#246 – Peter Woit: Theories of Everything and Why String Theory is Not Even Wrong

Podcast Summary

• The Emergence of a Grand Unified Theory of Mathematics and Physics: Mathematics and physics may appear to be different, but they are becoming increasingly intertwined as a result of a shared understanding of deep mathematical concepts. This is leading to a more unified theory of physics.

  Physics and mathematics have a conventional understanding that they are different things, but there is a significant overlap between them. Mathematicians make rigorous statements about abstract things and prove them rigorously, while physicists do experiments and test various models. However, a grand unified theory of mathematics and physics is emerging with the same mathematical objects appearing in both fields. This unification is based largely on deep mathematics that bring together geometry, number theory, and representation theory. These ideas are quite alien to our everyday understanding, but their discovery provides a unified set of ways of thinking that allow us to make a unified theory of physics.

• The Intersection of Geometry and Physics: Exploring Dimensions Beyond Human Perception: Math and physics reveal that our everyday experiences only scratch the surface of the complexity of the world. While physicists focus on practical examples, mathematicians create abstract objects to solve problems. Simplification is key.

  Math and physics have discovered geometries that are not obvious from human everyday experiences. While humans are used to three spacial and one time dimension, recent developments in number theory suggest that physics is four-dimensional. Mathematicians can work in any dimension, but physicists are interested in specific examples. While physicists have made the mistake of trying to go to higher dimensions, which leads to the problem of how to get rid of all the extra dimensions, mathematics thrives on creating abstract objects. When trying to solve a difficult problem, mathematicians and physicists both rely on simple examples that capture the fundamentals of the problem.

• Understanding Complex Ideas in Math and Physics with Visualization and Experimentation: Breaking down complex concepts into simpler situations can aid in comprehension. Visualization and experimentation build intuition. While higher-dimensional structures present challenges, beauty can be found in the ongoing search for unification in math and physics.

  In order to gain insight into complex ideas in math and physics, it can be helpful to break them down into simpler situations and try to really understand them. Visualization and experimentation can also aid in building intuition. However, when dealing with higher-dimensional structures, it can be challenging to fully comprehend them with the limitations of the human mind. Despite this challenge, there is still beauty in the ideas and the ongoing search for unification in math and physics. Inspiration can be found in both fields, as successful ideas in fundamental physics often lead to deeper exploration in mathematics and vice versa.

• The Langlands Program: Unifying Mathematics through Ideas of Symmetry, Groups, and Representations.: The Langlands program seeks to link different areas of mathematics by using concepts of symmetry and groups to study number theory problems. One fundamental idea is that algebra can be thought of as the space of functions on geometry.

  The Langlands program in mathematics is an area that unifies different fields like number theory, geometry, differential geometry, and topology through ideas about symmetry, groups, and representations. This program aims to obtain new insights in geometry by studying number theory problems. However, even most mathematicians may not fully understand the complex concepts involved in this area of study, including recent breakthroughs in local problems in number theory reformulated through geometric Langlands. One beautiful and fundamental idea that can explain the connection between algebra and geometry is that you can think of every algebra as the space of functions on some geometry. For example, the integers can be seen as a function on the space of prime numbers.

• The Underlying Connection between Algebra and Geometry in Mathematics: Algebraic gadgets can be thought of as functions on a space, illustrating the power of simple ideas in capturing the fabric of reality in modern number theory and solving difficult mathematical problems.

  Peter Woit explains how the fundamental idea of connecting algebra with geometry underpins much of mathematics. It involves thinking about functions on a space and realizing that abstract algebraic gadgets can also be thought of as functions on a space. The beauty of an idea is measured in how much power and information it packages into something simple. Ideas become uglier and more complicated as more elements are added to make them do what we want. In terms of simplicity, beauty, and truth, simpler theories are more likely to capture the fabric of reality. This idea is at the basis of modern number theory and has allowed for the proof of many difficult mathematical problems.

• The Importance of Self-Consistency and Simplicity in Developing Theories.: Developing theories requires self-consistency and simplicity to ensure consistency with experimental data. It is crucial not to fool oneself into thinking an idea is more simple or beautiful than it is, and to fix any inconsistencies with experimental observations.

  Physicist Peter Woit believes that there is something about the universe that is fundamentally simple, and that the best theories are ultimately relatively simple. However, he also cautions that it is easy to fall in love with an idea and fool yourself into thinking it is more beautiful or simple than it actually is. He agrees with physicist Sabine Haas that self-consistency is a better guide to developing theories than simplicity or beauty alone. If a theory is not consistent with experimental observations, then there is something about it that needs fixing. Ultimately, the goal is to develop theories that are both simple and consistent with experimental data.

• Challenges in Pursuing a Theory of Quantum Gravity: Without experimental data, consistency testing through thought experiments is one way to pursue a theory. However, this approach may lead to multiple consistent theories that cannot be experimentally distinguished. String theory is criticized for lacking experimental validation.

  Peter Woit discusses the challenges in arriving at a theory of quantum gravity, since quantum gravitational effects are tiny and difficult to observe experimentally. He suggests that one way to pursue a theory in the absence of experimental data is to search for consistency, which involves testing ideas with thought experiments to check if they offer a consistent picture of what would happen in a particular situation. However, the danger is that this approach may lead to multiple consistent theories that cannot be experimentally distinguished. Woit also touches on the topic of string theory, which he criticizes for being difficult to define and lacking experimental validation.

• Understanding String Theory: Unifying General Relativity and Quantum Mechanics: String theory proposes that everything is made up of tiny, vibrating strings and there are 10 dimensions in the universe. While there's no experimental evidence, it's sparked a lot of interest and led to beautiful mathematics and new ideas in physics.

  String theory is a theoretical framework that attempts to unify general relativity and quantum mechanics. The theory suggests that everything in the universe is made up of tiny, vibrating strings, and that there are 10 dimensions in the universe, including the familiar four dimensions of space-time. However, a major problem with string theory is that there is no experimental evidence to support it. In addition, the theory has a problem with providing a clear and consistent definition, and there are an infinite number of ways to get rid of the six extra dimensions, which makes it difficult to make real-world predictions. Despite these challenges, string theory has sparked a lot of interest and has led to the discovery of beautiful mathematics and new ideas in physics.

• The Unobservable Dimensions Predicted by String Theory: Physicists have tried various approaches to solve the problem of unobservable dimensions predicted by string theory. While some hope for new technologies, the current consensus is that the dimensions are unobservable.

  The problem with string theory is that it predicts that there are six extra dimensions beyond the four dimensions we can observe. To solve this problem, physicists have tried different approaches, including the "clubby ow postulate" and compact suffocation, which shrinks the six dimensions to a size that is unobservable. However, the challenge is that there are too many possible ways to combine the dimensions, making it difficult to pick out the ones that explain why we don't see them. The hope is that with a better understanding of string theory, physicists can find a solution to this problem that goes beyond perturbed expansion. While some physicists may leave the door open to the possibility of new technologies allowing for the observation of extra dimensions, the current consensus is that they are unobservable.

• Exploring the Inverse Square Law and Its Implications for Physics: The inverse square law explains how gravitational force decreases as distance increases. Scientists are studying this law to see if there are any extra dimensions that could affect it. Edward Witten's work has contributed to understanding physics beyond string theory, particularly the challenges of integrating gravity with other fundamental forces.

  The inverse square law is a fundamental law of physics that describes the decrease in gravitational force as distance increases. Scientists are trying to measure this law at smaller and smaller distances to see if there are any extra dimensions that would cause the law to fail. While no evidence for extra dimensions has been found yet, this work is ongoing. Physicist Edward Witten is known for his incredible contributions to mathematics and physics, but most of his greatest work has had nothing to do with string theory. The standard model of physics is generally successful, but has some aspects that are not elegant and require the addition of many extra parameters to make it work. The biggest problem with the standard model is integrating gravity with the other fundamental forces.

• The Complex Debate Over String Theory: Understanding Its Potential Contributions to Science: While the debate over string theory may be complex, it has led to fruitful ideas about mathematics and physics that hold core truths. It is important to understand its potential contributions to science.

  String theory, as a theory of the real world, introduces a Higgs field that requires a large number of parameters to make sense of all the masses and behaviors. While some argue that this complexity may just be the way the world is or may vary across multiple universes, many believe there is a deeper concept related to the origin of the Higgs field that we have yet to discover. Despite its lack of a well-defined proposal and the sociological mess it has become, string theory has led to many fruitful ideas about mathematics and physics that may hold some core truths that should not be ignored. Overall, the debate over string theory is complex and requires a nuanced understanding of its history and potential future contributions to science.

• The Downside of String Theory: Lack of Authenticity and Transparency: String theory has failed to provide experimental validation, hindering progress in the field. A successful unification of gravity and quantum mechanics will require a deeper understanding of physics and math.

  Peter Woit discusses the problem with string theory, where the initial understanding failed to work out. However, people keep referring to it as the starting point and inspiration of the whole subject. He believes that it deforms the whole way of making progress due to the lack of transparency and authenticity in communicating past failures. Experimental validation is necessary to be convinced of a new idea about unification, to see if it tells something true about the real world. Unifying gravity and quantum mechanics is a combination of physics and math problem, not an engineering problem.

• The Misleading Terminology of Theory of Everything: The theory of everything only explains certain specific things and cannot be used to understand complex systems like biology, psychology, and artificial intelligence. It is a reductionist point of view that has limitations.

  The problem with finding a theory of everything is not that we don't have access to the necessary physical or mathematical ideas, but rather that the problem itself is unclear. The theory of everything seeks to describe all objects and how they interact with each other at a fundamental level. However, this is a reductionist point of view that only explains certain specific things and cannot be used to understand emergent behavior. Solving the theory of everything will not give us a complete understanding of the world, as complex systems like biology, psychology, and artificial intelligence require their own theories of everything. The terminology of theory of everything is therefore somewhat misleading.

• The Importance of Developing New Ideas and Ways of Thinking in Different Levels of Explanation: Understanding the whole requires different ways of thinking, even when we know how individual things interact. Computational tools are crucial in solving complex systems, and choosing the right problems to focus on is vital.

  Peter Woit discusses the concept of developing new and different ideas as we move towards different levels of explanation. He mentions Phil Anderson's slogan that "more is different" and asserts that even when we understand how individual things interact with each other, understanding the whole becomes a completely different problem requiring different ways of thinking. He further dismisses the idea of a theory of everything emerging from cellular automata, saying that it goes against the unification of math and physics that he sees around certain deep ideas of geometry. He emphasizes the importance of choosing which problems to spend time thinking about and how computational tools will play an increasingly important role in solving complex systems.

• The Future of Science: Computers Doing Their Own Research: By exploring new ways for computers to conduct scientific research, we may gain a better understanding of complex physics problems. However, developing a theory of everything remains a significant challenge for scientists.

  Researchers are exploring new kinds of science that involve computers doing science on their own computational systems, a process that may help in understanding complex physics problems. While this may be decades away, it could open up new facets of physics exploration. However, the road to developing a theory of everything remains a significant challenge for scientists. The string theory has similar problems as other theories that try to put everything into a bigger structure for unity to explain things. The challenge is getting back to the objects we have seen, which requires a good idea of how to break big structures down into simpler, understandable forms.

• The Challenge of Understanding Theoretical Physics, Mathematics, and AI Development: Understanding theoretical physics and mathematics, as well as AI development, can be challenging. Twister theory offers a new perspective on fundamental concepts, such as light cones and spheres, but can be technically advanced and requires further development.

  Theoretical physics and mathematics can be difficult for even seasoned professionals to understand, and may range from amateurish to academic work. AI development is more straightforward, as long as the idea is good, it can be utilized in engineering to plan and build intelligent systems without the need for approval. Twister theory, developed by physicist Roger Penrose, provides a new perspective on the fundamental objects in space and time, namely light cones and spheres of light rays. It rethinks physics, with degrees of freedom living on light rays rather than points in space-time. This theory has provided new insights into physics, although it may be technically advanced, and some ideas are yet to be developed.

• Understanding Twistor Theory and Its Concepts: Twistor theory uses complex numbers to describe fundamental particles and spinners are more fundamental than vectors. Penrose diagrams and Henry's drawings are helpful for beginners to understand twistor theory.

  Twistor theory uses a kind of mathematics that goes back to the 19th century among mathematicians. It involves complex numbers instead of just real numbers, which can make it harder for most people to understand. However, it brings us closer to the way the human brains perceive reality. One important concept in twistor theory is spinners, which came out of mathematics and physics when physicists realized that fundamental particles were described by pairs of complex numbers instead of wave functions. Spinners are more fundamental than vectors, and you can build vectors out of them. To understand more, you can start by looking up the Penrose diagrams and Henry’s drawings as an introduction to the subject.

• Understanding Twister Theory: Spinners and Twister Space-Time: Twister theory is a complex concept that explains spinners in space-time, with the potential to lead to a theory of everything. It simplifies the understanding of electrons and quantum physics.

  Twister theory is a fundamental piece of geometry that explains the concept of spinners, which cannot be visualized in terms of vectors. A spinner is a point in twister space, which can be described as a two-dimensional complex plane. The mind-blowing aspect of twister theory is that it answers the question of what a spinner is by defining it as a point in space-time. Using twister theory simplifies the description of electrons and helps in the creation of quantum physics theories. While twister theory is hard to visualize, it provides a unique perspective on geometry that can lead to a theory of everything.

• A New Mathematical Move to Simplify Quantum Theories: By using a factor of scrubber, a new mathematical approach simplifies traditional theories and allows for a more consistent way of viewing quantum theories. However, a successful theory of everything may not be imminent due to difficulties in conducting experiments at higher energies.

  In an interview with physicist Peter Woit, he discusses how certain formulas in traditional theories have very odd behavior and require delicate, singular limits to get the correct answer. However, a new move in mathematics involving using a factor of scrubber to minus one, wherever you see the time coordinate, simplifies the formulas and allows for a more consistent way of looking at quantum theories. This move fundamentally changes the structure of the Aerie and allows for two different times to fit nicely into a twisty theory, resulting in structures that look like the standard model. Woit also comments on the likelihood of a successful theory of everything and believes that due to the difficulty in doing experiments at higher energies, it is relatively unlikely we will have one in the near future.

• Quantum Computing, Living in a Simulation, and the Fascinating Science of Physics: Quantum computing has potential for solving physics problems but not for understanding the theory behind them. Living in a simulation is interesting for engineering, but not for physics. Real physics can be just as fascinating as science fiction.

  Quantum computing may provide a solution for calculating strong coupling behavior in physics, but it may not be able to resolve the problem of understanding the underlying theory of physics. The concept of living in a simulation is interesting from an engineering perspective, particularly when considering the resources required to construct a simulation that is indistinguishable from reality. However, from a physics perspective, it may not be particularly useful. Finally, while science fiction can be entertaining, the actual science of physics can be just as fascinating and unusual, making it unnecessary to rely on fiction for excitement.

• Exploring Science Communication and Inspiration Through Popular Science Books: Popular science books can help bridge the gap between complex scientific concepts and the general public by telling the human stories behind scientific developments. Science is shaped by a combination of factors and is constantly evolving.

  Peter Woit discusses the role of popular science books in communicating complex concepts to the general public. He believes that books that delve into the human stories behind the development of scientific ideas can be particularly inspiring. Additionally, he explores the question of whether science is driven by lone geniuses or a network of ideas, citing examples where both have been true. He also wonders whether aliens, with a different kind of mind, would arrive at different fundamental physics ideas or mathematical structures. Overall, science is a constantly evolving field, shaped by a combination of factors including creative individuals, experimental data, and societal influences.

• The danger of promoting failed ideas in physics: It's important to accurately represent ideas in science and not promote failed concepts as successes, to maintain the integrity of the scientific enterprise and inspire excitement about the field.

  Peter Woit, a mathematician and physicist, cautions against promoting ideas in physics that have failed and calling them successes. He explains that physics has gotten itself into a "historically unusual state," where the field is banging up against hard problems without anything from experiment to help. While it is okay to oversimplify or slightly misrepresent ideas to explain them better, it is not okay to promote failed ideas as successes. Woit points out that this can discredit the scientific enterprise and is not a good way to get people excited about science.

• The danger of over-hyping unproven scientific theories: Inspiring people is important but honesty and transparency about flaws and mistakes of past theories are crucial. Best students should have access to accurate information to avoid being misled. Accuracy and credibility should not be overshadowed by public interest.

  The conversation highlights the danger of over-hyping unproven scientific theories, such as string theory. This can lead to a loss of trust in science and damage to the subject itself. While inspiring people is important, there must be honesty and transparency about the flaws and mistakes of past theories. It is crucial that the best students in the field are not misled and that they have access to accurate information, rather than being led down a blind alley. The unusual fascination and public interest in physics should not overshadow the importance of accuracy and credibility in scientific research.

• Importance of Diversity of Thought for Graduate Students: To become an expert in your field, question the past and strive for a wider range of ideas. Be humble enough to acknowledge when you are wrong, but have enough confidence to make progress on problems. Diversity in research is essential.

  Diversity of thought is essential for graduate students and those seeking to become experts in their field. It is important to question the ways of the past and strive for a wider range of ideas. Humility is essential to acknowledge when you are wrong, but also have enough lack of humility to believe that you can make progress on some of the problems. While mathematics may not provide insight into the meaning of life, exploring beautiful things through mathematics may offer some sense of finding meaning. It is essential to have diversity in research and explore a wider range of ideas.

• Reflection on Mortality Can Help You Appreciate Life More: By meditating on the finite nature of our existence, we can prioritize our goals and appreciate the positives in life. Let's make the most of our time and achieve our dreams.

  As we age, we realize that we may have less time ahead of us than behind us, which can motivate us to prioritize and focus on our goals. Meditating on mortality can help us appreciate life's beauty more intensely, according to the Stoics. While it's important to acknowledge our mortality, we should also take time to enjoy life and appreciate the positives. Life is amazing, and we should be grateful for the opportunities and experiences it offers. As Richard Fineman said, we must not fool ourselves, since we are the easiest person to fool. Let's make the most of our time and achieve our dreams.