re: Does Force really equal Mass X Acceleration? I think not.

Imagine a glass of water near an ant like. Its is a constant. The ant can have no real physical effect on it. But it is a visible physical object to him.

You reach out, and you shatter the glass. You change it's physical form with your body. Something the ant can't do.

Physical.


A dolphin is in a tank. Swimming. Floating. He can have little real effect on the water of this tank. You decide to drain it and hit a button. His once constant physical reality is changed using a method he can't comprehend.

A drain. A hole outside of his understanding.


Now imagine yourself looking up at the sky at night. You see stars, planets, moons.

A higher dimensional being decides to start removing things. Planets, stars, everything disappears on its whim.

Its method, unknown, its reasoning, unknown, it's distance, unknown.



Yet we pretend to be so much more advanced that the lower creatures.

quote:

---

we pretend to be so much more advanced that the lower creatures.

---

Yeah, it's some deep stuff. We might all be floating around on a speck of dust in some Goddess's Vacuum cleaner, trying to figure out the rules of an Environment that we really have no control of, but what the hell else are you gonna do? It's man's nature to ponder things and base theories off what he thinks has already been proven, by happening so many times. Something could change though, suddenly and without warning, The Sun might come up in the west one morning.

Who could predict it? It never happened before. You got to go with what you have.

mc = Hammertime



And his Caucasian Cousin

You can’t really "prove" F = ma; it’s a fundamental model of how interactions between observed phenomena change their kinematic states. As pointed out a few posts down, it is possible to derive the canonical form of Newton's second law from a more fundamental principle, the principle of least action; but the point would remain the same, it is just a mathematical representation of our reality. Asking for a rigorous mathematical proof of the constitutive equations of physics tends to be a foolish endeavor, as the equations tend to be empirically based on our observations of reality.

There are more sophisticated models that are more appropriate given the circumstance compared to Newton's second law, like special/general relativity which use Einstein’s field equations

quote:

---

You can’t prove F = ma; it’s a fundamental model of how interactions between observed phenomena change their kinematic states.

---

You can though, principle of stationary action leads to the Euler-Lagrange equations which are equivalent to Newton's laws. Lagrangian mechanics and such.

quote:

---

You can though, principle of stationary action leads to the Euler-Lagrange equations which are equivalent to Newton's laws. Lagrangian mechanics and such.

---

Fair point, and perhaps different language should have been used in my post, and I'll edit accordingly. All I was really getting at is that physics is a series of models, and asking for proof really comes down to asking for the fundamental constitutive equations and just taking on faith that those equations are adequate to model our reality.

But yes, you are correct that Newton's second law can itself be derived via the more fundamental principle of least action. The same discussion is simply shifted up a level though, in that "you can't prove the principle of least action, it is just a fundamental model of our reality" becomes the new dialog.


It's not often I happen upon someone who knows about Lagrangian mechanics on this board. Are you a ME perhaps?

Damn, I hope you guys get in some good discussions on here, just so I can see how much I can understand.