Is Probability conserved in RQM?

In summary: The proof is essentially the same.Oh. Then yes, it is conserved in relativistic quantum field theory in exactly the same way. The proof is essentially the same.In summary, the conservation of probability (or probability current) in RQM/QFT is considered a sign of consistency in the theory, as probabilities are expected to add up to one at all times. However, there are cases where this conservation does not hold, such as in the production of photons. The concept of position probability is also not conserved in QFT, as particles are indistinguishable and can exist in multiple locations simultaneously. The Born rule, which is used to compute probabilities in both QM and QFT, is not considered fundamentally true, but rather a
  • #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.
 
Physics news on Phys.org
  • #2
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. Or it's a sign that the quantity that you thought of as probability isn't really a probability (which was the case with the current derived from the Klein-Gordon equation)
 
  • Like
Likes bhobba
  • #3
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.
 
  • #4
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.

I should have said "Is the position probability conserved?".
 
  • Like
Likes Demystifier
  • #5
referframe said:
I should have said "Is the position probability conserved?".

In quantum field theory, there is not a definite number of particles. And particles of the same type are indistinguishable. So in QFT you would not ask "What is the probability that this particle is at location [itex]x[/itex]?" Instead, you would ask: What is the probability of finding a particle at location [itex]x[/itex], with the understanding that finding a particle at one location doesn't preclude the possibility of finding an identical particle at another location at the same time.
 
  • #6
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.

The problems with probability in relativistic QM were all resolved when going to Quantum Field Theory. Doing so also showed how they could be resolved in things like the Klein Gordon equation. Since QFT requires antiparticles negative probabilities in a current density are positive probabilities of the antiparticle.

Thanks
Bill
 
  • #7
referframe said:
I should have said "Is the position probability conserved?".
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?
 
  • #8
referframe said:
I should have said "Is the position probability conserved?".

Um... No it's not. The probability of finding a particle at a position isn't conserved. Why would you ever think it was? Particles move around.

I think you are struggling to ask a different question. Maybe you could ask what it is you are really trying to ask.
 
  • Like
Likes bhobba
  • #9
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?

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?
 
  • #10
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?

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?
 
  • Like
Likes bhobba
  • #11
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.

Just on that you might like to look into Gleasons Theorem.

Thanks
Bill
 
  • #12
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?

The Born rule works as well in QFT as in QM. In both cases, we have states, and we use the states to compute probabilities for measurement results, using the Born rule. The difference is that in single-particle, nonrelativistic QM, the "state" is described by a wave function giving a probability amplitude for finding that particle at a particular position, while in QFT, the "state" describes an indefinite number of particles.
 
  • #13
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?

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
 

1. What is RQM?

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.

2. How does RQM differ from traditional quantum mechanics?

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.

3. What is meant by "conservation of probability" in RQM?

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.

4. Is probability truly conserved in RQM?

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.

5. How does the concept of conservation of probability impact our understanding of the quantum world?

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.

Similar threads

  • Quantum Physics
Replies
1
Views
797
Replies
17
Views
2K
Replies
3
Views
1K
  • Quantum Physics
Replies
9
Views
1K
  • Quantum Physics
Replies
34
Views
3K
Replies
10
Views
966
  • Quantum Physics
Replies
22
Views
1K
Replies
0
Views
710
  • Quantum Physics
Replies
1
Views
1K
  • Quantum Physics
Replies
27
Views
804
Back
Top