# What does it mean to create particles by applying creation operator

This question will be a way to ask if quantum mechanics is just a mathematical framework to predict physical outcomes without talking about the 'actual', maybe even 'deterministic' phenomena, such that the equations never make the wrong predictions. The main reason is that its language is quite mathematical, and just mathsy in the sense I can't relate it to things that I call physical processes. Recently I was reading about creation operators and vacuum states in QFT, and the book says the following (I can't find a way to use mathjax here, sorry. If you can let me know of a link for it)

There exists a vacuum state and creation operator indexed by momentum. Applying this operator to the vacuum state gives a 1 particle state with the index momentum.

Now, what I don't understand is, what did really happen? In real life there shouldn't be a operator (at least I think) and somehow we produce a particle out of air. I mean, say I produced a 1 particle state. I don't think I used a mathematical entity , operator, to do it but I guess the statement is that maths of this process looks like operation on vectors with operators and such but we never really talk about the physical process itself. In this sense, quantum mechanics looks like a framework rather than theory.

Is this interpretation correct or is reality made out of vectors and such?

• When you turn on a light bulb, photons are created that weren't there before! Does that concern you? Commented Aug 16, 2023 at 1:56
• Hmm, well I am not very knowledgeable about particle or quantum nature of photons, but from wave view (based on classical EM) there is no particle really created. Maybe if EM field has probabilities to produce different photons, as in QM, (I just don't know QED), I would imagine still there is only fields not particles. Still, this is a good question Commented Aug 16, 2023 at 2:03

Every theory of physics is a framework; it's just that quantum mechanics is specially removed from day to day experience.

Operators in quantum mechanics don't represent actual experimental actions on the system. They are a way of encoding the several observables that we can measure and their probability of measurement. For example, the creation operator is a way of encoding how many particles (or quanta of some system) are present in that system. Nothing "happens" when you apply the creation operator.

As for your last question, I regret to inform you that physics has no answer for you. It cannot tell you about reality at all. All it can do is employ models to test our experience against. As to the reality that hides behind it, if you can talk about it meaningfully at all, it can't tell you if it's vectors and such, it can only tell you if vectors and such are successful at modelling it.

• I understand. I will wait a bit for other answers as well, but I was also waiting to learn or see if anyone would say that QM is a framework rather than reality itself, a model that black-boxes the reality using its own maths, bcs ig we often learn QM as if it is the reality too without talking much about it Commented Aug 16, 2023 at 2:08
• @MahammadYusifov At the risk of simply repeating the answer: physics is not reality. Not just quantum mechanics, but all of physics is "just" a framework for predicting experimental observations. The experimental observations, not our mathematical models of them, are the reality.
– d_b
Commented Aug 16, 2023 at 2:12
• Well, actually I have one related question to your answer. It is very popular to say that QM is also as natural as other theories if we were accustomed enough but the thing is I think most people would agree that complex numbers are not something that we would get accustomed to even if we were subatomic beings. Yes, there are questions if real numbers are really not abstract themselves either but somehow it seems quantum is really not the reality but just a way to encode whereas previous theories are encoding the reality as it 'has to' be. Commented Aug 16, 2023 at 2:16
• @MahammadYusifov You seem to think that some models are not models or encode "more reality" just because you like them better or can better relate to them, but I think that if you reflect hard enough you'll see you're just picking and choosing. Complex numbers are as natural as real numbers and as anything else in maths; they are a construction, either designed because it was interesting or to solve some problem. For example, complex numbers are the most natural for describing 2D rotations. Have you ever seen a natural number? Measured a vector? I'd think not. Everything is a model. Commented Aug 16, 2023 at 2:29
• My first sentence is wrong. I meant to say that what you say is important and I think that some courses in philosophy of science would help many students/researchers, to be forced to think about what we actually can conclude from our successful theories and models. I agree to your comment, tho. Commented Aug 16, 2023 at 14:29

This question will be a way to ask if quantum mechanics is just a mathematical framework to predict physical outcomes without talking about the 'actual', maybe even 'deterministic' phenomena, such that the equations never make the wrong predictions.

Every physical theory is “just” a mathematical framework to predict physical outcomes. Every framework only talks about the actual phenomena in the sense of what we can “actually” predict and observe. Quantum mechanics just feels unusual because there are things which we might have liked to predict and thought should have been there, but the theory makes no mention of such things. You should see look at Bell’s theorem, discussions of (local) hidden variables, and interpretations of QM to learn more about this.

such that the equations never make the wrong predictions

Well, if the equations made the wrong predictions, then we would assume we had the wrong equations and go looking for the other (right) ones. We are assuming that slices of reality are fundamentally rational and can be predicted with logical axioms and mathematical models - there is no reason reality had to be that way but so far this assumption has been very useful!

I think maybe what you are trying to express here is the feeling that the theory is so general that it could be used to model anything, and is thus not much of a model at all. The point to remember though is that the theory is constrained; namely, the assumption (in ordinary QM) that physical states are vectors (actually rays) and observables correspond to Hermitian operators does limit the types of things we are allowed to expect (which is a good thing)!

I am not as familiar with QFT, but similar considerations apply. The creation of a particle is modeled by a creation/annihilation operator, but we also assume this is a linear operator acting on a rigged Hilbert space. This gives some structure to “reality.”

Now, what I don't understand is, what did really happen?

Again, you should look at interpretations of QM for an attempt to answer this question. At present, there is no consensus among physicists as to what “really happened.”

Finally, as a general point, no language or mathematical model of reality is equivalent to reality itself, but we still expect some (approximate) homomorphism between the theory and reality. In other words, the theory tells us somewhat what reality must be like —- even if it is not reality itself. Similarly, a good map tells us what the actual territory is like, but the map isn’t reality.

• "the theory tells us somewhat what reality must be like —- even if it is not reality itself" - yes, but only as far as experimental predictions go. If you assume that the theory- at least in some restricted sense - corresponds to something "real", then that is an assumption, e.g. converging realism. For example, you can talk about electrons, magnetic fields, quantum fields etc. without giving these things a "real meaning", i.e. you do not have to assume these things are really out there. But if you do so, that is a "believe" in these sense that this is nothing you can observe. Commented Aug 16, 2023 at 6:50