I am really perplexed by the fact that Newton's equation is time reversal?
Newton's equation of motion is time reversally invariant, evident from the equation itself:
$$m\dfrac{d^2x}{dt^2} = F(x).$$
My question is why?
Is there some deep reason they come out to be time reversally invariant(may be connection to Principle of Least action, which is a global picture by the way, instead of being local which is the case of Newton's equation)? or connection to something else(which is more evident)?
In the equation of motion(eom) because of the acceleration term, instead of velocity or other(which defy TRI). Is there a reason of it coming out to be like this? Links from geometry(variational principle) or where I see clearly that, it has to be like this(very basic and physically intuitive).
A bit detailed explanation will be of great use(origin of such symmetry here).
Forgive me, if question is unclear(make it clear, if asked) or if it has been asked(I checked but not my question), any help is highly appreciable.
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