UP regarding value of a field and its rate of change

Suwailem
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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?
 
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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).
 
Thank you mvp_plate.
 
If the momentum is always positive (or non-negative), then the analogy of momentum with rate of change will not be one to one?
 
Suwailem said:
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.
 
Nugatory said:
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.
 
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