Is modelling REALLY impossible in quantum mechanics?

[ZuzaMagda]

I am not a physicist, so please excuse the gaps in my knowledge.

I am writing a would-be philosophical essay about models in different fields of research. In most general terms, my task is to consider how modelling can be useful in the pursuit of knowledge in the widest understanding of the word.

I have heard that in Newton's times (after him making the observation that analogies can be drawn between the motion of a planet and that of a ball attached to a piece of rope) it was thought that it is possible to model all true phenomena. However, I hear this view was abandoned with the advent of quantum physics. There, observations made for scale models did not apply in the case of actual phenomenona.

However, obviously, the three-dimensional scale model built of balls or ropes or anything else we could throw or drop or roll on a smooth table is not the only possible type of model. After all, there are also textual models, mathematical models, etc., etc.; generally, a model could be defined as "a simplified representation of something by something else".

What I am wondering about is whether this "impossibility to model" in quantum mechanics only relates to tangible, three-dimensional scale models (such as balls and ropes) and it is actually possible to construct more abstract models?

Or is it really completely impossible to model anything in quantum mechanics? Examples?

 

[gluefish]

Well, as you define it, mathematics is a formal system that is used to model many things, including quantum physics. If you meant more along the lines of a tangible model, than you are correct. Any model that would behave accurately would be impossible to observe, as explain by the uncertainty principle.

However, it comes to mind that a digital simulation of the universe (or rather, a small partition of the universe) could be created with known values for the un-observable quantities. This would simply be an embodiment of mathematics, and not necessarily tangible.

The reason modeling works for other things is that you are able to accurately simulate all the necessary variables for a representation (like gravity). But to build a physical model of the quantum world would require either a massive reduction in accuracy or an inclusion of many, many variables; it would not be likely to accurately represent any quantum principle in a simple system.

For your purposes, making observations in a simplified system would not necessarily carry over to the complex reality of quantum mechanics. Plus, reality cannot be observed to check if the predictions made from the models are correct. If you cannot directly observe the phenomenon, how would observing a model of questionable accuracy help?

 

[Antiphon]

It is possible within the limits of numerical error (and for simple problems to model exactly) some problems in QM.

In principle, all problems can be modeled exactly.

Example: hydrogen atom.

The problem for philosophers is understanding what that exact solution means. It means computing a very precise and definite STATISTICAL PROBABILITY of measuring a particular outcome when performing an experiment. Unless that mathematical probability is 0 or 1, you do not know and cannot predict the actual outcome of the experiment. (this is a simplified explanation that is accurate for philosophical purposes.)

 

[ZapperZ]

I am not a physicist, so please excuse the gaps in my knowledge.

I am writing a would-be philosophical essay about models in different fields of research. In most general terms, my task is to consider how modelling can be useful in the pursuit of knowledge in the widest understanding of the word.

I have heard that in Newton's times (after him making the observation that analogies can be drawn between the motion of a planet and that of a ball attached to a piece of rope) it was thought that it is possible to model all true phenomena. However, I hear this view was abandoned with the advent of quantum physics. There, observations made for scale models did not apply in the case of actual phenomenona.

However, obviously, the three-dimensional scale model built of balls or ropes or anything else we could throw or drop or roll on a smooth table is not the only possible type of model. After all, there are also textual models, mathematical models, etc., etc.; generally, a model could be defined as "a simplified representation of something by something else".

What I am wondering about is whether this "impossibility to model" in quantum mechanics only relates to tangible, three-dimensional scale models (such as balls and ropes) and it is actually possible to construct more abstract models?

Or is it really completely impossible to model anything in quantum mechanics? Examples?

This is a very strange question.

When we try to make a theoretical description of the band structure of solids, for example, we ARE doing modeling. Not sure what you consider as a model here. Modeling of many phenomena in condensed matter is a common practice. One only needs to look at, say, Phys. Rev. B, on any given edition. So this question is rather puzzling.

Zz.

 

[Fredrik]

...this "impossibility to model" in quantum mechanics...

As ZZ pointed out, the claim that QM can't model anything (if that's what you're saying) is probably too strong. Another example is the hydrogen atom. A calculation of the energy levels gives us a mathematical description of some features of the atom. So I would say that some things can be modeled by QM.

I would also say that some things can't be modeled by QM. See e.g. my comments in this post.

 

[Dr Lots-o'watts]

After all, there are also textual models, mathematical models, etc., etc.; generally, a model could be defined as "a simplified representation of something by something else...Or is it really completely impossible to model anything in quantum mechanics? Examples?

What is impossible is a macroscopic-scale physical model. (balls and springs don't work)

It is certainly possible to model mathematically, and that is precisely what qm is: a successful mathematical model of qm.

 

[ZuzaMagda]

Yes, what I have heard to be impossible to do is to model a quantum phenomenon with a scale physical model (balls, strings, smooth surfaces). I take it that it is possible to create mathematical models of quantum phenomena. Are there other types of models that could be either possible or impossible in QM apart from the a) tangible ones and b) mathematical ones? Verbal descriptions, perhaps?

(...) the claim that QM can't model anything (if that's what you're saying) is probably too strong. (...) So I would say that some things can be modeled by QM. (...) I would also say that some things can't be modeled by QM.

What I meant was modelling phenomena in QM rather than modelling phenomena by QM (there is a difference, isn't there?).

 

[The_Duck]

You can use a classical double-slit experiment to create a large-scale analog of a quantum double-slit experiment. Fill a rectangular tray with water and divide it in two with a wall, but leave two breaks in the wall. Set up a wave in the water on one side of the tray. The wave will travel to the wall; bits of the wave will go through the two holes, spread out, and interfere with each other. Something very similar happens with the probability wave describing a particle in quantum mechanics if you shoot it at such a wall.

Is this "modeling a quantum phenomenon with a scale physical model"?

 

[Dr Lots-o'watts]

Are there other types of models that could be either possible or impossible in QM apart from the a) tangible ones and b) mathematical ones? Verbal descriptions, perhaps?

Verbal descriptions and written text are models and can model anything, but they are not as accurate or universal as mathematical ones.

Strictly speaking, the act of thinking about QM is creating a model: thinking about an atom means that our brain neurons connect such that we visualize an atom. The visualization could be said to be a model, but this is starting to get off-topic.

By definition, physics is about accurate modeling, and this practically means the use of mathematics.

 

[Dr Lots-o'watts]

You can use a classical double-slit experiment to create a large-scale analog of a quantum double-slit experiment. Fill a rectangular tray with water and divide it in two with a wall, but leave two breaks in the wall. Set up a wave in the water on one side of the tray. The wave will travel to the wall; bits of the wave will go through the two holes, spread out, and interfere with each other. Something very similar happens with the probability wave describing a particle in quantum mechanics if you shoot it at such a wall.

Is this "modeling a quantum phenomenon with a scale physical model"?

Somewhat, but it is modeling of a (probability) wave function by a a water wave, not a scaled-up wave fonction. It is the wave functions that cannot be scaled-up.

On the other hand, a water wave can be scaled.

 

[webplodder]

At the end of the day, we can know nothing of 'reality' outside of or perceptual apparatus, which in effect, means we have to 'invent' (in a way) what we find out about our experiences with it. The experiments with which science uses to test hypotheses are themselves based on human invention so that you might say reality, for us, must be a rather parochial experience. Even mathematics is a human invention (although many people do not agree with this) so again, even the most abstract maths is really an analogy or model of human sensory and intellectual experience. In fact, it is a well known truism that nothing can really be said to exist without it first being measured. A quantum object has no definite position or momentum till measured by some kind of intelligent observer so it all really comes down to what an observer can define as 'reality.' Sorry if this seems to be straying in philosophy, but there it is.

The rather startling conclusion from the foregoing is that we, as active participants, are in reality 'forming' the universe by the way we measure or observe it or, put another way, by the kind of questions we pose to it.

 

[Deric Boyle]

I want to just ask the expert that do they remember anything about liquid helium or superfluid?
It's a great example of a macro-quantum states.
And dear Zuza chemists use modelling in QM for chemical reactions, but these are all probabilistic.It is being also employed for quantum computing and in the modelling of Casimir oscillators.
Only the problem is that they require a rigorous mathematical formulation which is very difficult to interpret in common man's language.