Bridge Between Quantum and Classical Bremsstrahlung & Why Bremsstrahlung Asymmetry Could Exist Considering Symmetry Axes

<p dir="ltr">Bremsstrahlung Electron. (0000-0002-0829-0749).</p><h2>Abstract</h2><p dir="ltr">This article uses a formula for Action, the path that minimizes energy, which can be written in the Lagrangian form as ∫(T − V )dt, which has a solution of a whole number multiple of the quantum of action "nh". Hence, ∫(T − V )dt = nh where n is a whole number multiple, and h is Planck’s constant. The article uses nh = ∫mvds and substitutes the position vector that incorporates the bremsstrahlung asymmetry quantity, R, inside. The article rearranges the formula to find the relationship between bremsstrahlung asymmetry, R, as a function of the whole-number multiple of the quantum of action "n", R(n). This is thought to be possible due to angular momentum, which has the same units as action, using a similar procedure to Bohr used when he decided to discretize the angular momentum. Finally, following a similar tuning procedure as Planck did to get Planck’s constant, h value, this report tunes the parameter, a whole multiple of quantum of action "n" until it gets the correct scale of the graph which is from Figure 1c to Figure 1d matching and describing the classical prediction of Bremsstrahlung asymmetry in Figure 1a. This allowed predicting the whole number multiple of quantum of action "n" which follows the Bohr correspondence principle, that when the quantum number “n” becomes very large, the quantized behaviour predicted by quantum mechanics should start to look like the smooth, continuous behaviour described by classical physics.</p><h2>Plain Language Summary</h2><p dir="ltr">Physical systems naturally follow the “path of least effort” as they move or change. Effort is the difference between motion energy and stored (potential) energy, added up over time. Quantum mechanics tells us that this total “effort” can’t be just any value; it comes in fixed chunks equal to multiples (n) of Planck’s constant (h). Hence, the motion we see in tiny systems only happens in those discrete steps. The same logic applies to spinning motion (angular momentum), and it, too, can only exist in those same fixed, indivisible units. If the particle flew straight, you’d see two pairs of radiation lobes, two pointing forward and two backward, that are mirror images of each other. But when the particle follows a curved path, the two pairs of lobes in each direction aren’t mirror images anymore. This extra asymmetry occurs only when the trajectory bends. This is quantified using the parameter Bremsstrahlung Asymmetry, R. When this is substituted into the quantum angular momentum equation, we can predict the same Bremsstrahlung asymmetry, R, from the quantum scale that is predicted before using classical physics by finding the correct multiples (n) of chunks of discrete quantum steps. This is the Bohr correspondence principle.</p>