Heisenberg's Uncertainty Principle

[Chirag]

I am supposed to do an essay on the following prompt:

 

Heisenberg claims that you cannot know both the position and momentum of an electron with total certainty. Choose two other concepts that cannot be known simultaneously and discuss the implications. (Do not consider yourself limited to the field of physics).

 

Here's my response:

 

 

Though quirky in its origin, Heisenberg's Uncertainty Principle is a reflection of the laws of physics, and like other reflections of the laws of physics, it can be best explained as a statement about symmetry. Formally, symmetry is defined as invariance under transformation; x is symmetric if it is impossible to tell whether or not a given transformation has been applied to x. German mathematician Emmy Noether, a contemporary of Albert Einstein, declared that every symmetry of the laws of physics leads to a conservation law, and every conservation law arises from a symmetry of the laws of physics. Thus, translational symmetry of space and time leads to the laws of conservation of momentum and Energy and so on. But Emmy's insight goes even deeper than that. After some fairly deep mathematical business, one can conclude that there exists an uncertainty relation linking every symmetric quantity and its corresponding conserved quantity. Thus, in the case of Heisenberg's Uncertainty Principle, the translational symmetry of space leads to the conservation of momentum and to the uncertainty relation linking ∆X (position) and ∆P (momentum). So, is there an uncertainty principle connecting ∆t (time) and ∆E (Energy)? Absolutely! ∆t.∆E>h. The more accurately we know the energy of a body (∆E is small), the less accurately we know how long it possessed that energy (∆t is big). The energy can be known with perfect precision (∆E = 0), only if the measurement is made over an infinite period of time (∆t = ∞). It also implies that in extremely small time elements (∆t is small), the uncertainty in the energy of the particle (∆E) is significant. This has major implications for Connective Physics, Hyper dimensional Physics, The fifth point, Casmir Effect, and Zero point Energy.

 

How would you rate it on a scale of 1 to 9? Have I got all the facts correct? Thank you