# For collision, physical contact is not a necessary condition. Why?

In my textbook, it is written that

"For collision, physical contact is not a necessary condition".

How can collision occur without physical contact? If there is no physical contact, then there would be no contact force between particles to act as impulsive force.

What would act as impulsive force in such a collision where there is no physical contact between the particles?

Can you give an example of such a collision?

• Consider a spaceship doing a gravitational slingshot off a planet. At no point does it touch the planet, but it's still a collision, in the sense that it's a relatively rapid event that conserves momentum. Sep 6, 2017 at 7:10
• Still, that's a pretty vague statement and I'd recommend you get a new textbook. Sep 6, 2017 at 7:10
• To be nitpicky, "physical contact" is a very tough statement to really understand in itself. Try to define what a "touch" actually is, and you'll end up concluding that nothing ever really touches anything. Sep 6, 2017 at 7:57
• @Steeven To expand on your nitpicking, physical contact is actually an electromagnetic interaction between the atoms at the surfaces of either material. It's still sort of at a distance. Your textbook could have been even less helpful by reminding you that bodies can exert force on each other via any of the fundamental interactions, the "distance" connotations being an exercise for the reader. Sep 6, 2017 at 10:38
• If you confine the discussion to the realm of Newtonian mechanics, you do need contact for a collision. In fact, the two are synonyms for bodies with delta-v. If you leave the realm of Newtonian mechanics all the terms are "not even wrong". There are no particles if you look close enough, hence no possibility for any "contact" in a meaningful sense of the word. There is not even the same space or time for the "entities" involved which are more like state parameters at time-space coordinates. So: In Newtonian mechanics, the statement is wrong; in quantum mechanics, it's meaningless. Sep 7, 2017 at 10:06

In science, language is specific and unambiguous. That means that terms are defined in ways often different from colloquial usage.

I'll quote Wikipedia on the definition of a collision. "A collision is an event in which two or more bodies exert forces on each other for a relatively short time." Note that there is no requirement for contact.

Of the four fundamental forces, both electromagnetism and gravity are long range. Despite being long range, they both fall with the inverse square of the distance (for simply distributed objects). This means you can mostly ignore the effects of the force at large distances relative to their closest approach.

A charged particle being deflected by another charged particle as they pass by each other is an example of a collision where no contact takes place. A gravitational slingshot where a small object moves around a much heavier object to gain speed is another example.

• I'd argue that your examples for electromagnetism and gravity don't fit your definition. "Relatively short time" is obviously extremely vague and up for interpretation. That said, gravity and electromagnetism don't disappear as you go away. There is always an (increasingly small) force between the two bodies. You couldn't define when they collide without having an arbitrary force as a cutoff point. I don't think those are good examples of collisions because it's not really clear where the collision starts and ends, or what the time it takes is.
– JMac
Sep 6, 2017 at 10:39
• "In science, language is [ideally] specific and unambiguous[, but sloppy usage is common enough to mess with everybody's heads]." Fixed that for 'ya. As a matter of practice some specific and unambiguous meansing are used nearly universally and others are ignored willy nilly. In my experience this one is a middle case, with many precises usages but also enough colloquial vagueness to cause trouble. Sep 6, 2017 at 14:34
• @JMac In the context of doing, say, a nuclear physics experiment the word in entirely appropriate because while E&M is nominally long range the presence of the rest of the target material means that the time for which the interaction with any particular scattering center is not washed out by other effects is quite short. Sep 6, 2017 at 14:39
• I think the key to the vague definition of "a relatively short time" is the word "relatively." We can model an interaction as a collision if the period of time is short enough that we aren't too concerned with the details of what happens during that time. It's relative to everything else that is going on. If the interaction took 1 month, and the timescale for everything else happening is centuries, it may be very reasonable to model that interaction as a collision. Likewise, if an interaction took a microsecond, but you're interested in nanosecond level interactions,... Sep 7, 2017 at 1:26
• ... it may not be effective to model that interaction as a collision, even though it was "brief" by human standards. Sep 7, 2017 at 1:26

This may be a somewhat pedantic answer, but I think for the purposes of cultivating clear language, I'd call into question the notion of "physical contact" as implied by the textbook's usage of the word and instead answer as follows: If the "collision" of two or more relatively moving bodies (as it implies) means a mutually wrought-on-one-another change of motion state, then there has been physical contact, by definition. There has been exchange of momentum and or angular momentum and energy by dint of some interaction.

When we say "physical contact" colloquially, we mean a particularly strong interaction wrought by particularly tight nearness of the two bodies to one another, with a cluster of results that evokes our intuitive idea of "physical contact", such as: triggering of the sense of touch, if one of the bodies is a sentient animal, sharp deformation and possibly fracture of some of the bodies at their points of nearest approach, permanent, plastic deformation such as scratching, scoring or warping and clearly hearable "contact" sounds. But, at the most basic level, such an interaction is different from any other interaction through the four basic forces of nature only through the strength of the interaction. There's no real fundamental qualitative difference at all: when we "touch" a body, we're simply feeling the deformations of our own body wrought by fundamental forces - electromagnetism - between our bodies and what we're touching. Whether we're feeling the Coulombic repulsion between our finger and the atoms of the table it is resting on, or the Coulombic repulsion between the charged ball we are holding and a like charged one several centimeters from "physical contact" with the former, there's nothing really different that is happenning at a fundamental level.

When trying to define what makes "physical contact" different from other interactions, we quickly discover there is no rigorous definition that will differentiate it from other interactions.

All scatterings are examples of collisions. You may consider the example of Rutherford's alpha scattering in which there is no physical contact between alpha particle and the nucleus.

The problem here is one of definition. It's discussing "collisions" and "contact" but doesn't carefully define them. The problems you get are:

• There is no clear-cut difference between a collision and many other forms of interaction.

• There isn't a good definition of "contact" either. Look closely and things don't contact each other. They just come close and move apart.

• Whatever size the objects we are discussing may be, at an atomic scale they are all made up of tiny quanta/"particles" which aren't solid, and don't "collide" at all. Ever. They exchange force carriers and exert forces on each other. Technically it's hard to describe what exists. This isn't relevant at day to day level but is a big part of the reason why its hard to define these words. (You may hear this stated as "everything is mostly empty space")

• Although we call a lot of things "collisions", it's a vague term when you look carefully at it, because physically things interact rather than collide. We think of them as "collisions" because we see them on a timescale that makes them look like instant events. If we saw them closer up, we would see they involve many interactions that gradually build up and gradually dissipate, all while the objects are at a distance. A "collision" is a kind of conceptualisation. Which is fine, except that you're then trying to apply the term "contact" which isn't a similar concept.

An example of this is Brownian Motion. You can see dust particles move in the air, and particles in water (under a microscope), suddenly change direction. It certainly looks like they have had collisions, because they suddenly change direction. Even in classes we say they collided. But they never actually came in contact. They might have come within tiny fractions of a millimeter, but before they could actually touch, the interaction had done its job and momentum/energy was transferred, so they moved apart.

Its the same with large scale collisions, just harder to see, and less obvious. Because we generally don't care when 2 cars collide, whether their particles came into contact or just within a tiny fraction of a millimeter, enough to pass on momentum and deforming forces, we say they "collided" and came into "contact". But technically neither is true, or at least, you would have to define what counts as "collision" and “contact" to decide whether it was true according to that definition.

## Thought experiment/example of a "quite close" answer

Here's a thought experiment for you, in place of a definitive answer.

Suppose you played pool or snooker just with the cue ball and black, and somehow both balls were either all the same electrical charge (all + or -) or all the same magnetic monopole (north or south magnet) without breaking apart, exploding the earth, or breaking physics. Being the same charge or magnetic pole, they repel each other very strongly when they get close.

You hit the cue ball at the black. It seems to smack one side of the black, and both balls move apart as usual in pool/snooker. But ultra-slow motion shows that the black ball started moving away and the cue ball started to change its path, when they were 3.5mm apart, and both balls rapidly changed their motion so they never actually got closer than 0.25mm, so rapidly that it looked like a normal game of pool.

Would you say this was a "collision" and if so, was there "contact"?

In close-up, that is what every collision you see is like, and the kind of movement that's really happening.

That is my attempt to show why it's a difficult question to answer.

• Great explanation, without getting deep into technical vocabulary. This deserves more attention. Sep 7, 2017 at 3:04
• Great thought experiment, it perfectly highlights that a collision is a transfer of momentum, without having to fuss about what "contact" means. Deserves more votes! Sep 8, 2017 at 7:52

Short term magnetic repulsion (e.g. between same poles of magnets) is also one example of collision without physical contact.

What does "physical contact" mean anyways? The atoms of two cars colliding never "touch" each other! The idea of "touch" is really our human inability to comprehend sizes smaller than a fraction of a millimeter.

Once you accept that physical contact is a mere question of scale, you give it up and then all collisions are "touch-less". Two cars colliding can exchange paint, sure, but they never really touch in the sense that the atoms don't even have a defined surface with which to touch one another!

(Mathematically, we can define touch as two object's surfaces sharing a least a point. But that doesn't work in physics because atoms don't have surfaces)