This "wonders of the Big Little Problem" resource is dedicated to my grandchildren - it is a work in progress like the "Big Little Problem" itself
The Big Little Problem is to characterize the space time continuum from the scale of the Cosmological horizon (The Big (Bang))(and potentially beyond) to Plancks length (The Little) A trillion trillion times smaller than an atom) (and potentially beyond.)
The Big Little Problem is an open problem. It is about the deepest layers of reality. Since the beginning of our species we have grappled with how to make sense of our world and to survive. This has necessitated mapping our world and therefore measuring it. To measure it, is to map it; to map it is to measure it. The earliest record we have of this is the Ishango bone - a tally stick.The earliest conceptual leap necessary for this measurement was pre-mathematics and involved "one to one correspondence".
The Big Little Problem is part of ontology - the philosophical study of being. It is sometimes referred to as the Hierarchy Problem and is related to the fine-tuned universe problem.
Modern physics has characterized elements of the universe in terms of the current known as the Standard model. The Standard Model of particle physics is the theory describing fundamental forces. There are four fundamental forces at work in the universe: the strong nuclear force, the weak force, the electromagnetic force, and the gravitational force (not really a force). They work over different ranges and have different strengths. Gravity is the weakest but it has an infinite range.
The Standard model has been refined over time but remains incomplete in various ways. Various other disciplines like cosmology have characterized in various fragmented ways space at various scales and the "rules" that apply in those spaces but there appears to be no agreed upon,integrated view of the space at various scales and the implications of what is possible in those spaces.This has been a function of our lack of tools for measurement. We cannot, by way of example, "see" dark matter
Dark Matter is an inferred missing mass energy in the universe. In the standard lambda-CDM model of cosmology, the mass–energy content of the universe is only 5% ordinary matter.
Particle physicists have been looking inward and astronomers have been looking outward.
The human species lives at the nexus of the Big Little venturing "outward" and "inward" through instrumentation to tap the resources at various scales where the laws of the universe provide different potential resources. What we lack are the necessary tools as well as mental models.
Mathematics is essential to a deep understanding the Big Little Problem. It provides the platform for discovery and for expressing the key ideas and perspectives required to understand reality.
One aspect of the Big Little Problem is the seeming intractability of the certain mathematical problems. Another is imposed by current computational systems limits.
Infinity and the problem of emergence are also related.
1 Our ability to sense, never mind measure (metrology), at very small scales is central to articulation of the big little problem.
The Planck scale (\(10^{-35}\) meters, \(10^{19}\) GeV) represents the limit where current physical theories, specifically General Relativity and quantum mechanics, break down and become incompatible. Key problems include the lack of experimental access, the emergence of untameable mathematical infinities, the potential inaccuracy of fundamental constants, and the unknown nature of gravity at that scale.
You Tube - Talks and Presentations
Acquiring a feel for the space time continuum.
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YT: Visualizing the Planck Length: The Smallest Scale of the Universe (June 16, 2025)(12 min)
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YT: The Scale of the Universe | From Planck Length to the Observable Universe (4 min)(2018)
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YT:
Universe Size Comparison | 3d Animation Comparison | Stars Real Scale Comparison ( October 19, 2022 )(4.5 min)
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YT: The Planck Length: The Resolution of the Universe? (8 min)(2021)
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YT: The Scale of Everything - The Big, the Small and the Planck (18 Min)(Curious Droid)(2021)
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YT: The Planck scale: Is there a fundamental limit to space and time? (Physics Explained) (28 min) (2023)
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YT: The Royal Institution: Dr. David Tong: The Universe at the smallest scale - quantum gravitational field (Plank Length)(59 min) (March 25, 2024
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YT: The Kavili Prize: Lisa Randall, Scale Matters (52 min)(March 2023
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YT:
Quanta Magazine: Vijay Balasubramanian: Space-Time: The Biggest Problem in Physics: The Planck length, an intro to space-time (19 min) (September 25, 2024)
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YT: Why don't electrons fall onto the nucleus? (22 min)(March 2024
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YT: The surprising reason behind electron spin! (They don't REALLY spin) (16 min)(March 2024)
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YT:Smallest Particle in the Cosmos Discovered | Neutrinos can cross Earth without Resistance (6 min)(April 21, 2024)
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YT:Microchip Scaling Beyond 1nm
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YT:24 04 03 talk by Prof. Neil Turok - a surprisingly economical description of the universe on both very small and very large scales (April 5, 2024)
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YT:24 04 03 Particles Unknown: Hunting Neutrinos | Full Documentary | NOVA | PBS(April 24, 2024)
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YT: Sean Carroll, "The Biggest Ideas in the Universe: Space, Time, and Motion", Harvard Science Book Talks and Research Lectures (March 8, 2023)
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YT:Sean Carroll, "Quanta and Fields: The Biggest Ideas in the Universe", Harvard Science Book Talks and Research Lectures (June 1, 2024)
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YT: The Royal Institution: The quantum revolution - with Sean Carroll (October 1, 2024)
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YT: What Happens Beyond the Planck Length? (September 20, 2023)
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YT: Physics Surrounding Black Holes (January 25, 2025)
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YT: Perimeter Institute: Niayesh Afshordi: Battle of the Big Bang: The New Tales of Our Cosmic Origins (June 4, 2025) (106min)
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YT: Terence Tao on how we measure the cosmos | The Distance Ladder Part 1 (February 8, 2025) (28 min)
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YT:First Results from the Vera C. Rubin Observatory equipped with the largest digital camera ever built.
(June 23, 2025) (127 min)
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YT: Scott Manley
Millions of New Asteroids - How The Vera Rubin Telescope Changes Everything
(June 25, 2025) (127 min)
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YT: How We Mapped The Infinite Universe With Jim Al-Khalili
(June 19, 2025) (59 min)
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YT: Can Something Come From Nothing? Exploring The Universe's Origins With Jim Al-Khalili
(June 26, 2025) (59 min)
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YT: What If The Universe Has No End? Exploring Infinite Scales With Jim Al-Khalili
(June 25, 2025) (59 min)
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YT: PBS Digital Studios: The Crisis In Physics: Are We Missing 17 Layers of Reality?
(June 12, 2025) (32 min)
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YT:Nima Arkani-Hamed, Gopal Prasad Professor, School of Natural Sciences, Institute for Advanced Study, Beyond Space - Time and Quantum Physics from Little C (10 -17cm) to Big C (Cosmology) 10 +27 cm
(July 15, 2025) (20 min)
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YT: Richard Feynman Nothing Doesn't Exist: Why the space between atoms is not empty (18 min)
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YT: David J. Gross: Quantum Field Theory Past, Present, Future
(July 14, 2025) (108 min)
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Its About Time, and Space
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Quanta Magazine: What Is Entropy? A Measure of Just How Little We Really Know. (December 13, 2024)||("What’s really going on is there’s macroscopic order forming at the expense of microscopic disorder,")
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APS: January 1928: The Dirac equation unifies quantum mechanics and special relativity
A seminal paper by Paul Dirac, who relied on mathematical intuition, laid the foundation for quantum electrodynamics. (November 19, 2024)
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Attosecond science: Nobel-worthy nonlinear optics on steroids (November 1, 2024)
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Femtosecond fieldoscopy accesses molecule fingerprints at near-infrared spectral range (October 22 , 2024)
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arxiv: Quantum phenomena in attosecond science (March 8, 2024)
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Gravity experiments on the kitchen table: why a tiny, tiny measurement may be a big leap forward for physics (March 3, 2024)
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Big Think: A great many cosmic puzzles still remain unsolved. By embracing a broad and varied approach, particle physics heads toward a bright future. (March 28, 2024)
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Report of the 2023 Particle Physics Project Prioritization Panel
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Wiki: Hilbert's problems
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Daily Galaxy: 125-Year-Old Physics Puzzle Finally Cracked by Mathematicians (April 28, 2025)
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arxiv.org: HILBERT’S SIXTH PROBLEM: DERIVATION OF FLUID EQUATIONS VIA BOLTZMANN’S KINETIC THEORY YU DENG, ZAHER HANI, AND XIAO MA (March 3, 2025)
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YT: Simons Foundation Talk: Yu Deng: The Hilbert Sixth Problem: Particles and Waves (December 6, 2024) (April 8, 2025) (49 min)
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Simons Foundation: Quanta Magazine: Epic Effort to Ground Physics in Math Opens Up the Secrets of Time (June 11, 2025)
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Theoretical physicists completely determine the statistics of quantum entanglement (March 26, 2025)
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Wiki Exponentiation
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Wiki: The Halting Problem
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Wiki: Complexity Theory
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Royal Society Open Science: A Master Equation for Power Laws (December 7, 2022)
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Matrices in Deep Learning
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No evidence for fractal scaling in canopy surfaces across a diverse range of forest types (December 18, 2023)
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Wiki: Metabolic theory of ecology (+ Metabolic Scaling Theory)
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Constructal Theory
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Quanta Magazine: "In both aperiodic tilings and quantum error-correcting codes, learning about a small part of a large system reveals nothing about the system as a whole."
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Wiki: Measure Theory
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Researchers using pulsar measurements to probe dark matter find Milky Way galaxy is highly dynamic (February 26, 2024)
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"Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms.
It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science."
"Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms.
It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science."
New Theory of Quantum Gravitation
Electromagnetism - part of the Big Little puzzle
The influence of dark matter (DM), which constitutes around 85% of matter in the Universe, has been firmly
established by astronomical observations.
"For perspective, the lightest known particle is the neutrino, which is about 500,000 times lighter than an electron. In the most extreme models, the lightweight dark matter can be billions of times lighter than a neutrino.
If dark matter has such a small mass, it will behave in unexpected ways. For example, instead of zipping around the cosmos like particles, it would slosh around like waves."
Metrology - the science of measurement - the necessary tool for understanding reality.
Mathematics, metrology and physics have marched hand in hand since the beginning. Metrology provides the conceptual scafolding for the abstractions necessary to map reality. If you can't measure it, it you can't understand it. If you can't understand it you can't harness it.
Particle Experiments - exploration of the "little"
Physicists and Mathematicians focused on the Big Little Problem
News at infinitesimal scales - On the Little Frontier
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