Too much info for multiparticle wave function?

[MichPod]

Let me start with a short disclaimer - I am not saying that QM is wrong or things like that. And I very well understand that my argument is not physical, more philosophical one, which may be considered as inappropriate here. Still, my intentions are good and I hope for some understanding.

When a wave function of a single particle is considered in QM it is somehow analogous to a classical field, i.e. it defines a particular value (complex amplitude) for each point in the 3-dimensional physical space. This looks quite "natural" - it looks natural that for each point in the space a value may be defined.

Things get less natural when a multiple particle wave function is considered in QM - for N particles we would need a 3*N-dimensional space in which for each point a particular amplitude is defined.

Now, I fail to understand, what "real" thing may stay behind such a "big" object. Where and how these amplitudes may be "stored"? (I am a software engineer, so let me think in these terms) Again, for single particle it is very intuitive that each amplitude may be "stored" in a point of our 3-dimensional space but where would the Nature store the amplitudes of 3*N-dimensional space? Looks like too much information to be stored in our world.

I know nothing about QFT, but as far as I could understand, there the amplitude is defined per each "classical" field configuration, which hardly helps to resolve the problem, rather making it worse. So, my uneducated guess is that QFT does not resolve this particular problem, providing more "natural" objects than QM with its multyparticle wavefunction.

If my argument is somehow correct, are there any attempts to resolve this problem? If not correct - I would be much interested to understand why the wave function of multiple particles may be considered as a "natural" object.

PS: of course, my intuition about what is "natural" and what is not may be completely wrong. Still, a function defined on each point of 3*N-dimensional space looks quite "unnatural", too "big" to fit anywhere.

 

[Drakkith]

I'm not an expert in Quantum Theory, but my understanding was that this is resolved by understanding that a wavefunction is an abstract mathematical concept and solutions and amplitudes aren't "stored" anywhere in this context.

 

[MichPod]

Whether a wave function is a mathematical concept or something real, the wave function is what ultimately defines the state of the system. In this sense, two different (multiparticle) wave functions define two different states. It then still remains unclear how such a "big" state may exist, just for the same reason.

 

[Drakkith]

I'm not sure I see how. If wavefunctions are purely abstract and not "real", then how is it unclear? It would seem that nature doesn't need to "store" anything about the wavefunction at all. After all, there are plenty of n-dimensional mathematical abstractions used all over the place in math and physics.

 

[MichPod]

But there must be something in reality which stores this big number of amplitudes - after all, because each distinct wave function correspond to distinct state of real quantum system, this data should be somehow "stored" in the state.

In classical mechanics you may define the state of your system (upd: better to say, coordinate, not the state) as a point in 3*N configuration space, but that is just one point, i.e. 3*N values which pretty well fit into our 3-d space where position of N point objects is defined precisely with 3*N values. In QM we have an amplitude defined per EACH point of 3*N space, it is a field defined in 3*N dimensional space and for each such a field we actually have a distinct physical state.

 

[Mmm_Pasta]

The wave function can be represented in many ways, including a one-particle wave function. Your description in the first post describe a wave function represented in position space. However, you could have represented it in momentum space as well. The wave function for a particle with spin also would not fit your "natural" view. To represent the spin of a particle requires a spinor. The coordinates representing spin exist in "spin space". In other words, the spin of a particle has its own internal structure which requires a different coordinate system than the three-dimensional euclidean one you are accustomed to.

Also, a field is any physical quantity that has a value at every spacetime point. This physical quantity can be represented by a number, vector, spinor, or tensor (and perhaps other objects that I am unaware of). I mentioned the spin of a particle; the spin of the particle can change from one point in spacetime to another, however, the actual spin of the particle is represented by its own internal structure, a spinor. You can think of the wave function (one- or multi-particle particle) in a similar way (although, the spin is also a part of the overall wave function). The wave function has its own internal structure and the structure is not necessarily the three-dimensional euclidean structure that you appear to be trying to think of.

These are just mathematical ways to represent nature. A cartesian coordinate system is also a mathematically convenient way to represent the physical space around us as well. I personally feel the abstract spaces we use such as "spin space" are just as physical as "euclidean space" - these spaces are just objects that we aren't quite accustomed to in our day-to-day experience, so they seem "strange". I don't find it strange since nature is rather interesting and new experiences that we don't expect pop up here and there. However, many people would disagree with me.

 

[MichPod]

I meant to consider here just a simplistic model. Having wave function for a (single!) particle with spin is not a problem as well as it is not a problem to have a tensor as a value in the point and not just a scalar. It is even not a problem to have some "hidden" dimensions i.e. to have a full multidimensional space per each point of our 3D space.
Also, I meant to consider a representation of the wave function in the coordinate space just as an example, as representation in other spaces would not change the situation.
I.e. additional details of real QM may be added to my simplistic description, no problem. That still does not address the problem, as far as I can see.

 

[Drakkith]

I.e. additional details of real QM may be added to my simplistic description, no problem. That still does not address the problem, as far as I can see.

Personally, I'm not convinced there even is a problem. You're assumption is that nature "stores" values, but to be honest I'm not quite sure what you mean by that in this context. We can certainly make models which require us to assign values to different aspects or properties, but is nature required to do the same thing? Does nature also store every digit of pi in our base 10 decimal system somewhere?

 

[LeandroMdO]

Whether a wave function is a mathematical concept or something real, the wave function is what ultimately defines the state of the system.

The "state" in this case is just a way to write down the experimenter's best information available about the physical system in question. What features of that representation carry over to the actual ontology is a wholly different question. There could quite conceivably be a large redundancy in our representation of the physical state. It wouldn't be the first time.