entropic gravity


Luca Mazzucato


An interview with Erik Verlinde. The Dutch physicist, now at the Institute for Theoretical Physics, University of Amsterdam, was recently awarded the $2.5 million Spinoza Prize for his recent idea on entropic gravity. We sat down with him after a colloquium at RenTec, the hedge fund based in Setauket.

A new revolutionary proposal for the theory of quantum gravity, motivated by the holographic principle, links gravity to entropy and information theory. And it shows a new direction for string theory, departing from a meeting at a hedge fund headquarter…

Every so often, the doors of the Setauket based hedge fund Renaissance Technology LLC (whose founder made the SCGP happen) open to host a scientific colloquium, featuring the most recent developments in physics, biology, and other disciplines. This might sound slightly odd at first: what does a hedge fund, temple of the financial enterpreneurship, have in common with advance science?

The mistery is easily unveiled. Many RenTec’s employees are Maths or Physics PhD’s, that often left academy to join the financial company. Some of them were at the very top of their research field back in their academic days. Once a month, they still enjoy checking what is hot in the scientific community and organize a seminar at their facility. This time they invited the famous dutch physicist Erik Verlinde. We could not help but ask him about his recent breakthroughs and what happened at the hedge fund.

What was it like to give a seminar in a hedge fund?

It was really fun. Before the seminar I was kept the whole afternoon, meeting and discussing with many of the employee’s. Many of them are former physicists, even some string theorists that I know quite well. They were really interested in my work, and asked good and clever questions. I also again met an old friend of mine with whom I spent some years at the Institute for Advanced Study and who now works for this hedge fund. Finally, it is also nice that they can afford to pay an attractive honorarium for giving a seminar.

Let us get to your recent work. For almost a century, the holy grail of theoretical physics has been the search for a unified theory of all interactions. In your recent paper, you suggest a completely different direction. What is your new take on gravity?

Gravity is usually regarded as one of the four fundamental forces. And indeed, most physicist believe that its fundamental description is found by unifying quantum mechanics with Einstein’s theory of general relativity. Yet, there are many indications that gravity is not a fundamental force, but is the result of a microscopic dynamics that takes place at a much more elemental level. Matter but even space and time are made out of elementary building blocks (“degrees of freedom”) that obey microscopic rules that do not contain gravity. Most of these degrees of freedom and their rules are invisible to us. So we only see the net effect of this microscopic dynamics, and this is how gravity arises. It is only the net resulting force.

A good example is the motion of gas in a room. Microscopically it is the consequence of the motion and collisions between individual molecules. But at macroscopic scale it is much more practical to describe the motion of the gas in terms of pressure and temperature. These quantities do not exist at a microscopic level, but are defined as averages in terms of the motion of the molecules. Gravity is like that.

An even better analogy is osmosis. Suppose one separates a mixture of two kinds of gas molecules by a membrane, that only allows one kind of molecule to pass. If the concentration of the other molecule is higher on one side then the other, there will be a net force. One can calculate that force using statistics. In my paper I show that Newton’s law of gravity can be derived in a very similar way. It is the consequence of a change in probability when two massive objects are being displaced with respect to each other.

Is there any compelling evidence in favor of your entropic explanation?

The evidence is mostly theoretical. If one studies the equations of gravity near black holes, one clearly sees the analogy with the laws of thermodynamics that describe the motion of a gas. But there are also results in string theory that, if one looks at them in the right way, clearly show that gravity can be derived by averaging over microscopic degrees of freedom. So I have very little doubt that my idea is correct. But I do not have a complete theory yet.

Can you make any predictions to test your ideas?

Before trying to make predictions it is necessary first to further develop the theory. Predictions will have to come from deviations from Einstein’s theory of general relativity. I am hopeful that such deviations will indeed be found. Especially in the context of cosmology. For instance I believe these ideas may shed important new light on the nature of dark energy and dark matter. If one succeeds in understanding these cosmological mysteries in a new way it can very well lead to testable predictions.

You are suggesting that physicists have been pursuing the wrong track so far, in the quest for unification… Why do you think that mainstream physics is headed in the wrong direction?

This has to do with the historical development. At the beginning of this century we only knew about two forces: gravity and electromagnetism. Einstein’s theory of gravity appeared, and it has been dominating our thinking about gravity ever since. But after the discovery of the weak and strong nuclear forces, and the development of the standard model, people tried to unify this with Einstein’s theory of gravity. One assumed that this should be done using the same paradigm.

What has been ignored for too long are all the signs that gravity is not a fundamental force. It’s equations look and smell like thermodynamics and hydrodynamics. If one does not draw the only and most obvious conclusion from this, namely that gravity is emergent, than indeed one keeps going in the wrong direction. That doesn’t mean that the physics one is doing is wrong: only the direction is wrong. One should take a different starting point: one has to try and understand where gravity comes from, instead of assuming its presence and simply describe it.

Over the last decade the mainstream physics community has mostly been busy with developing tools for doing calculations. But the theoretical questions that have to do with gravity also need developments at a more conceptual level. This kind of thinking has been ignored for too long.

You have been a leading figure in the theoretical physics community for many years. Based on your experience do you think string theory is going to be useful to explore the entropic nature of gravity?

Yes, my idea arises from string theory. In fact, everything I know about string theory is consistent with my idea. All I have done is look at the general lessons that string theory is teaching us, and extracted the essence and most universal statement from it. Currently I am using tools from string theory to make my idea more precise and concrete.

But I do believe that to further develop string theory one should change direction: one should try to understand the basic laws, even those of string theory, starting from first principles. Assuming that the world is made out of strings is not the right starting point. It is much nicer if we can understand where strings, if they exist, come from. I am convinced that string theory, as we know it now, is itself an effective theory. It emerges from an underlying much more general formulation. We have already seen many hints in string theory that this is the case. One should take those hints seriously.

Now some speculations. Do you believe that there is such a thing as a theory of everything, or a fundamental theory of nature? Is there any simple principle that will be at the core of such deep understanding?

I believe that Nature does have microscopic building blocks and microscopic rules. But I think that we as human beings will never be able to fully discover those, let alone grasp what all the microscopic rules are. There is simply a limit to what we can understand. Believing that we can build the final theory of everything sound likes hubris to me.

But that does not mean that we can not understand the world around us. The point of view we should take is that we try to derive our effective laws of physics from first principles, using only very general properties of a possible underlying theory. This is exactly how one works in statistical physics: the laws of thermodynamics can be derived from only a few very general assumptions. In this way one discovers universal laws that apply to many situations. I believe our current laws of physics can be derived in such a universal way, from a very general starting point.

Is this underlying theory going to look anything like the physics we know today? Are the current theoretical tools inadequate?

I think we already have many tools in place, but there are also many new concepts that need to be developed. In particular, we should change our views on the nature of space and time. Space and time should not be part of the basic and general underlying theory. They should arise as an effective description at a more macroscopic scale.

The starting point we have to choose will therefore be much more abstract than what we have been using up to know. It is likely that we should develop new mathematical tools as well. Quantum mechanics may be part of the underlying theory, but gravity and general relativity should be completely seen as “emergent”. This means that gravity only appears after we also introduced the notions of space and time.