Why Does the System of Natural Units Consider the Reduced Planck Constant as 1 Instead of the Normal Planck Constant?

When discussing the system of natural units in theoretical physics, one often encounters the reduced Planck constant, denoted as ?, set to 1. This choice is not arbitrary; it is a strategic maneuver aimed at simplifying the mathematical formulations of physical laws. This article will delve into the reasons behind this decision, explaining its practical and theoretical benefits.

Convenience and Clarity in Equations

Whether you choose the reduced Planck constant or the normal Planck constant, it is a matter of convenience. However, the reduced form, denoted as ?, is often preferred because it reduces the prevalence of factors involving 2π in equations. This simplification makes the equations less cluttered and more manageable.

The adoption of natural units, including setting ? 1, represents a conscious decision to streamline the intricacies of mathematical formulations. This choice simplifies the equations by eliminating certain numerical factors, thereby making the physical laws more elegant and easier to understand.

Enhancing Elegance and Parsimony

By setting ? 1, theoretical physicists can write equations in a more concise and elegant manner. For instance, the famous relation from special relativity, E mc2, can be simplified to E m under these units. Similarly, the energy of a quantum system, E ?ω, can be simplified to E ω.

Practical Implications and Simplicity

The choice of natural units, including setting ? 1, is not without practical implications. It makes the equations shorter and more manageable, which is particularly useful in theoretical physics and advanced research. However, it is important to note that this choice does not alter the underlying principles of physics. It is simply a methodological approach to enhance clarity and convenience in mathematical discourse.

When setting units for documentation, physicists have the freedom to choose them as long as everyone is aware of the system of units being used. By setting ? 1 and the speed of light c 1, equations become more concise, as seen in the simplified forms of the famous equations mentioned above.

For example, the energy-momentum relation E mc2 becomes simply E m under the adopted units, while the relationship between energy and angular frequency E ?ω becomes E ω. These simplified forms make the equations easier to work with and understand, which is crucial in theoretical physics.

While such simplifications are highly valuable in the realm of theoretical physics, it is essential to recognize that they might not be directly useful in everyday applications. For instance, trying to buy 5 times 1035 electron volts of apples would not make practical sense, as it is far beyond the scale of everyday experience.

In conclusion, the decision to set the reduced Planck constant to 1 in natural units is a strategic choice that simplifies mathematical formulations without altering the fundamental principles of physics. This choice enhances the clarity and elegance of physical equations, making them more accessible and easier to analyze in the realm of theoretical research.