At the macroscopic level, we are all quite familiar with the concept of a physical surface.

From wikipedia: https://en.wikipedia.org/wiki/Surface_(topology)

In mathematics, a surface is a geometrical shape that resembles to a deformed plane. The most familiar examples arise as boundaries of solid objects in ordinary three-dimensional Euclidean space ...

The concept of a "boundary of a solid object" becomes quite hazy at a subatomic level - so can anyone explain how we would define a physical surface at that scale ?

For my understanding, perhaps it would be best if someone could unpack the following scenario in terms of the fundamental interactions:

A hammer strikes the head of a nail and drives it into a block of wood.

  1. At the subatomic level, what do we mean by:

    • the "surface of the head of the hammer" and
    • the "surface of the head of the nail"
  2. At the subatomic level, in terms of the fundamental forces/interactions:

    • how exactly is the momentum transferred from the hammer to the nail

I found this explanation which satisfies me partially - but that isn't the whole picture:

Subatomic particles don't collide in the same way as macroscopic objects like billiard balls: they do not literally touch one another. Instead, as two subatomic particles approach one another they exchange force-carrying bosons (photons, gluons, W or Z particles) with each other. This is what enables them to interact and scatter off of one another. ~ Elizabeth H. Simmons, Particle Theorist, Dean, and Physics Professor at Michigan State University

What I am trying to understand exactly is:

  • What do the surfaces of the hammer and nail head look like at this level ?

  • Are they well defined boundaries, or are they "clouds of subatomic particles" that interact or are exchanged at a certain proximity ?

  • $\begingroup$ It depends on what you mean by "subatomic level". For scenarios not involving chemical and nuclear reactions and for reasonably long time scales these surfaces can be approximated by mean field potentials. Atomic force microscopy can image these potentials beautifully, down to the resolution of a fraction of an atom. If we let go of these simplifying assumptions it gets pretty complicated very quickly. $\endgroup$
    – CuriousOne
    Commented Jul 29, 2016 at 10:03
  • $\begingroup$ Even in the context of mean field potentials, there isn't a single agreed-upon definition for 'surface'. In some contexts it refers to the atoms with undersaturated bonds, in other cases (e.g. when speaking of surface stress) it may refer to atoms within a certain distance (typically ~ 1 nm) of the outer-most atoms. Note, by the way, that all of these definitions break down when you consider sufficiently small nanoparticles. $\endgroup$
    – lemon
    Commented Jul 29, 2016 at 10:10

2 Answers 2


What do the surfaces of the hammer and nail head look like at this level?

STM Image of Iron

enter image description here

In your post title, you ask for details at the subatomic level, which I don't think anybody can provide you with.

So I have cheated a bit, and displayed a Scanning Tunnelling Microscope Image at the atomic level, which may be on the scale of the best image we can currently obtain.

What I find interesting about this image, is that is corresponds exactly with what we would expect to see classicaly, all nicely lined up and ordered neatly.

I would doubt that the subatomic level is even possibe to visualise, in other words, an electron is supposed to be an point shaped particle, that takes a 720 degree rotation to get back to its starting point, I have no idea how to visualize that.

The nearest image I can provide you with, where quantum effects start to come into play, is the one below.

enter image description here

From Wave Like Motions

The concept of wave-like motion for electrons has been very difficult to imagine or visualize. What does it mean for a particle to move like a wave? But we can visualize it. Very recently, scanning tunneling microscopy (STM) has been used to take images that clearly reveal this wave-like character. The STM mechanism can be used to literally pick up and place metal atoms in specific arrangements on metal surfaces. For example, iron atoms have been arranged to form a closed circle on a copper surface. An image of the resultant structure then taken using the STM shows not only the ring of iron atoms but also conspicuous waves inside the ring, which result from the motion of electrons moving within the ring and reflecting off of the walls formed by the iron atoms. Two of the original images taken at IBM of these so-called “quantum corrals” are shown below.

This Wikipedia STM article explains the details of the STM, and how it uses the the quantum tunnelling effect to display an image, not of the atoms themselves, but of the electric charge surrounding them.

Any corrections / clarifications to the above statement will be welcomed.

Are they well defined boundaries, or are they "clouds of subatomic particles" that interact or are exchanged at a certain proximity ?

On a subatomic scale, they are not well defined boundaries, and I am pretty certain we cannot visually image an electron, all we can do as in the above images, is produce an image based on the indirect effects of their electric charge on our instruments.

As far as proximity relates to interactions, you should read this Overlapping Orbitals post and the comment by CuriousOne below it, on the factors that influence whether an interaction will occur or not.

How exactly is the momentum transferred from the hammer to the nail?

By exactly the same method as we are able to walk across on a floor, that is the electrical repulsion of similar negative charges, as the electrons repel (or attract) each other by momentum exchange mediated by photons.

QED, our theory of how particles and forces interact, is well summarised by Wikipedia.

  • $\begingroup$ Cool thanks ... you address the most important points of my pondering, and have given some useful links. Marked answer as Correct / and Vote +1 $\endgroup$
    – TaoRich
    Commented Jul 30, 2016 at 12:36
  • $\begingroup$ Thanks very much, just check I am right about what you are actually seeing with the STM, I am 99% sure it's a cgi based on the charge around the atom. The QED article is informative about transfer of momentum $\endgroup$
    – user108787
    Commented Jul 30, 2016 at 13:00

The term surface may be not applicable to this level. As surface is just some our approximation. We see something which looks like continous surface, but, really, that is some kind of the grid with very small nodes.


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