The cause of this line of thought is the drama surrounding the match between Tochinoshin and Asanoyama in the latest sumo tournament. The outcome on the match hinged on whether Tochinoshin’s heel had touched the sand on the outside of the ring or not before his opponent hit the ground. They specifically have finely-swept sand outside the ring to be able to tell if contact is made, but in this case the falling opponent obliterated any evidence of whether the heel touched down earlier. Video evidence (which contrary to most things in sumo, was introduced much earlier than in other sports simply because of how important these things are) was entirely inconclusive. There were plenty of photos that showed the heel wasn’t touching, but video evidence was less precise and it certainly seemed possible that the heel touched down very lightly at least. In the end the five judges deferred to the one who was closest to the action, who said he was sure the heel had touched out. For various reasons, this drove most foreign sumo fans into a virtual riot. See https://www.reddit.com/r/Sumo/comments/bsg1ry/asanoyama_vs_tochinoshin/
I recall seeing someone saying he tested with sand and his own sense of touch, and there was no way that he could be sure that he had touched the sand without leaving a mark, but I suggest that it may be reasonable to suggest that the only reason that sense is recorded is that the sand actually moves. But I could also see the line that it’s possible in theory with the sand to touch your body, have it be sensible in some way, yet not actually disturb the sand. And along this line of thought, it’s possible that two objects may indeed “touch”, but that it would not be sensible at all, but that goes down the line of what it means for two objects to touch, or to be in contact.
The problem with saying that “their valence electrons interacted with each other” is that all charged particles are theoretically influencing every other charged particle in the universe through its disturbance in the electromagnetic field. Is there any consensus what exactly needs to happen for objects to be in contact? Is there an area of where there’s no clear disturbance of one body by the other, but the electron clouds have some nontrivial amount of overlap? Electron clouds are fundamentally probabilistic, so in some sense every electron cloud overlaps every other one with an extremely tiny probability.
Perhaps the reason I can find no information as to whether this has been rigorously defined is that scientists simply don’t care. It may be that when you get down to the level of considering the electron cloud probabilistically, macroscopic notions of “contact” are not relevant any more. But it leaves all definitions of things being in contact in a state of indefiniteness when it’s really really close. Surely there’s no way that we would be able to have enough evidence in a sports match to say exactly how close the nuclei in the atoms of each object got, but on a fundamental level, as someone who studied lots of advanced math in school and is now interested in learning more fundamental physics, while at the same time enjoying sports that have rules involving macroscopic effects which are ill-defined on the smallest level, it leaves me a bit unsettled.
So is there a universal definition rigorous down to the quantum scale of when two objects are touching, or because it’s impossible to make such measurements when it matters, no one else has put any thought into it?
In tennis, they used to rely on someone’s eyes to judge whether a ball had hit the line or not. In the 1970s there were several electronic systems proposed and patented to remove the human element, but it was in 1980 that Cyclops, which used infra-red horizontal beams of light was officially accepted. The advent of high-definition TV has enabled Hawkeye which is also used in cricket where similar fine judgements about stepping over a line have to be made. I imagine that Baseball might also have the same problem and solution.
Since we are usually referring to a line on the ground, which may be painted on grass; it hardly needs accuracy down to the molecular level. Just a system that is demonstrably unbiased and reasonably accurate.
I’m not sure there is actually any known way that subatomic particles actually ever can be considered to touch - ever. Well maybe in the singularity of a black hole. The use of sand is clearly intended to provide one definition. If the sand is undisturbed it wasn’t touched with enough force. But clearly it could be touched with a tiny amount of force that was within the elastic deformation of even piled sand grains. The definition of touched should probably be done, not in abstract terms, but as “no discernible disturbance to the sand.” The alternative is a well known joke:
There are three umpires at a baseball game. One is an engineer, one is a physicist and one is a mathematician. There is a close play at home plate and all three umpires call the man out. The manager runs out of the dugout and asks each umpire why the man was called out.
The physicist says, “He’s out because I calls 'em as I sees 'em.”
The engineer says, “He’s out because I calls 'em as they are.”
The mathematician says, “He’s out because I called him out.”
Baseball uses replay for some things, but still uses the umpire’s eyes to say if a batted ball is fair or foul.
What baseball will probably do is automate the calling of balls and strikes. When you watch a game on TV, they always have a way to show the audience where the pitch went. And they show that missed calls are endemic. Baseball players know this was well. So it’s only going to be a matter of time before they’ll introduce a system for calling them in the game itself.
When two objects are in contact you’ll hear one of shout from the back seat “He’s touching me!”. The other object is likely to follow up with “He was looking at me!”.
I fully realize that. I’m wondering if there’s some definition people have come up with to say when two macroscopic objects have touched based on the interaction of their smallest constituents.
The sports note was merely for motivation of why I’m asking the question. I know full well that what I’m asking is not applicable for making sports calls. I mainly just got to thinking about how we might rigorously define macroscopic touching, in cases where it’s unclear, based on what we know of how the microscopic world works.
It’s not that scientists don’t care. It’s that the word “touch” seems more definitive than it is. Check out “Lennard-Jones potential” and “atomic force microscopy” and “quantum tunneling”. The world of very small distances doesn’t fit the definitions implicit in sports.
