How universal is Heisenberg uncertainty?It can be extended to time energy, coordinate momentum,what else?What is the connection between it and Noether's theorem?

2 Answers

1. It is not clear what the author of the question means by the word “universal?“. The Heisenberg uncertainty principle is a fundamental property of the quantum system and of the particles themselves. The principle is not related to the accuracy of devices that simultaneously measure conjugate variables (coordinates and momentum) with the desired accuracy.�

   ➢ … time — energy, coordinate-momentum … what else?� The Heisenberg uncertainty principle also applies to:�

   • Particle angular momentum and orientation (angle),
   • Phase of the electromagnetic wave and the number of photons,
   • Electric potential and charge density,
   • Magnetic potential and current density,
   • Electric field and polarization density,
   • Newtonian gravitational potential and mass density.

   ➢ Noether's theorem has nothing to do with Heisenberg's uncertainty principle. Due to its fundamental nature, the theorem states that in classical and quantum mechanics, the invariance of equations with respect to certain symmetries guarantees the fulfillment of certain conservation laws. Thus, the law of conservation of energy corresponds to the homogeneity of time, and the law of conservation of momentum corresponds to the homogeneity of space.

   Log in to Reply

2. Tell me where you can find the most complete list of physical quantities associated with Heisenberg uncertainty. Or how to display them yourself. Who did this?� Thank you.

   Log in to Reply