Law of force:
Newton found that force is proportional to acceleration. Acceleration is second derivative of position. It seems so obvious result that it is very hard to doubt further. My query is:
“Why nature chose second derivative of position to be proportional to Force? Why not third derivative of position? Can we develop a consistent physical world in theory with force proportional to third derivative of position?”
If there is a very obvious explanation for it please let me know.
Nature contains particle. And particle can’t exist without certain properties such as position, movementum, energy and mass. And these properties have interdependencies. If you fix one property then automatically others get a constraint over their values.
One of these dependency is uncertainty principle. It says there are interdependent pair of properties in the nature. If you are certain about one property then other get loose its certainty in its value. Mathematically speaking, product of uncertainty of the pair of properties can’t be less then a known value. Such pair of properties are (position, monument am) or (Energy,Time).
My feeling asks: “ Why there are exactly two quantities whose uncertainty product should be lower bounded? Why not product of three quantities?”
If you play with the equations of the quantum physics you will feel that this uncertainty principle is implication of 2-dimensions of imaginary number space. If you tight your solution in one dimension it will set loose in other dimension.
The reason behind why quantum physicist chose imaginary number as base of quantum equations seems to me is completeness of the imaginary number space.
Does completeness of imaginary number space imply uncertainty principle with only two components?
Nature has some master plan which implied uncertainty principle and also completeness of imaginary number. We humans just got a chance to put them together.
All mathematician are invited to answer my confusion. 🙂