# Is all motion really the result of fundamental forces?

1. Jan 4, 2014

### Trickstar

I'm in 11th grade of high school and I'm currently in Advanced Pre-Calc and AP Stats and I am teaching myself Physics from a textbook at home (which is Algebra based) because of my intense interest in physics. I also taught myself how to differentiate (on Wikipedia) because of the boredom I felt in what we are covering in Pre-Calc (Trigonometric proofs). Well what made me ask this questions was reviewing Instantaneous velocity and acceleration. These are the only two derivatives of in position mentioned. From what I learned from Wikipedias derivative example, instantaneous velocity is really the derivative of time and position, and acceleration is the derivative of velocity and time. Well this caused me to ask the question, whats the derivative of acceleration? I found the answer to be jerk, which caused me to ask what the derivative of jerk was, which is jounce and so on. Well then I realized you could keep deriving forever. So then I asked the question, is there a final derivative to position and time? This caused me to find a post that said that atoms have a force that extends out into infinity, so for every derivative of position there will always be another "deeper" derivative. The force at far distances are so low that they could be considered zero, but in reality they would still have a force if your measured it sensitively enough.

Anyway this caused me to think about the forces produced by the atoms. When you jump, is it in reality the electromagnetic/weak and strong forces that gives your atoms properties giving you your kinetic energy? The same thing with collisions. And the motion of astronomical objects a combination of those forces and gravity? I think the simple way to ask my question is, are all forms of motion caused ultimately by the fundamental forces? Like you jumping is ultimately a result of the forces holding your atoms together and keeping them separate.

Also, I'd like to know if it is possible to directly measure any of the nth derivatives of motion (past jounce)?

2. Jan 4, 2014

### voko

You have a bunch of unrelated questions.

First, the "final" derivative. What does "final" even mean? I can think of two different meanings. One, some n-th derivative becomes zero identically. All subsequent derivatives will also be zero. This only happens for functions known as polynomials. There is one very important polynomial motion: projectile motion close to the surface of the earth. Its acceleration is constant, so all further derivatives will be zero. Another interpretation of "final" is that an n-th derivative simply does not exist. This is possible in pure mathematics, but in physics we believe that such motion is impossible.

A more important question is why do you care about higher derivatives? The laws of physics deal with only two derivatives, so bothering about higher derivatives of motion is usually pointless.

Regarding your question about forces, everything you experience in "normal life" is the product of electromagnetic forces and gravity. Atoms in your body are held together by electromagnetic forces. The Earth is held together largely by gravity. Objects on the Earth interact with other objects and the Earth through gravity and electromagnetic forces. At subatomic scales, other forces play an important role. They are what hold atomic nuclei together and, sometimes, make them transmutate. At astronomical scales, however, we understand that we may be missing something. It appears that there are "dark matter" and "dark energy". We call them "dark" because we cannot see or detect them directly, we only infer their existence indirectly. We do not currently understand - or at least there is no commonly accepted agreement - what those are, which might mean there are some unknown forces, or our known forces behave differently than we expect.

3. Jan 4, 2014

### Bandersnatch

Depends on what you mean by "to cause" and "motion".

You can "cause" yourself to be in motion through space by choosing an appropriate reference frame. E.g., when traveling by train you can equivalently say that you're motionless with respect to the train, and moving with respect to the train station, and furthermore moving at completely different velocity with respect to the Moon, the Sun, the Galactic centre, the second train passing you by, etc.

Then you've got the expansion of space, which does cause distances to increase without any of the fundamental forces participating, but also without any actual motion through space. You may count that as motion, but not in the sense it's described by Newton's equations.

I don't know about measuring higher derivatives of acceleration, but in principle it's just a matter of measuring the rate of change of the previous derivative(jounce is the rate of change of jerk, and so on).

4. Jan 4, 2014

5. Jan 4, 2014

### voko

It is important to understand that "suddenly put force on" is an idealization. In reality, a force is not put on suddenly. It is always applied gradually, even if transition from "no force" to "full force" is very fast. So the graph of that is not given by a step function with sharp corners, but a smooth curve, which has derivatives everywhere, unlike the step function.

I do not see how that answers the bit with the step function, and whether the step function thing asked any question to begin with.

Yes, that is fundamentally correct. We flex our muscles by electromagnetic forces.

6. Jan 4, 2014

### cryora

You can continue taking derivatives over and over, and they will still take on the meaning of "the rate of change of the previous derivative." Mathematically, there's no defined end to it, just like there is no end to the number of dimensions you can define for an Euclidean vector space by giving the vectors more and more real components. Since Force is defined using acceleration (the derivative of momentum actually, but dm/dt=0 is the more common case) in Newtonian physics, the usefulness of higher derivatives will probably depend on a case-by-case basis as there isn't a lot of theory out there for them.

I can imagine two planets falling towards each other, adhering to the equation F = GMm/r^2. Since their distances are decreasing over time, their acceleration is increasing. In this situation, the planets would have positive jerk. In order to find out what jerk is though, whether it's a constant or a function of another quantity, I reckon this would be an application of differential equations, which I haven't studied yet.

Jumping off the ground is a consequence of the repulsion between electron shells of the atoms on your feet and the ground, which is due to the electromagnetic force. The electromagnetic force is what gives molecules their structure.