Physics Without Forces

[ydoaPs]

Forces are, after all's said and done, only a description of what actually happens. You can do all of Physics without the concept of force

 

And tvp45 for ALOT (if not nearly all) mechanics problems not using forces normally works out easier (reduces the complexity of the differential equations that need to be solved)...

 

 

How do we do physics without forces?

[gcol]

How do we do physics without forces?

 

Why not begin by giving at new, physics specific name? Force surely had a traditional meaning long before physics as a science was invented. Physics is great at inventing new words, let it find its own. Perhaps define force without using the word force. Might give a clue as to a fresh, modern way of looking at things.

[ajb]

Forces are really a Newtonian concept. When dealing with mechanics from a Hamiltonian or Lagrangian formalisms you don't need the concept of a force. You do of course have potentials and so the idea of a "generalised force".

[Klaynos]

My comment was infact directly relating to what ajb said

[h4tt3n]

Well, when it comes to one of my favourite hobbies, making physics simulation programs, it is quite common to use impulse as a way of indirectly transferring force from one object to another. For instance when dealing with rigid body collision it would be a pain in the arse to actually figure out the forces involved ^^

 

Here's a funny java example with a pretty good explanation: http://www.myphysicslab.com/collision.html

 

(Just get me right, here - I'm definitely NOT saying that it can be done entirely without using the concept of force!)

[thedarkshade]

How do we do physics without forces?

It's not really like we're doing physics without forces, we're just excluding force as a concept, as a definition. Everything includes forces, so the fact that force is actually everywhere is understood, so we don't need to mention that every time, that's why tvp45 said that you can do all the physics without the concept of force. BUT YOU CANNOT DO PHYSICS WITHOUT FORCE. That's like doing maths without multiplication or addition.

[ydoaPs]

Could I get a simple example of how a mechanics problem is solved without the concept of force?

[thedarkshade]

Could I get a simple example of how a mechanics problem is solved without the concept of force?

Sure! For example you have a question like this: "If a car moving with a velocity of 12m/s, for 10 sec reaches an acceleration of 15m/s^2, then what's the final velocity?"

It is understood that some force causes this increase in energy, or this acceleration, bur to solve this you don't need to know how much force is put on the car. All you got to do is find final velocity, and to do that you absolutely don't need the concept of force!

[ydoaPs]

Sure! For example you have a question like this: "If a car moving with a velocity of 12m/s, for 10 sec reaches an acceleration of 15m/s^2, then what's the final velocity?"

It is understood that some force causes this increase in energy, or this acceleration, bur to solve this you don't need to know how much force is put on the car. All you got to do is find final velocity, and to do that you absolutely don't need the concept of force!

 

So, it's no different than the rectilinear motion I learned about in my high school physics class?

[thedarkshade]

So, it's no different than the rectilinear motion I learned about in my high school physics class?

Well there are a lot more complex things, but yeah, it's no different. After all, movement is a product of force, so how could it not be!

[timo]

A not-so-simple but interesting example would have been my WiSci article on the derivation of the GR equation of motion which got deleted with WiSci (and the backup later being deleted with the crash of my computer's HD) .

 

A simple example: A point-sized particle in a potential. The Lagrangian function L for this system is [math] L = T - V = mv^2/2 - qV(x) [/math] with T being kinetic energy, V being potential energy, m being the mass (so obviously classical physics, here), v the velocity, q the charge associated to the potential (e.g. mass in a gravitational potential) and V(x) the potential. The equation of motion is derived via the Euler-Lagrange equations

[math] \frac{d}{dt} \frac{\partial L}{\partial \vec v} - \frac{\partial L}{\partial \vec x} = 0 [/math] (note that that the differential wrt. to a vector is just a lazy notation of mine, technically, you have to satisfy this eqn for each coordinate seperately).

Plugging in the L above

[math] \Rightarrow \frac{d}{dt} \left( m \vec v \right) + q\frac{\partial V}{\partial \vec x} = m \vec a + q\frac{\partial V}{\partial \vec x} = 0 [/math]

[math] \Rightarrow \vec a = \frac{q}{m} \frac{-\partial V}{\partial \vec x} [/math].

A specific example: When V is a gravitational field [math] V(\vec x) = g (\vec e_z \cdot \vec x)[/math] with [math]\vec e_z [/math] being the unit vector in z-direction (well, just "up"), then

[math] \vec a = -\frac{m}{m} g \vec e_z = -g \vec e_z [/math]. In other words, the object falls down with an acceleration of g, just as you would expect from the Newtonian F=ma=mg.

Note that using the way shown the concept of force did not explicitely appear and was "replaced" with the concept of a potential.

[Klaynos]

*looks at Atheist* you beat me this time... I was just about to make a near identical post

[timo]

Darn, I had surely spotted a sign-error somewhere.

[tvp45]

Could I get a simple example of how a mechanics problem is solved without the concept of force?

 

When I answered the OP, I was responding to the question "Why...". I hold that force is an operational definition rather than a foundational concept and, thus, completely outside any question of why. One might as well ask "Why are there sevens?" My answer would be, you can do arithmetic without them just fine. It'll be a pain in the neck doing the US currency or the SI units, but one could do it.

 

I understand that many (most?) problems are easier when using forces. But problems and concepts are very different. Think about how many people think Faraday's Law says that a changing magnetic field induces current. That is conceptually deficient, yet some of the most sophisticated electromagnetic motors in the world are built by people who use that idea. Go figure.

[Physia]

How do we do physics without forces?

 

Remove the word 'forces.'

Or, don't do Physics at all.