Holography as a metaphor for the emergence of spacetime

Spacetime can expand, contract and be created. Matter can change and be created. The theoretical conception of these events can be explained by the String Theory, the only one able to unify the four forces of matter (electromagnetism, weak and strong interactions, and gravity) in microscopic conditions.

Physicist Tadashi Takanayagi, from the Kyoto University's Yukawa Institute for Theoretical Physics (YITP), said that a good analysis model for these conceptions are black holes, a metaphor for the analyses of 3D-realities from the observable information on 2D-surfaces, with the help of the Holographic Principle. The professor spoke during the Physics Workshop of the second phase of the Intercontinental Academia (ICA), on March 9.

Theoretical physicist Tadashi Takanayagi

He explained that the Standard Model, a traditional approach of particle physics, works perfectly for three forces of matter: electromagnetism, strong interaction (nuclear power) and weak interaction (beta decay, neutrino). But it does not describe the action of the fourth force (gravity). "In the microscopic field, gravity behaves completely different from the other three forces."

This difficulty led to the String Theory, according to Takayanagi. As the strings rapidly vibrate, they give rise to heavy particles. As they vibrate slowly, they produce light particles. "With this approach, the theories on matter are consistent with the unification of the four forces: the open string describes electromagnetism, and the strong and weak interactions; simultaneously, the same string describes gravity when closed."

To check whether the String Theory is true, it is necessary to find a phenomenon that can only be explained by it, Takanayagi said. Some aspects of black holes are good cases for research, especially from the microscopic point of view: "We want to use a theoretical microscope to enlarge a black hole and see what is inside."

He said that this concern eventually resulted in the development of the Holographic Principle, "one of the most important advances in this theoretical field in the last 20 years."

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The concept of spacetime is defined by a four-dimensional coordinate system (x, y, and z for space, and t for time). The Einstein's General Theory of Relativity considers this concept. "The question is whether this description system of spacetime is real and if it is the best framework for understanding the universe."

Perhaps the analysis of very microscopic structures indicates that space is emerging, and maybe even time is emerging, warns Takanayagi. For him, this kind of consideration leads to the idea that spacetime is equivalent to the information of matter.

Once that massive objects form a black hole, the information in it is not accessible to outsiders. The amount of non-accessible information is called entropy, explains the physicist, adding that the String Theory can solve the problem by playing the role of a microscope to extract information from the black hole. "Among the massive particles there are open strings and one can extract their behavior information. This makes it possible to explain the entropy of the black hole."

Takayanagi showed the formula that defines the amount of entropy of a black hole, proposed by Jacob Bekenstein and Steven Hawking, and stressed that one of its terms, represented by the letter A, corresponds to the surface area of the black hole.

"This is not common. If we observe any matter agglomerate (gas, liquid or solid), entropy is proportional to the volume, not to the surface. But the information seems to be on the surface of a black hole. This is similar to what happens in an hologram, where a 3D-image is encoded on a 2D-surface, but the mechanism is totally different, just an analogy. "

Takayanagi said that physicists Gerard 't Hooft and Leonard Susskind have conjectured that the gravitational theories are equivalent to microscopic theories of "a certain matter" on its border.

According to him, this idea is quite popular and intuitive, but the String Theory proposes something beyond that. He commented that in 1997 Juan Maldacena proposed that the Holographic Principle must be understood as a Gauge / Gravity Duality in the String Theory, meaning that there is an equivalence between gravity (closed strings) and matter (open strings).

At the same time, the Holographic Principle states that spaces can emerge from matter in gravity. Gravity would function as a series of sieves with different frame sizes, allowing the passage of information according to the granulation accepted by each sieve, said Takanayagi.

Toy model

He said that physicists use a toy model to express the hidden information in a black hole: a white dot or a black dot (similar to 0 or 1 in computers). The information unit based on these dots (or "coins") is called one qubit.

For the whole system it must be considered that possibly both the white dot and the black dot are inside and outside the black hole, with a 50% probability for each occurrence. "It follows that if within the black hole there is a white dot then out of it there will always be a white dot (and vice versa). If we can not look inside the black hole, then we can not know the outside of it (hidden information, for example)."

This phenomenon is called quantum entanglement and it is said that "the interior and the exterior are entangled." The amount of "coins" (or qubits) is called entropy of the entanglement (Sent), which measures the amount of hidden information.

Thanks to holography, it appears that the entropy of the black hole is equal to the entropy of the entanglement. In fact, Takanayagi adds, the entropy of the entanglement is equal to the area of any surface, even without any black hole. The formula that Takanayagi proposed with Shinsei Ryu in 2006 implies that spacetime consists of qubits of information.

The Holographic Principle states that the spaces in gravity emerge from matter (or information). In the String Theory, the holography allows us to say that the gravity in the 3D-universe is equal to the matter in the 2D- spacetime. In the gravity of the 3D-Universe spacetime can expand, contract and even be created. Considering the matter in the 2D-spacetime, spacetime is not dynamic, but matter can change and be created.