# UP regarding value of a field and its rate of change

Gold Member
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).

Gold Member
Thank you mvp_plate.

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

Mentor
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.

Gold Member
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.