# Are space and time emergent or fundamental

## The atoms of space-time

The field equations of gravity have the same status as the equations of elasticity or fluid dynamics. ”This sentence from a scientific review article a few months ago may not sound particularly exciting to laypeople, perhaps even cryptic. But it contains explosives that can literally tear apart the physical notions of space, time and gravity as well as the foundations of the universe. Not practical, of course, but in theory. And that would be brutal and revolutionary enough.

One can read this sentence as a hypothesis. But for his author it is more - in a sense the quintessence of twelve years of research. And this author is not an extravagant esoteric, but a multiple award-winning physics professor at the Inter-University Center for Astronomy and Astrophysics in Pune, West India, former President of the Cosmology Commission of the International Astronomical Union and an expert in general relativity and cosmology with a great reputation: Thanu Padmanabhan.

Talent and non-conformism were, as it were, placed in the Indian's scientific cradle: at the age of 20, the 57-year-old published his first research article on a topic of general relativity. A little later he did his doctorate with Jayant Narlikar, who had written his dissertation in the 1960s with the famous British astrophysicist Fred Hoyle and used him to research cosmological models without the big bang, which he is still doing.

### The whole and its parts

Like Narlikar, Padmanabhan also attacks ingrained ideas - but without maneuvering himself into an outsider position. “We need a fundamental revision in the consideration of gravity,” he says. "Gravity could just be an emergent phenomenon."

In physics, “emergent” means system properties that can in principle be traced back to the components and interactions of the system, but in practice are recorded on a higher level of description with an effective theory, not a fundamental one.

One such emergent phenomenon is the property of water to be liquid under certain pressure and temperature conditions and solid or gaseous under others. This cannot be seen in a single H2O molecule, although it can be theoretically deduced from a precise knowledge of its properties and interactions. In this respect, the “whole” is more than its parts.

Other examples of emergence are elasticity and gas dynamics. For this purpose, physicists have found formulas that are used, for example, to build bridges or describe the movement of air on an airplane wing. These long-standing equations work well. But they don't point to the deeper reality: the molecules and atoms. To describe them, a more fundamental theory is necessary, the quantum theory.

### "Superficial" theory of relativity

Padmanabhan sees parallels here with the general theory of relativity. He does not consider this to be fundamental either, but merely an effective description, as physicists say. Accordingly, the force of gravity would emerge - and space-time itself. That would have drastic consequences for the long sought-after theory of quantum gravity, sometimes also called the “world formula”, a little exaggerated.

"If the emergence concept is correct, then most previous attempts to quantize Einstein's equation have been in the wrong direction - similar to trying to find atomic physics by quantizing the laws of elasticity," says Padmanabhan. "Variables such as metrics and curvature in the description of spacetime in relativity theory are analogous to density, velocity and so on in fluid dynamics, and they have no meaning on the microscopic level of description." to reveal the microscopic structure of spacetime, how quantizing the density and velocity of a liquid helps understand molecular dynamics. "

That is a radical view. Because it follows that space-time itself consists of smaller units and gravity is not a fundamental force, but a derived quantity - ultimately an illusion. For the common sense, this is an almost grotesque conclusion. After all, everyone feels the gravitational pull of the earth - especially in the early morning when the alarm goes off. But the idea is actually not new. Because within the framework of the theory of relativity, gravity is not described as a force, but as a geometric property of spacetime.

"Einstein himself taught us that there is no such thing as gravity," says Padmanabhan. “Matter bends space-time, which appears to us as a force. Hence, all that needs to be explained is how the relationship between matter and space-time curvature can be understood in the thermodynamic framework. "

The basic idea of a relationship between gravity, thermodynamics and "granular" spacetime has been around for a while. In an essay only two pages long, the Soviet physicist and later dissident Andrei Sakharov had already speculated about it in 1967. In the 1980s, Kip Thorne and Thibault Damour came to similar conclusions in a different way, discovering an analogy between the "surface" properties of black holes and hydrodynamics. In 1995, Ted Jacobson caused a sensation when he proposed a thermodynamic derivation of general relativity. And since 2009, for example, Erik Verlinde from the University of Amsterdam has been arguing from the perspective of string theory that gravity is an “entropic force”, as he puts it - an emergent phenomenon. However, Verlinde's model has been heavily criticized for purely mathematical reasons, for example by Matt Visser of Wellington University in New Zealand, and Padmanabhan considers it "algebraically inadequate".

### Hot horizons

Thanu Padmanabhan has developed Jacobson's approach since 2002. The starting point was the knowledge of Bill Unruh, Paul Davies, Jacob Bekenstein, Stephen Hawking and other physicists on the thermodynamics of horizons in the theory of relativity. Such horizons arise at the outer borders of black holes, but also with accelerated movements. Unruh and Davies calculated independently of one another that a fictitious observer could register a temperature of the room that is proportional to its acceleration (see box on the right “The temperature of the vacuum”). In practice it is immeasurably small: the value of the acceleration due to gravity on earth (9.8 meters per second squared) would only correspond to 10–46 Kelvin in a vacuum. But it is a real quantum effect that could, in principle, slightly heat a glass of water.

"If a space-time horizon moves by a small amount, it is analogous to the change in the volume of a gas," summarizes Padmanabhan his discovery. "Einstein's equations, which describe spacetime, then correspond exactly to the first law of thermodynamics." This law of conservation of energy links changes in mechanical work, internal energy and entropy, which is a physical measure of the disorder of a system. The pressure of a gas in a vessel can do work when it moves a piston - for example in an internal combustion engine. In addition, energy can be exchanged with the environment, for example when heat “flows”, which changes the entropy of the system.

Space-time horizons, such as the imaginary surface of a black hole, also have entropy and therefore a temperature. The larger the horizon, the greater the entropy - because it hides the "disorder" or the amount of information behind it.

### The density of spacetime

Therefore, according to Padmanabhan, a logic applies here that Ludwig Boltzmann had already successfully applied in thermodynamics or in the statistical mechanics he co-founded: If something can be heated, it has a microstructure. The Viennese physicist interpreted temperature as the random movement of discrete microscopic objects - molecules or atoms. For example, the faster you whiz around in a gas, the hotter it is. It is only because of this microstructure that a system can store energy and exchange it with its environment. Entropy describes the microscopic information content of such a system.

"There must be clearly microscopic degrees of freedom in space-time that are responsible for its thermal behavior," transfers Padmanabhan Boltzmann's logic. Because the balance-wheel effect means, so to speak, a warming of space-time. “The connection between thermodynamics and gravity is not a mathematical curiosity, but a physical reality. An adequate description of gravity should start from the entropy density of spacetime or, what is equivalent, the density of the atoms of spacetime. "

Padmanabhan is even convinced that the density of microscopic degrees of freedom can be estimated from the macroscopic dynamics. This is also analogous to thermodynamics - because at a certain temperature, each degree of freedom stores an amount of energy proportional to the temperature. As early as the 19th century, this made it possible to estimate the number of particles in a certain amount of gas - the so-called Avogradro number. Admittedly, nobody knew what this meant at the time. "We are in a similar situation with the atoms of space-time," comments Padmanabhan. Only with a quantum gravity theory could this more fundamental reality be described directly.

According to Padmanabhan, gravity can be explained thermodynamically, as it were, depending on the entropy density and thus the number of microscopic degrees of freedom - similar to how a gas can be characterized by the macroscopic variables of volume, pressure and temperature and the kinetic energy of the molecules can be deduced from this.

If a thermodynamic system is in equilibrium, then its entropy is maximal. The same applies to gravitational systems, as Padmanabhan and Aseem Paranjape have shown: "A space-time fulfills Einstein's equations because the atoms of space-time maximize entropy - just as a gas obeys the laws of gas because its atoms maximize entropy." Thermodynamics is therefore more than an analogy, the two physicists conclude: It enables a look into a deeper reality - just as Boltzmann was able to infer the existence of atoms with his statistical thermodynamics in the 19th century, although this was unobservable for the technology of the time were small.

“Instead of talking about space-time atoms, one can also talk about physical degrees of freedom. Both expressions are mathematically equivalent if there is a pre-defined space - and if not, the degrees of freedom description still works, ”says Padmanabhan. "The number of degrees of freedom can be calculated - within the framework of the theory of relativity, but also in alternative theories of gravity."

As assumed by other approaches to a theory of quantum gravity, this granularity of spacetime is on the Planck scale: in the order of magnitude of 10–33 centimeters and 10–4 3 seconds. This is so tiny that spacetime appears as a unit for everyday viewing, but also for the most powerful particle accelerators in the world. This can be compared to a photo that looks homogeneous when viewed from a distance - but if you look closely, you will see that it is composed of individual pixels.

### Quantum Gravity and Dark Energy

Padmanabhan is convinced: Because the “atoms of space-time” have not yet been identified and described with a new quantum theory, decades of attempts to quantize gravity were doomed to failure from the outset. With the current understanding, he still considers it difficult to make statements about the density of spacetime atoms or their changes. However, in his current work, the physicist has presented ideas on how the emergence of spacetime can be understood in the context of the expansion of space.

Moreover, the mysterious dark energy that is currently accelerating this expansion can possibly also be explained in the context of Padmanabhan's approach. That this dark energy - for example Einstein's cosmological constant - exists but is only very small is one of the greatest puzzles in physics. If Padmanabhan's ideas are correct, a small cosmological constant almost inevitably turns out to be a relic of quantum gravity. With a theoretically sharpened view, one could look at both the realm of the very smallest and the dynamics of the universe as a whole. •

### The temperature of the vacuum

The discovery of connections between apparently widely spaced areas of physics has proven time and again to be the key to a deeper understanding of the world. Therefore, Thanu Padmanabhan's interpretation of the field equations of gravitation as equilibrium conditions of space-time is very promising. At first glance, the theory of relativity appears to be far removed from thermodynamics and quantum theory. The classical field equations of gravity do not contain Planck’s quantum of action h, which is essential in quantum theory. The balance wheel temperature T, which an observer accelerated in a quantum vacuum could in principle measure, is based on h. It is T = ha / 2pckB, where kB denotes the Boltzmann constant, a the local acceleration of the observer and c the speed of light. (The Hawking temperature of a black hole is described with the same formula, only here a means the acceleration due to gravity at the event horizon.) Because T depends on h and the entropy of a horizon on the reciprocal value 1 / h, this quantity is canceled out. This is the only reason why the relationship between gravitation and thermodynamics can be established in the first place.

### Higher dimensions

The analogy between thermodynamics and gravity applies not only to the general theory of relativity, in which entropy is proportional to the area of a horizon, but also to other theories of gravity, such as higher-dimensional ones. (The temperature of the horizon is independent of the respective theory of gravity, the entropy is not.) Einstein's field equations can be generalized to more than three spatial dimensions. The British physicist David Lovelock proved this in 1971, building on the work of the Hungarian physicist Cornelius Lanczos in the 1930s. "This generalizability to Lanczos-Lovelock theories suggests that the idea of spacetime atoms meets something physically real," says Thanu Padmanabhan. For the same reason, however, he is skeptical that there is a connection to loop quantum gravity, which also assumes that space-time is made up of more fundamental units. Because it only works in three spatial dimensions. Padmanabhan has more sympathy for the higher-dimensional string theory with its additional spatial dimensions. Especially since it also describes a connection between a “surface” - like a horizon - and a space around or inside (“holographic principle”), as it also plays a role in Padmanabhan's approach, but not in loop quantum gravity.

### Compact

· The equations of general relativity are strangely similar to those for energy, entropy and work.

· This indicates that space and time are not fundamental, but are built up from smaller "components" - perhaps a guide to the world formula.

### The fire behind Einstein's equations

The laws of thermodynamics agree amazingly with those of general relativity: energy, entropy and work can be described in a similar way to gravity. Gravity would therefore be a derived quantity like temperature. Because there is a deep thermodynamic connection between horizons in the theory of relativity - for example the outer "limit" of a black hole - and the volume of a gas at a certain pressure. If this is enlarged, its entropy density increases - just like a black hole, the "surface" of which grows proportionally to its entropy.

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