# Smallest distance

Have you ever wondered how the hell we actually "feel" things without touching them. The atoms in my fingers and the atoms of the keyboards get extremely close to each other, but you can always imagine them getting closer and closer without actually touching.

How is it then that I am able to type this post, if my fingers technically never touch the keyboard? I am thinking that this requires there to be a smallest distance; either that or the electromagnetic repulsive force is "jumping" the very small space between the atoms.

Has anybody ever thought of this?

Well, what we call "touching" is simply the point where electron resistance becomes high enough to convey kinetic energy, right? So we do touch things.

Yes, but how is that "signal" information transferred between space, if it has to jump very small distances, to impart kinetic energy? Do you get what I'm saying.

Your fingers electrons push the keyboards electrons with a repulsive force this forces range is infinetly ling but the closer your hand gets too the keyboard the harder the repulsive force.

G01
Homework Helper
Gold Member
Yes, but how is that "signal" information transferred between space, if it has to jump very small distances, to impart kinetic energy? Do you get what I'm saying.
The force from the electrons in your hand is transferred to the keyboard through the electromagnetic field, like every other electromagnetic interaction.

The reason why this force is only felt at small distances is because, on the whole, your body and the keyboard are both electrically neutral. So, when they are far away, your hand looks like a neutral object to the keyboard, and vice-versa. Thus, the net force between the two is 0.

When your finger is very close to the keyboard, the electrons in the keyboard can start to feel the interaction from the electrons on the surface of your hand. At this close range, the effect of the positive charges in your hand is less, since the electrons in both the surface of your fingers and the surface of the keys are much closer to each other than they are to the positive charges.

In this example, we can say that the interaction is "screened" by the presence of the positive charges i.e. you can feel it at very short distances, but it's strength drops off rapidly as the distance between the two objects increases. (Effectively, we are left with a "hard-core" repulsion potential, which drops off like 1/r^11.)

Consider this simpler example:

When two atoms are far apart, there is no net force between them, as they are electrically neutral.

When you bring the atoms together, the electron clouds will, at very short distances, be closer to each other then to their respective nuclei, and thus the atoms will feel a net repulsion.

EDIT:

I've been talking with a friend about this question and realized, for instance, we will also have the Van der Waals force, which will tend to attract the two bodies (drops off as 1/r^7). However, as it does not cause repulsion, I'll continue to ignore it for this educational example.

Secondly, my fellow grad student also pointed out that Pauli exclusion also probably plays a role, but, I think it's fair to focus on the electrostatic repulsion effects for this elementary discussion.

Finally, A huge part of the confusions come into play because we don't really have a good definition of what we mean by "touching." For this thread, I'll suggest touching be defined as when hard core repulsion becomes non-negligible. (Which, when you think about it, is really an obvious definition.)

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I guess I miscommunicated my question to you guys. I'm not confused about the electric forces between my keyboard and fingers.

What I'm trying to understand is the following:

Imagine two very sharp pencil heads pointing at each other, touching one another. Draw a circle between both tips and zoom in. Repeat this process until you are zoomed in so close that there is a space between them. Now you will say that the electromagnetic forces are jumping this small gap and causing the sensation of "touch", but again, zoom in on the forces themselves.

What you end up with is a seemingly paradoxical gap even between them because you can keep zooming in forever. Yet we still have sensations of touch, and so on. So, at the infinitely smallest scale something has to give and the smallest unit of "information" has to teleport two unimaginably tiny points in space.

Now do you understand my question?

G01
Homework Helper
Gold Member
What I'm trying to understand is the following:

Imagine two very sharp pencil heads pointing at each other, touching one another. Draw a circle between both tips and zoom in. Repeat this process ...What you end up with is a seemingly paradoxical gap even between them because you can keep zooming in forever. Yet we still have sensations of touch, and so on. So, at the infinitely smallest scale something has to give and the smallest unit of "information" has to teleport two unimaginably tiny points in space.

Now do you understand my question?
No information is "teleported" from one point in space to the other. There is no action at a distance when we think in terms of fields.

The gap between the pencil tips is spanned by the electromagnetic field, which is the entity that transports the "information" from one tip to the other. The field transports this information at the speed of light, thus everything is ok, in terms of causality. This is what it means to say that the field mediates the interaction between the two objects.

Ok, but what if you considered, just as an example, only two mediators of the electromagnetic force between each pencil?

Call this m1 (for mediator 1) and m2 particles.

Now, how close can the particles m1 and m2 get? Can they ever "touch"? I don't think so. And if they can't touch, then there has to be again yet another mediator between them.

Thus a mediator, within a mediator? Get my point?

I'm not even sure we're talking physics at this point, maybe my question is more philosophical.

G01
Homework Helper
Gold Member
Ok, but what if you considered, just as an example, only two mediators of the electromagnetic force between each pencil?

Call this m1 (for mediator 1) and m2 particles.

Now, how close can the particles m1 and m2 get? Can they ever "touch"? I don't think so. And if they can't touch, then there has to be again yet another mediator between them.

Thus a mediator, within a mediator? Get my point?

I'm not even sure we're talking physics at this point, maybe my question is more philosophical.
You are getting terminology confused. The mediator of the force is not the particles. The particles experience the force, but the force is mediated by the electromagnetic field.

We are not talking physics or philosophy at this point. Basically, it is just semantics now.

What is your definition of touching? Apparently, it's not when the two objects are close enough to feel a repulsive hard core potential?

Thus a mediator, within a mediator? Get my point?
Not at all. Sorry.

Drakkith
Staff Emeritus
The very idea of "touching" to most people is actually nothing like the real world is. In everyday life we think of things as solid, while in reality things are merely interacting particles and fields with huge empty spaces in most matter. As you get down to the quantum level, there is no such thing as touching. Just varying strengths of fields that interact with everything. Things can occupy the same space if the conditions are right, can pass through other things, and other crazy ideas. Two atoms could never "touch" since there is no such thing.

Now, from what I understand about your orignal question, there might be a smallest distance called the Planck distance. From wikipedia: "In some theories or forms of quantum gravity, it is the length scale at which the structure of spacetime becomes dominated by quantum effects, giving it a discrete or foamy structure, but other theories of quantum gravity predict no such effects."

So who knows...

some say the planck length is or may be the smallest possible or at least smallest meaningful distance

some say the planck length is or may be the smallest possible or at least smallest meaningful distance
Right.

But the Planck length is much, much smaller than what the OP is asking.

As the electron 'clouds or smears' of the surface atoms of the keyboard and the surface atoms of your fingers come closer, more and more photons are exchanged until the strength of the electromagnetic force is so great that either your finger getssquashed or the keyboard breaks.

If you had the (incredible) strength to actually force the two together to actually result in a 'physical; contact', you'd have a nuclear reaction, which would certainly not be good for your fingers or the keyboard. :D

10 to the -33rd power cm i believe it the planck length but that would have nothing to do with fingers or the keyboard interaction, this is macroscopic probing not individual atoms. That is referring to the smallest amount of distance, which is known as a meaningful distance on a quantam scale. This relative to the planck time which is 10 to the -43rd power seconds, the time it takes energy to traverse a planck length. Messenger particle photons transfer information, creating kinetic energy from potential energy, from the electrons of the keyboard to that of your fingers so no they don't every actually touch. Didnt read the whole thread sorry.