Why does every action have an equal and opposite reaction?
Because the Lagrangian of mechanical processes is invariant under translations.
Heh heh.Actually I am a high school student.So, I don't really understand what you mean.Could you please explain?Any way,thanks for replying.
This was a completly inapproiate response to a students question. I will not tolerate such garbage here.
Thats a tough question because it is something that seems (to me at least) to be self evident: It just does. So let me turn it around - is there something that leads you to believe it wouldn't?
The best reason I can come up with is because it does. This is an observation of Newtons and is incorporated in his fundamental laws. The goal of physics is to make predictions based upon observations. This is the observation. We cannot discuss why, it simply is.
i know it sounds totally nuts but maybe it was because somebody told Newton to say so
but was aplied in the wrong context
There exists a casual geometrical explanation of action, reaction and theit subsequent resultant(s).
Specifically, every force has an equal and opposite force. This is because of conservation of momentum. Force is a change in momentum over time. If momentum is conserved, then it cannot change with time. That means that if you apply a force to change the momentum of part of a system, there must be an opposing change in momentum (force) to keep the total change in momentum equal to zero.
So, your question has been reduced to the question, "Why is momentum conserved?" If you study the Lagrangian formulation of mechanics, you learn that conservation laws are due to symmetries. (This is known as "Noether's theorem".) In this case, the law of conservation of momentum is due to a spatial translation symmetry. In plain terms, the outcome of an experiment should not depend on where it is performed. So if you move from one place to another ("translation in space"), the laws of physics are unchanged ("the laws of physics are invariant under spatial translation"). Noether's theorem says that there must then be a conserved quantity, which we call "momentum".
So, your question has been further reduced to the question, "Why are the laws of physics the same at all locations?" We don't know. Maybe they aren't ... they are as far as we know, but we can't know for sure.
Where you repeat experiments in the 'exact' manner, results show no deviaition from observed effects, you do something and something happens as a result, technically you cannot repeat any 'event' in exactly the same 100% way, Entropy will force you to comply to its natural path!
Now what is interesting is if you get a different angle on the possible number of ways you can do 'exact' experiments?.
For instance lets say Galilleo performs an experiment on the leaning tower of pisa, he drops a cannonball, it falls to Earth. If he goes back up and does the experiment again, he could deduce the time taken for the cannonball to drop to the ground, and make some basic assumptions based on the experiment.
Now if Galilleo, instead of retrieving the cannonball and goes back up the tower, he digs a hole into the ground next to the cannonball to a similar height of the Pisa Tower, and then drops the cannonball into the hole whilst peering over the edge taking notes, this a variation on the effects of Gravity, the original setup has changed, so the observed effect alters in a small way to compensate for difference's.
This experiment differs from the original, although the effect of the falling cannonball is governed by the same force, the slight difference in experimental setup, produces a differing 'observed' effect.
So every SIMILAR ACTION has a SIMILAR REACTION which is dependant on the exactness of the enviromental setup. Most of Earths enviroment is similar to us, but differs vastly to that of say a dynamical Jupiter.
We are confined to our limited, but satisfactionary observations of a wider dynamical Universe and its constraining governing Effects.
Re: Re: reaction
This is has been the best formal anwer yet.
"Conservation of momentum" sounds much like "conservation of energy." I would informally extrapolate from those statements a "conservation of inerta" as well.
Why these three and others are conserved is due to the physical Universe being a finite integral whole.
Why are the laws of Universe the same everywhere in Universe as far as we know?
Beacuse if they werent the integrity of our physically finite whole of Universe would not exist.
Re: Re: Re: reaction
Conservation of energy is due to invariance under time translations.
There isn't any symmetry that gives rise to "conservation of inertia". But in relativity, conservation of energy becomes conservation of mass-energy, and mass-energy is representative of inertia in some senses.
It's due to the laws of physics in the universe having certain symmetries.
Well, you can appeal to the weak anthropic principle, but there isn't any theoretical reason why a universe without these symmetries couldn't exist.
Re: Re: reaction
That isn't true for static forces as there is no momentum or energy change.
Integral really said it best: it is observed to be true.
Re: Re: Re: reaction
It is true for static forces. That there is no momentum or energy change is my whole point: that is why for every force, there is an equal but opposite force. If A exerts a static force on B, then B exerts an equal but opposite static force on A, to ensure no net momentum or energy change.
Separate names with a comma.