The Role of Theories, Models, and Laws in the Scientific Process

[Frasch]

What role do theories, models, and laws play in the scientific process? Is there a clear dividing line between a theory and a law? Are models used in both theories and laws? All theories and laws? Do our best current models perfectly represent reality to the best of our knowledge, or are they a simplified version of what we understand to be reality so that they can be used as tools to predict future events?

 

[Geofleur]

Here are some ways to think about these terms. They are not the only ways, but I have found them helpful:

Model - A simplified picture of a part of reality, used to explain some observation or set of observations. Think of a map. A map that represents absolutely everything would be too complex and probably not very useful. Simplicity can aid understanding. Accounting for more and more of real-world complexity if often in tension with this goal.

Theory - A network of interrelated and very successful hypotheses, which can be used to predict and understand a wide variety of phenomena. The theory of evolution is a good example. Plate tectonics is another.

Law is sometimes used to mean a statement that is universally valid, but sometimes it is just a conventional name, as in Ohm's law. Arguably the most fundamental laws of physics are of the former type!

By these definitions, theories can contain or give rise to many models. Evolution, for example, acts as a framework that can be used to generate models. Newtonian mechanics, likewise, is a framework that can be used to generate models.

 

[Frasch]

Must models always be a simplified version of our perception of reality? Bohr's atomic model for example isn't entirely correct. It is only approximately accurate. Are all models simplified and approximate in this way? Is our current model, the quantum mechanical model simplified in this way?

 

[russ_watters]

It must be assumed that all models are simplified versions of reality, since it is inherrently impossible to prove that they are totally accurate.

 

[Frasch]

It must be assumed that all models are simplified versions of reality, since it is inherrently impossible to prove that they are totally accurate.

But are there any known simplifications with our current models? Also are there laws or theories that we don't use models to understand?

 

[axmls]

Are all models simplified and approximate in this way?

"All models are wrong, but some are useful." - George Box

Yes, every single model is approximate, and even if it wasn't, our measurements are only approximate. The question is: is my model accurate enough where it can be applied? If the answer is yes, then you've got a good model.

 

[Frasch]

But are our best and most current models only approximate because we don't have perfect knowledge of how things really work, or is it also because we have simplified the models and made them less accurate and more approximate in order for them to be useful? Also, what are some examples of models and theories? I mentioned the Bohr and electron cloud models of an electron, what theory is associated with them? What models are associated with the Big Bang theory?

 

[russ_watters]

But are our best and most current models only approximate because we don't have perfect knowledge of how things really work...

But are our best and most current models only approximate because we don't have perfect knowledge of how things really work,

Right. Since it is impossible to test everything and impossible to have perfect accuracy, it is impossible to know for sure if the models are 100% accurate.

or is it also because we have simplified the models and made them less accurate and more approximate in order for them to be useful?

No, we'd certainly not intentionally do that. We may simplify things for use when the accuracy isn't needed, but for learning how the universe works, scientists make things as complex as needed.

Also, what are some examples of models and theories? I mentioned the Bohr and electron cloud models of an electron, what theory is associated with them? What models are associated with the Big Bang theory?

Theories and their associate mathematical models generally don't have different names, unless the theory is sort of a meta-theory like the Big Bang, which incorporates several theories (such as General Relativity).

 

[jtbell]

But are our best and most current models only approximate because we don't have perfect knowledge of how things really work

If we ever did find out how things "really work", how would we know it? (as opposed to merely finding another approximate model?)

 

[jbriggs444]

or is it also because we have simplified the models and made them less accurate and more approximate in order for them to be useful?

Possibly not completely on point, but we continue to use the model of Newtonian mechanics because it is simple in spite of the fact that we have more accurate models (special and general relativity) available. Meteorologists use simplified models of the Coriolis force (assuming that it applies only tangential to the Earth's surface) in order to simplify their calculations. The vertical component is dwarfed by the effect of gravity and buoyancy. In fluid mechanics, a number of simplifications are possible. For instance, the assumption of incompressable flow or ideal gasses. When analyzing a spring, we might use Hooke's law even though experiment would likely show it not to be completely accurate.

 

[Frasch]

I understand that we can never be sure that we have a perfect model, I'm more curious about the models that we use that have errors that we are aware of. Something like hooke's law for example. If I'm correct it's an approximate model that we still use. Is that only because it's an old model that is still useful, or was it known to be an approximation when it was discovered? Also, is there any modeling going on in laws such as the conservation of momentum?

 

[russ_watters]

I understand that we can never be sure that we have a perfect model, I'm more curious about the models that we use that have errors that we are aware of. Something like hooke's law for example. If I'm correct it's an approximate model that we still use. Is that only because it's an old model that is still useful, or was it known to be an approximation when it was discovered?

Most theories are established when the data on them is still pretty thin, so their limitations are not known. The limitations (if any) are only discovered later.

However, both can be true: some are used that have known real inaccuracies and sometimes it is just that the situation is more complicated than the model takes into account. A real spring doesn't follow Hooke's law very closely not because of a problem with Hooke's law, but rather because of issues with the spring (geometry, mostly) that add other components to the motion or just make it hard to analyze properly. When scientists are testing a theory, they do their best to design an experiment that eliminates such issues and focuses just on what they are trying to test.

Now, a theory can cross that bridge or even be on either side. Newton's gravity, for example. It is still perfectly accurate (to within the limit of our ability to measure) in certain situations (no motion), but it tends to be used in a lot of situations where it is known to be inaccurate, as long as the known inaccuracy is too small to matter.

Also, is there any modeling going on in laws such as the conservation of momentum?

All physics laws have models. All mathematical statements in physics are models. So yes. M1V1+M2V2=M3V3, for example.

 

[rootone]

If the plan is to build a bridge then using Newton's mechanics is fine for that purpose, even though we know it isn't fully accurate.
Using relativity would not result in a better bridge, and would most likely give the construction engineers an aweful headache.