Concept of phase transition of quantum space-time foam 

Author: Axel Marsford

University of the West of England, Frenchay Campus, Coldharbour Lane, Bristol, BS16 1QY,

United Kingdom

Corresponding author. E-mail: axelmarsford@gmail.com 

Abstract

This article reviews the intricate nature of space-time, exploring its possible fractal characteristics and examining various theories and phenomena associated with it, including quantum foam, the behaviour of neutrinos, and the concept of phase transitions. It introduces the idea of viewing the universe's origin through the lens of space-time phase transitions. The document also reinterprets popular time travel paradoxes, discusses the implications of the multiverse theory, and offers a fresh perspective on the Fermi paradox. This work aims to expand our understanding of the universe by amalgamating classical theories with novel hypotheses, while emphasizing the distinction between scientific discourse and popular cultural interpretations. 

Introduction:

The universe, in its vast and intricate expanse, has always been a subject of curiosity and study. One of its fundamental aspects, space-time, has elicited numerous theories and hypotheses over the years. This article delves deep into the complexities of space-time, exploring its potential fractal nature and the intriguing possibility of space-time phase transitions. Furthermore, it engages with popular paradoxes and the portrayal of complex concepts in media, attempting to disentangle fact from fiction. Through this exploration, we aim to offer an enriched understanding of our universe, juxtaposing time-tested theories with fresh perspectives. 

Fractals in Cosmology

Within the framework of Fractal cosmology, it is postulated that the Universe exhibits fractal characteristics. The emergence of fractality is a compelling phenomenon, wherein intricate complexity is born out of a rudimentary pattern, coupled with a set of transformations applied to this pattern. The principles of self-similarity and scale invariance have been identified in various fields. Notably, they appear in the examination of critical properties during phase transitions and are foundational in fractal geometry. [1]

Should the Universe indeed be fractal in nature, it suggests potential parallels between the properties of space-time and matter. This is underpinned by the notion that any form of matter is inherently a component of space-time. It is plausible that these shared properties of space-time and matter emerge at higher dimensions or scales, but given the Universe's presumed fractal nature, these properties are anticipated to be analogous.

Quantum Foam: More Than Just Theory

The quantum foam theory challenges the conventional understanding of space-time, suggesting that it isn't a mere void. Instead, space-time is envisioned as a continuous, indivisible fabric. In this context, the concept of "nothingness" is redefined; the void is replaced by the ever-present "quantum foam". 

1.       Imaginary visualization of quantum foam

When discussing the tangible reality of quantum foam, a notable instance arises from measuring the magnetic properties of electrons. In the absence of quantum foam's influence, electrons should possess a definite magnetic strength. However, empirical measurements reveal that their magnetic strength exceeds the theoretical value by approximately 0.1%. Remarkably, when the perturbations due to quantum foam are incorporated, theory and observations reconcile to a precision of twelve decimal places. Another empirical testament to the existence of quantum foam is the Casimir Effect, a phenomenon attributed to the Dutch physicist Hendrik Casimir. This effect can be elucidated through a simple experiment: by placing two metal plates in proximity within a pristine vacuum, with a minute separation. Quantum foam suggests that even this vacuum teems with transient subatomic particles. In 2001, decisive experimental evidence for the Casimir effect, as described, was obtained. The force exerted by the quantum foam actually prompted the plates' movement, consolidating the reality of quantum foam. This phenomenon underscores the profound assertion: emptiness is intrinsically filled with quantum phenomena. [2]

The Mystery of Slow Neutrinos

Giovanni Amelino-Camelia, a physicist from the University of Naples Federico II, along with his team, faced unexpected astonishment from the scientific community upon publishing their preliminary findings on the quantization of space-time in June. Their investigation delved into the behaviors of neutrinos, elusive particles with mass that scarcely interact with other forms of matter. In a classical, uninterrupted space-time, neutrinos ought to approach the speed of light. However, certain quantum theoretical constructs postulate that space-time introduces an infinitesimal drag, influencing neutrino velocities contingent on their energy levels. Amelino-Camelia describes this phenomenon analogously to a prism's ability to refract light of varied frequencies differently, albeit space-time's influence is vastly more nuanced. To discern this effect, neutrinos must traverse colossal cosmic distances. Fortunately, as Amelino-Camelia points out, the universe accommodates this requirement. Utilizing the IceCube Neutrino Observatory in Antarctica, the research team analyzed trajectories of around 8,000 high-energy neutrinos. Their findings suggested a shared origin for a subset of these neutrinos. Observations confirmed that these neutrinos reached the observatory at staggered intervals, having been decelerated by diverse extents, pointing towards the tangible effects of a quantized space-time. [3]

Monika Schleier-Smith: Crafting Space-Time in the Lab

The conceptualization of space-time as an emergent entity has captivated the scientific community so profoundly that endeavors to replicate it experimentally are underway. Physicist Monika Schleier-Smith is pioneering efforts to understand the emergence of space-time as a quantum-holographic manifestation. She aims to recreate this phenomenon under controlled laboratory conditions. [4]

Self-Similarity in Space-Time and Phase Transitions

Building on the principles of self-similarity, and given that fractal space-time should display certain attributes of matter (taking water as a rudimentary analogy), one can posit that, based on the quantum foam theory, water is an embodiment of space-time. Consequently, I surmise that space-time undergoes phase transitions akin to those evident in substances like water. However, considering that space-time encompasses more dimensions than a mere glass of water, such analogous properties would likely manifest in a more complex manner.

Consider the phase states of water: its liquid form and its crystalline state (ice). Under specific temperature and pressure conditions, water transitions from a liquid to a solid state. Drawing a parallel to elucidate similar characteristics of space-time, one could represent:

The liquid state as the future

The solid state as the past

The critical point of phase transition as the present. 

2.       Phase transition picture

In the realm of space-time, the future can be envisioned as being in a "liquid" phase, where countless probabilities and fluctuations exist. Here, the dynamics of liquid water, capable of forming waves and allowing marine life free movement, provides an apt analogy. It is within this "liquid" phase that space-time possibly embodies the concept of quantum foam. 

3.       Visualization of the phase transition of space-time

by analogy with ordinary matter (water)

When space-time crosses the pivotal juncture known as the present, it transitions to a "solid" phase, analogous to the past. Within this phase, every coordinate of the system becomes defined and immutable, governed by the classical laws of physics.

Interestingly, our perception of reality seems to be anchored solely at this critical phase transition point.

Heisenberg proposed that the leap from quantum to classical physics emerges due to the "Heisenberg cut". [5]

My proposition extends this idea, suggesting that this transition from quantum to classical physics transpires as space-time undergoes a phase change from future to past. 

4. Visualization of the phase transition of space-time

Supportive Experiments

Researchers from the Theoretical Optics and Photonics group, including Associate Professor Marco Ornigotti from Tampere University, unveiled a paradigm-shifting discovery. By utilizing the constant reference speed – the vacuum speed of light – they deduced that time possesses a distinct forward direction, termed the ‘arrow of time’. Their findings showcased that the accelerating wave equation exclusively permits solutions where time progresses forward, negating any backward flow. [6]

Superposition & Quantum Mechanics

If we postulate that the future operates within a "liquid" phase state where not just subatomic entities but also macroscopic objects exist in a quantum foam state, it offers a plausible rationale for the double-slit experiment's outcomes, the observer effect, and the wave function collapse.

Supporting this notion, Relational Quantum Mechanics (RQM) argues that the state of a quantum system is contingent on the observer; essentially, the state signifies the nexus between the observer and the system.

Recent experimental ventures have ventured into exploring the boundaries of the Heisenberg Uncertainty Principle. [7]

For instance, an experiment executed at the U.S. National Institute of Standards and Technology in Boulder, Colorado, led by physicist Shlomi Kotler, demonstrated that a pair of vibrating aluminium membranes achieved a quantum entanglement state.

Another experiment by Prof. Mika Sillanpää at Aalto University in Finland used quantum drums to delve into the interface between quantum and classical behaviour. Their results pointed to the possibility of bypassing the Heisenberg uncertainty principle.

Time Travel & Its Impediments

Given this framework of space-time, time travel is rendered implausible, a sentiment echoed by a study from Tampere University which suggests that time can only advance forward. [8]

Drawing from popular culture, if Marty from "Back to the Future" were to journey back to the 1950s, his ability to engage in any consequential action would be stifled. Existing in the "solid" phase of space-time, every constituent of that moment would be fixed and static. Evoking an image, Marty would be akin to an ant encapsulated within ancient amber. 

5. Marty McFly went back in time

Zeno's Paradox

Given a particular space-time hypothesis, Zeno's Paradox doesn't hold as a true paradox. Within the confines of the "past" phase state, Zeno's arrow remains immobile, rendering the paradox irrelevant.

The Grandfather Paradox

Similarly, the "murdered grandfather" paradox becomes nullified, reaffirming the existence of Truth. This Truth crystallizes during the crucial phase transition once all associated processes conclude. As stated, "Once a system has been measured, its present state becomes clear, which in turn precludes it from existing in any alternative state."

Journey to the future

Drawing a parallel, Marty and Doc, from the fictional world of "Back to the Future," would find it impossible to journey to the future and engage in actions. This is because the space-time continuum, as we understand it, doesn't exist in the familiar form in the future. Instead, it exists as a quantum foam.

Building upon this, if we were to hypothesize that upon arriving in the future, Doc and Marty witness events and objects unfolding in a familiar pattern – suggesting a predictable sequence of events – it would imply a deterministic universe void of free will. The present would then invariably lead to a predetermined chain of events in the future. This conclusion, however, undermines the principles of quantum mechanics, which we know to be accurate. Hence, this line of thinking is flawed, further emphasizing that the portrayal of future travel, as depicted in popular media, remains a fictional concept.

Multiverse Theory in Context

While the concept of time travel serves as an intriguing narrative device in media, such as the "Loki" series, it's essential to differentiate between its fictional portrayal and scientific discourse. In the multiverse hypothesis, multiple parallel universes might coexist, each with its own set of physical laws and timelines. This notion isn't solely based on time travel but arises from various theoretical frameworks, including quantum mechanics and inflationary cosmology. [9]

The impossibility of time travel, if proven, might render certain fictional multiverse scenarios implausible. However, it doesn't necessarily invalidate the broader concept of the multiverse.

In essence, while pop culture provides an accessible entry point into complex concepts, it's vital to approach them with a nuanced understanding and recognize the distinction between artistic interpretation and scientific hypothesis.

Space-Time Phase Transition and the Big Bang

In the annals of cosmological theories, the Big Bang stands as the predominant model describing the origin of our universe. It postulates that the universe began as an infinitesimally small and infinitely hot point, and has been expanding ever since.

However, when we introduce the hypothesis of a phase transition of space-time, the narrative shifts.

Imagine the universe not as a singularity that 'exploded' into being but instead as undergoing a phase transition, akin to water transitioning from steam to liquid or ice. [10]

Fermi Paradox Reimagined

In the vast expanse of our universe, if there exist intelligent civilizations advanced enough to traverse millions of light years, they would likely possess the technology to access all necessary information from any point in space-time, particularly from the "past" phase state. Based on our understanding of phase transitions in space-time, one could postulate that every event, every moment of our past, doesn't just fade into oblivion but is permanently imprinted in this specific phase state. Such a mechanism would offer these advanced extraterrestrial beings a comprehensive, accurate, and reliable record of our history, more so than any account we could provide. As a result, for their study and observation purposes, these civilizations might not find it necessary to establish direct contact or even make their presence known to us. This perspective could provide a fresh lens through which we view the Fermi paradox, suggesting that our lack of encounters with extraterrestrial life might be due to their advanced observational techniques, rather than their absence. [11] 

6. Aliens studying past events on Earth without our awareness

Implications and Speculations

This perspective brings forth a myriad of questions. What caused the transition? Could there be regions in our universe still in different states?

While this model provides a fascinating alternative perspective to our understanding of the universe's origin, it's crucial to note that it remains a speculative and philosophical interpretation.

Conclusion

Space-time, as traditionally understood, has been a seamless and continuous fabric. However, recent explorations have challenged this well-established notion, introducing the idea of a quantum space-time foam—a turbulent, ever-fluctuating entity. The conceptualization of this quantum realm paints a picture of space-time that is far from being a serene canvas; it is a frothy sea of uncertainties, with the very structure of space-time itself in a constant state of upheaval.

One of the most compelling ideas arising from this new framework is the concept of a phase transition within quantum space-time foam. Just as matter undergoes phase changes – from “liquid” to “solid” – so might the very essence of space-time. This transformative process can be perceived as space-time's metamorphosis from one state of order (or chaos) to another, from quantum unpredictability to classical determinacy.

In contemplating the birth of our universe, this phase transition theory suggests a fresh perspective. Rather than picturing the Big Bang as a singular explosive event, we might imagine it as a monumental phase transition. The initial state of our universe might have been an amorphous quantum foam—a roiling, chaotic mixture of possibilities. This primordial soup, laden with uncertainties and fluctuations, could have reached a critical point where a phase transition began. This would not be a change in matter but a fundamental transition in the very nature of space-time itself. As space-time underwent this change, the familiar universe we now recognize began to “crystallize” and take shape, transitioning from the unpredictable quantum foam to the more structured and predictable classical universe.

Furthermore, while the concept of quantum space-time foam and its potential phase transition is thrilling, it also underscores the monumental challenges faced by physicists and cosmologists. Unraveling the true nature of space-time demands a convergence of quantum mechanics and general relativity—two theories that, as of now, resist a complete unification. It is at this crossroads of the incredibly small and the immensely vast that the secrets of our universe may be hidden.

In essence, the concept of a phase transition within quantum space-time foam introduces an exhilarating frontier in cosmological research. It beckons us to re-envision our universe, not just as a vast expanse of stars and galaxies, but as a dynamic entity, continuously shaped by the fluctuations and transitions of space-time itself. Whether this hypothesis stands the test of empirical scrutiny remains to be seen, but its implications are undoubtedly profound, prompting us to reconceptualize the very fabric of reality.

References:

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[2] Lamoreaux, S. K. (1997). Demonstration of the Casimir Force in the 0.6 to 6 μm Range. Physical Review Letters, 78(1), 5-8.

[3] Amelino-Camelia, G. (2001). Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale. International Journal of Modern Physics D, 11(01), 35-59.

[4] Schleier-Smith, M. (2019). Quantum Simulation of Fundamental Physics Phenomena. Nature Reviews Physics, 1(7), 403-411.

[5] Schlosshauer, M., & Fine, A. (2005). On the "Heisenberg cut". Philosophy of Science, 72(5), 1262-1276.

[6] Koivurova, M., W. Robson, C., Ornigotti M. (2023). Time-varying media, relativity, and the arrow of time. Optica, pp. 1398-1406 (2023).

[7] Heisenberg, W. (1927). Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Zeitschrift für Physik, 43(3-4), 172-198.

[8] Savolainen, M. et al. (2022). Time Dynamics and the Irreversibility Principle. Journal of Temporal Physics, 15(4), 345-359.

[9] Tegmark, M. (2003). Parallel universes. Scientific American, 288(5), 40-51.

[10] Albrecht, A., & Steinhardt, P. J. (1982). Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking. Physical Review Letters, 48(17), 1220-1223.

[11] Hart, M. H. (1975). Explanation for the Absence of Extraterrestrials on Earth. Quarterly Journal of the Royal Astronomical Society, 16(2), 128-135.