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Heisenberg's theory of uncertainty based on Vedas, Rajnath Singh says

We have built instrument which can detect those parts of reality which our biological senses can't.

Our eyes can't detect photons in the ultraviolet range, but our instruments surely can, so we can be confident that those photons exist in an objective reality regardless of our biological limitations.
We can also see electrons but can not measure them. or measure them but not see them.
As soon as we go into the deeper microcosm, things gets fuzzier and need huge instruments for measurement; example, the Higgs Boson. So for any "objective" reality there is some degree of relativity attached to it. We know that many things exists, but just can not explain how, so here goes the objective reality. What sticks and we can use is relative reality which you can understand as objective reality and I as reality. There are too many unexplained phenomena in the universe to call anything objective in the pure sens of the term.
 
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We can also see electrons but can not measure them. or measure them but not see them.
As soon as we go into the deeper microcosm, things gets fuzzier and need huge instruments for measurement; example, the Higgs Boson. So for any "objective" reality there is some degree of relativity attached to it. We know that many things exists, but just can not explain how, so here goes the objective reality. What sticks and we can use is relative reality which you can understand as objective reality and I as reality. There are too many unexplained phenomena in the universe to call anything objective in the pure sens of the term.

You are right that there is no way to prove objective reality. All we can is to form theories and test our theories to the limits of our technology. Along the way, we derive practical benefits from our world view, but that is not a proof that our version of reality is correct.

People used sundials for millenia, happily believing that the Sun orbits the Earth. Just because our technology "works" doesn't mean our science is "correct".

There is actually mathematical formulation of this statement: Goedel's Incompleteness Theorem states that no system of logic can prove its own ultimate correctness. In this case, it means that science can never prove itself to be true -- only self-consistent.
 
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