Is probability a mathematical artifact or do things literally exist in probabilistic states?

ChatGPT said:

The question of whether probability is a mathematical artifact or whether things literally exist in probabilistic states touches on deep philosophical and foundational issues in both physics and mathematics. There are two main perspectives to consider:

1. Probability as a Mathematical Artefact:

In this view, probability is a tool or construct we use to model uncertainty in systems where we don’t have complete knowledge or where the outcomes are not deterministic. Here, probability is understood as a formal mathematical framework for reasoning about randomness, uncertainty, or likelihood, but it does not imply that things themselves are inherently probabilistic.

• Classical Probability (frequentist interpretation): In this perspective, probability describes the long-run frequency of events occurring in repeated trials. It does not suggest that the events themselves are probabilistic, but rather that the model we use to understand them involves probabilities.

• Bayesian Probability: In this approach, probability is a measure of belief or subjective uncertainty about the state of the world. The probability distribution is a reflection of our knowledge (or lack thereof) about a situation, and the events themselves are not considered to have inherent probabilistic properties.

2. Things Literally Existing in Probabilistic States:

This view suggests that the world, or at least some aspects of it, is inherently probabilistic, and probability is not just a tool but a reflection of the underlying nature of reality. In this interpretation, probability is fundamental to describing the behavior of systems, particularly at microscopic or quantum scales.

• Quantum Mechanics: One of the most well-known examples of this is found in quantum mechanics. In quantum theory, particles do not have definite positions or velocities until they are measured. Instead, they exist in a superposition of states, with the probability of finding the particle in a specific state governed by a probability distribution (the wave function). This suggests that at a fundamental level, particles do not have definite properties until they are observed, and the probabilities reflect this indeterminacy in the system.

• Many-Worlds Interpretation: In the context of quantum mechanics, the Many-Worlds Interpretation (MWI) further posits that all possible outcomes of quantum events actually occur in separate branches of reality, meaning the universe itself splits into multiple parallel realities, each corresponding to a different outcome. Here, the probabilistic nature of quantum events becomes a reflection of the many potential realities that are "real" in a certain sense.

Reconciling the Two Views:

Some interpretations of quantum mechanics, such as the Copenhagen interpretation, suggest that the probabilistic nature of quantum mechanics is a result of the limitations of our ability to measure and know everything about a system. On the other hand, objective probabilistic interpretations (such as the de Broglie–Bohm theory) maintain that probability reflects a real feature of the quantum world, not just a consequence of human ignorance.

Conclusion:

• Mathematical Artefact View: Probability is simply a tool we use to represent uncertainty and model complex systems. Things themselves are deterministic or follow hidden variables we don't know about.

• Literal Probabilistic States: Probability describes a fundamental feature of reality, particularly in quantum systems, where events do not have definite outcomes until they are observed, and the world operates in a probabilistic way.

In the context of quantum mechanics, the idea that things "literally exist in probabilistic states" is widely accepted. However, in everyday macroscopic contexts, it’s more common to treat probability as a way of dealing with uncertainty rather than an inherent property of the universe.