Question

For context: Through my reading on Lagrange’s development of his celestial mechanics theory in the Newtonian gravitational context, and then of Einstein and Co.’s GR, which significantly diverged from the Newtonian construct and represented a paradigm shift in gravity theories, it seems that GR fundamentally rejected the Lagrangian-Newtonian solar system orbital construct in a number of ways. With one of these ways rooted in Mach’s concept of 'distant masses of the universe' and the error of trying to understand all the pattern motions of the solar system as though it’s a fully isolated system, which unjustifiably disregards other locationally-concentrated influential forces "out there" beyond our SS.

So then I wonder, if we can see the Lagrangian celestial mechanics model as one that almost all physicists would agree has for over 100 years been replaced by General Relativity – and not just in a "minor updates" way but in a paradigm-shifting way – is it then not logically awkward to reconcile that with the extent to which modern quantum mechanics / QFT fundamentally incorporates the mathematics that Lagrange used to model planetary orbits (or quite similar orbit/oscillation pattern models) into it’s own overall theory model?

Answer 1

Lagrangian celestial mechanics model and General Relativity (GR) are two different theories that explain the motion of celestial bodies. While GR challenged Newtonian gravity and introduced a paradigm shift, some mathematical tools from Lagrangian celestial mechanics are still applicable in modern quantum mechanics and Quantum Field Theory.

Step-by-step explanation:

Lagrangian celestial mechanics model and General Relativity (GR) are two different theories that explain the motion of celestial bodies in the universe.

Lagrangian celestial mechanics model, which is based on Newtonian gravitational context, was widely used in physics for a long time.

However, when Einstein proposed his theory of General Relativity, it fundamentally challenged the Newtonian construct of gravity and led to a paradigm shift in gravity theories.

GR rejected the idea of considering the solar system as a fully isolated system and introduced the concept of distant masses of the universe, which play a role in the motion of celestial bodies.

This change in perspective is rooted in Mach's concept and acknowledges the influence of other locationally-concentrated forces beyond the solar system.

On the other hand, modern quantum mechanics and Quantum Field Theory (QFT) do incorporate mathematical tools and concepts, such as those used by Lagrange to model orbital patterns of celestial bodies.

However, it is important to note that the incorporation of these mathematical techniques does not mean that Lagrangian celestial mechanics is still the dominant model for describing the motion of celestial bodies.

Rather, it highlights the usefulness and applicability of certain mathematical tools across different theories.