- #1
LarryS
Gold Member
- 345
- 33
Is probability (or probability current) conserved in RQM/QFT? I have never seen a simple answer to this question.
As always, thanks in advance.
As always, thanks in advance.
DEvens said:Is probability of what conserved?
QFT conserves lots of things. Momentum, energy, angular momentum, various charges.
Other things are not so straightforward.
https://en.wikipedia.org/wiki/Lepton_number
https://en.wikipedia.org/wiki/Weak_hypercharge
Some things simply are not conserved. You can pretty much produce as many photons as you are prepared to expend the effort to produce. So the probability of observing a photon is not conserved.
referframe said:I should have said "Is the position probability conserved?".
stevendaryl said:I think it's usually considered to be a sign of an inconsistency in a theory if probabilities don't add up to one at all times.
There is no simple answer because there is no simple answer to an even more elementary question: What is the position operator for RQM/QFT?referframe said:I should have said "Is the position probability conserved?".
referframe said:I should have said "Is the position probability conserved?".
Demystifier said:There is no simple answer because there is no simple answer to an even more elementary question: What is the position operator for RQM/QFT?
referframe said:Obviously, since it includes SR, QFT/RQM is considered physically more accurate than the original non-relativistic QM. So does that mean that the Born Rule is a nice approximation of reality but not fundamentally true?
DEvens said:Depending on how you look at it, the Born rule is either a postulate of, or a derivable consequence of the rest of, quantum mechanics.
referframe said:Obviously, since it includes SR, QFT/RQM is considered physically more accurate than the original non-relativistic QM. So does that mean that the Born Rule is a nice approximation of reality but not fundamentally true?
DEvens said:The first sentence has nothing to do with the second sentence. So it clearly does not mean that. Whatever you may mean by "fundamentally true" as opposed to true.
https://en.wikipedia.org/wiki/Born_rule
Depending on how you look at it, the Born rule is either a postulate of, or a derivable consequence of the rest of, quantum mechanics.
Again, it seems like you are struggling to ask some other question. Could you please ask that other question?
referframe said:I am referring to the "conservation law for probability in quantum mechanics" as referred to in the link:
https://en.wikipedia.org/wiki/Probability_current#Continuity_equation_for_quantum_mechanics
RQM stands for Relational Quantum Mechanics. It is a theory that approaches quantum mechanics from a relational standpoint, meaning that it focuses on the relationships between objects rather than the objects themselves.
RQM differs from traditional quantum mechanics in several ways. Unlike traditional quantum mechanics, RQM does not use a wave function or rely on the concept of a single observer making measurements. Instead, it views measurements as interactions between multiple objects. Additionally, RQM does not require the concept of an external, absolute time.
In RQM, conservation of probability refers to the idea that the total probability of a system remains constant over time, even as individual probabilities may change. This is similar to the concept of conservation of energy in classical mechanics.
There is ongoing debate and research on whether probability is truly conserved in RQM. Some argue that the theory does not fully account for all aspects of quantum mechanics, while others believe that it provides a more complete understanding of the nature of probability.
The concept of conservation of probability in RQM challenges traditional notions of causality and determinism in quantum mechanics. It suggests that the relationships and interactions between objects are more fundamental than the objects themselves, and that the behavior of quantum systems cannot be predicted with certainty. This has implications for our understanding of the nature of reality and the role of observers in the quantum world.