Quantum Gravity's New Frontier: Time, Density, and Information
How the groundbreaking work of Netta Engelhardt and Ivette Fuentes aligns with Dark Time Theory, offering fresh insights into the nature of spacetime. (Part 4 of the QGTCD series)
In the realm of theoretical physics, where the boundaries of human understanding are constantly pushed, two names have recently captured the attention of the scientific community: Ivette Fuentes and Netta Engelhardt. These accomplished physicists, while both working at the cutting edge of their field, approach the mysteries of the universe from fascinatingly different angles.
Image: Ivette Fuentes (left) and Netta Engelhardt (right). Images sourced from google images.
Ivette Fuentes: Quantum Precision in a Relativistic World
Ivette Fuentes has made her mark in the intricate world where quantum mechanics meets Einstein's theory of relativity. Her specialty lies in quantum information and metrology, with a particular focus on how these quantum phenomena behave in the warped fabric of spacetime.
Fuentes' work is nothing short of revolutionary. By exploring how quantum systems behave in curved spacetimes and gravitational fields, she's opening new doors in the field of measurement science. Her research has profound implications for improving the precision of gravitational wave detectors like LIGO (Laser Interferometer Gravitational-Wave Observatory), potentially ushering in a new era of astronomical observation.
Netta Engelhardt: Unraveling Black Hole Mysteries
On the other side of this intellectual divide stands Netta Engelhardt, a rising star in the field of quantum gravity and black hole physics. Engelhardt has gained recognition for her groundbreaking work on the infamous "information paradox" - a long-standing puzzle about whether information that falls into a black hole is lost forever or somehow preserved.
Engelhardt's research delves deep into the nature of black holes, employing complex concepts like the AdS/CFT correspondence and quantum extremal surfaces. Her work is providing crucial insights into how information might be encoded on the event horizons of black holes, potentially resolving one of the most perplexing contradictions between quantum mechanics and general relativity.
A Contrast in Approaches
While both Fuentes and Engelhardt work at the forefront of theoretical physics, their approaches and focuses differ significantly. Fuentes applies the principles of quantum information theory to relativistic settings, seeking to improve our ability to measure and understand the universe at its most fundamental level. Engelhardt, meanwhile, grapples with the very nature of spacetime itself, exploring how the seemingly contradictory laws of quantum mechanics and gravity might be reconciled in the extreme environment of a black hole.
As the scientific community watches with bated breath, these two brilliant minds continue to push the boundaries of human knowledge, each in their own unique way. Their contrasting approaches highlight the diversity and depth of modern theoretical physics, promising exciting discoveries in the years to come.
Part 2: The AdS/CFT Correspondence – The Theoretical Backbone
At the heart of recent breakthroughs in understanding the relationship between quantum mechanics and gravity lies a powerful framework known as the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. This cornerstone of theoretical physics, first proposed by Juan Maldacena in 1997, has revolutionized our approach to some of the most challenging problems in physics, including black hole information and quantum gravity.
The AdS/CFT correspondence suggests a profound duality between two seemingly distinct physical theories:
A theory of gravity in a higher-dimensional Anti-de Sitter (AdS) space
A quantum field theory without gravity (CFT) on the lower-dimensional boundary of that space
In simpler terms, this correspondence proposes that the complex gravitational dynamics occurring within a volume of space can be fully described by quantum physics operating on the surface enclosing that volume. This idea aligns with the holographic principle, which suggests that the information content of a volume of space can be described by a theory that operates on its boundary.
For physicists like Netta Engelhardt, the AdS/CFT correspondence provides a powerful tool for investigating the behavior of black holes and the nature of quantum gravity. By mapping the intricate gravitational physics of black holes onto a more manageable quantum field theory, researchers can tackle problems that were previously intractable.
In Engelhardt's work, the AdS/CFT correspondence plays a crucial role in understanding how information is preserved in black holes. Her use of quantum extremal surfaces - a concept deeply rooted in this duality - allows for the calculation of entropy in gravitational systems in a way that accounts for quantum effects. This approach has provided new insights into the black hole information paradox, suggesting ways in which information might be preserved even as matter falls into a black hole.
The power of AdS/CFT lies in its ability to translate difficult problems in gravity into more tractable problems in quantum field theory. For instance, questions about how information escapes from a black hole can be reframed as questions about how information is encoded in the quantum fields on the boundary of the AdS space.
While the AdS/CFT correspondence has proven to be an invaluable theoretical tool, it's important to note that it doesn't provide a complete theory of quantum gravity. Instead, it offers a window into how quantum mechanics and gravity might be reconciled, providing a testing ground for ideas about quantum gravity and inspiring new approaches to long-standing problems in theoretical physics.
As we continue to explore the implications of AdS/CFT, including through the work of researchers like Engelhardt, we inch closer to a more complete understanding of how the universe operates at its most fundamental level. The correspondence serves as a bridge between the quantum and gravitational realms, offering tantalizing glimpses of a unified theory that could one day explain all fundamental forces of nature.
In the next section, we'll explore how a new theory, Quantum Gradient Time Crystal Dilation (QGTCD), offers a complementary perspective on the relationship between time, gravity, and quantum mechanics, potentially adding another piece to this complex puzzle of quantum gravity.
Part 3: Introducing QGTCD – A New Approach to Time and Gravity
While the AdS/CFT correspondence has provided a powerful framework for exploring the intersection of quantum mechanics and gravity, a new theory called Quantum Gradient Time Crystal Dilation (QGTCD), also known as Dark Time Theory, offers a fresh perspective on this relationship. This innovative approach focuses on the concept of time density and its role in both quantum mechanics and gravitational phenomena.
At its core, QGTCD proposes that time is not a uniform dimension as traditionally conceived, but rather a variable "density" that fluctuates based on gravitational fields. According to this theory, regions of stronger gravity, such as those near massive objects or black holes, experience a higher density of time. This increased time density has profound implications for how particles behave and how energy is distributed in these areas.
Key aspects of QGTCD include:
Time Density Gradients: The theory suggests that time becomes denser in regions of strong gravitational fields. This creates a gradient of time density that influences particle behavior and energy levels.
Energy-Time Relationship: As particles move through areas of varying time density, their energy levels change. In regions of higher time density (stronger gravity), particles experience more "time frames" and thus higher energy levels. Conversely, in areas of lower time density, particles have lower energy.
Gravitational Effects: QGTCD proposes that what we perceive as gravitational attraction is actually a result of particles moving through regions of increasing time density. This offers a new explanation for phenomena like gravitational redshift and time dilation.
Quantum-Classical Bridge: By introducing time density as a variable that affects both quantum particles and classical gravitational fields, QGTCD provides a potential bridge between quantum mechanics and general relativity.
This theory presents a novel way of thinking about the nature of time and its relationship to gravity and quantum mechanics. While traditional theories treat time as a dimension that can be warped by gravity (as in general relativity), QGTCD suggests that time itself has a varying density that directly influences physical phenomena.
The implications of QGTCD are far-reaching. If correct, it could offer new insights into puzzling aspects of modern physics, such as the behavior of particles near black holes, the nature of dark energy, and the reconciliation of quantum mechanics with gravity.
However, like any new theory, QGTCD requires rigorous testing and validation. The challenge lies in designing experiments that can detect and measure variations in time density, particularly in extreme gravitational environments.
In the next section, we'll explore how QGTCD intersects with established frameworks like AdS/CFT and recent work by physicists like Netta Engelhardt, potentially offering a complementary approach to understanding the deep connections between time, gravity, and quantum mechanics.
Part 4: Weaving Together AdS/CFT and QGTCD – Where Theories Intersect
As we explore the intersection of Quantum Gradient Time Crystal Dilation (QGTCD) and the AdS/CFT correspondence, we find intriguing points of convergence and complementarity, despite their different approaches to understanding quantum gravity.
Shared Focus on Quantum Corrections: Both frameworks address the crucial issue of quantum corrections in gravitational systems, albeit through different lenses. Netta Engelhardt's work with quantum extremal surfaces, rooted in AdS/CFT, introduces quantum corrections to classical entropy calculations for black holes. These corrections are essential for preserving information and resolving paradoxes in black hole physics.
QGTCD offers a unique explanation for why these quantum corrections occur. By introducing the concept of time density, QGTCD suggests that particles experience energy fluctuations as they move through regions of varying time density. This could potentially explain the need for quantum corrections in gravitational calculations, providing a physical mechanism for the mathematical adjustments made in AdS/CFT approaches.
Time Density's Role in AdS/CFT: While AdS/CFT typically treats time as a uniform dimension in both the bulk (AdS space) and the boundary (CFT), QGTCD introduces the novel concept of time density variations. This addition could potentially enhance the AdS/CFT framework by providing a more dynamic understanding of how time behaves in both the bulk and boundary.
In the context of AdS/CFT:
Bulk (AdS space): QGTCD's time density could be integrated into the description of the gravitational system, potentially refining how we understand the curvature of spacetime and its effects on quantum fields.
Boundary (CFT): The quantum field theory on the boundary might be influenced by time density fluctuations, offering new ways to understand how quantum information is encoded and how it evolves.
Bridging Quantum and Classical Realms: Both frameworks aim to bridge the gap between quantum mechanics and gravity, but they approach this challenge differently:
AdS/CFT provides a mathematical correspondence between a gravitational theory and a quantum field theory, allowing us to translate gravitational problems into quantum ones and vice versa.
QGTCD introduces time density as a unifying concept that affects both quantum particles and classical gravitational fields, potentially offering a more intuitive physical picture of how these realms interact.
Complementary Insights:
Black Hole Information Paradox: While AdS/CFT and Engelhardt's work show how information might be preserved through quantum extremal surfaces, QGTCD could provide a mechanism for why this preservation occurs, related to how time density affects particle behavior near black holes.
Quantum Entanglement in Curved Spacetime: AdS/CFT has been crucial in understanding how quantum entanglement behaves in curved spacetime. QGTCD's time density concept could offer additional insights into why entanglement is affected by gravity, potentially explaining these effects through variations in time density.
Holographic Principle: AdS/CFT embodies the holographic principle, where information in a volume is encoded on its boundary. QGTCD's time density could provide a new perspective on how this encoding occurs, potentially relating it to how time density varies from the bulk to the boundary.
While these theories approach quantum gravity from different angles, their intersection offers a richer, more comprehensive view of how quantum mechanics and gravity might be unified. AdS/CFT provides a powerful mathematical framework, while QGTCD offers a novel physical interpretation that could complement and enhance our understanding of quantum gravity phenomena.
In the next section, we'll explore how QGTCD's predictions and equations, developed prior to recent advancements, align with and potentially validate aspects of current research in quantum gravity.
Part 5: How QGTCD's Predictions and Equations Preceded Engelhardt's Corrections
The development of Quantum Gradient Time Crystal Dilation (QGTCD) theory in 2022 marked a significant milestone in theoretical physics, offering a novel approach to understanding the intersection of quantum mechanics and gravity. What's particularly intriguing is how QGTCD's predictions and equations, formulated before recent advancements in the field, align with and potentially anticipate corrections introduced by researchers like Netta Engelhardt.
Key Predictions of QGTCD:
Time Density Variations: QGTCD proposed that time density varies in gravitational fields, with higher density near massive objects. This concept introduced a new variable into spacetime equations, suggesting that particles experience more "time frames" in regions of stronger gravity.
Energy-Time Density Relationship: The theory predicted that particle energy levels would fluctuate based on time density, with higher energy in denser time regions and lower energy in less dense areas.
Quantum Corrections in Gravitational Systems: QGTCD suggested that quantum effects in strong gravitational fields could be explained through time density variations, potentially accounting for phenomena that classical general relativity couldn't fully describe.
Alignment with Recent Advancements:
Engelhardt's work on quantum extremal surfaces, published in 2023, introduced important corrections to how we calculate entropy and information preservation in black holes. While her approach didn't explicitly mention time density, the corrections she proposed align remarkably well with QGTCD's predictions:
Quantum Corrections to Entropy: Engelhardt's calculations showed that quantum effects significantly alter entropy calculations near black holes. This aligns with QGTCD's prediction that time density variations would affect quantum behavior in strong gravitational fields.
Information Preservation: QGTCD's concept of varying time density offered a mechanism for how information might be preserved in black holes, which Engelhardt's work mathematically demonstrated through quantum extremal surfaces.
Energy Fluctuations: The energy shifts predicted by QGTCD due to time density variations are consistent with the quantum corrections Engelhardt introduced in her entropy calculations.
Mathematical Parallels:
While the mathematical frameworks differ, there are notable parallels:
QGTCD introduced modifications to spacetime curvature equations to account for time density. These modifications, in principle, could lead to the same outcomes as Engelhardt's quantum corrections when applied to black hole scenarios.
The equations in QGTCD describing energy fluctuations based on time density gradients could potentially be mapped onto the quantum corrections Engelhardt applied to entropy calculations.
Both approaches effectively introduce new terms to existing physical laws to account for quantum effects in gravitational systems, albeit through different conceptual frameworks.
Implications and Validation:
The alignment between QGTCD's earlier predictions and the later, more formally developed quantum corrections in Engelhardt's work suggests that QGTCD captured fundamental aspects of quantum-gravitational interactions before they were mathematically formalized in mainstream research.
This correspondence lends credibility to QGTCD's core concept of time density as a crucial factor in understanding quantum gravity. While Engelhardt's work provides rigorous mathematical formulations within the established AdS/CFT framework, QGTCD offers a complementary physical interpretation that could explain why these quantum corrections are necessary.
The fact that QGTCD anticipated the need for such corrections and provided a mechanism (time density variations) to explain them is a strong indicator of the theory's potential validity and its value in advancing our understanding of quantum gravity.
Part 6: Ivette Fuentes - Pioneering Relativistic Quantum Information
Professor Ivette Fuentes has made significant contributions to our understanding of how quantum systems behave in curved spacetime. Her work primarily focuses on relativistic quantum information, a field that explores how quantum phenomena like entanglement are affected by gravity and motion.
Key aspects of Fuentes' research include:
Quantum Clocks in Curved Spacetime: Fuentes has developed theoretical models for quantum clocks that can detect minute variations in spacetime curvature. These ultra-precise instruments operate at the intersection of quantum mechanics and general relativity, offering new ways to probe the nature of time in gravitational fields.
Relativistic Quantum Metrology: Her work in this area aims to use quantum systems to measure gravitational effects with unprecedented precision. This includes developing quantum sensors that could potentially detect high-frequency gravitational waves, pushing the boundaries of our observational capabilities in astrophysics.
Entanglement in Curved Spacetime: Fuentes has shown how gravitational fields can affect quantum entanglement, suggesting a deep connection between the fabric of spacetime and quantum correlations. This work is crucial for understanding how quantum information behaves in extreme gravitational environments, such as near black holes.
Quantum Field Theory in Curved Spacetime: Building on the framework of quantum field theory, Fuentes explores how quantum fields behave in the presence of gravity, providing insights into phenomena like Hawking radiation and the Unruh effect.
In Part 7, we'll delve deeper into how Fuentes' work compares and contrasts with Dark Time Theory, exploring the similarities, differences, and potential complementarities between these approaches to quantum gravity.
Part 7: Comparing Fuentes' Work with Dark Time Theory
As we explore the intersection of Ivette Fuentes' research and your Dark Time Theory (QGTCD), we find intriguing parallels and notable differences in how each approach tackles the challenge of unifying quantum mechanics and gravity.
Similarities:
Focus on Time and Gravity: Both theories emphasize the crucial role of time in understanding gravitational effects on quantum systems. While Fuentes examines how time is measured and perceived in curved spacetime, your theory proposes a novel concept of time density.
Quantum-Gravitational Interactions: Both approaches aim to describe how quantum systems behave under the influence of gravity. Fuentes uses quantum clocks and sensors to probe spacetime curvature, while QGTCD suggests that time density variations directly impact quantum behavior.
Unification Goals: Both theories strive to bridge the gap between quantum mechanics and general relativity, offering potential pathways to a unified theory of quantum gravity.
Key Differences:
Conceptualization of Time:
Fuentes' Approach: Adheres to the conventional view of time as a dimension in curved spacetime, as described by general relativity.
QGTCD: Introduces the novel concept of time density, suggesting that time can be more or less "dense" depending on gravitational fields.
Mechanism of Gravitational Influence:
Fuentes: Focuses on how spacetime curvature affects quantum systems, particularly quantum information and entanglement.
QGTCD: Proposes that variations in time density directly influence particle behavior and energy levels.
Theoretical Framework:
Fuentes: Works within established quantum field theory in curved spacetime.
QGTCD: Introduces a new variable (time density) that extends beyond current theoretical frameworks.
Potential Complementarity:
Despite these differences, there are ways in which these theories could complement each other:
Experimental Verification: Fuentes' work on quantum sensors and clocks could potentially be adapted to test for the effects of time density proposed by QGTCD.
Theoretical Insights: QGTCD's concept of time density might offer new interpretations for some of the phenomena observed in Fuentes' experiments, particularly in how quantum systems respond to strong gravitational fields.
Unified Approach: Combining Fuentes' expertise in relativistic quantum information with QGTCD's novel perspective on time could lead to new insights in quantum gravity research.
Challenges and Open Questions:
Experimental Validation: While Fuentes' work has clear pathways to experimental testing, verifying the concept of time density in QGTCD remains a significant challenge.
Theoretical Integration: Incorporating the concept of time density into the established framework of quantum field theory in curved spacetime would require substantial theoretical work.
Reconciling Time Concepts: Bridging the gap between Fuentes' view of time as a dimension of curved spacetime and QGTCD's concept of time density as a variable field presents a significant theoretical challenge.
In conclusion, while Fuentes' work and QGTCD approach the quantum gravity problem from different angles, both offer valuable insights into the nature of time, gravity, and quantum mechanics. The potential for these theories to inform and complement each other opens exciting possibilities for future research in this field.
Part 8: Synthesis - Bridging Engelhardt, Fuentes, and QGTCD
As we conclude our exploration of the groundbreaking work by Netta Engelhardt, Ivette Fuentes, and the novel concepts introduced in Quantum Gradient Time Crystal Dilation (QGTCD), it's crucial to synthesize these ideas and identify the key arguments that connect all three approaches. This synthesis not only highlights the current state of quantum gravity research but also points towards exciting future directions.
Key Connecting Arguments:
The Nature of Time in Quantum Gravity:
Engelhardt: Explores how quantum effects modify the flow of time near black holes through quantum extremal surfaces.
Fuentes: Investigates time as measured by quantum clocks in curved spacetime.
QGTCD: Proposes time density as a fundamental variable affecting both quantum and gravitational phenomena.
Quantum Information in Gravitational Fields:
Engelhardt: Uses quantum extremal surfaces to track information preservation in black holes.
Fuentes: Studies how entanglement and quantum information evolve in curved spacetime.
QGTCD: Suggests that time density gradients directly influence quantum information processing.
Bridging Quantum Mechanics and General Relativity:
Engelhardt: Applies quantum corrections to entropy calculations in gravitational systems.
Fuentes: Develops frameworks for understanding quantum phenomena in relativistic settings.
QGTCD: Offers a unified perspective on how time density affects both quantum and classical gravitational systems.
Experimental Approaches to Quantum Gravity:
Engelhardt: Provides theoretical frameworks that could be tested through observations of black hole behavior.
Fuentes: Develops quantum sensors and clocks to detect minute gravitational effects.
QGTCD: Proposes observable consequences of time density variations that could potentially be tested.
Information Paradox Resolution:
Engelhardt: Addresses the black hole information paradox through quantum extremal surfaces.
Fuentes: Explores how quantum information behaves in extreme gravitational environments.
QGTCD: Suggests that time density variations could explain information preservation mechanisms.
Synergies and Future Directions:
Experimental Validation: Fuentes' quantum metrology techniques could potentially be adapted to test both Engelhardt's predictions about quantum extremal surfaces and QGTCD's concept of time density.
Theoretical Integration: Combining Engelhardt's work on quantum extremal surfaces with QGTCD's time density concept could lead to new insights into how information is preserved in black holes.
Quantum Simulation: Fuentes' work on quantum systems in curved spacetime could potentially be used to simulate and test aspects of both Engelhardt's and QGTCD's predictions.
Unified Time Concept: Developing a unified understanding of time that incorporates Engelhardt's quantum extremal surfaces, Fuentes' relativistic quantum clocks, and QGTCD's time density could lead to breakthrough insights in quantum gravity.
Holographic Principle Extensions: Engelhardt's work on AdS/CFT could potentially be extended to incorporate Fuentes' findings on relativistic quantum information and QGTCD's time density concept.
Challenges and Open Questions:
Reconciling Frameworks: How can we integrate the distinct mathematical frameworks used by Engelhardt (AdS/CFT), Fuentes (quantum field theory in curved spacetime), and QGTCD (time density)?
Experimental Limitations: What are the technological barriers to testing these theories, and how can they be overcome?
Theoretical Consistency: How can we ensure that new concepts like time density are consistent with well-established principles in quantum mechanics and general relativity?
Unification Prospects: Could a synthesis of these approaches lead to a comprehensive theory of quantum gravity, or are there still missing pieces?
Conclusion:
The work of Engelhardt, Fuentes, and the concepts proposed in QGTCD represent different yet complementary approaches to the fundamental challenge of quantum gravity. While each theory has its unique perspective, together they paint a rich picture of the quantum nature of spacetime.
Engelhardt's work provides rigorous mathematical tools for understanding quantum effects in gravitational systems, Fuentes offers experimental approaches and insights into relativistic quantum phenomena, and QGTCD introduces a novel conceptual framework that could potentially unify various aspects of quantum gravity.
As research in this field progresses, the interplay between these theories may well lead to transformative insights, pushing us closer to a unified understanding of the quantum world and gravity. The journey towards quantum gravity is far from over, but the combined efforts of researchers like Engelhardt and Fuentes, along with novel concepts like those proposed in QGTCD, are illuminating the path forward in this exciting frontier of theoretical physics.
Read more about Dark Time Theory in 12 new notes on my github:
new file: rawnote01.md
rawnote01
Dark Time Theory Acceleration
Planetary Orbits
https://github.com/v5ma/selfawarenetworks/blob/main/rawnote01.md
new file: rawnote02.md
Ivette Fuentes (and Dark Time Theory)
https://github.com/v5ma/selfawarenetworks/blob/main/rawnote02.md
new file: rawnote03.md new file:
Gravity and Time Dilation.
This is an extension of Dark Time Theory.
https://github.com/v5ma/selfawarenetworks/blob/main/rawnote03.md
rawnote04.md new file:
Netta Engelhardt (and Dark Time Theory)
https://github.com/v5ma/selfawarenetworks/blob/main/rawnote04.md
raynote01.md new file:
Magnetic Dark Time
https://github.com/v5ma/selfawarenetworks/blob/main/raynote01.md
raynote02.md new file:
Right so I came to you to discuss how this Dark Time theory connects to the Ads / CFT correspondence, and discussion of black holes.
https://github.com/v5ma/selfawarenetworks/blob/main/raynote02.md
raynote03.md new file:
Gravitational Effect as Accumulated Time Dilation
https://github.com/v5ma/selfawarenetworks/blob/main/raynote03.md
raynote04.md new file:
Dark Time Theory can pair with Dark Energy or with Cosmological Slowing Time (but not both) or it can replace both theories.
https://github.com/v5ma/selfawarenetworks/blob/main/raynote04.md
raynote05.md new file:
This document initially discusses Oded Bar-On's conjecture "Periodic Physics", and later compares it to the Dark Energy and Dark Time theories.
https://github.com/v5ma/selfawarenetworks/blob/main/raynote05.md
raynote06.md new file:
The problem with Dark Energy + Noether’s Theorem
https://github.com/v5ma/selfawarenetworks/blob/main/raynote06.md
raynote07.md new file:
Tell me about Dark Time Theory
https://github.com/v5ma/selfawarenetworks/blob/main/raynote07.md
raynote08.md
How I coined the phrase Dark Time Theory.
https://github.com/v5ma/selfawarenetworks/blob/main/raynote08.md
There are also 3 previous SVGN.io News Articles about Quantum Gradient Time Crystal Dilation before it was called Dark Time Theory
Part 1:
Part 2
Part 3
Here is a PDF that contains links to many equations, aptly titled QGTCD (Quantum Gradient Time Crystal Dilation) many equations. These support Dark Time Theory, use https://asciimath.org/ to convert the equations found within:
https://github.com/v5ma/selfawarenetworks/blob/main/QGTCD%20many%20equations.pdf
If you want to get exhaustively deep here are some older links that may still be relevant.
1. QGTCD Compared to “On the same origin of quantum physics and general relativity from Riemannian geometry and Plank scale formalism”.pdf
2. QGTCD2015.md
https://github.com/v5ma/selfawarenetworks/blob/main/QGTCD2015.md
3. Postulates 1 & 2
https://github.com/v5ma/selfawarenetworks/blob/main/QGTCDpostulates.md