Definition of collision

Question

I was going through my book when I noticed this definition

"A collision is said to occur when the motions (of two or more bodies) are influenced by the forces they exert upon one another."

Well, I later realised some strange application of this definition. Consider an elementary charge moving in free space. There is another charged body (of much greater magnitude). Now due to the electric field of this charged body, the motion of the elementary charge has been influenced. As a result the trajectory of the elementary charge changes.

Now, if consider our definition in this case, we should be able to say that the elementary charge is colliding with the charged body. This statement is definitely false. Similar examples can be set up in gravitational fields as well.

So, what can we consider as a "trusty definition" for collision?

In case I have hypothesized something incorrectly, then kindly guide me.

While giving your respective insights upon this topic, kindly consider the example of an object following a parabolic trajectory in the gravitational field of Earth. Is it colliding with Earth as well?

Answer 1

A collision is said to occur when the motions(of two or more bodies) are influenced by the forces they exert upon one another.

Generally, for it to be what is commonly referred to as a collision, would be one for which the interaction lasts for a small amount of time. For example, when two billiard balls collide, they briefly exert an impulsive force on each other.

Now, if consider our definition in this case, we should be able to say that the elementary charge is colliding with the charged body. This statement is definitely false.

Why? Even though one charge is significantly greater, this does not mean the greater charge experiences no force or recoil. In fact, it does according to the Coulomb force law and Newton's third law. The same is true for gravitational force, regardless of the masses.

So, what can we consider as a "trusty definition" for collision?

As above, one where the interaction time is small. For macroscopic collisions the objects would come in contact briefly, and for smaller charged/interacting objects, they would interact briefly.

Answer 2

There are several ways to define collision, and the choice of the definition depends on the type of the problem and the field of physics. The possibilities that come to mind are:

• Finite range and/or time The objects interact in a particular region of space or during a finite period of time. This is often used as an operational definition, e.g., when describing collisions in statistical physics, hard-sphere scattering cross-section in atomic physics, emission/absorption of light by atoms, etc. However, this definition immediately poses problems, if we consider, e.g., particles interacting via infinite-range forces, such as Coulomb or gravitational force - when dealing with collisions of charges or stellar bodies.
• Asymptotically free One can define a collision in asymptotic sense, that the particles are freely moving at $t\rightarrow -\infty$ and when they are far from each other, and that they separate after the collision and can be again regarded as free at $t\rightarrow +\infty$.
• Boundary conditions In quantum mechanics and QFT the above definition of collision is usually reformulated in terms of boundary conditions - that is, the problem described by the same Hamiltonian can be treated as an eigenvalue problem or a scattering problem, depending on the boundary conditions and the normalization we use (normalizing the number of particles in eigenvalue problems or normalizing the incident/outgoing flux in scattering problems).

Answer 3

I would opine that you make a conceptual error when you say that your example of two charged bodies interacting is not a collision. If we consider two snooker balls approaching each other- a classic example of a collision, you might think- their interaction at the point of contact is mediated by nothing other than the same electrostatic forces that appear in your example. The only difference between the two cases is relative scale. In the case of the snooker balls, the distance over which the forces have a measurable effect is very small compared with the size of the balls themselves.

Now, imagine that the two snooker balls are in space, and each contains a significant net positive charge. If you arrange for them to collide, their distance of closest approach will depend open the values of the charges- if you repeat the experiment while gradually dialling up the net charge on each ball, you will reach a point at which the distance of closest approach between the balls becomes large compared with the size of the balls. At what point during that series of experiments does the interaction between the balls cease becoming a collision?

Answer 4

In colloquial English a collision (literally, not a metaphor) is a rapid contact between objects, so that they touch and their motion is altered. Physics needs more specific terms. The general connotation is that the interaction is quick and has some effect on motion. I wouldn't say a comet "collides" with Earth just by having its trajectory altered: the period of influence stretches over a significant time. If you're using it to mean "influence due to proximity" to avoid some more awkward phrasing, just say so in your paper.

Answer 5

Intuitively, when two bodies "collide", one of them "hits" the other. That is, they are understood to have actually touched.

But at the subatomic level, what does it mean to say that two bodies "touch" each other?

They come close enough for the electromagnetic forces which bind the atoms of one of the bodies together to interact with the electromagnetic forces which bind the atoms of the other body together.

When it comes down to it, a "collision" is just an interaction of the electron shells of the individual atoms of one, with the electron shells of the individual atoms of the other.

Do the electrons themselves actually "touch"? My understanding is that an electron is so small, the electric field around it is very large as you get really close to it. So large, in fact, that you just can't get two electrons to "touch".

Yes I know it's far more complicated than that because of "quantum" an' all that ... but the best you can say is that perhaps some of the electrons (and indeed atoms) migrate from one of the bodies to the other, and vice versa, during this "collision" incident -- but again, nothing actually "touches" anything else. Their only interactions, at the atomic level, are as a result of the electromagnetic force.

The same, even more so, at the subatomic level, where you have not only the electromagnetic force to worry about, but also even the strong force, which spreads only to the limit of the size of a nucleus. And of course the weak force, about which I don't really know enough about (intuitively) to comment on.