2 More Reasons for Classical Mechanics

by landonlehman

Link to the first two reasons.

Reason #3 to study classical mechanics: the link to quantum mechanics.  Many of the concepts and formalisms used in quantum mechanics are easier to understand if you know about them from classical mechanics.  For example, there is a correspondence principle between Poisson brackets in classical mechanics and commutators in quantum mechanics.  This principle was formulated by Dirac in 1925 (see Sakurai, 2nd. ed., pg. 48):

[\; , \; ]_{\text{classical}} \rightarrow [\; , \; ]/(i \hbar) .

There is also the idea that if a quantum mechanical system has a classical counterpart, the equations of motion for the classical system should be attainable by taking the limit \hbar goes to 0 in the quantum system.  This is somewhat heuristic – one might run into problems with phases and the answer might depend on exactly how \hbar is taken to be small.  But it is often a useful shortcut.

Another example is the group structure of rotations.  This shows up in both classical and quantum mechanics.

Reason #4 to study classical mechanics: it is a necessary part of physics as a practice.  This will require a bit of explanation.  I am using the word “practice” in the sense defined by Alasdair MacIntyre in his book After Virtue:

“By a ‘practice’ I am going to mean any coherent and complex form of socially established cooperative human activity through which goods internal to that form of activity are realized in the course of trying to achieve those standards of excellence which are appropriate to, and partially definitive of, that form of activity, with the result that human powers to achieve excellence, and human conceptions of the ends and goods involved, are systematically extended.” (pg. 187, 3rd ed.)

Goods “internal” to the practice of physics are just goods which cannot be obtained except by doing physics.  MacIntyre goes on to say:

“To enter into a practice is to enter into a relationship not only with its contemporary practitioners, but also with those who have preceded us in the practice, particularly those whose achievements extended the reach of the practice to its present point.” (pg. 194, 3rd ed.)

Some of “those whose achievements extended the reach” of physics include Galileo, Newton, Lagrange, Kepler, Poisson, Laplace, etc.  These masters of physics worked primarily in what today would be classified as classical mechanics.  So if the goal is to fully “enter the practice of physics,” at least a cursory understanding of classical mechanics is one of the stepping stones on the path towards achieving that goal.

To put Reason #4 in another, less precise way: classical mechanics is part of the “culture” of physics, some understanding of which is necessary to function well as a physicist.

 

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