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This is a very heuristic argument, but here goes. I believe it is wise to search for determinism in physics, simply because although the physical world we measure appears to contain some elements of indeterminism, the ability to measure anything would not be possible without some degree of placing determinism in our logic. If we measure the position of a ...


0

I'd like to point out that knowing $2n$ quantities and the equations of motion are not enough to determine the solution. Even at the level of $L=T-U$ for just one particle ($n=1$). Consider $T=\frac{1}{2}m\left(\frac{dx}{dt}\right)^2,$ and $U=-C\frac {9m}{2}x^{4/3}.$ Then, for your equations of motion, you get ...


3

Observe that, knowing $\ddot{q}$, to get $\dot{q}$ and then $q$ you have to integrate twice. This introduces $2n$ integration constants you have to know to fully describe the system, which is the same amount of freedom you get when solving the Euler-Lagrange equations, where you need initial conditions for $q$ and $\dot{q}$.


1

When defining the uncertainty principle one has first of all to be very careful with the domain of definitions the operators have: in particular, if $A, B$ are the observables whose uncertainties we want to measure together, what needs to be calculated is the commutator $\left[A,B\right]$. In order this commutator to be well defined we must have that the ...



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