Living in a hologram

Most of us have watched a holographic photograph that shows 3D image printed on a flat surface. Imagine the whole cosmos being painted on a distant celestial horizon, the three space dimensions we experience are illusion and rather hologram encoded in two dimensions. This sounds crazy but actually there are some clues in the nature that indicates the universe being a hologram.

The laws of relativity forbid anything that went inside the event horizon of a black hole from coming out again. In the simplest case, the horizon is a sphere, whose surface area is larger for more massive black holes. If a piece of matter drops inside its energy is added to mass of black hole and energy conservation is upheld. Another fundamental law, the second law of thermodynamics, appears to be violated. This law summarizes the familiar observation that most processes in nature are irreversible: a teacup falls from the table and shatters, but it never gets spontaneously fixed again. In the other words, entropy of a closed system always increases. If one fixes the teacup its entropy gets lower but then the system is not closed anymore and external energy and notably information is needed to do it. If a teacup drops to a black hole one can think its entropy vanish. Actually, the extreme gravity would crush it first to the smallest know pieces as a particle soup while all information of its original form is lost. In the other words, its entropy gets to maximum. In 1971, Stephen Hawking theorized that in a black hole merger the area of the new event horizon should not be smaller than the total horizon area of its parent black holes. In 1972, Jacob Bekenstein proposed that entropy of a black hole is proportional to the area of the event horizon. The gravitational wave measurements from the black hole merger proved Hawking's theory 50 years later and confirms that the generalized second law of thermodynamics holds in black holes. To comply with the laws of thermodynamics a black hole has Bekenstein-Hawking entropy; precisely one quarter of the event horizon's area measured in Planck areas. As a consequence, there's a bound on the maximum information density that is proportional to the area, not to the volume.

Gerard t Hooft in 1993 and further Leonard Susskind in 1995, applied black hole thermodynamics for general holographic principle of nature; the maximum possible entropy depends on the boundary area instead of the volume of space. The real universe is a 4-D system: it has volume and extends in time. If the physics of our universe is holographic, there would be an alternative set of physical laws, operating on a 3-D boundary of spacetime somewhere, that would be equivalent to our known 4-D physics. But what surface should we use as the boundary of the universe? One model is antide Sitter space (AdS) that possesses a boundary, which is located at infinity. It is the de Sitter universe derived from the general relativity but the repulsive cosmological constant is replaced by an attractive one. However, the observed universe is expanding, not contracting, and the most cosmologist think to be infinite without boundary. Holographic principle derived from black holes just does not seem to fit for the whole cosmos. 

The problems with the AdS space were circumvented by the AdS/CFT correspondence theory introduced by Juan Maldacena in 1998. The conformal field theory (CFT) is a type of quantum field theory, which gives rise to gravity without the curves of AdS space. The quantum gravity theories appearing in the AdS/CFT correspondence are typically obtained from string theories by a process known as compactification. This produces a theory in which spacetime has effectively a lower number of dimensions and the extra dimensions are "curled up" into tiny circles. To illustrate this, a garden hose looks one-dimensional far away but a closer look reveals it to be two-dimensional. In 2022, theoretical physicists of Kyoto University published novel approach that uses the holographic principle to describe the expanding universe in de Sitter space. Their model, which excludes gravity, describes a two-dimensional framework approximating the expansion of our three-dimensional universe. The results produced from the computational model demonstrated that basic quantities agreed between general relativity and CFT. The celestial CFT would be even more ambitious than the corresponding theory in AdS/CFT. Since our universe appears to be flat, it would live on a sphere of infinite radius, which breaks down concepts of space and time. As a consequence, the CFT wouldn’t depend on space and time; instead, it could explain how space and time come to be.  However, if everything is infinitely far from everything else, the meaning of locality and time becomes questionable or even meaningless.

Recent research results have given physicists hope that they’re on the right track. These results use fundamental symmetries to constrain what this celestial CFT might look like. Researchers have discovered a surprising set of mathematical relationships between these symmetries — relationships that have appeared before in certain string theories, leading some to wonder if the connection is more than coincidence. Monica Pate and Sabrina Pasterski (2021) used quantum gravitational low-energy scattering problems as the starting point to determine some of the rules the hypothetical celestial CFT must obey. They look patterns the particles make on the detector, which correspond to rules or symmetries the scattering process must obey. The symmetries demand that if you apply certain transformations to the detector, the outcome of a scattering event should remain unchanged. They discovered that the group of symmetries on the celestial sphere obeyed a thoroughly studied and well-established algebra — one that has already appeared in certain string theories and is related to the description of well-known quantum systems such as the quantum Hall effect. In 2019, Sean Cooper et.al explored the possibility that certain high-energy holographic CFT states correspond to black hole microstates with a particular structure that terminated at an end-of-the-world (ETW) brane. In string theory and other related physics theories, a brane is a dynamical object that can propagate through spacetime in accordance with quantum mechanics laws. In 2021, Stefano Antonini showed an end-of-the-world brane sitting far enough from the black hole horizon to possibly support gravity localization.

Both black hole entropy and AdS/CFT correspondence are giving clues that information of multiple dimensions can be encoded by lower dimensions. The latter states that every entity in one theory has a counterpart in the other theory, and there is a dictionary between those. The string theories, quantum gravity and general relativity all may describe the same reality with different amount of dimensions. Especially, spacetime could be given by the boundary of AdS space, which encodes all the information of the universe with maximum density further described by string theory in the smallest scale. If the spacetime itself emerges from a two-dimensional surface, the effects of gravity, dark matter, and the expansion of the universe driven by dark energy could be more like illusion. On the other hand, if time exits and the universe had its early development as described in the blog, the total entropy of the universe has increased all the time since the end of cosmic inflation. We can speculate if the size of the observable universe has been proportional to the total entropy, and the cosmological horizon encodes all the information inside it. Furthermore, the spherical area of the horizon has been as small as the entropy in the beginning. It is estimated that during the cosmic inflation the entropy was around 10¹⁵ kB and immediately after that jumped extremely to 10⁸⁸ kB. For the current universe it has only increased to 10¹⁰³ kB  and after 10²⁰ years will reach its maximum about 10¹²¹ kB. While amount of the entropy has increased it could show up as expansion of the universe. This year, Paul Gough proposed that information energy can account for the dark energy causing the accelerating universe expansion, which effectively solves the cosmological constant problem, allowing the cosmological constant to take the zero value. As the information dark energy density will eventually fall, the model predicts that the universe expansion will revert back to deceleration as was occurring prior to the present dark energy dominated epoch. This again reminds that some sort of cosmic coupling may exist.