Discussion Overview
The discussion revolves around the nature of probabilities in quantum mechanics (QM) and the implications of obtaining non-rational probabilities, such as ##1/\sqrt{2}##. Participants explore whether such probabilities can be considered real if they cannot be verified through finite experimental results, and they touch upon philosophical considerations regarding realism and idealizations in models.
Discussion Character
- Debate/contested
- Conceptual clarification
- Exploratory
Main Points Raised
- Some participants propose that a probability of ##1/\sqrt{2}## from QM cannot be verified since experiments yield only rational numbers with finite digits.
- Others question whether this implies that such a theory cannot be real, suggesting it would require an everlasting experiment for verification.
- A participant introduces the idea that all models are idealizations and argues that the real world is discrete, contrasting with the notion of fuzzy reality.
- Another participant asserts that predictions in theories do not need to be accurate to infinite precision, except in pure mathematics.
- A hypothetical example involving reindeer is presented to illustrate that a theory's verification may depend on an infinite number of trials, raising questions about the nature of empirical evidence.
- There is a challenge regarding whether the reindeer theory's outcome is conditioned on specific factors, such as the presence of a red nose.
Areas of Agreement / Disagreement
Participants express differing views on the implications of non-rational probabilities and the nature of reality in relation to theories. There is no consensus on whether such probabilities undermine the reality of the theories in question.
Contextual Notes
Participants highlight limitations in the verification of probabilities and the dependence on definitions of reality and idealization in models. The discussion remains open-ended regarding the philosophical implications of these points.