# What is required for change? Force or Energy?

1. Oct 30, 2009

### runner108

I'm wondering what is more fundamental to the concept of something changing, force or energy. As I see it, energy is the capacity of a system to do work. Also if we don't have energy in the universe, there is no physical universe for us to experience. Must be pretty fundamental. On the other hand if I separate the notion of 'what' changes from 'the process of change' it seems force is a bit more fundamental. Force is the space derivative of energy. An object at rest stays at rest unless a force is acted upon it.

2. Oct 30, 2009

### magpies

Id go with change.

3. Oct 30, 2009

Staff Emeritus
I think this will turn into a discussion on what "fundamental" means.

4. Oct 30, 2009

### mikeph

It has everything to do with time and nothing to do with anything else, IMO. change = d/dt, anything can have non-zero d/dt, and it is not fundamentally more linked to one "thing" than another, just as one function is not more fundamentally linked to one point in its domain than another. Very philosophical.

5. Oct 30, 2009

As far as I understand the subject, Hamiltonian and Lagrangian mechanics are expressed in terms of a potential energy function, and all forces internal to the system are derivatives of this potential function.

It never ceases to bug me though, because doing that constrains the type of systems you can express without contrived time dependence terms to forces expressable with a potential function. Not all fields in general have a potential, only irrotational ones.

There are tons of problems in engineering where you have loss terms, or source terms, or boundary conditions, and as far as I understand the subject yet, you can't give a hamiltonian for something with loss terms. Any situation where you don't have the last, most fundamental, complete accounting of your system is not going to be perfectly conservative, and the nonconservativeness of it is going to be important.

So why in the world did physicists decide to take Hamiltonian mechanics, rather than the more general Newtonian mechanics when they moved forward with reletavistic and quantum mechanics? Didn't they worry they were going to be missing something eventually when they ran into a nonconservative situation?

Last edited: Oct 30, 2009
6. Oct 30, 2009

### vanesch

Staff Emeritus
Indeed. When there's friction, you cannot use these methods (well, there are some extensions where you can still tweak things so that you can emulate some sort of friction, but in all generality you are right).

Well, their bet was that on the most fundamental level, things ARE conservative. And apparently they made the right bet. So these techniques are indeed only useful if we consider things on their most fundamental level (that is, when we do not neglect degrees of freedom which play a role).

7. Oct 30, 2009

### runner108

i guess to clarify I can just state my opinion and the more knowledgeable folk can correct me where I go astray.

In order to have change a force has to be acted on something. What is this something? Force is both:

a) the space derivative of energy
b) time derivative of momentum.

Reworded it seems: if we see something change. It is either due to a change in energy as it relates to space or a change in momentum as it relates to time.

Thanks..

8. Oct 30, 2009

That's sort of what Hamilton's equations say:

dp/dt = -d/dq H(p,q,t)
dq/dt = d/dp H(p,q,t)

where H, under certain restrictions, is the system energy

The time rate of the momentum is equal to the coordinate change rate of the potential function.

9. Oct 30, 2009

### Staff: Mentor

An object in motion will continue to change its position without additional force or energy. So in that sense neither force nor energy are required for change.

10. Oct 30, 2009