Is negative 20 psi / 1.5 bar possible? If I understand correctly, negative pressure usually means relative pressure: the difference between inside and outside.
If outside is normal (1 bar, 15 psi, 100 kPa etc), how low can the (relative) pressure inside be? Can it be -20 psi / -1.5 bar / -150 kPa?
Absolute pressure can't be negative, right?
 A: You're right, absolute pressure can't be negative.  Of course, you can easily have a $20\: \mathrm{PSI}$ pressure differential (although not without pressure above $1\: \mathrm{ATM}$ since that's $14.22\: \mathrm{PSI}$ at sea level).  Check out Wikipedia on the zero-reference:

  
*
  
*Absolute pressure is zero-referenced against a perfect vacuum, so it is equal to gauge pressure plus atmospheric pressure.
  
*Gauge pressure is zero-referenced against ambient air pressure, so it is equal to absolute pressure minus atmospheric pressure. Negative signs are usually omitted. To distinguish a negative pressure, the value may be appended with the word "vacuum" or the gauge may be labeled a "vacuum gauge."
  
*Differential pressure is the difference in pressure between two points.
  

A: You can absolutely have negative absolute pressure in solids or liquids. Think of an elastic solid being forced to expand due to adhesion to the walls of some chamber. That has negative pressure even if the comparison is a total vacuum. Depending on the bulk modulus of the material being stretched and the strength of the interaction with the walls of the chamber holding the material, you may be able to get to several negative atmospheres of pressure.
Dark energy also creates negative pressure in otherwise empty space.
See this veritasium video for more about negative pressure in trees.
