We are well aware by now of the observer problem in quantum mechanics. Human subjectivity appears to play a key role in the results of quantum experiments. However, the observer problem reaches far beyond just quantum mechanics, argues Edward Frenkel.
In the episode The Path to the Black Lodge of David Lynch’s iconic series Twin Peaks, Annie (played by Heather Graham) recites to Dale Cooper (Kyle MacLachlan) a famous quote by the great German physicist Werner Heisenberg, “What we observe is not reality itself but reality exposed to our method of questioning.”
This quote elegantly encapsulates what is often referred to as “observer-dependence” in quantum mechanics: Depending on how we set up an experiment, quantum reality will expose itself in various ways, with different experimental setups revealing different, seemingly contradictory forms. For example, in the famous double-slit experiment, electrons will reveal themselves as waves if we don’t put detectors behind the slits but will appear to us as particles if we do put the detectors. Thus, our choice of experimental protocol influences what pattern of behavior we observe. This makes the first-person perspective an integral part of modern physics.
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Is there room for the first-person perspective in mathematics as well?
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