Of quarks and international borders

[MisterTrilby]

At what point does an atom cross an international border, and can it exist on the cusp, not in either country?

I would say that the border, not being a material object as such, is infinitesimally thin. So the atom can't possibly be as thin as the border, therefore there will be a time at which the atom can be said to be on one side of the border, straddling the border at another time, and finally on the other side of the border. The atom can be straddling the border partially, exactly on the border with half on one side and half on the other, or fully on one side or the other. No matter what, then, some part of the atom is always in a country. These are the conclusions I can draw from my limited knowledge of such things.

Thinking about this answer has raised more questions than I had before. This usually happens when I arrive at any answer. I assume that a border be infinitesimally thin, but is it that true, or even possible? Is it pointless to talk of anything that exists being thinner than the thinnest thing possible, i.e. a quark? (Is a quark the thinnest thing possible?) If so, are borders one quark thick? In which case, while an atom is going to be in one of the positions I mentioned above (straddling, 50/50 or completely over the border) a single quark could exist exactly on the border and not be in either country, right? And what about the uncertainty principle - wouldn't this make it impossible to determine the exact position of the quark anyway? And if quarks are pointlike, does this mean they have no width at all?

 

[ZapperZ]

Can you tell me why you are THIS concerned about where an atom is across a man-made imaginary line?

Zz.

 

[masudr]

Atoms have a finite size. Quarks, and all leptons (which include electrons) for that matter, are theoretically treated as pointlike objects, although being quantum objects, they will necessarily have some uncertainty in position.

Man-made borders generally have a region of uncertainty too; some of these borders aren't even decided. However, we can take them as being of zero width if we wanted to. Just specify a line in some set of co-ordinates.

 

[MisterTrilby]

Can you tell me why you are THIS concerned about where an atom is across a man-made imaginary line?

Zz.

I want to know because a friend of mine is a lawyer, and this had come up in a recent case. I came up with my own answer, but it opened up more questions, as so often happens. The more you know, the less you know! And the pursuit of knowledge is an end in itself.

I didn't realize that questions needed justifying on this forum; I'll know better should I decide to post again in the future.

 

[masudr]

I didn't realize that questions needed justifying on this forum; I'll know better should I decide to post again in the future.

I don't think ZapperZ was looking for justification. Sounds like he was just curious about a relatively bizarre question instead. I suppose I should let him speak for himself, anyway.

 

[ZapperZ]

I want to know because a friend of mine is a lawyer, and this had come up in a recent case. I came up with my own answer, but it opened up more questions, as so often happens. The more you know, the less you know! And the pursuit of knowledge is an end in itself.

I didn't realize that questions needed justifying on this forum; I'll know better should I decide to post again in the future.

masudr is correct. I was just very curious as to why "an atom" crossing the boundary of an imaginary line would be an issue. It is rather bizzare, and I don't think even in a court of law, such an issue would even be considered (at least, I hope not if it has any degree of rationality). I mean, once you start disecting which part of the atom is across this imaginary line (that is yet to be physically defined) up to the quark level, then it has gotten into an absurd realm.

It is certainly not a physics problem. I hate to think how that lawyer would do if he/she finds out that a quantum particle can actually occupy several places at once.

Zz.

 

[MisterTrilby]

While the line itself is 'imaginary', there is still a definite point at which one is in one country and not in another. Another example might be the equator: there is no real line, but the part of the planet closest to the sun is a real place.

 

[vanesch]

While the line itself is 'imaginary', there is still a definite point at which one is in one country and not in another. Another example might be the equator: there is no real line, but the part of the planet closest to the sun is a real place.

It is most of the time not on the equator, and worse, it follows a non-continuous path (jumping from hill to hill... unless you also count the atmosphere, up to what density ?)...
See, once one starts to nit-pick, the approximations that are entirely valid on a rougher scale become absurd on a smaller scale. Also, there is a tiny but entirely crucial point that Zapperz mentionned: our current understanding is that:
1) quarks are indeed point particles
2) they are at several places simultaneously
(this last point is what gives rise to the Heisenberg uncertainty you worried - correctly - about).

Also, who's defining, on the femto-meter scale, where exactly the borderline between two countries resides ? I guess legal documents have specifications which don't have that precision. So how do we decide on that scale, where the border is ? If we have no way to decide, that means that the border line is UNDEFINED at that precision, and that hence any question that depends on it, becomes meaningless.

I fully agree with Zz that if this is part of some legal debate, then one should quickly flee the country where such debate has the power of law, because the people in power became nuts !

 

[ZapperZ]

While the line itself is 'imaginary', there is still a definite point at which one is in one country and not in another. Another example might be the equator: there is no real line, but the part of the planet closest to the sun is a real place.

It isn't definite, at least not to the atom, because nature couldn't care less where our human political boundaries are. This is what I meant by "imaginary".

Any lawyer who thinks an argument can be based on when an atom crosses such an imaginary line, up to the scale of the atom itself, needs to be disbared from practice.

Zz.

 

[MisterTrilby]

It isn't definite, at least not to the atom, because nature couldn't care less where our human political boundaries are. This is what I meant by "imaginary".

Any lawyer who thinks an argument can be based on when an atom crosses such an imaginary line, up to the scale of the atom itself, needs to be disbared from practice.

Zz.

Hahahaha! I'll tell him that!

I get the impression that the argument isn't just about who owns which atoms, but he's unwilling to elaborate on the case.