Where does Newton's stuff stand today?

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Newton's three laws of motion remain valid as fundamental principles for speeds much lower than the speed of light (c) and energies above the continuum limit. However, they are not applicable at relativistic speeds or in quantum mechanics, where Einstein's equations provide a more accurate description. At relativistic speeds, Newton's laws serve only as first-order approximations. The discussion raises questions about the applicability of the first and third laws as speeds approach c and seeks clarification on the continuum limit's impact on these laws. Overall, while still relevant in classical mechanics, Newton's laws have limitations in modern physics contexts.
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Besides the second law's issue with SR, are Newton's 3 laws still considered to be true FUNDAMENTAL laws of motion? If not, why?
 
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All of Newton's laws are considered valid given speeds much smaller then c and energys above the continum limit. That means we do not use them at relativistic speeds and for quantum mechanics. Within their realm they are as valid today as they were 400yrs ago.

At relativistic speeds Newtons laws are only a first order approximation to the full equations derived by Einstein.
 
"All of Newton's laws are considered valid given speeds much smaller then c and energys above the continum limit. That means we do not use them at relativistic speeds and for quantum mechanics."

For clarification... are you saying that the first and third law also have problems when approaching c? Also, what is the continuum limit, and why does it present problems for the 3 laws?
 

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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