Sunday 16 March 2025
For decades, scientists have been searching for a way to unify classical and quantum mechanics. These two theories describe how the world works at different scales, but they don’t always agree. Classical mechanics is great for understanding big objects like planets and cars, while quantum mechanics is better suited for tiny particles like atoms and electrons.
Recently, a new approach has emerged that combines elements of both theories to create a more complete picture of reality. This approach, known as complex classical mechanics, uses complex numbers – numbers with both real and imaginary parts – to describe the motion of objects.
In traditional classical mechanics, the position and velocity of an object are described using only real numbers. But in complex classical mechanics, these quantities are represented by complex numbers, which can be used to describe more nuanced and subtle motions.
One of the key benefits of this approach is that it allows for a more natural description of non-conservative systems – systems where energy is not conserved over time. This is important because many real-world systems, such as engines and electrical circuits, are non-conservative.
The complex numbers used in this approach also allow for a deeper understanding of the relationship between classical and quantum mechanics. In traditional quantum mechanics, particles like electrons can exist in multiple places at once, which seems strange and counterintuitive. But in complex classical mechanics, this phenomenon is reinterpreted as a manifestation of the complex structure of space-time.
Another advantage of this approach is that it provides a new way to understand dissipative systems – systems where energy is lost over time due to friction or other forces. This is important because many real-world systems, such as engines and electrical circuits, are dissipative.
The theory also has implications for our understanding of time and space. In traditional classical mechanics, time is thought of as a fixed, one-way dimension that flows from past to future. But in complex classical mechanics, time is reinterpreted as a more dynamic and flexible concept that can be influenced by the motion of objects.
One of the most exciting aspects of this theory is its potential to unify our understanding of the universe at all scales. By combining elements of both classical and quantum mechanics, scientists may be able to develop a single, consistent framework for describing everything from the smallest particles to the largest galaxies.
This new approach is still in its early stages, but it has already generated a lot of excitement among physicists.
Cite this article: “Unifying the Scales: A New Approach to Classical and Quantum Mechanics”, The Science Archive, 2025.
Classical Mechanics, Quantum Mechanics, Complex Numbers, Non-Conservative Systems, Dissipative Systems, Space-Time, Time, Energy, Unified Theory, Physics
Reference: Sergio Giardino, “Classical and quantum complex dynamics” (2025).
