Do different masses ever combine?

[magpies]

Ok so basicaly what I am asking is... Can two different masses *separated by vaccume/empty space* physically touch? I am under the understanding that they would not be able to physically touch because of 1. electromagnetic reasons and 2. because vaccume/empty space between them would pervent it. My guess is that the vaccume perventing the objects from making contact would be what holds the electromagnetic fields and perhaps it might be the electromagnetic fields itself. Is this understanding fairly accurate and if so where is it wrong in theory?

 

[vanesch]

I rembered when in high school disturbing my high school mathematics teacher once, by asking him the question: a material object, should we think of it as an open or a closed geometrical set ?

In fact, the answer is that we don't know whether objects "touch", simply because to the best of our ability, on a truly microscopic scale, objects become "fuzzy" for different reasons. First of all, we have to think of objects as "made up of particles". In as far as we know, these "particles" are to be "point particles" even though we know that this picture cannot be exactly right. But the way we describe matter is by considering it to be made up of (point) particles, or of particles that themselves consist of "point particles" (say, protons consist of quarks and gluons and some other mess). That in itself already makes it difficult to say when two objects "touch", because the "objects" are swarms of point particles.

But worse, we cannot exactly give a well-defined position to each of these (moving) point particles. That's due to quantum theory. So the exact location of those point particles doesn't have a meaning.

And still worse, on small enough scale, the number of point particles isn't even well-defined, because they are created and disappear constantly into the vacuum.

All this means that there's no way of even knowing exactly what it would mean, on a sufficiently microscopic scale, to say that two objects "touch each other".

Summary:
- objects are made of point particles
- we know that the idea of point particle cannot be exactly right, but it works well up to now
- the exact position of point particles doesn't make sense beyond a certain precision
- even the number of point particles doesn't make sense beyond a certain precision.

 

[Bob S]

The space between the two oxygen nuclei in an oxygen molecule is mostly vacuum. It is the electromagnetic force that binds the two neutral atoms together, and also prevents the two nuclei from ever touching.
Bob S

 

[Pyrocyon]

Hmm.. @Vanesch, would you be able to consider the superfluid spots at the cores of Neutron Stars, or the hypothetical state of matter in Black Holes to fulfill the criteria of @Magpies' question? Or is that a different thing entirely?

 

[vanesch]

Hmm.. @Vanesch, would you be able to consider the superfluid spots at the cores of Neutron Stars, or the hypothetical state of matter in Black Holes to fulfill the criteria of @Magpies' question? Or is that a different thing entirely?

For superfluids, what happens is that the quantum state of the set of particles doesn't separate into individual particle states, so they are highly correlated. In a way you could "redefine" the concept of "touching" as "being quantum-mechanically correlated", but then you have the problem that you can also have such a state for geometrically well-separated particles (in EPR experiments for instance). I was more aiming at resolving the concept of "touching" in a strictly geometrical sense, and then you encounter the problem that, according to our current understanding of the structure of matter, this geometry is ill-defined to allow for a clear concept of "touching".

Touching in a geometrical sense would be: you can represent objects by compact subsets of Euclidean space, and touching objects have common points in their border.

Well, current understanding of the structure of matter doesn't allow you to represent objects as compact subsets, for the reasons I noted earlier: they are made up of point particles, we don't know exactly where they are and even whether their "precise position" makes sense, they are not even a fixed number, etc...

Of course, on a coarse approximation, like in machining and tooling, we can still think of objects as geometrically being compact subsets of Euclidean space, but with a "geometrical tolerance" of the order of nanometers or so at least. And this tolerance makes that it is impossible to define strictly "touching".

As to the "hypothetical matter of black holes" I wouldn't even know what it is, or what theory describes it, so I won't say anything about it.