2010 paper [arXiv:1001.0785] I clarified the origin of the inertia force and its relation to the microscopic entropy in space, assuming that this is given by the area of an artificial horizon. After this work I started thinking about cosmology, and learnt about the observations that indicate a close connection between the acceleration scale in galaxies and the acceleration at the cosmological horizon, which is determined by the Hubble parameter. I immediately realised that this implied a relation between the observed phenomena associated with dark matter and the presence of dark energy.

### Your paper is 50 pages long. Can you summarise it here?

The idea is that gravity emerges by applying an analogue of the laws of thermodynamics to the entanglement entropy in the vacuum. Just like the normal laws of thermodynamics can be understood from the statistical treatment of microscopic molecules, gravity can be derived from the microscopic units that make up space–time. These “space–time molecules” are units of quantum information (qubits) that are entangled with each other, with the amount of entanglement measured by the entanglement entropy. I realised that in a universe with a positive dark energy, there is a contribution to the entanglement entropy that grows in proportion to area. This leads to an additional force on top of the usual gravity law, because the dark energy “pushes back” like an elastic medium and results in the phenomena that we currently attribute to dark matter. In short, the laws of gravity differ in the low-acceleration regime that occurs in galaxies and other cosmological structures.

### How did the community react to the paper?

Submitting work that goes against a widely supported theory requires some courage, and the fact that I have already demonstrated serious work in string theory helped. Nevertheless, I do experience some resistance – mainly from researchers who have been involved in particle dark-matter research. Some string theorists find my work interesting and exciting, but most of them take a “wait and see” attitude. I am dealing with a number of different communities with different attitudes and scientific backgrounds. A lot of it is driven by sociology and past investments.

### How often do you work on the idea?

Emergent gravity from quantum entanglement is now an active field worldwide, and I have worked on the idea for a number of years. I mostly work in the evening for around three hours and perhaps one hour in the morning. I also discuss these ideas with my PhD students, colleagues and visitors. In the Netherlands we have quite a large community working on gravity and quantum entanglement, and recently we received a grant together with theorists from the universities of Groningen, Leiden, Utrecht and Amsterdam, to work on this topic.

### Within a month of your paper, Brouwer *et al.* published results supporting your idea. How significant is this?

My theory predicts that the gravitational force due to a centralised mass exhibits a certain scaling relation. This relation was already known to hold for galaxy rotation curves, but these can only be measured up to distances of about 100 kilo-parsec because there are no visible stars beyond this distance. Brouwer and her collaborators used weak gravitational lensing to determine the gravitational force due to a massive galaxy up to distances of one mega-parsec and confirmed that the same relation still holds. Particle dark-matter models can also explain these observations, but they do so by adjusting a free parameter to fit the data. My prediction has no free parameters and hence I find this more convincing, but more observations are needed before definite conclusions can be drawn.

### Is there a single result that would rule your theory in or out?

If a dark-matter particle would be discovered that possesses all the properties to explain all the observations, then my idea would be proven to be false. Personally I am convinced this will not happen, although I am still developing the theory further to be able to address important dynamical situations such as the Bullet Cluster (see “How dark matter became a particle”) and the acoustic oscillations that explain the power spectrum of the cosmic microwave background. One of the problems is that particle dark-matter models are so flexible and can therefore easily be made consistent with the data. By improving and extending the observations of gravitational phenomena that are currently attributed to dark matter, we can make better comparisons with the theory. I am hopeful that within the next decade the precision of the observations will have improved and the theory will be developed to a level that decisive tests can be performed.

### How would emergent gravity affect the rest of physics?

Our perspective on the building blocks of nature would change drastically. We will no longer think in terms of elementary particles and fundamental forces, but units of quantum information. Hence, the gauge forces responsible for the electroweak and strong interactions will also be understood as being emergent, and this is the way that the forces of nature will become unified. In this sense, all of our current laws of nature will be seen as emergent.