Actually getting kicked up the arse is incredibly complicated from a fundamental physics point of view. So this post will be long.
Let's take two metals blocks hitting each other, an approximation to your arse. Fundamentally all matter (basically) is made up of atoms which are a central charge, the nucleus, with electrons going around them. All that will really matter are the electrons.
Electrons are isolated "lumps" of the electron field that fills the entire universe. This field is fermionic, which means that you have to perform a 720 degree rotation for it to look the same again (unlike objects in everyday life which take 360 degrees). Tthe individual lumps of this field, the electrons, are also fermionic.
Like all quantum mechanical particles electrons exist as a probability wave spread over space, rather than existing in one place like in classical mechanics. This probability wave gives the chance of finding an electron in a certain location. The probability wave is usually called a wavefunction.
There is a mathematical result known as the Spin and Statistics theorem which tells us that because electrons are fermionic, their probability waves don't overlap in a certain sense. Specifically if the electrons have the same spin, then the probability of them being in the same place is zero. This means it takes energy to push electrons near each other, because they "exclude" each other. Which is known as the Pauli Exclusion principle.
Due to this, electrons pile up inside atoms and materials, in a certain way, arranging themselves so as to obey the Pauli-Exclusion principle. These arrangements have a lot of energy:
1,000,000,000,000,000 times the energy of typical arrangements you get from things which don't obey the Pauli-exclusion principle.
When one thing hits another it has to fight against this energy to crush it. Without the Pauli exclusion principle most things things would be easy to crush, for instance if I could "switch off" the Pauli exclusion principle in a bar of titanium a baby could easily crush it.
Hence because of this "most" of the energy from the kick can't go into rearranging atomic configurations, so it has to go elsewhere.
Now let's step back for a bit. Since the electrons of the two objects are both just different parts of the electron field, the moment of the kick is just one collection of excitations of this field coming near another collection. Since the electron field is connected to other fields, such as the electromagnetic field, these fields will start getting excited near the point of contact. Basically because there is lots of electrons.
The electromagnetic field's presence will change the way the electron field evolves, and will cause it to redistribute the probabilities among the electrons. During the kick, all the electron field is doing, from an objective point of view, is redistributing the probabilities for the electrons to be in certain locations because of the presence of the electromagnetic field. Due to the Pauli exclusion principle above, very little probability goes to configurations where the material remains in place but is significantly crushed. Most "flows" into configurations where the kicked object as a whole is moved slightly away from the kicking object.
Hence, from our perspective, the kicked object will move away.
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