Classical physics is generally considered deterministic, meaning the future state of a system is entirely determined by its present state. However, certain situations appear non-deterministic due to our practical limitations. These include chaotic systems, where tiny uncertainties in initial conditions are amplified exponentially, making long-term predictions impossible, despite the underlying deterministic nature. Other examples involve systems with a vast number of particles, like gases, where tracking individual particles is infeasible, leading to statistical descriptions and probabilistic predictions, even though the individual particle interactions are deterministic. Finally, systems involving measurement with intrinsic limitations also exhibit apparent non-determinism, arising from our inability to perfectly measure the initial state. Therefore, non-determinism in classical physics is often a result of incomplete knowledge or practical limitations rather than a fundamental property of the theory itself.
The Stack Exchange post explores the intriguing question of whether determinism, the principle that future states are fully determined by present conditions, truly holds within the realm of classical physics. While classical physics is often presented as a deterministic framework, the discussion reveals several nuanced situations where this deterministic picture may falter or require careful consideration.
One prominent point of discussion centers around systems with chaotic behavior. In these systems, even minuscule uncertainties or imprecisions in the initial conditions can lead to vastly divergent outcomes over time, making long-term predictions effectively impossible, despite the underlying equations of motion being deterministic. This phenomenon, often illustrated by the butterfly effect, highlights the practical limitations of predictability in deterministic chaotic systems. The post elaborates on how chaotic systems, though deterministic in principle, exhibit a sensitive dependence on initial conditions, leading to practical non-determinism.
Furthermore, the discussion delves into the role of measurement in classical physics. It raises the question of whether the act of measurement itself introduces an inherent uncertainty, thereby disrupting the deterministic chain of cause and effect. While classical physics generally assumes that measurements can be made with arbitrary precision, in practice, limitations in measurement apparatus and techniques introduce a degree of uncertainty. This inherent uncertainty in measurement, while often negligible, can be a source of apparent non-determinism.
Another aspect considered is the conceptual challenge posed by systems involving infinite quantities or singularities. For instance, when dealing with phenomena like the collapse of a wave in a perfectly inelastic string or the behavior of particles at singularities, the classical equations of motion may become ill-defined or yield multiple solutions. These situations highlight the potential limitations of classical physics in handling extreme scenarios and can lead to ambiguities that challenge a strictly deterministic interpretation.
Finally, the concept of thermal equilibrium is examined. While the macroscopic properties of a system in thermal equilibrium appear stable and predictable, the microscopic motion of its constituent particles is inherently random. This statistical nature of thermal equilibrium introduces an element of randomness into the microscopic description, even within the framework of classical physics. Therefore, while the macroscopic behavior appears deterministic, the underlying microscopic dynamics exhibit probabilistic characteristics.
In summary, the post elucidates several scenarios within classical physics where determinism, while often assumed, can be challenged. These include the practical unpredictability of chaotic systems, the inherent uncertainty associated with measurement, the breakdown of classical descriptions at singularities and infinities, and the statistical nature of microscopic behavior in thermodynamic equilibrium. While the fundamental equations of classical physics are typically deterministic, these nuances demonstrate that determinism in practice can be a complex and sometimes elusive concept.
Summary of Comments ( 66 )
https://news.ycombinator.com/item?id=43058198
Hacker News users discuss deterministic chaos and how seemingly simple classical systems can exhibit unpredictable behavior due to sensitivity to initial conditions. They mention examples like the double pendulum, dripping faucets, and billiard balls, highlighting how minute changes in starting conditions lead to vastly different outcomes, making long-term prediction impossible. Some argue that while these systems are technically deterministic, the practical limitations of measurement render them effectively non-deterministic. Others point to the three-body problem and the chaotic nature of weather systems as further illustrations. The role of computational limitations in predicting chaotic systems is also discussed, along with the idea that even if the underlying laws are deterministic, emergent complexity can make systems appear unpredictable. Finally, the philosophical implications of determinism are touched upon, with some suggesting that quantum mechanics introduces true randomness into the universe.
The Hacker News post "What situations in classical physics are non-deterministic?" has generated several comments discussing the concept of determinism in classical physics.
Some users argue that true non-determinism doesn't exist in classical physics, pointing to chaotic systems as examples of systems that appear random due to our limited computational ability to predict their long-term behavior, but are fundamentally deterministic. They suggest that with sufficient information about initial conditions, one could theoretically predict the future state of a classical system. This includes systems like dice rolls or roulette wheels.
Others bring up the idea of systems with a "practical" non-determinism, acknowledging that while classical physics may be theoretically deterministic, limitations in measurement and computation often force us to treat certain systems as non-deterministic for practical purposes. This aligns with the concept of chaos mentioned earlier, where even tiny uncertainties in initial measurements can lead to vastly different outcomes, making long-term predictions impossible.
One user introduces the philosophical implications of determinism and free will, connecting it to the discussion of unpredictability in classical systems. This tangent explores the potential conflict between a deterministic universe and the subjective experience of choice.
Another point of discussion revolves around the interpretation of statistical mechanics. Some users argue that while individual particles within a gas might follow deterministic Newtonian laws, the vast number of particles makes it practically impossible to track them individually. Therefore, we rely on statistical methods, which introduce probabilistic descriptions and appear non-deterministic. The underlying argument is that this statistical approach is a tool for dealing with complexity, not an indication of true randomness in the system itself.
Finally, the role of quantum mechanics is briefly touched upon. Some users highlight how the probabilistic nature of quantum mechanics contrasts with the deterministic nature often ascribed to classical physics. However, this comparison isn't a central theme in the discussion.