In physics, we do not generally talk of objectivity vs. subjectivity in research. We expect research to be as objective as possible, and by that we mean that the researchers must make their best efforts to remove personal biases, opinions and specifics from the results. This does not mean that physicists do not have opinions or debates - we often clash in interpretations and predictions. It does mean that a result should follow the principle of repeatability. If two instances of a single experiment conducted by different researchers but under the same conditions yield differing results, we would probably say that something has gone wrong with that experiment.
So is there anything left to wonder?
Yes.
For one, interpretation matters. An example of this is with the quantum wave function, a mathematical expression of a particle's probable location as a wavy distribution in space. Some theorists believe that the wave function is a part of physical reality that happens to collapse when we measure it, which explains why we see particles behaving in wavy ways until we measure their position, at which point they are very clearly located at single points. Others believe that the wave function is a convenient shortcut for describing probabilities but has no basis in physical reality.
The questions come up even more often in theoretical particle physics, where different interpretations, such as string theory and supersymmetry, try to forge ahead towards a grand unified theory (GUT) of everything. One primary purpose of the LHC is to develop new experiments that will allow us to prove or disprove some of these theories.
On a more abstract level, I am curious about the implications of the incompleteness theorems for theoretical physics. Ideally, we would like to find a GUT that predicts everything and has the shortest possible form. We can't necessarily know when we have the shortest possible formulation of the laws of the universe, as the ability to compute the length of the shortest formulas may create a paradox via Chaitin's Incompleteness Theorem. I also wonder if Godel's Incompleteness Theorem implies that even if we measure everything measurable about the universe, we will still be able to formulate multiple interpretations with similar complexity.
So I propose that the great debate in physics is not subjective vs. objective, but a question of how we should go about working with different interpretations of experiment and to what extent multiple interpretations of the same result may depend on philosophical differences.
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