Fractional quantum Hall effect 5/2 Updated +Created
Grand Unified Theory Updated +Created
Appears to be an unsolved physics problem. TODO why? Don't they all fit into the Standard Model already? So why is strong force less unified with electroweak, than electromagnetic + weak is unified in electroweak?
High-temperature superconductivity Updated +Created
As of 2020, basically means "liquid nitrogen temperature", which is much cheaper than liquid helium.
Figure 1.
Timeline of superconductivity from 1900 to 2015
. Source.
Strong CP problem Updated +Created
Theory of everything Updated +Created
As of 2019, the Standard Model and general relativity are incompatible. Once those are unified, we will have one equation to describe the entirety of physics.
There are also however also unsolved problems in electroweak interaction + strong interaction, which if achieved is referred to as a Grand Unified Theory. Reaching a GUT is considered a sensible intermediate step before TOE.
The current state of Physics has been the result of several previous unifications as shown at: en.wikipedia.org/wiki/Theory_of_everything#Conventional_sequence_of_theories so it is expected that this last missing unification is likely to happen one day, potentially conditional on humanity having enough energy to observe new phenomena.