New limits on prediction: Exploring Unknowability in Physics
The idea of a **'Laplace's demon'**, an entity with complete knowledge of the present and thus capable of predicting the entire future, has long been a philosophical cornerstone in physics. However, modern discoveries are challenging this notion, revealing fundamental limits to predictability.
The Quantum Realm and Chaos Theory
The first blow to deterministic predictability came with **quantum mechanics**, which introduced the concept of inherent fuzziness in the position and momentum of particles. Later, **chaos theory** showed how minute uncertainties can be amplified, rendering long-term predictions virtually impossible.
Undecidability: A New Frontier of Unknowability
Recently, a new limitation called **undecidability** has emerged. It suggests that even with perfect knowledge of a system's state, some questions about its future behavior are inherently unanswerable. This concept, well-established in mathematics and computer science, is now finding its way into physics.
Physicists like Toby Cubitt and mathematicians like Eva Miranda are at the forefront of this exploration, linking unknowable mathematical systems with physical ones, thereby mapping the boundaries of knowledge.
The Undecidable Machine
A prime example of undecidability is Cris Moore's theoretical pinball machine. This machine, designed to mimic a **Turing machine**, can perform any computation, but its long-term dynamics are inherently unpredictable. Even with complete knowledge of the machine's setup, it's impossible to determine whether a particular arrangement of bumpers will trap the ball or steer it to the exit.
Implications for Physics
The discovery of undecidability in physical systems has profound implications. It suggests that there are limits to what we can know about the universe, even with unlimited resources. While it doesn't negate our ability to predict specific properties of specific systems, it proves that no single method can work for all systems.
Researchers are finding new limits on predictability not only in quantum physics but also in classical systems like fluid dynamics. Eva Miranda's work, for instance, demonstrates that fluids can flow in ways that make trajectories through them undecidable.
The Role of Infinity
Undecidability arises in idealized systems that involve infinity, such as infinitely long tapes or infinitely divisible spaces. While real-world experiments are always finite, these infinite theories are essential approximations of reality, helping us make sense of the finite.
Ultimately, the realization of undecidability in physics forces us to accept that while we can discover the laws governing the universe, those laws may not always provide shortcuts for predicting every aspect of its future. Some aspects may remain forever hidden, challenging our ambition to achieve complete knowledge.
Source: Wired