BUBBLES OF NOTHING AND THE CREATION OF THE UNIVERSE

When we hear about the Big Bang theory, we always ask ourselves the same question: What was there before the big bang? How could our vast universe emerge from nothing? Until very recently, nothingness was merely a vague philosophical or metaphysical concept with no place in our real world. However, as has happened with many other concepts, modern physics has managed to include within the field of physics phenomena that no one thought could be addressed by science.

In this article, we'll try to understand what the concept of nothingness really means. We'll study the so-called "nothing bubbles" and see what role these bubbles may have played in the creation of our Universe. We'll also try to answer the transcendental question: Could our Universe have emerged from nothingness? Welcome to "nothingness," a "place" where neither space nor time exists!

The instability of the Kaluza-Klein vacuum

"Nothing" first appeared in modern physics in 1982 in a groundbreaking paper by Edward Witten entitled "The Instability of the Kaluza-Klein Vacuum." In this paper, Witten showed that a 4-dimensional Universe similar to our own, but with an additional hidden dimension wound into a circle, is unstable. At a given moment, the vacuum of this Universe undergoes, through quantum tunneling, a transition to another vacuum state of lower energy. This transition

it implied something incredible, the curled up extra dimension begins to "deflate": a bubble is formed inside which there is nothing, no energy, no quantum fields, not even space-time! This bubble begins to expand accelerating to almost the speed of light and turning the entire Universe into literally a huge bubble of nothing! In an intuitive way "roughly" we can consider our 4+1 dimensional Universe as a huge circular "donut" without a hole. The "donut" is (classically) stable due to the action of two opposing forces: on the one hand, curling up the extra dimension produces a positive curvature that produces an inward gravitational attraction (remember that gravity is actually curvature of space-time) and on the other hand, compacting the new dimension produces an additional scalar field called "radion" that produces a repulsive force. When the vacuum decays to the true vacuum state, this equilibrium is broken, and a topological transition occurs: a small hole appears in the donut with nothing inside, and this hole begins to expand. The donut without a hole has become a torus. The expansion of this bubble of nothingness is totally destructive: the "wall" that delimits the bubble expands at almost the speed of light.

and any particle that collides with it will be ejected back into the interior. The key question now is: How can we physically interpret this bubble of nothingness?

The first drawing represents the 4D Universe with an extra dimension wrapped around a circle. The second represents a cross-section of the cylinder: the vertical coordinate represents the extra dimension, and the horizontal coordinate represents our usual four dimensions. The third drawing represents the appearance of a bubble of nothingness: the extra dimension "deflates" at the point r=0, so that any section along the r axis includes a hole. This hole contains nothing, not even space-time.

Nothingness and the Universe with negative curvature

The universe described by Witten gives us little information about the true nature of the bubble of nothing. Recently, physicists have investigated possible universes with curled-up extra dimensions to see if the formation of a bubble of nothing was also possible. The simplest and best studied of these

Universos is the 6D Universe of the Einstein-Maxwell theory. In this Universe, the two extra dimensions are compacted into a 2-sphere and are stable due to the action of two opposing forces: the positive curvature of the sphere, which creates a gravitational force, and the new scalar fields, which produce a repulsive force. The most interesting thing about this Universe is that there is no single solution to the phase transition that leads to the bubble of nothingness. Instead, there is a whole continuous family of solutions. By studying the trend, that is, the limit to which this family of solutions tends, we can see what happens as we slowly approach the bubble of nothingness. As we approach the limit, the two-dimensional "slices" of the extra dimensions become positively curved, while the four-dimensional "slices" of the usual dimensions become negatively curved.

At the limit, the Universe undergoes a topological transition, but this transition is geometrically smooth. Now we'll try to visualize nothingness. Seen from an observer in the usual (4D) dimensions, the Universe has increasingly more negative curvature. The Universe with negative curvature is like a chair.

of riding: if we consider the central point of the saddle and gradually increase the negative curvature, the volume of the interior becomes smaller and smaller. The more we increase the curvature, the more volume is "expelled" outwards until, at the limit, we have a surface with no interior volume! A clearer way to understand this is the following: a circle in a space-time with positive curvature encloses a two-dimensional "volume" greater than the surface of the circle (the angles of a triangle measure more than 180º). A circle in a space-time with zero curvature (a plane) encloses a two-dimensional "volume" equal to that of the surface (Πr2). A circle in a negative space-time (saddle) encloses a two-dimensional "volume" smaller than that of its surface. That is, in a space-time with negative curvature, the 2-volume enclosed by a circle is smaller than the surface of the circle.

This means that as we increase the negative curvature, the volume decreases more rapidly than the surface area, so in the limit we obtain something truly counterintuitive: a finite surface with zero volume. Now we can explain what a bubble of nothing is. Physically, it's a negatively curved surface with no interior volume. That is, a surface whose interior has been emptied of all space-time dimensions.

Bubbles of Nothing and the Creation of the Universe

At this point the following transcendental question naturally arises: If the Universe can undergo a phase transition to a bubble of nothing, could the reverse process from nothing to a D-dimensional Universe occur? This process could be involved in the creation of our own Universe! Although not yet

We have a quantum theory of gravity, and we have a semiclassical formulation featuring the so-called Coleman-De Luccia (CDL) formalism. This formalism is used to calculate the probability of quantum transitions in dynamical spacetime. Consider a quantum field with the following potential:

The CDL formalism tells us that the probability of a quantum transition from A to B is: Pab=e-dS/h where dS=S(instanton)-S(A). Although it may seem incredible, this formalism tells us that the same process that mediates the transition from A to B mediates the transition from B to A, that is, in principle, the process would be the same in both

directions! In fact, the probability of the quantum transition from B to A is described by the same expression above, only in this case dS=S(instanton)-S(B). Although it may seem small, this difference is crucial: in flat spacetimes or with negative curvature, quantum systems are finite, with finite volumes and finite entropies,

However, in positively curved spacetimes, two states can have an infinite entropy difference, that is, S(B) would have an infinite value in this case. This implies something very important: The quantum transition from flat or negatively curved spacetimes to D-dimensional Universes is impossible, which leads us to

to the following conclusion: The transition from a bubble of nothingness to a Universe like ours is not possible. Although both are described by the same process, in the case of the transition from B to A the transition probability we obtain is zero. Moreover, in principle, any transition from a Universe with negative or flat curvature (AdS or Minkowski) to a Universe with positive curvature (de Sitter or dS) would be prohibited.

Conclusions

Despite this last conclusion, three very important aspects must be taken into account:

- The Bubble of Nothing teaches us how we should truly understand a region without space-time. It explains what the concept of nothing means in physics and reveals something transcendental: space-time seems to be something physical, something that can be curved, measured, and transformed (giving the impression of appearing or disappearing).

- The final conclusion failed to take into account the nonperturbative aspects that must be included in a quantum theory of gravity. There are some indications that still unknown quantum gravity effects involving a "backreaction" could make possible a quantum transition from a bubble of nothingness to an expanding Universe like ours. If this were possible, we would have an explanation for how our Universe was created from "nothingness."

There is another type of "nothing bubble" in which it would theoretically be possible to transition from a bubble of nothing to a D-dimensional Universe. These bubbles use the Vilenkin wave function in the formalism described by Linde. Unfortunately, this new type of nothing is still not well understood by physicists, and its characteristics are more difficult to analyze.

Although we haven't yet found the correct answer, these works allow us to begin to glimpse new, abstract concepts of enormous physical importance, such as the concept of "nothing." One thing seems clear: to understand why there is something rather than nothing, we must first understand what that "nothing" means.

Sources: On nothing , Instability of Kaluza-Klein vacuum