As far as I know, this law has been extensively observed in experiments, and is proved through Newton's second law of motion (F = ma) or some other physical principles such as energy conservation. All of these proofs are of experimental and observational nature, however, I am enthusiastic to know whether there is a fully FUNDAMENTAL and THEORETICAL proof for this substantial law in physics without which the creation of many branches of Engineering might be impossible.
Yes, while originally an empirical law, Newton’s third law is now both theoretical justified through conservation laws and validated experimentally in a wide variety of settings. In modern physics, it’s seen as a reflection of deeper principles like momentum conservation and spatial symmetry.
Raymond Alex Ekemube The conservation laws are all experimental, not theoretical. Furthermore, I pointed out the conservation laws in my original question, myself, and emphasized that I am seeking a theoretical proof of the Newton's third law of motion. In addition, I don't know a lot about spatial symmetry, but I know that the symmetry is considered as an assumption or principle in physics and doesn't have a theoretical proof.
Yes, Newton's Third Law has been theoretically proven and consistently validated through the framework of classical mechanics and conservation laws. It is deeply rooted in the law of conservation of momentum, which has been derived and supported by numerous physicists, including Leonhard Euler and Joseph-Louis Lagrange in the 18th century through analytical mechanics. Modern physics, including quantum field theory, also respects action-reaction symmetry at fundamental interaction levels.
Proof and Explanation of Newton’s Third Law
Newton’s Third Law of Motion states: Whenever one body exerts a force on a second body, the second body exerts an equal and opposite force on the first—
mathematically, if body A exerts a force F⃗ABFAB on body B,
then body B exerts a force F⃗BA=−F⃗ABFBA=−FAB on body A236.
Can Newton’s Third Law Be Proven?
Strictly speaking, Newton’s third law is a fundamental postulate of classical mechanics and cannot be "proven" in the mathematical sense. Instead, it is supported by extensive experimental evidence and its consistency with other physical laws, especially the conservation of momentum17.
"You cannot 'prove' laws of physics in an absolute sense—you can only show that they are consistent with observed truths and with each other. In that spirit, you can readily prove Newton's third law by considering energy conservation. If the result of two bodies interacting was that one gained more energy than the other lost... energy would not be conserved."
https://www.perplexity.ai/search/proof-of-newtons-third-law-0W5r5uUPTO2.suzamSNjGw
"without which the creation of many branches of Engineering might be impossible."
Huh??!!
Just how many entire branches of Engineering do you want to create ?
Do ANY branches of Engineering exist solely founded on a single law or proof ? There would likely be a lot of "borrowing" from other branches ;-)
If your question is: Is There a "Proof" Without Any Empirical Basis?
No, because physics is fundamentally an empirical science. Even the most abstract theories (like QFT or General Relativity) are validated through experiments.
However, Newton’s Third Law is not arbitrary, it is deeply tied to spatial symmetry and self-consistency in physical theories.
If Newton’s Third Law were violated, momentum would not be conserved, leading to absurdities (e.g., perpetual motion, violation of causality).
Hope it helps :-)
Hafiza Noor Us Sabah You are right. Every theory in physics should be validated through experiments. However, these theories should have mathematical or physical proofs based on the well-established and basic physical concepts or equations.
Spatial symmetry, and momentum and energy conservation, are all validated through experiments and observations, however, violating them doesn't mean violating the concepts mathematically or logically accepted for the human. Furthermore, causality is admitted only whenever the human mind allows that causality relationship to be held and the human mind issues this permission only whenever that relationship is already experimented or observed by the human.
What I am seeking is to prove and confirm the Newton's Third Law based on the clearly known and basic physical concepts and equations.
Farshad Rezaei
Perhaps begin by refuting / rebutting / answering these (from above) :
Strictly speaking, Newton’s third law is a fundamental postulate of classical mechanics and cannot be "proven" in the mathematical sense. Instead, it is supported by extensive experimental evidence and its consistency with other physical laws, especially the conservation of momentum17.
"You cannot 'prove' laws of physics in an absolute sense—you can only show that they are consistent with observed truths and with each other. In that spirit, you can readily prove Newton's third law by considering energy conservation. If the result of two bodies interacting was that one gained more energy than the other lost... energy would not be conserved."
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