Mathematical analysis of a physics problem requires data.
If there is no data there can be no analysis, and no solution.
Experimental observation supplies data. This requires activation of the biological senses or artificial detector. The sense organs or detector are at the Prime reality interface between objective and subjective reality.
If information crosses the interface so that it may be processed or analysed, then there may be knowledge derived from that information via external mathematical solutions or direct analysis via brain function.
If no information crosses because it does not reach a necessary threshold for detection or it is not the kind of information that those sensors are able to detect, then there can be no knowledge of that information, no mathematical analysis and no solution.
This is the real limit for the scientific method and mathematics. Science and mathematics can not explain or analyse the unknowable. This is a true boundary.
As I have mentioned elsewhere a photon is the disturbance needed to move a electron in space. This does not prove that there can not be lesser disturbances. Only no effect can be detected and therefore it is not incorporated into the subjective reality model.
Likewise the objective reality of the void or "vacuum" may supply no information across the Prime reality interface to inform the subjective reality, (that is formed from information processing and analysis.) That is not proof that there is no material substance to the void in objective reality.It only shows that no information has been detected and processed.
Any true theory of everything must acknowledge the unknowable and the limit of science. Subjective reality is just one side of the Prime reality interface. There may be even more on the objective side of the interface. This is because the subjective reality that is experienced, and in which scientific investigation is performed, is limited by the information received across the Prime Reality Interface.