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if using hbar=c=1 and ev for mass/energy what are appropriate distance units? Wikipedia talks about inverse energy without really explaining them
Setting Hbar c=1 is a common practice in theoretical physics and allows for simpler and more elegant equations. It essentially means that the speed of light (c) and the reduced Planck's constant (Hbar) are equal to 1. This simplification is useful when working with high energy or small scale phenomena.
Inverse energy units, such as the electron volt (eV), are commonly used in physics to describe the energy of particles. When Hbar c=1, it means that energy and mass are interchangeable, so inverse energy units can also be used to describe mass. This allows for easier conversions between units and simplifies calculations.
eV is a convenient unit to use in physics calculations because it is equivalent to a very small amount of energy, making it suitable for describing the energy of subatomic particles. It is also a more manageable unit compared to Joules or ergs, which are much larger units and would require more decimal places for precise calculations.
Sure, one example is the famous equation E=mc^2, which relates the energy (E) of an object to its mass (m) and the speed of light (c). When Hbar c=1, this equation becomes E=m, showing the equivalence between energy and mass. This concept is also used in quantum mechanics equations, such as the Dirac equation.
Besides simplifying equations and allowing for easier conversions between units, setting Hbar c=1 also helps in unifying different theories in physics. For example, it allows for the unification of special relativity and quantum mechanics, which are both based on the speed of light and Planck's constant. This concept has also been used in attempts to unify the four fundamental forces in physics.