B Energy vs. Force: Understanding the Relationship and Implications in Mechanics

[FallenApple]

I understand that the energy equations are derived from f=ma.

From what I understand, this was reformulated under lagrangian and hamlitonain mechanics. So force here is merely a consequence or at least equal to the energy changing with respect to position.

So an apple falling from a tree does so only because its energy changed, with respect to distance. We don't have to consider forces at all, for forces are only mathematically tantamount to changes in energy. That is the appearance of "forces" are ascribed to energy changes.

Maybe we can even say that its the changes in energy that causes the motion, instead.

This is very different philosophically. But what is the more accurate picture? F=ma came first and then the reformulations came after.

However, I'm sure if history scientific discovery was different, maybe everything we conceive would be energy based instead, without much conception of push pull forces.

 

[Drakkith]

But what is the more accurate picture?

I'd say neither way is more accurate. Forces are very useful in solving certain types of problems and energy is very useful in solving others.

 

[FallenApple]

I'd say neither way is more accurate. Forces are very useful in solving certain types of problems and energy is very useful in solving others.

I think mathematically, they are equally accurate.

But in the modern sense, wouldn't the concept of energy be more philosophically sound? Since, gravity is already fictitious under GR. And all interactions are merely actions at distance. So saying that invisible things cause motion makes less sense than merely observing that a configuration has changed.

 

[Drakkith]

But in the modern sense, wouldn't the concept of energy be more philosophically sound? Since, gravity is already fictitious under GR. And all interactions are merely actions at distance. So saying that invisible things cause motion makes less sense than merely observing that a configuration has changed.

Is energy not an "invisible thing" too?

 

[FallenApple]

Is energy not an "invisible thing" too?

True. But energy is measured in terms of concrete things. Like Mgh. g is a constant, M the property of the object, and height is a spatial quantity. All those we can see and observe with our senses. Except perhaps the constant g( which can be obtained by experimentation)

So in a sense, energy is less invisible, even though it is a human made construct.

 

[Drakkith]

My bathroom scale would argue that force is a very concrete thing. Otherwise how am I being held up by the surface of the scale against gravity?

Edit: Keep in mind we can find the force using the equation F=MA, where both the mass and acceleration are easily measured. I assume you have no issues with either mass or acceleration being less-than-concrete?

 

[FallenApple]

My bathroom scale would argue that force is a very concrete thing. Otherwise how am I being held up by the surface of the scale against gravity?

Edit: Keep in mind we can find the force using the equation F=MA, where both the mass and acceleration are easily measured. I assume you have no issues with either mass or acceleration being less-than-concrete?

No, mass and acceleration are concrete. It's just forces. It seems like Newton's formulation implies that a force causes the acceleration. The energy only view observes those concrete things changing, without ascribing a cause.

There is empty space between the bathroom scale and you.

We can only observe that you are not accelerating in your own frame. That is, the energy(configuration) is somehow not changing.

 

[A.T.]

But what is the more accurate picture?

Your interpretation of neither is accurate, as neither implies any cause-effect relation.

...more philosophically sound? ...energy is less invisible...

This drifts into the esoteric. Energy is more broadly applicable than forces, so you could say that it's more general or more abstract. But those classifications have no consequence on accuracy of the concepts.

 

[Dale]

This is very different philosophically. But what is the more accurate picture?

These are two different formulations of the same physics. Any experiment which confirms one confirms the other. Any experiment which contradicts one also contradicts the other. So experimentally they are equally accurate.

You say that they are philosophically different, but doesn't philosophy use logic? They are logically equivalent, so they are not that different. Whatever minor philosophical differences there might be are in things that cannot be measured. Nature simply doesn't care about such unimportant things and you are free to use either.