Here is the English translation of the section "III. Cosmological Constant and Zero-Point Energy":
III. COSMOLOGICAL CONSTANT AND ZERO-POINT ENERGY
Zero-point energy refers to the inherent energy of the quantum vacuum, even in the absence of real particles. This energy is not merely theoretical: it has observable and significant effects [6], with profound physical implications. Unlike energy in states with real particles, zero-point energy remains constant and cannot be completely eliminated. This concept is fundamental to understanding the underlying dynamics in quantum mechanics and particle physics, and is crucial in the framework of quantum field theory, especially in contexts such as curved space [7].
Zero-point energy has several important implications that generate some paradoxes. One of the most well-known is its relationship with the Casimir effect, where an attractive force is observed between two uncharged neutral plates in a vacuum due to quantum fluctuations. This observation evidences how the energy of the vacuum can have tangible physical effects [8]. Additionally, its connection to the cosmological constant poses significant challenges in cosmology, where there is a notable discrepancy between the theoretical and observed values of vacuum energy [9]. These implications are fundamental in questioning and expanding our current understanding of the universe.
Zero-point energy plays a crucial role in quantum field theory, where it is an essential component in calculating the energies of quantum fields in space. In this framework, each type of elementary particle is associated with its own quantum field, and zero-point energy represents the lowest possible energy of these fields. This concept is essential to understand how particles and fields interact at quantum scales, influencing phenomena such as renormalization, a mathematical process necessary to handle the infinities that arise in the calculations of quantum field theory.
Moreover, from the perspective of statistical mechanics, zero-point energy provides a more complete view of quantum systems. In this context, it is considered that even at absolute zero temperatures, quantum systems retain a minimum energy due to zero-point energy. This contradicts the classical notion that all motion ceases at absolute zero. Zero-point energy, therefore, is crucial for understanding the behavior of systems at low temperatures, affecting properties such as heat capacity and quantum phase transitions [10].
Together, the theoretical implications of zero-point energy illustrate its importance not only in theoretical physics but also in our broader understanding of the nature of the universe at microscopic and macroscopic scales. The zero-point energy of the quantum vacuum and its relationship with deep cosmological problems, such as the cosmological constant, are of great interest, and gain relevance in the context of "dark energy": a mysterious component believed to be responsible for the acceleration of the universe's expansion [11].
If the universe were like a balloon that is inflating, the cosmological constant is a number that allows us to understand how fast this balloon is inflating, that is, how fast the universe is expanding. In this context, vacuum energy could be thought of as the air that inflates the balloon, in such a way that the equation of the cosmological constant relates this vacuum energy to the speed of the universe's expansion.
The cosmological constant, which Einstein introduced and later prematurely discarded as his "biggest blunder," has resurfaced in modern cosmological theories as a possible explanation for dark energy. Zero-point energy could provide clues about the nature of this dark energy, offering a connection between the theories of quantum physics and massive astrophysical phenomena and the very structure of space-time.
Zero-point energy is a central concept in quantum physics and arises from the interpretation of quantum mechanics of fields and particles. Unlike classical mechanics, where a system in its lowest state would have zero energy, quantum mechanics predicts that even in its lowest energy state (the ground state), a system possesses a finite amount of energy, known as "zero-point energy". This energy can be mathematically represented as:
E = 1/2 ℏω
where E is the zero-point energy, ℏ is the reduced Planck constant, and ω is the angular frequency of the quantum harmonic oscillator. This concept is crucial for understanding the quantum vacuum, as it suggests that the vacuum is not truly "empty" but is filled with these fluctuating energies. These energy fluctuations are responsible for real and observable physical effects, such as the Casimir effect, which manifests as an attractive force between two neutral conducting plates in a vacuum.