# Newtons third law and quantum mechanics

1. Jun 10, 2014

### shivakumar06

dear sir,
we know that third law of motion says that every action has a equal and opposite reaction. quantum mechanics tells us that it is possible not predict the position as well as the speed of electron. i like to know if electrons ,protons and neutrons form a system called atom. each of the components interact with each other and we also know where the protons and neutron are in nucleus and their speed. my question is if i am correct why can not we have a equation for path of electron?

2. Jun 10, 2014

### HomogenousCow

Newtons laws are not correct in the quantum realm.
In fact Newton's third law isn't even correct for many systems in the Newtonian realm.

3. Jun 10, 2014

### hilbert2

In quantum mechanics, reference is usually not made to the concept of force like in Newton's mechanics. The relevant concept in QM is that of energy, similar to classical Lagrangian and Hamiltonian mechanics.

It is possible to demonstrate by several experiments, like the double slit experiment, that a particle can "be in several places at once" between consequent measurements of its position. Therefore, its useless to try to make a theory where electrons have a definite trajectory.

4. Jun 10, 2014

### hilbert2

Yes, in a system with magnetic forces the 3rd law is not valid in its original form.

5. Jun 10, 2014

### DrDu

and we also know where the protons and neutron are in nucleus and their speed. [/QUOTE]
No, we don't know the position of neither the protons nor of the neutrons but the uncertainty of the position of these particles is usually smaller to the uncertainty of the position of the electrons due to the larger mass of protons and neutrons. To show that Newtons third law is valid in QM one can express the force F acting on an electron as $F=\frac{i}{\hbar} [H,p]$ and the corresponding force acting on a nucleus as $\frac{i}{\hbar} [H,P]$, where p and P are the momentum operators of the electron and nucleus, respectively. Now as $P+\sum p$ is a constant of motion for an atom also in QM (i.e. it commutes with H), the force acting on the nucleus must equal the sum of the forces acting on the electrons.