UP regarding value of a field and its rate of change

[Suwailem]

I am just a hobbyist and try to learn for myself.

I understand that the value of a field and its rate of change play the same role of position and momentum of a particle with respect to Uncertainty Principle, i.e. both pairs are conjugate variables. My question is: does the rate of change of a field extends to the negative domain, so that it could take negative values, or is it always non-negative?

 

[mpv_plate]

Derivative of a field can be negative and it often is negative. If it were always positive (or zero), the field value would be always and forever growing (or not changing).

 

[Suwailem]

Thank you mvp_plate.

 

[Suwailem]

If the momentum is always positive (or non-negative), then the analogy of momentum with rate of change will not be one to one?

 

[Nugatory]

If the momentum is always positive (or non-negative), then the analogy of momentum with rate of change will not be one to one?

Momentum is not always non-negative. Consider two bodies of equal mass moving in opposite directions: their momenta will be of equal magnitude but opposite sign, so the total momentum of the system is zero.

 

[Suwailem]

Momentum is not always non-negative. Consider two bodies of equal mass moving in opposite directions: their momenta will be of equal magnitude but opposite sign, so the total momentum of the system is zero.

Thank you Nugatory.