# Are all kinds on Forces between particles only dependent on the distance between the particles?

The 'total energy' of a particle in an isolated system is conserved only if all the forces on it are conservative. For a conservative force, we need a force dependent only on the current position of the particle, right? Is every force in the universe like that? Coloumb and Gravitation Forces are like that, and I think the forces which we use to push/pull in daily lives are also coloumbic forces at their core. What about weak forces and nuclear forces? Are they also of this type?

• Have you read this? – J.G. Mar 12 at 7:53
• @J.G. The link talks about Friction, but that's also conservative if we account for heat as kinetic energy and deformation as potential energy – Ryder Rude Mar 12 at 7:57
• Exactly, "conservative" depends on how you look at it. You may wish to clarify your question based on that issue. – J.G. Mar 12 at 7:59
• @J.G. I don't think there are any "real" non-conservative forces, because they'd cause an isolated system to lose energy – Ryder Rude Mar 12 at 7:59
• @J.G. Conservative means only dependent on position such that a potential can be defined with respect to the Force. I've mentioned this in the question. Conservation of energy can't work without the 'potential' part of the equation, and the 'potential' part needs a Force only dependent on position. – Ryder Rude Mar 12 at 8:00

No, not all of them, actualy most of them do not. Coulomb and Gravitational Newton force have such simple form because they describe interaction between particles at rest (unmoving) and with no other qualities that scalar electric charge and mass. The situation they are supposed to describe is so simple there isn't much that then can depend on.

For example the magnetic force (which is an aspect of electromagnetic force) also depends on the velocities of the particles. What's more, because of the limited speed of propagation of the electromagnetic field, it actualy depends on how they were moving in the past.

Same with gravitation: if you consider the full equations of General Relativity, you can see that the force depends on the velocity of the object, it's just that for low velocities it can be approximated with the force desbribed by Newton's equation of gravity.

Weak interaction depends on a certain quantum property of particles called chirality. It doesn't affect right-chiral matter particles and left-chiral antimatter particles at all - it only affects left-chiral matter and right-chiral antimatter.

The field that describes strong interaction (gluon field) follows so complicated equations, that it's difficult to describe this interaction as forces between particles. we have a number of particles affecting the gluon field, and gluon field affecting the particles back, but often in a way than cannot even be calculated, only simulated.

• But then how is the total energy of a particle defined? The equation needs 'Potential energy' which can only be defined if the acceleration of the particle is only dependent on position. – Ryder Rude Mar 12 at 8:13
• Most of these forces are not conservativate, that is they are not just a gradient of some potential. As an effect there's no notion of potential energy either. Instead, what can defined is 'the energy of the field' - the amount of energy that is contained within the given field configuration (for example, the energy of electromagnetic wave). And the law of energy conservation states then that the sum of kinetic energy of particles and the energy of the field remains constant. – Adam Latosiński Mar 12 at 8:22
• I have seen some equations of quantum mechanics equations contain a potential energy term. I don't have any understanding of the subject. Do we just use potential energy whenever it can be defined, or is the Potential energy in QM different from the 'Force integral potential energy' in classical physics? – Ryder Rude Mar 12 at 9:05
• @RyderRude Electromagnetic field can be full described by a pair: scalar potential also so called vector potential. So the sclar potential, which gives the usual potential energy is still there, and it still appears in the equations. But it's not all there is, and there are also other terms that also describe electromagnetic interaction. There are also situations when we consider quantum particles on a classical, external background. In such case we can for example, consider a special case where the external background is purely electrostatic field, and use the notion of potential energy. – Adam Latosiński Mar 12 at 22:12