As close as possible, without touching

[Warp]

Snooker rule:

"When the nominated colour is potted, the player will be awarded the correct number of points. The colour is then taken out of the pocket by the referee and placed on its original spot. If that spot is covered by another ball, the ball is placed on the highest available spot. If there is no available spot, it is placed as close to its own spot as possible in a direct line between that spot and the top cushion, without touching another ball."

So, how close is "as close as possible without touching another ball" in terms of physics?

 

[Dale]

"Touching" isn't a well defined physics term.

 

[jbriggs444]

"Touching" isn't a well defined physics term.

"As close as possible without touching" does not work in mathematics either.

 

[aheight]

This is an interesting phenomenon in Nature. Like the paradox of crossing a road taking 1/2 the length then 1/2 of that and so on. In purely mathematical terms we of course never get to the end. And similarly, there is no "closest" real number to the number 1. Physically however, I suppose molecular orbitals get in the way of each other when we press two objects close to one another and perhaps the strength of those orbitals dictates just how close is "as close as possible". Maybe this would be an interesting question to pose in the Quantum Mechanics section?

 

[ZapperZ]

This is an interesting phenomenon in Nature. Like the paradox of crossing a road taking 1/2 the length then 1/2 of that and so on. In purely mathematical terms we of course never get to the end as there is no "closest" real number to the number 1. Physically however, I suppose molecular orbitals get in the way of each other when we press two objects close to one another and perhaps the strength of those orbitals dictates just how close is "as close as possible". Maybe this would be an interesting question to pose in the Quantum Mechanics section?

This HAS been posted there. In fact, if you do a search, there have been several incarnations and re-incarnations of this type of question throughout the years.

The issue here isn't what happens when atoms get closer, materials get closer etc... We study that and we know what happens in many cases. The problem with this type of question is the DEFINITION of what the OP is asking. As has been stated, the question made use of the word "touch", which we ALL know the meaning of in everyday life. However, in the context of physics, it HAS to be defined. Often times, in cases like this, the question has no valid meaning (it is like asking "how soft is 5 meters?").

Usually, question like this is a great introduction to new members, and non-scientists to start being aware of the nature of the question that is being asked. Physics had to this type of re-calibration many times in its history. It is a good exercise for everyone else as well.

Zz.

 

[aheight]

This HAS been posted there. In fact, if you do a search, there have been several incarnations and re-incarnations of this type of question throughout the years.

Ok, here's one: https://www.physicsforums.com/threads/circle-sphere-touching.845552/#post-5303541

The wave functions extend to infinity so in this regard, I suppose the matter of "touching" is not a well-defined (discrete) event.

 

[fresh_42]

"... without touching" is context sensitive. In this case you may assume a piece of paper. It is only meant as to guarantee that the according red ball can be played without having to move the colored ball.

@ Ronnie: I'm not very confident after your performance yesterday with this rather risky kind of your play, but I wish you the best for the sixth!