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Primacy of conservation laws 
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#37
Nov1112, 06:49 PM

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Wherever you choose, that is one of the decisions you have to make when you define a reference frame.



#38
Nov1112, 06:53 PM

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If we let the velocity of the particle be v or 10^{10}v, what difference would it make to this universe (or the particle)? 


#39
Nov1112, 06:59 PM

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#40
Nov1112, 07:32 PM

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In Classical Mechanics, a particle has a determinate position x,y,z for any given time t. I can take position between two times and obtain velocity. That's it. If you insist that velocities are relative, then you are the one who is not sticking to the constraints of Classical Mechanics. Now, you might be tempted to bring up Galilean Relativity, but it's not true relativity in sense that it is indistinguishable from preferred system. Just because I can rewrite equations doesn't mean that particles doesn't have an intrinsic absolute velocity. It is only when you start considering motion of light relative to other objects that the concept of velocity as relative quantity becomes irrefutable. But by now you've ventured into Special Relativity where force is a relative quantity as well. 


#41
Nov1212, 02:10 PM

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Isn't it simpler to just write down mass times acceleration, and be done with it? 


#42
Nov1212, 04:01 PM

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Mass times acceleration is easier when you have a trivial degree of freedom with a trivial constraint. The more general problem becomes, the more effort it becomes to write out the correct equations for each DoF. In contrast, you can always write down the Lagrangian with the same amount of effort, and get the equations of motion by differentiating. 


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