Is there a difference between Newtonian mechanics and classical mechanics?

I have heard the terms "Newtonian mechanics" and "classical mechanics" used interchangeably, but is there a difference between them? If so, what is it?

In advanced physics circles, "classical mechanics" always means something very specific, and it doesn't mean "Newtonian." Classical means not quantum. Newton's theory of gravity is just one example of a classical theory. Einstein's general relativity is also a classical theory. Any theory which says gravitation is due to the exchange of gravitons would be a quantum theory. In this usage of the term, all theories are either classical or quantum. The quantum theories are the more fundamental ones, and the classical theories are in some sense approximations of them.

• Can you give some examples of classical theories that are non-Newtonian? May 4 at 21:50
• Einstein's theory of general relativity is one such example. May 4 at 21:50
• Oh, that's not quantum? Hmmm I suppose it isn't. May 4 at 21:50
• Isnt, classical mechanics the same as Newtonian mechanics ? I know classical physics / classical theory is much more than newtonian mechanics. But the OP said classical "mechanics" . So, does classical "mechanics" involve anything else other than Newtonian mechnaics as well ? May 5 at 5:24
• @silverrahul It seems like Newton is to classical mechanics as Kleenex is to tissue. heh. May 5 at 8:11

The term "Classical mechanics" sometimes describes brunch of physics or a course, which focuses on Lagrange and Hamiltonian formalism. This are a little bit advanced tools, which are widely used (Euler-Lagrange equations etc...).

Because this (mathematical) tools are a little bit harder, they are often taught on the example of something, which we understand very good and it's quite simple and this is simple mechanic (pendulums, objects on slopes, spinning-tops...). This course at uni is often titled "Classical mechanics". It focuses on describing Newtonian mechanics, but with different tools, which can be than applied on other fields of physics (often quantuum etc). Notable classical mechanics problems are spinning-top (precession, nutation), all components of Couriolis force, shape of pendulum, central potenitals, Euler-Lagrange equations, Hamilton's formalism, double pendulum...

Generally speaking, the term "classical physics" means "the physics laid down before a particular, more 'advanced', form of physics is considered". It signifies a conceptual change of some form from the preceding physics in terms of its basic assumptions.

For example, in the transition from Newtonian to relativistic mechanics, the relevant conceptual change is that information propagation speed is no longer unlimited ($$c < \infty$$). From Newtonian to quantum mechanics, that information content is no longer unlimited ($$\hbar > 0$$). Hence with respect to either one, Newtonian mechanics is "classical mechanics". But then when you get to relativistic quantum field theory (RQFT), where both of these conceptual changes are incorporated, both Newtonian and non-quantum special/general relativity become "classical mechanics"! And finally, if and when we get to quantum gravity, then all preceding physics will be "classical" in that context.

That said, you are not wrong to think that the term can also have more than one meaning, and so if "classical mechanics" or "physics" is referred to generally as a subdiscipline in physics as opposed to being used in a more specialized context, then yes, it means Newtonian mechanics and related theories that operate with the same background conceptual framework, such as continuum mechanics (fluid and solid statics and dynamics), and relativistic, quantum, RQFT and QG physics all belong to so-called "modern physics".

Newtonian mechanics is valid for single-particle systems but classical mechanics is valid for both single as well as n-particle systems. Newtonian mechanics is the part of classical mechanics