Is Popper's Falsifiability Test Reasonable?

Popper states in Knowledge Without Authority (1960):

• The empirist’s questions “How do I know? What is the source of your assertion?” are wrongly put. They are questions which beg for an authoritarian answer.
• I propose to replace, therefore, the question of the sources of our knowledge by the entirely different question: “How can we hope to detect and eliminate error?

This is Popper’s falsifiability test: A theory is considered scientific as long as it is not falsified in the sense that there is a consequence or prediction of the theory, which does not match with observation of reality.

Popper’s test thus does not ask for justification or positive evidence that the theory is correct, only for negative evidence as lack of falsification.

Popper’s test represents a break with classical rational science based on positive evidence and reason, and one may ask what made Popper take the bold step from positive evidence to lack of negative evidence?  Does it reflect the break from classical rational deterministic physics into the modern physics of statistical mechanics and quantum mechanics which took place at the turn to the 20th century?

Yes, there seems to be substantial positive evidence supporting this idea: The fundamental reason seems to be that the basic assumptions of modern physics being based on statistics, cannot be directly tested and justified and thus a weaker test is needed to be able to claim that modern physics is science, which Popper then offers in the form of his falsifiability test.

The basic assumption of molecular chaos of statistical mechanics can thus according to Popper be adopted without positive evidence, and can be viewed to be valid as long as no consequence of the assumption contradicts observation.

But to draw consequences from molecular chaos is difficult since it requires solution a Boltzmann’s equation, which is impossible except in a few simple cases. This makes statistical mechanics into a scientific theory according to a very weak test.

But viewing a theory with weak support as a scientific theory with solid support, is potentially dangerous since the theory may give grossly incorrect predictions.

Comparing with a legal case, we know that to convict someone for murder it is necessary with some positive evidence which connects the suspect to the deed, like fingerprints. We know that lack of negative evidence, such as lack of alibi, is not enough for conviction to the electric chair. It should neither be enough to convict a theory to the heavy burden of being scientific.

Popper’s negativism expresses his criticism of positivism, which serves the purpose of making modern physics based on statistics acceptable as science.