Meaning: The quote by Arthur Eddington, a renowned physicist and mathematician, encapsulates the fundamental nature of modern physics and its relationship with determinism and probability. In essence, Eddington is highlighting the inherent uncertainty that is embedded within the framework of modern physics, rendering it impossible to make precise deterministic predictions. To fully comprehend the significance of this quote, it is essential to delve into the context surrounding the development of modern physics, the concept of determinism, and the role of probabilities in shaping our understanding of the physical world.

At the heart of Eddington's quote lies the contrast between determinism and probability, two concepts that have long been central to the discourse in physics and philosophy. Determinism, in the context of physics, refers to the idea that the state of a system at a given time uniquely determines its state at any future time. In other words, if one possesses complete knowledge of the initial conditions and the laws governing the system, it should be possible to predict its behavior with absolute certainty. This notion of determinism held sway in classical physics, where the laws of motion formulated by Isaac Newton seemed to provide a deterministic framework for understanding the behavior of physical systems.

However, the advent of quantum mechanics in the early 20th century ushered in a paradigm shift in our understanding of the physical world. Quantum mechanics, with its probabilistic interpretation of the behavior of subatomic particles, introduced a level of indeterminacy that challenged the deterministic worldview of classical physics. This indeterminacy was famously encapsulated in Werner Heisenberg's uncertainty principle, which posits that certain pairs of physical properties, such as position and momentum, cannot be simultaneously measured with arbitrary precision. Instead, the more precisely one property is measured, the less precisely the other can be known.

Eddington's assertion that modern physics deals with probabilities from the outset reflects this fundamental departure from determinism. In the quantum realm, the behavior of particles is described by wave functions that encode probabilities of finding the particles in different states. This probabilistic nature of quantum mechanics has profound implications for our understanding of the physical world, as it implies that, at the fundamental level, the behavior of particles is intrinsically uncertain and unpredictable with absolute certainty.

Moreover, the probabilistic nature of modern physics extends beyond the realm of quantum mechanics. In statistical mechanics, a branch of physics that deals with the behavior of large ensembles of particles, probabilistic methods are employed to describe the collective behavior of systems comprising a vast number of individual constituents. This statistical approach gives rise to fundamental concepts such as entropy and the second law of thermodynamics, which govern the evolution of macroscopic systems and underpin our understanding of phenomena such as heat transfer, chemical reactions, and phase transitions.

In light of these developments, it becomes evident why Eddington emphasizes the impossibility of trapping modern physics into predicting anything with perfect determinism. The probabilistic nature of quantum mechanics and statistical mechanics permeates our understanding of the physical world, challenging the notion of deterministic predictability that held sway in classical physics. This recognition of inherent probability and uncertainty underscores a profound shift in our conception of the nature of reality, prompting a reevaluation of our assumptions about the predictability and determinism of physical phenomena.

In conclusion, Arthur Eddington's quote encapsulates the profound transformation that has occurred in our understanding of the physical world with the advent of modern physics. By highlighting the intrinsic probabilistic nature of modern physics, Eddington challenges the traditional notion of deterministic predictability, signaling a shift towards a worldview that embraces uncertainty and probability as fundamental aspects of the natural order. This recognition of the limitations of determinism and the embrace of probability have not only reshaped the foundations of physics but have also reverberated across disciplines, prompting a reevaluation of our conceptions of causality, predictability, and the nature of reality itself.