The Most Difficult Physics Problem, Ranked

Voting rules: Choose the problem you think is the most difficult!

Updated on May 3, 2024 06:25

Physics often poses challenges that push the boundaries of understanding and innovation. Grasping the complexities of some problems in this field can be daunting even for seasoned professionals. By collectively evaluating which issues are the most perplexing, we can better focus our intellectual resources where they are most needed. This community-driven ranking offers a unique opportunity for experts and enthusiasts alike to voice their opinions on the scale of difficulty of various physics problems. By voting, you contribute to a clearer picture of where collective confusion or interest lies, potentially guiding future educational and research priorities.

What Is the Most Difficult Physics Problem?

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73
votes
The Navier-Stokes equations

These equations describe the motion of fluids and are notoriously difficult to solve. In fact, they are one of the seven Millennium Prize Problems, offering a $1 million reward for a solution.
The Navier-Stokes equations are a set of partial differential equations that describe the motion of fluid substances. They are named after Claude-Louis Navier and George Gabriel Stokes, who independently derived them in the 19th century.

Equation type: System of nonlinear partial differential equations

Fluid motion: Describes the motion of viscous fluids

Conservation laws: Includes conservation of mass, momentum, and energy

Vector field: Involves the velocity vector field and the pressure scalar field

Applications: Used in various fields such as aerospace engineering, fluid dynamics, and weather forecasting
The Navier-Stokes equations in other rankings
- Position 4 of 10 in Most difficult Calculus problem
- Position 9 of 10 in Most popular equation
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50
votes
The Three-Body Problem

This problem involves calculating the motion of three celestial bodies, such as planets or stars, under the influence of gravity. It is considered one of the most difficult problems in classical mechanics.
The Three-Body Problem is a classical physics problem that involves calculating the motion of three celestial bodies under gravitational forces. It seeks to determine the positions and velocities of the three bodies at any given time as they interact with each other.

Number of Bodies: 3

Algorithm Complexity: O(n^2)

Chaotic Behavior: Yes

Analytical Solutions: Very limited

Numerical Solutions: Commonly used
3

16
votes
The Holographic Principle

This principle suggests that the universe may be a hologram, with all the information contained on its surface. While it has not been proven or disproven, it poses significant theoretical challenges to physicists.
The Holographic Principle is a concept in physics that suggests that the information contained within a region of space can be fully described by the information on its boundary. It proposes that the laws of physics and the description of a particular volume of space can be encoded or projected onto its bounding surface or lower-dimensional space.

Information Encoding: The principle suggests that all the information within a given volume can be encoded on the boundary of that volume.

Boundary Projection: The holographic principle proposes that the 3D information of a physical system can be projected onto a 2D surface.

Black Holes: The principle is often linked to black holes, suggesting that the information inside a black hole is encoded on its event horizon.

String Theory: The holographic principle is closely related to string theory and is significant in understanding the nature of the holographic dualities that arise in the theory.

Quantum Entanglement: The principle highlights the role of quantum entanglement, suggesting it plays a crucial role in the holographic encoding of information.
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23
votes
The Grand Unified Theory

This theory seeks to unify the fundamental forces of nature into a single, coherent framework. While progress has been made, a complete theory has yet to be developed.
The Grand Unified Theory (GUT) is a theoretical framework in physics that aims to unify the three fundamental forces of nature: electromagnetism, the strong nuclear force, and the weak nuclear force. It seeks to explain how these forces are fundamentally interconnected and how they can be described by a single set of equations. By achieving this unification, GUT could provide a deeper understanding of the fundamental laws governing the universe.

Unification of Forces: The Grand Unified Theory seeks to unify electromagnetism, the strong nuclear force, and the weak nuclear force into a single mathematical framework.

Symmetry: GUT postulates symmetry principles that govern the behavior of the fundamental particles and forces.

Particle Interactions: It describes the interactions between three types of particles: leptons, quarks, and gauge bosons.

Predictions: GUT makes various predictions, such as the existence of new particles and phenomena that could be observed in particle accelerators.

Energy Scale Unification: It suggests that at extremely high energies, the three forces can be described by a single unified force.
5

21
votes
Quantum Gravity

This is the attempt to reconcile quantum mechanics with general relativity, which governs the behavior of gravity. It is an active area of research, but a complete theory has yet to be developed.
Quantum gravity is a theoretical framework attempting to reconcile quantum mechanics and general relativity into a consistent theory of gravity at the smallest scales, where quantum effects become significant. It aims to describe the behavior of gravity using the principles of quantum mechanics, which govern the behavior of particles at the microscopic level.

1: Combines quantum mechanics and general relativity

2: Attempts to explain gravity at the quantum level

3: Seeks to unify the fundamental forces of nature

4: Involves the study of hypothetical particles called gravitons

5: Addresses the behavior of gravity in the early universe and near black holes
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8
votes
The Theory of Everything

This is a hypothetical theory that would explain everything in the universe, from the smallest subatomic particles to the largest structures. While progress has been made, a complete theory has yet to be developed.
The Theory of Everything is a hypothetical physics theory that aims to explain and unify all fundamental forces and particles in the universe into a single framework. It seeks to provide a comprehensive understanding of the behavior of our physical reality at both the macroscopic and microscopic levels.

Unification: The theory aims to unify the four fundamental forces of nature: gravity, electromagnetism, the weak nuclear force, and the strong nuclear force.

Quantum Mechanics: It incorporates the principles of quantum mechanics, which describe the behavior of particles at the smallest scales.

General Relativity: The theory seeks to reconcile and merge general relativity, which explains gravity on a large scale, with quantum mechanics.

Grand Unified Theory (GUT): The Theory of Everything is often related to Grand Unified Theories, which attempt to unify the strong nuclear force, weak nuclear force, and electromagnetism.

String Theory: It connects to various forms of string theory, where particles are envisioned as tiny vibrating strings.
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12
votes
The Black Hole Information Paradox

Stephen Hawking

This paradox involves the loss of information when matter falls into a black hole, which seems to violate the laws of quantum mechanics. It remains an unsolved problem in physics.
The Black Hole Information Paradox refers to the theoretical conflict between quantum mechanics and general relativity that arises when discussing what happens to information that falls into a black hole. According to classical physics, once information enters a black hole, it is lost forever due to the irreversibility of black hole evaporation, known as Hawking radiation. However, this conflicts with the principles of quantum mechanics, which state that information cannot be destroyed. Resolving this paradox is one of the important unsolved problems in modern physics.

Paradox type: Information paradox

Proposed: 1975

Field: Quantum physics and general relativity

Solution status: Unresolved

Quantum gravity implications: Relevant
8

9
votes
Aflafla1WikiHelper1982 (French translation) · CC0

Dark Matter

This is matter that does not emit, absorb, or reflect light, and is therefore invisible. It is thought to make up 85% of the matter in the universe, but its nature is still unknown.
Dark matter is a form of matter that does not emit, absorb, or reflect electromagnetic radiation, making it invisible to direct observation. It is believed to make up approximately 85% of the matter in the universe and is thought to play a crucial role in the formation of galaxies and the structure of the cosmos. Although its existence has been inferred through its gravitational effects, its precise nature and composition remain unknown.

Abundance: Dark matter is estimated to make up about 85% of the total matter in the universe.

Invisible to Electromagnetic Radiation: Dark matter does not emit, absorb, or reflect electromagnetic radiation, making it difficult to detect directly.

Gravitational Effects: Its existence is inferred through its gravitational effects on visible matter and its influence on the large-scale structure of the universe.

Unknown Composition: The exact particles that make up dark matter are still unknown, and several potential candidates are being studied.

Non-baryonic: Dark matter is believed to be non-baryonic, meaning it does not consist of ordinary matter particles such as protons and neutrons.
Dark Matter in other rankings
- Position 10 of 10 in Most popular show on Syfy
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5
votes
Dark Energy

This is a mysterious force that is causing the expansion of the universe to accelerate. Its nature is also unknown, but it is thought to make up 68% of the universe's total energy.
Dark energy is a mysterious and hypothetical form of energy that is believed to permeate all of space and contribute to the accelerated expansion of the universe. It accounts for a significant portion of the total energy content of the universe, but its nature and origin remain poorly understood.

Nature: Unknown

Origin: Uncertain

Energy Type: Negative pressure

Influence: Causes accelerated expansion of the universe

Density: Low but constant
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8
votes
The Arrow of Time

This is the concept that time only flows in one direction, from past to future, and cannot be reversed. While it is well-established in physics, the underlying reason for this phenomenon is still not fully understood.
The Arrow of Time refers to the distinction between the past and the future in physics, indicating the directionality of time. It is a concept that explains why events in the universe seem to occur in a particular sequence, with a clear distinction between cause and effect. The Arrow of Time is often associated with the concept of entropy, which is a measure of disorder or randomness in a system.

Irreversibility: The Arrow of Time implies that certain processes in nature are irreversible, meaning they can only occur in one direction and cannot be reversed.

Entropy: Entropy tends to increase over time, meaning that systems become more disordered and random as time progresses.

Thermodynamics: The Arrow of Time is closely connected to the second law of thermodynamics, which states that the entropy of an isolated system will always increase or remain constant.

Expanding Universe: The observed expansion of the universe, as described by the Big Bang theory, also contributes to the concept of the Arrow of Time.

Time Reversal Symmetry: While individual physical processes may be reversible, the overall macroscopic behavior of systems tends to exhibit time irreversibility.

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Ranking factors for difficult problem

Conceptual complexity

The problem should involve a deep understanding of the fundamental concepts in physics, such as classical mechanics, electromagnetism, statistical physics, quantum mechanics, or relativity. The more advanced and abstract the concepts, the more difficult the problem is likely to be.
Mathematical complexity

Difficult physics problems often involve advanced mathematical techniques and methods. The difficulty can depend on the level of mathematical sophistication required to tackle the problem, such as calculus, linear algebra, differential equations, or tensor analysis.
Number of steps or sub-problems

Problems that require multiple steps or sub-problems to be solved can be more difficult, as they require a greater level of organization and problem-solving skills.
Pervasiveness of approximations

Some physics problems are inherently more difficult because they involve complex systems or phenomena where approximations are either impossible or only limited in their usefulness. In these cases, an exact or highly accurate solution may be challenging to obtain.
Presence of non-intuitive aspects

Physics problems can be challenging if they involve non-intuitive phenomena or require a deep understanding of counterintuitive concepts. For example, problems involving quantum mechanics or relativity can be especially difficult for students, as they involve principles that are not encountered in everyday experiences.
Ambiguity or lack of clear information

Physics problems can be challenging when they present ambiguous or incomplete information, requiring the problem solver to make educated guesses, assumptions, or approximations to arrive at a solution.
Requirement of computational resources

Some physics problems are so complex that they require significant computational resources to solve numerically, which can add to the overall difficulty of the problem, especially when a closed-form or analytical solution is not available.
Real-world applicability

Problems that involve real-world scenarios and constraints may be considered more difficult, as they require not only a deep understanding of the relevant physics principles but also an ability to apply them in practical situations.
Novelty or originality

Difficult physics problems may require a creative approach to problem-solving, especially when they involve new or speculative ideas that have not been addressed extensively in the literature.
Interdisciplinary nature

A problem that integrates concepts from different branches of physics or requires knowledge and skills from other scientific disciplines, such as mathematics, chemistry, or biology, can be considered more difficult because it requires a broader understanding and more diverse problem-solving skills.

About this ranking

This is a community-based ranking of the most difficult Physics problem. We do our best to provide fair voting, but it is not intended to be exhaustive. So if you notice something or problem is missing, feel free to help improve the ranking!

Statistics

4376 views
186 votes
10 ranked items

Voting Rules

A participant may cast an up or down vote for each problem once every 24 hours. The rank of each problem is then calculated from the weighted sum of all up and down votes.