Contact at the Quantum Level

[Hyd]

Query:

 

When we touch an object, we are not actually touching it.

 

Thus, when we sit on a chair, we are actually floating on the chair (very, very small distance above)

 

How can this be explained at the quantum level?

[DQW]

<non-rigorous argument follows>

 

This can be explained in terms of the wavefunction of a pair of particles. Consider a pair of identical particles with the distance from particle 1 to particle 2 being 'x'. The square of the wavefunction is the probability density, and this should not chage for the particles by swapping their positions - since they are identical, swapping them should make no difference.

 

Mathematically, you could write this as

 

[math]|\psi (-x)|^2=|\psi (x)|^2[/math]

[math]\implies \psi (-x) = -\psi (x) ~or~\psi (-x) = + \psi (x) [/math]

 

Of these two possibilities, the first case is satisfied by particles known as fermions - which include electrons and protons.

 

In this case, let's see what happens when we set x=0 (ie:at zero separation).

 

[math]\psi(-0) = -\psi(0)~but~-0=0,~so~\psi(0) = -\psi(0) [/math]

[math]but~k=-k ~ \implies k=0,~so~here,~\psi(0)=0 [/math]

 

What this is saying is that there is zero probability that the two particles can be at zero separation (making contact). In other words, fermions can not make contact.

 

Since all the atoms in our bodies and other objects are essentially swarms of elecrons (which are fermions) around a nucleus, no electron from my large collection of swarms may make contact with any of the electrons in the chair's collection of swarms.

 

Notice that the second case (the one I left out) does not impose this "no contact" rule. That case is satisfied by bosons - such as photons, which we know have no such qualms about "touching each other". :biggrin:

[lethalfang]

In a more classical picture, electrons repel each other when they get close, so do the nucleus of the atoms.

In a QM level (totally unnecessary), the probability of you (zillions of particles) passing through the chair (a mighty wall) is like 10^-100000000000000000000000000000000000.