Quantum field theory (QFT) is the fusion of three core concepts of modern science - quantum mechanics, relativity, and field theory. In quantum field theory, the vacuum state is not truly empty—it represents the lowest possible energy state of a quantum field. This distinction leads to the intriguing concept of a "false vacuum," a metastable state of the universe that has drawn significant interest in the study of quantum phenomena.
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The False Vacuum Hypothesis
In classical physics, a vacuum is traditionally understood as an empty space devoid of particles and energy. However, insights from quantum physics and a deeper examination of Maxwell's equation reveal that, in reality, the vacuum state represents the system of fields at its minimum energy level rather than a complete absence of energy. The vacuum state is a complex state containing “virtual particles”, which can be generated and blink out of existence at any time due to Heisenberg’s uncertainty principle.
The concept of “False Vacuum” was pioneered by Coleman and his research team as they studied the stability of a physical system. The research study explained that physical systems can sometimes exist at a local minimum energy state, which is differentiated from the absolute minimum potential energy state by an effective potential barrier. The absolute minimum energy state is the “true vacuum” state while the local minimum energy state is referred to as the “false vacuum” state.2
Experts believe that the universe exists in a “False vacuum” state and the early universe was too cold for a thermal transition towards the “True vacuum” state.
Key Theories and Concepts Explaining Vacuum Instability
The Higgs field is the only known scalar field in nature, playing a fundamental role in particle physics. Scalar fields like the Higgs are also essential in cosmological models, particularly in explaining theories of inflation and (p)reheating, which describe the universe's rapid expansion and energy redistribution in its early life. As the universe approaches an approximate De Sitter phase, theoretical models suggest that the current vacuum state may be metastable rather than truly stable. This implies that, while it appears stable on observable timescales, it could eventually transition to a lower-energy state under the right conditions. Interestingly, the observed values of the Higgs boson and top quark masses, along with other parameters, indicate that meta-stability is already a feature of the Standard Model (SM).
Prediction of Metastable Universe by Higgs Field
By extending the loop-corrected renormalization group evolution of SM parameters to high energy scales, researchers have found that the Higgs coupling turns negative at energies above approximately 1011 GeV. This suggests that the SM vacuum is metastable, placing the Universe at the critical boundary between stability and instability. Additionally, the small Higgs mass squared keeps the SM near the threshold between phases with broken and unbroken electroweak symmetry.
Models of scalar field landscapes, such as the Higgs potential model, introduce the concept of vacuum transitions between different local minima.3 The symmetry phase of the Higgs potential in the early universe pointed to massless particles. However, the electroweak symmetry breaking led to the Higgs field acquiring a nonzero vacuum expectation value. These calculations lead towards quantum vacuum decay, allowing the universe to transition towards a lower-energy “True Vacuum”.4 Exploring the implications of a metastable SM vacuum could provide deeper insights into the evolution and long-term fate of our Universe.
Quantum Machine-Led Simulations: A Game Changer
Advantages of Modern Quantum Simulations for Studying Quantum Dynamics
Quantum computing platforms have become a key technology for simulating complex quantum processes. Operators describe the systems containing the encoded information, characterized by a continuous spectrum. It is also known as Continuous-Variable Quantum Computing (CVQC).5
Quantum optical frameworks of CVQC have become popular in recent times. CVQC is an established platform for efficiently simulating the dynamics of quantum systems, particles, and fields. CVQC implements Gaussian gate operations successfully, and allows the manipulation of quantum states while preserving their Gaussian character, allowing machine-led simulations of quantum field dynamics.
With the implementation of non-Gaussian operations, higher-order interactions are modeled accurately, paving the way for universal simulation of quantum dynamics through quantum computing and simulations. The successful simulation of the time evolution of quantum systems has allowed experts to investigate phase transformations, and energy spectra, proving to be the core technology to study quantum reactions, the evolution and stability of quantum systems, and the early universe in great detail.6
Quantum Simulations Model Vacuum Decay and Bubble Nucleation
False vacuum decay has been studied extensively, building on the original research by Coleman et. al. and using the key concepts of Langer’s theory of bubble nucleation. Classical simulation systems have been programmed to calculate the bubble nucleation rate in field theory by solving equations of motion. This method is not sufficient to simulate strongly coupled quantum systems.
In a recent research article, experts presented a better system to simulate vacuum decay. The research team postulated that vacuum decay is a problem defined in real-time, which can be easily formulated on a closed-time path. Modern simulation systems employing this efficient method calculate the time evolution of the order-parameter field, tracking its progression from an initial metastable phase to its final low-energy, stable state.
The simulation system used by the research team utilized non-equilibrium quantum evolution equations to study the dynamics of the quantum field and simulate bubble nucleation. This new method allows modern quantum systems to capture transitions between energy levels not possible by classical systems.
This becomes a crucial step in connecting the non-equilibrium field theory with the Euclidean approach for studying vacuum decay. This also allows to efficiently study the dynamics of false vacuum decay by accurately characterizing it in terms of time-dependent potential, controlling the shift from meta-stable condition to true vacuum state.7
Bubble Nucleation and Fate of the Universe
The decay of a false vacuum state is generally found to be a first-order transition, with experts discovering that bubbles nucleate by following specialized paths in the quantum field. The bubble nucleation events occur through special trajectories. It has been demonstrated that the presence of classically allowed paths connects the initial quantum false vacuum state with a subsequent state comprised of nucleated bubbles of stable lower energy state or “true vacuum”. Bubble nucleation has been shown to arise from initial vacuum fluctuations, leading to the formation of localized regions of "true vacuum." These regions then expand, gradually replacing the surrounding false vacuum.
Bubble Nucleation Simulations and Cosmic Implications
The simulations setup using this concept allows us to accurately investigate the vacuum decay rates and the study of interactions between nucleated bubbles in a high-ordered coupled system. The existence of specialized paths for bubble nucleation from high energy initial quantum state is a demonstration of complex self-decoherence phenomena of the quantum field, giving insights about the quantum fluctuations during the inflation processes.8 This is key for studying cosmological evolution, and the simulation of bubble nucleation events opens up avenues for using neural networks, and machine learning (ML) events to predict the likelihood of false vacuum decay during cosmological processes, revealing key information related to the fundamental nature of our universe.
Observational Evidence
Many cosmic bodies and signatures are proof of vacuum instabilities. Research studies proposed that Primordial Black Holes (PBHs) could trigger first-order transitions, and make the electroweak vacuum unstable. PBHs are not present in vacuum regions, and recent studies have revealed that there exists no thermal equilibrium between PBHs and their surroundings.
PBHs deposit energy at localized spots in the thermal plasma employing Hawking radiation, leading to the formation of hot spots. These hot spots lead to the formation of true electroweak vacuum bubbles and act as the foundation for false vacuum decay. Experts have developed accurate methods to calculate false vacuum decay rates around PBHs, showing that vacuum stability is not a myth.9 Furthermore, a detailed analysis of dark matter associated with PBHs, and cosmic rays could also prove to be key in confirming the decay rates and gathering concrete data regarding vacuum instability.
Challenges
However, the false vacuum decay and emergence of PBHs are extremely rare events, which can’t be predicted with complete confidence. Quantum simulations powered by ML algorithms have improved our ability to calculate quantum field dynamics and recognize patterns to predict vacuum instabilities at a localized spot to predict the occurrence of black holes. However, there is still a lack of confidence among scientists regarding the data interpretation and isolation of gravitational waves associated with PBHs from other cosmic rays. Additionally, the long timescales involved in studying cosmological false vacuum decay, the difficulty of verifying evidence, and the high costs associated with astronomical observations present significant challenges to testing these hypotheses.
The integration of quantum mechanics and machine learning into interdisciplinary fields like quantum ML is advancing the study of quantum dynamics in astronomical processes, offering new insights into the early universe and its evolution. However, despite improvements in computational speed, data processing, and calculations of false vacuum decay rates, many fundamental questions from classical theories and the Standard Model remain unresolved. Perhaps the biggest mystery of all still lingers: is our reality a temporary quantum state?
Further Reading
- Aitchison, I. (1985). Nothing's plenty the vacuum in modern quantum field theory. Contemporary physics, 26(4), 333-391. Available at: https://doi.org/10.1080/00107518508219107
- Urbanowski, K. (2017). Properties of the false vacuum as a quantum unstable state. Theoretical and Mathematical Physics, 190(3), 458-469. Available at: https://doi.org/10.1134/S0040577917030151
- Horn B. (2020). The Higgs Field and Early Universe Cosmology: A (Brief) Review. Physics. 2(3). 503-520. Available at: https://doi.org/10.3390/physics2030028
- Sher, M. (1989). Electroweak Higgs potential and vacuum stability. Physics reports, 179(5-6), 273-418. Available at: https://doi.org/10.1016/0370-1573(89)90061-6
- Adesso, G. et. al. (2014). Continuous variable quantum information: Gaussian states and beyond. Open Systems & Information Dynamics, 21(01n02), 1440001. Available at: https://doi.org/10.1142/S1230161214400010
- Abel, S. et. al. (2024). Simulating quantum field theories on continuous-variable quantum computers. Physical Review A, 110(1), 012607. Available at: https://doi.org/10.1103/PhysRevA.110.012607
- Batini, L. et. al. (2024). Real-time dynamics of false vacuum decay. Physical Review D, 109(2), 023502. Available at: https://doi.org/10.1103/PhysRevD.109.023502
- Braden, J. et. al. (2019). New semiclassical picture of vacuum decay. Physical review letters. 123(3). 031601. Available at: https://doi.org/10.1103/PhysRevLett.123.031601
- Hamaide, L. et. al. (2024). Primordial black holes are true vacuum nurseries. Physics Letters B, 856, 138895. Available at: https://doi.org/10.1016/j.physletb.2024.138895
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