The Probability Distribution of a Bosonic Field when Emitted

[JohnH]

If a bosonic field is probabalistic, and if it can be emitted (suddenly coming into existence), what determines its probability distribution when it is emitted from a fermion? In other words, one thinks (or at least I think) of a fermion field as already being in existence and already having some probability distribution as a given, but boson fields are different in that seemingly mid calculation, so to speak, they can be emitted such that their probability distribution is not a given from the outset. So what determines its probability distribution?

 

[PeterDonis]

if it can be emitted (suddenly coming into existence)

It can't. Quantum fields don't "suddenly come into existence". "Emission" just means the field transitions from one state to another--in the simplest case, from the vacuum state to a state containing a quantum (for example a photon).

boson fields are different in that seemingly mid calculation, so to speak, they can be emitted such that their probability distribution is not a given from the outset

This is not correct and I don't know where you are getting it from.

 

[JohnH]

Quantum fields don't "suddenly come into existence".

So in other words, in places in a Feynman Diagram where emission or absorption occurs, it's not that anything has been created or destroyed but instead that it always existed or continues to exist in the vacuum state?

 

[PeterDonis]

in places in a Feynman Diagram where emission or absorption occurs, it's not that anything has been created or destroyed but instead that it always existed or continues to exist in the vacuum state?

Feynman diagrams are not diagrams of real processes. They are mathematical conveniences that help with calculations. So no, when you see "particles" being "created" or "destroyed" in Feynman diagrams, it does not mean real quantum fields are being created or destroyed. (Note that if it did, this would apply just as much to fermions as to bosons, since it is perfectly possible to have Feynman diagrams in which fermion lines are created or destroyed.)

Single Feynman diagrams do not correspond in any simple way to real quantum field state transitions. Only sums of multiple diagrams (actually an infinite number of them in the limit where we insist on an exact solution) tell you anything about real processes.

 

[JohnH]

Only sums of multiple diagrams (actually an infinite number of them in the limit where we insist on an exact solution) tell you anything about real processes.

I find this quite confusing. So you're saying that QED, the most successful theory in physics--how do you say it--almost coincidentally gets the correct answer? You're saying that this convoluted mathematical process predicts the right outcome and yet has absolutely nothing to do with the actual process itself?

If we're talking about how multiple probabilistic fields might evolve over time, it seems to me that such an approach might be described as "realistic." Would I be, in my ignorance, the only one who sees it that way? Is there some logical wall that has prevented the entirety of all serious physicists from going down that road? Does the logical problem have to do with what you were saying:

it does not mean quantum fields are being created or destroyed. (Note that if it did, this would apply just as much to fermions as to bosons, since it is perfectly possible to have Feynman diagrams in which fermion lines are created or destroyed.)

 

[PeterDonis]

So you're saying that QED, the most successful theory in physics--how do you say it--almost coincidentally gets the correct answer?

It's not a coincidence at all. I have no idea why you would think that.

You're saying that this convoluted mathematical process predicts the right outcome and yet has absolutely nothing to do with the actual process itself?

Not at all. I am saying that your understanding of what Feynman diagrams are is incorrect. Go read my post #4 again.

If we're talking about how multiple probabilistic fields might evolve over time, it seems to me that such an approach might be described as "realistic." Would I be, in my ignorance, the only one who sees it that way? Is there some logical wall that has prevented the entirety of all serious physicists from going down that road? Does the logical problem have to do with what you were saying

I have no idea what any of this means. Where are you getting all of this from?

 

[CoolMint]

I find this quite confusing. So you're saying that QED, the most successful theory in physics--how do you say it--almost coincidentally gets the correct answer? You're saying that this convoluted mathematical process predicts the right outcome and yet has absolutely nothing to do with the actual process itself?

If we're talking about how multiple probabilistic fields might evolve over time, it seems to me that such an approach might be described as "realistic." Would I be, in my ignorance, the only one who sees it that way? Is there some logical wall that has prevented the entirety of all serious physicists from going down that road? Does the logical problem have to do with what you were saying:

Conceptually, the field always has energy which is never zero(remember it came from the Big Bang and is still powering our own survival via the Sun). The field is in a state of superpositions of states which are not real. The argument is that if they were, they would have real world measurable effects. And they don't.
We only measure physical(observable) effects of the field(say the electromagnetic field) when the so called wavefunction "collapse" takes place.
Where does math come into all this?
The math connects the unphysical(unmeasured) with the measured physical outcomes in the form of probabilities.
It is no coincidence that it is successful at the quantum scales as math has always been the greatest tool of mankind for making exceptionally good models of nature and reality and valid predictions.

 

[PeroK]

I find this quite confusing. So you're saying that QED, the most successful theory in physics--how do you say it--almost coincidentally gets the correct answer?

It's not a coincidence. Feynman invented his diagrams to represent the series of integrals that emerge from a perturbative calculation of scattering processes in QFT/QED.

You're saying that this convoluted mathematical process predicts the right outcome and yet has absolutely nothing to do with the actual process itself?

The process, such as it is, is described by the interaction hamiltonian, which leads mathematically to the series of integrals and the Feynman diagrams.

If we're talking about how multiple probabilistic fields might evolve over time, it seems to me that such an approach might be described as "realistic." Would I be, in my ignorance, the only one who sees it that way?

The heart of the matter is whether QFT is a complete theory of nature, in the sense that it tells us about everything that is measurable and, by implication, everything this is knowable.

Some physicists would like a more "realistic" theory of nature. You can look up Bohmian Mechanics, for example.

Is there some logical wall that has prevented the entirety of all serious physicists from going down that road?

Most physicists accept that QFT is the best theory we have and accept what nature appears to be telling us. That the elementary interactions are probabilistic and cannot be described in classical, realistic terms. The alternative is to look for "realist" theories that meet preconceived human notions of how nature ought to be.

From my perspective, the more you study QM/QFT the more sense it makes and the more inevitable it seems that nature at the fundamental level cannot be like the classical, macroscopic world.

The problem with the alternative is that you are most likely wasting your entire working life, motivated by little more than a natural human prejudice.

 

[PeterDonis]

Conceptually, the field always has energy which is never zero(remember it came from the Big Bang and is still powering our own survival via the Sun).

If you are talking about the electromagnetic field, this is true. But the electromagnetic field is not the only field, or even the only bosonic field.

The field is in a state of superpositions of states which are not real. The argument is that if they were, they would have real world measurable effects. And they don't.

Are you referring here to virtual particles? If so, what you say here is not really correct. Virtual particles, like Feynman diagrams, are a calculational convenience. Conceptually, it is not correct to say that a quantum field is a superposition of virtual particle states.

 

[CoolMint]

Are you referring here to virtual particles? If so, what you say here is not really correct. Virtual particles, like Feynman diagrams, are a calculational convenience. Conceptually, it is not correct to say that a quantum field is a superposition of virtual particle states.

I was under the impression that in QFT even though quantum states have nothing to do with wavefunctions, they can still be in a state of superposition(in multiparticle Fock space). And this is generally how 'collapse' creeps in QFT(I assumed this is what is happening). Sorry if this is wrong/misleading.

 

[Demystifier]

The problem with the alternative is that you are most likely wasting your entire working life, motivated by little more than a natural human prejudice.

In my case, Bohmian mechanics helped me to easier accept standard QM/QFT, see the last section in
https://arxiv.org/abs/2205.05986

 

[Demystifier]

If a bosonic field is probabalistic, and if it can be emitted (suddenly coming into existence), what determines its probability distribution when it is emitted from a fermion? In other words, one thinks (or at least I think) of a fermion field as already being in existence and already having some probability distribution as a given, but boson fields are different in that seemingly mid calculation, so to speak, they can be emitted such that their probability distribution is not a given from the outset. So what determines its probability distribution?

Standard quantum theory does not give a probability of existence. It gives a probability of a given measurement outcome, if a measurement is performed. Without measurement, we cannot talk of existence of fields at all, not only for bosonic fields but for fermionic as well. The only thing that "exists" without measurement is probability, where "exists" should be understood in a mathematical (not physical) sense, meaning that probability is something that we can compute by our equations. So probability distribution of bosonic (or fermionic) field does not require the existence of the field itself.

 

[PeterDonis]

I was under the impression that in QFT even though quantum states have nothing to do with wavefunctions, they can still be in a state of superposition(in multiparticle Fock space).

Sort of. But even if we accept this as a heuristic description, it would not be a "superposition of states which are not real". Multiparticle Fock space states can in principle be observed, so they would count as "real" (unlike virtual particle states, which can't be observed even in principle).

And this is generally how 'collapse' creeps in QFT(I assumed this is what is happening).

No. "Collapse" in QFT just means we fix the "in" and "out" states at the start of our analysis (for example, in Compton scattering the "in" state is one electron and one photon and the "out" state is one electron and one photon). It does not appear anywhere in the analysis itself.

 

[JohnH]

From my perspective, the more you study QM/QFT the more sense it makes and the more inevitable it seems that nature at the fundamental level cannot be like the classical, macroscopic world.

I wasn't surprised that physicists didn't believe in what you might call intuitive, classical physics. I was surprised that physicists didn't believe in probability. For example, Demystifies said this about probability and I'm assuming it is the most common interpretation

"exists" should be understood in a mathematical (not physical) sense

Is it really all that uncommon for physicists to believe that probability exists in a physical sense?

 

[PeterDonis]

Is it really all that uncommon for physicists to believe that probability exists in a physical sense?

What would it mean for probability to exist in a physical sense?

 

[JohnH]

What would it mean for probability to exist in a physical sense?

It would mean that mathematics can map one to one and onto physical reality.

And if this discussion is going outside the bounds of the forum rules, I apologize. Just answering a question.

 

[PeterDonis]

It would mean that mathematics can map one to one and onto physical reality.

While this is a clear definition (and is false for all known physical theories), I don't see what it has to do with probability. But in any case...

And if this discussion is going outside the bounds of the forum rules, I apologize. Just answering a question.

No problem, but you are correct that this particular subthread should not go any further as it is off topic.

 

[vanhees71]

I think indeed, for many people who think that there were a "problem" with quantum theory (despite the only real physical problem that we don't have a consistent quantum theory of the gravitational interaction) it's that QT says that there is "objective chance" in nature. That's what's even called "non-realistic", i.e., that not all observables always take determined values, and that the probabilistic interpretation of the quantum state is "complete".

 

[Vanadium 50]

"problem" with quantum theory

Some folks confuse "I don't like it" with "there is a problem with the theory".

 

[vanhees71]

Well, Nature doesn't care whether you like it, how she behaves ;-)).

 

[JohnH]

QT says that there is "objective chance" in nature

Again, I totally agree.

 

[Hornbein]

I can say that it is easier to understand quantum physics if you wipe your mind clean and have no expectation. That is, don't try to relate what quantum objects do to anything in your experience. It will just mess you up. The only man to succeed in coming up with a useful simple model was Richard Feynman. I recommend his QED. But I don't believe that his model has anything to do with what is actually going on. As to what that might be, I don't think anyone knows.

On the other hand, I say the "it will forever remain unknowable" crowd are going too far. Who knows what the physicists of one million AD might have? How about one billion AD?

 

[vanhees71]

Feynman's QED (I guess you refer to the scientific textbook, not to the pop-sci book, which however is also among the better pop-sci accounts for QED, but still it's pop-sci) is on an amazingly conservative side of the existing literature. It's more or less following Fermi's old operator-methodological paper, and the interpretation is (fortunately) of the typical Feynman no-nonsense kind, i.e., "shutup and calculate".

Physics is not about "what is actually going on", whatever you mean by this phrase, but on what is observed in objective quantitative experiments/observations, and there what QED (as any relativistic QFT) delivers are S-matrix elements to evaluate scattering cross sections (for the so-called "vacuum QFT", which deals with scattering processes in contradistinction to many-body QFT which deals with many-body systems, usually in thermal equilibrium but also off equilibrium, which allows to calculate macroscopic properties like equations of state, transport coefficients etc.).

 

[JohnH]

Physics is not about "what is actually going on", whatever you mean by this phrase, but on what is observed in objective quantitative experiments/observations

This was what I was struggling to come to grips with but this is the clearest, and most reasonable explanation of why it makes sense I've heard yet. For some reason it never quite clicked that we were more or less ignoring "what is going on."

 

[JohnH]

Bell's inequality is a fact, not a theory. You'll hear no argument from me on the existence of probability in nature.

 

[vanhees71]

The violation (!) of Bell's inequality is a fact!

 

[JohnH]

The violation (!) of Bell's inequality is a fact!

Right! Haha, you know what I meant.