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Prathyush
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I am aware that physicists are trying to derive born rule from unitary evolution. Has there been any success? What is the current status of that program?
Prathyush said:I am aware that physicists are trying to derive born rule from unitary evolution. Has there been any success? What is the current status of that program?
Only if you believe kets are "fundamental".Jazzdude said:2) Circular: Many derivations introduce the Born Rule that they attempt to eventually get through the backdoor. Most do that by postulating the existence of ensemble descriptions in terms of density operators. That construction already contains the born rule,
I'm always confused when people insist this is an additional assumption: by the frequentist interpretation of probabilities, this is what probability means. Showing that the probabilities defined by QM correspond to frequentist probabilities is what we've been trying to do all along!3) Use of additional assumptions: ... For example you can postulate that you only are interested in the limit of infinitely many measurement iterations
Hurkyl said:Only if you believe kets are "fundamental".
If you take the probability distributions are "fundamental", then so long as you avoid a ket-based presentation of QM the Born rule simply doesn't enter the picture at all. The Born rule, then, simply becomes how we define the use of kets to represent states; if we wanted a different rule, we can! But the laws of physics would have a different form.
I'm always confused when people insist this is an additional assumption: by the frequentist interpretation of probabilities, this is what probability means. Showing that the probabilities defined by QM correspond to frequentist probabilities is what we've been trying to do all along!
Hurkyl said:Asking for the Born rule to be 'justified' is really the same question as asking for the Schrodinger equation to be justified.
Hurkyl said:I'm always confused when people insist this is an additional assumption: by the frequentist interpretation of probabilities, this is what probability means. Showing that the probabilities defined by QM correspond to frequentist probabilities is what we've been trying to do all along!
The_Duck said:For me this seems problematic because no one has ever done infinitely many measurements. Therefore showing that QM predicts a certain thing in the limit of infinitely many measurements doesn't actually predict anything about any experiments we have done or will do.
The Born rule, also known as the Born interpretation, is a fundamental principle in quantum mechanics that relates the mathematical description of a quantum system to the probability of obtaining a particular measurement outcome. It allows us to make predictions about the behavior of quantum particles and is essential for understanding the underlying principles of quantum mechanics.
Unitary evolution is a mathematical concept that describes how a quantum system evolves over time. It is based on the idea that the total probability of all possible outcomes must always equal one. The Born rule provides a way to calculate the probabilities of these outcomes based on the initial state of the system, thus connecting the unitary evolution to the actual measurements and observations we make in the physical world.
While the Born rule has been experimentally verified and is widely accepted in the scientific community, its origin and connection to other fundamental principles of quantum mechanics remain somewhat mysterious. By deriving the Born rule from unitary evolution, scientists hope to gain a deeper understanding of the underlying principles of quantum mechanics and potentially uncover new insights into the nature of reality.
There have been numerous attempts to derive the Born rule from unitary evolution, but it remains an open problem in physics. Some theories, such as the Everett interpretation, suggest that the Born rule is a consequence of the many-worlds interpretation of quantum mechanics. Other approaches involve modifying the fundamental equations of quantum mechanics to include the Born rule as an additional postulate.
If the Born rule can be successfully derived from unitary evolution, it would provide a more complete and unified understanding of the fundamental principles of quantum mechanics. It would also open up new avenues for research and potentially lead to a better understanding of the nature of reality at the quantum level. However, it is important to note that even if the Born rule is derived, it may not provide a complete explanation for all aspects of quantum mechanics.