> why would the temperature at any finite point will always be zero
Based on your answer of the temperature inside a neutron then maybe it won't be zero everywhere. Any finite point is going to either be inside a particle or outside of a particle. And since most of space is empty, and atoms are also mostly empty, the vast majority of finite points will be where there is nothing, and hence have no temperature.
> emptying space is stupid expensive
I don't what this means. Most of space is already empty.
If space is “empty”, then how come we can measure the temperature of the microwave background radiation?
Think about it…any direction we point an apparatus, we will get a reading — the static of a radio IS the CMB, and if you could take that radio into space, and have the ability to travel anywhere, that radio would still have static. As such, space cannot be “empty”, it’s filled with photons, electrons, and quarks, amongst other things.
To reach 0 Kelvin would take an infinite amount of energy (infinite is not exactly accurate but might as well be), hence “stupid expensive”. It would also create holes in the CMB. CMB has no holes, as such, there is stuff everywhere.
> how come we can measure the temperature of the microwave background radiation
Because that's the average temperature over an region not the temperature of a finite point. It's kind of like pressure; it really only makes sense at a macro level where you are averaging over a volume or region. The pressure at a singular finite point will also be zero because that singular infinitely small point will likely be in the empty space that makes up an atom.
The original comment was about scalar fields in which there is a value at every finite point. Temperature and pressure are not good examples of these. A better example would be like a magnetic or gravitational field which would have a specific value at every point in space.
Based on your answer of the temperature inside a neutron then maybe it won't be zero everywhere. Any finite point is going to either be inside a particle or outside of a particle. And since most of space is empty, and atoms are also mostly empty, the vast majority of finite points will be where there is nothing, and hence have no temperature.
> emptying space is stupid expensive
I don't what this means. Most of space is already empty.