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The forbidden city

Brazilian teams collaborate in the effort to bring together the physics of the infinitely small to that of the infinitely large

NASA / SMITHSONIAN ASTROPHYSICAL OBSERVATORYSeated in front of a table covered with papers full of mathematical formulae, the physicist Élcio Abdalla picks up two ball point pens and lightly hits one against the other causing a click. “A shock at this level of energy brings about deformations in the pens that we manage to describe using the laws of Newton”, says Abdalla, referring to the formulated mathematical expressions, almost 300 years old, described by the Englishman Sir Isaac Newton in order to explain the movement of  bodies on the surface of the planet or even in space. Nevertheless, Abdalla goes on, it would be necessary to resort to concepts of a more recent area of physics – Quantum Mechanics, established at the beginning of last century – in order to justify the transformations that occur in these pens in the case where one is launched against the other with sufficiently high enough energy to break them into pieces or even melt them together. Now, if it were possible to throw one pen against the other with energy elevated to the point of the impact pulverizing the pens’ atoms to their most elementary components, the quarks, the physicists would have no idea of what would occur next. “The theories that we make use of don’t manage to forecast the behavior of material at this energy level”, says Abdalla, a professor at the Physics Institute of the University of Sao Paulo (USP).

It has been calculated that to isolate the quarks that form a particle it would be necessary to heat it up to 2 trillion degrees, a temperature billions of times higher than the interior of the Sun. For it is only at this level of energy that the more elementary components of matter manage to overcome the four forces of nature – gravity and the electromagnetic forces, weak nuclear and strong nuclear – which keep them united in the nucleus of atoms. This energy size, clearly, it not found in whatever corner of the cosmos. It should only exist under very special circumstances, such as the first instances after the Big Bang, the gigantic explosion that occurred and gave origin to the Universe and even time, some 13.7 billion years ago or even in regions close to powerful black holes, the greatest devourer of material and energy in the cosmos.

Investigating these little common situations, Abdalla and other physicists from São Paulo, Campinas, São Carlos and Belém, in  the state of Pará, have over the last five years been uncovering phenomena that help to better describe black holes and the behavior of nature itself in the surroundings of these powerful cosmic aspirators from which not even light escapes. In this manner, they are attempting to bring together the physics of the infinitely small to that of the infinitely large. Obviously there is still a long way to go before finishing this work on the construction of another form of thinking on the origin and destiny of the Universe.

According to the Big Bang theory, as one goes back in time towards the moment of this primordial explosion, one finds the Universe hotter and hotter and denser and denser, with the material concentrating itself into a space that is smaller and smaller. But starting from a determined degree of condensation, the two theories that best describe the phenomena of nature and are considered the foundation stones of modern physics – Quantum Mechanics and General Relativity, which, respectively, deal with the world of particles and of the behavior of stars, planets and galaxies – simply stop working. And until this moment the physicists have not conceived a complete and consistent theory, acceptable to the majority of them, and capable of explaining what must have occurred in a period long before the first second of the life of the cosmos, in which all of the material and energy that exists today had already been compromised into a space trillions of times smaller than the point of a needle.

“On this scale one observes the confluence of  high energy particle physics and of cosmology, because it keeps the history of the times in which today’s infinitely large had been infinitely small”, comments the physicist Luiz Carlos de Menezes, from USP, who in the book entitled, A matéria – uma aventura do espírito: fundamentos e fronteiras do conhecimento físico [Material –  an adventure of the spirit: fundamentals and frontiers of  known physics] defines physics as a game in which one attempts to identify the totality where one only sees glimpses, to search for permanence where one can only perceive transformations and to cover the greatest number of phenomena with the least number of principles.

In this special environment one measures the main physical parameters (time, mass, energy and size) on a specific scale, the so-called Planck scale –  in reference to the units of measurement defined at the beginning of the last century by the German physicist Max Planck, the inventor of quantum mechanics. Starting from three major constants of the Universe, Planck managed to establish a type of metric measurement of nature, in which the units of measurement did not vary from one country to another, as had happened with the metric system, used in Brazil, or the mile system adopted to measure distances in the Anglo-Saxon countries. Alberto Vasquez Saa, a theoretical physicist at the State University of  Campinas (Unicamp), classifies as extremes the phenomena of the Plank scale. “They’re extremely rapid, extremely energetic and if they pass through space, extremely diminutive”, he says. Only to have an idea of how extreme these phenomena are, on this scale the energy of a single atomic particle such as an electron, would correspond to that of a car traveling at the incredible velocity of 7,000 k.p.h. –  if this car were to exist, it would go round the planet in less than six hours.

The interest of physicists for something so complex, goes far beyond the pleasure of spending various hours doing and redoing calculations that attempt to translate into numbers the phenomena of nature. “If there really is the intention of understanding why the Universe is as we know it today, it’s necessary to investigate what happened close to the Big Bang, and in this case, we have to know how to deal with this scale of energy’, says the physicist Daniel Vanzella, from USP’s Physics Institute in Sao Carlos, in the interior of the state of  São Paulo. Like the serpent that bites its own tail, this energy scale unites the beginning with the end, creation and destruction, and it is common both to the Big Bang and the black holes, especially in the final phase of their existence.

The major difficulty is that in order to clarify the phenomena on the Planck scale it is necessary to take into consideration the four forces of nature. And as yet a single theory does not exist, which is consistent and accepted by the majority of physicists, capable of this achievement. One of the most popular candidates over the last few years is the Strings Theory, considered elegant from the mathematical point of view, but seen with limitations by a good number of physicists because none of its forecasts have been proven up until now.

Whoever suspects that this is not the pathway is betting on a way out that is apparently more simple: the union of the two physics theories already consecrated: General Relativity, formulated some 90 years ago by Albert Einstein, with Quantum Mechanics, initially proposed by Max Planck and developed over the first three decades of the last century by physicists such as Niels Bohr, Paul Dirac, Werner Heisenberg and Erwin Schrödinger, among others.

Over the last fifty years it has been shown that it is not so simple to overcome this challenge because there is conceptual incompatibility between General Relativity, which deals with the phenomena of the macroscopic world in which gravity assumes a relevant role, and Quantum Mechanics, the physics of the sub-microscopic world, governed by the other three forces of nature. The most important difference between them is that the first considers space as a magnitude that is measured in continuous values – one can assume any value that one can image between two natural numbers, as, for example, between the numbers 2 and 3 there is the number 2.2 or that of 2.742. However, Quantum Mechanics describes the phenomena measured in discrete values, determined only by natural numbers. It is much easier to understand this difference by imagining each one of the theories as pathways that lead from the ground to a walkway over an avenue. Whilst for the first pathway there will be a ramp, on which one climbs up gradually and continually, the second has stairs on which one gains height in jumps, step by step.

Because of this incompatibility, even today the Theory of Everything is for the physicist like the Forbidden City, in the heart of Peking, was to the Chinese population, in the opinion of George Avraam Matsas, from the Theoretical Physics of the São Paulo State University (Unesp). Protects by thick walls, this grouping of palaces, wherein the Emperor lived, remained for centuries forbidden to the majority of  Chinese, even to relatives of the monarch. “Since we’ve still not found ways of getting across these walls, we attempt to imagine what is happening in the Forbidden City starting from what it is possible to see from the cracks in this wall”, compares  Matsas.

At the beginning of the decade of the 1970s until now some physicists – very few, it is true – discovered cracks in this wall and glimpsed what was occurring on the other side. They did not manage a complete union of  Quantum Mechanics with General Relativity, but they produced a hybrid theory that incorporates parts of both and is known as the Quantum Field Theory in Curved Spacetime, a complicated name to define the area of physics that studies the behavior of particles in regions of space in which the concentration of material or energy is very elevated, such as black holes – according to General Relativity, the concentration of material or energy does not generate a gravitational force, as Newton had stated, but brings about a curvature of space-time similar to what a rubber ball causes in an elastic layer.

One of the precursors of the Quantum Field Theory in Curved Spacetime, the American physicist Leonard Parker, from the University of  Wisconsin, in the state of  Milwaukee, began to see connections between Quantum Mechanics and General Relativity even during his doctorate degree studies, a little more than 40 years ago, and discovered that in regions with very intense gravitational fields, such as black holes or the Big Bang, there had also been the creation of particles.

A good part of the fame for the discovery that black holes were not simply chasms for material and energy, but also producers of particles returned into space, was due to another physicist, the Englishman Stephen Hawking, inheritor of the chair that was once that of Isaac Newton at the University of Cambridge. During this same era  Hawking verified that black holes emitted a special radiation –  today called Hawking radiation – in the form of heat, slowly evaporating, and he published these results in 1974 in Nature. “Before this discovery it had been believed that General Relativity was sufficient to describe, with precision, a black hole”, comments physicist George Matsas, from Unesp. “Hawking showed that we only have a precise idea of how these obscure objects of the cosmos function when these quantum ingredients [the production of particles] are added in”,  he says.

Analyzing the calculations that had led professor Hawking to identify this phenomena, the Canadian physicist William Unruh discovered another phenomenon of the microscopic world, which is independent of black holes, but can also be applied to them. Two years after the finding by professor Hawking, physicist Unruh verified that empty space (vacuum) could, in reality, not be so empty as thought and is replete with elementary particles, depending how one who observes this region moves him or herself. This phenomenon, known as the Unruh effect, comes directly from Quantum Mechanics.

According to this theory, the vacuum is not empty, as in general is imagined, but full of pairs of particles that come about and annihilate themselves so rapidly that they cannot be detected. But in regions of space in which the density of material and energy is sufficiently high to create frontiers of no-return, as in a black hole, everything changes: one particle or another can escape from the gravitational field and, instead of annihilating each other, become real. Unruh forecast that an astronaut who fell into a black hole – or that is to say, was free of the action of forces – would not see anything apart from empty space. But, if his ship were to have its engines running, counterbalancing the tendency to fall in the direction of the black hole, this same astronaut would perceive clouds of elementary particles. “This is an exotic effect of Quantum Mechanics that remained hidden for almost 50 years from a legion of physicists from the best laboratories in the world”, says Matsas.

Strange? Certainly. So much so that many physicists also doubted that it would be possible for elementary particles to exist for observers under a determined condition, but not under another. At times, nonetheless, it is necessary to place preconceived ideas to the one side in order to accompany the rational thinking of physicists and to attempt to understand how nature possibly works. Since it is not possible to send a spaceship into a black hole in order to evaluate this effect, Matsas and Daniel Vanzella decided to verify it in another way: they proposed, as is generally done in physics, an imaginary experiment that would prove that without the Unruh effect nature could not be as we know it. Tests in particle accelerators have already demonstrated that the proton – the particle with a positive electrical charge that is an integral part of the nucleus of atoms –  is stable when it travels at a constant velocity. But, this same proton disintegrates and transforms into a neutron, the particle without an electrical charge in an atomic nucleus, when it is submitted to a force that makes it move faster and faster or slows it down.

From a series of calculations published in 2001 in the magazine Physical Review D,  Matsas and Vanzella demonstrated that a proton under the action of a very intense force, such as that which would make it remain stationary and impede it from falling into a black hole, would exist for a very short period before it transforms itself into a neutron. This behavior would be obvious only to someone in free fall going into the black hole who would see the proton stopped in the proximity of this hole, under the action of a force that impedes the proton from being sucked in. It was necessary to discover what a stationary astronaut would find in relation to the proton.

In principle, the astronaut would not see the proton disintegrate, since they are stationary one in relation to the other. But here there would be a paradox because someone in free fall would observe the proton, stopped outside of the black hole, transform itself  into a neutron. And is this in fact what happens, since in nature the proton cannot at the same time disintegrate and remain entire? Matsas and Vanzella also proved that in this case the proton disintegrates in the same interval of time that had been forecast in previous work, originating a neutron, but through a different mechanism. As a consequence of the Unruh effect, an astronaut stopped with the proton observes on his return that cloud of particles predicted by Hawking. These particles, therefore, could interact with the proton and lead it to becoming a neutron. As the two physicists affirmed in an article in Physical Review Letters of 2001, the Unruh effect is fundamental for this paradox not to occur. “This result helps us to better understand not just the behavior of black holes, but also of elementary particles themselves”, comments Matsas.

In collaboration with Jorge Castiñeiras and Luís Crispino, from the Federal University of Pará, Alberto Saa, from Unicamp, and Atsushi Higuchi, from the University of  York, England, Matsas is continuing to test the limits of the Quantum Field Theory in Curved Spacetime, with the objective of knowing until what point it represents well nature’s phenomena without violating other laws of physics already proven. Recently, he and physicist André Rocha da Silva confirmed that these transformations suffered by particles in the proximity of  black holes do not go against, for example, the laws of thermodynamics formulated during the 19th century, which still today explain the transformations of different forms of energy and the heat exchanges observed in nature.

Blind bell ringer
Working with the second law of thermodynamics, according to which the degree of disorder or excitation of a system always increases with time, professor Abdalla and the physicists Bertha Cuadro-Melgar, Roman Konoplya and Carlos Molina attempted to quantify how this disorder varies in a black hole. Recently he discovered a way of calculating the dimensions of a black hole starting from the gravitational waves generated in response to the disturbance caused by an object drawn into its interior. “This is something like estimating the size of a lake starting from the waves that form on its surface”, compared professor Abdalla, “or even, a blind man who manages to know the size of a bell starting from the sound of a chime.”  In principle, the gravitational waves produced by the disturbances could be identified using experiments with a Mario Schemberg Gravitational Waves Detector, which began to function in the country in September of this year.

As all of these effects still need to be proven, Unruh proposed in 2005 a strategy that perhaps permits the reproduction in the laboratory of similar effects to those that, it is believed, must occur close to black holes, such as Hawking radiation. Unruh does not plan, of course, to reproduce a black hole at the physics study centers, but an analogous  phenomenon, named sonic hole. Invited during 1982 to give a course on hydrodynamics, a specialty with which he was little familiar, Unruh imagined that a structure capable of absorbing a fluid with a velocity greater than that of sound – for example, the super drain of a pool – would impede any noise in its interior overtaking the frontiers of the drain and escaping to the outside, in a similar manner to that which occurs with the light that falls into a black hole. “The production of an analogue of a black hole could provide us with more clues about the existence of  Hawking radiation”, says Matsas, who is also investigating other analogous models of black holes.

In São Carlos, Vanzella is now dedicating himself to the application of the Quantum Field Theory in Curved Spacetime in an investigation into another cosmic phenomenon: the current phase of accelerated expansion of the Universe, in which stars and galaxies move away from each other faster and faster, one from the other. In collaboration with Leonard Parker, Vanzella is developing the conceptual part of this model, according to which the vacuum itself will produce in the process of the creation and annihilation of virtual particles the force that overcomes gravity and makes the stars move away from each other in an accelerated manner. If the model were to be correct, Parker may have found the origin of the so-called black energy, corresponding to two thirds of all that exists in the cosmos. “We’re looking for a way to calculate the energy of vacuum”, says Vanzella. This is not an easy task, since one needs to carry out various approximations that can or cannot be justified from the physics point of view. “If they were to be justifiable”, continues Vanzella, “this model would fit into the same category as Hawking radiation: any theory that would be a candidate for the Theory of Everything, would have to forecast the existence of these two phenomena.”

The Projects
1. Quantum Theory of  Fields in Space-Time Curves (nº 01/09617-3); Modality Thematic Project; Coordinators George Avraam Matsas (Unesp) and Alberto Vasquez Saa (Unicamp); Investment R$ 104,000.00 (FAPESP)
2. Disturbances in General Relativity (nº 02/07916-6); Modality Thematic Project; Coordinator Élcio Abdalla (USP); Investment R$ 131,000.00 (FAPESP)