My teacher was teaching us about path of electrons around a nucleus. He told us that many theories have been proposed about path of an electron and the latest theory is somehow different from saying that electron revolves in a circular path around nucleus. Even though he used the circular-path theory (temporarily called so) to demonstrate other phenomenons such as Ionization Potential, vaporization etc and it all seems logical. He also said that other theories concerning to electronic path can also be used to demonstrate these phenomenons but I am using this for this is simpler.

But how this is possible? I am thinking that these things must be working under a single theory (may be one among them or one uncovered so far) naturally then why a question can be answered with several theories completely logically.

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    I observe that my keys are not in my hand. This is consistent with the theory that they are in my pocket, but also consistent with the theory that I left them on my desk. It is also consistent with the theory that I, in fact, have two sets of keys, one of which is in my pocket and the other one on my desk, as well as with the theory that I have no keys at all, and that any recollection I have of putting them in my pocket is just a figment of my imagination. Or that the keys have, in fact, fallen between the sofa cushions. Commented Jan 31, 2016 at 1:00
  • @IlmariKaronen Well said. The point is, I think, that we shouldn't confuse theories which explain a phenomenon or state of affairs, with the reason or cause for that state of affairs. In the former case, as you illustrate with the missing keys example, we can have many theories to one phenomenon. In the latter, we might say that there is only one true or necessary reason or cause.
    – M. le Fou
    Commented Jan 31, 2016 at 4:48

7 Answers 7


What you are mentioning is the problem of underdetermination of scientific theories (see here, and here).

The straight up answer to your question is: No, there can never be a single theory or model explaining a given set of experimental observations, there will always be multiple explanations. This was proven definitively by W.V.O. Quine in his landmark paper "Two Dogmas of Empiricism" and led to the famous statement "Every observation is theory laden", meaning that what we observe will always depend on theoretical presuppositions. Quine went on to adopt a form of holism, saying that we can never confirm individual theories or models, we can only confirm webs of interconnected theories.

See this post and the accepted reply for more information.

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    holsim -> holism
    – Ergwun
    Commented Feb 1, 2016 at 0:48

The model of electrons orbiting a nucleus has one severe handicap:

An electron orbiting the nucleus changes permanently the direction of its velocity, which means a permanent acceleration. According to Maxwell's theory of electrodynamics an accelerated electron creates an electromagnetic radiation which carries away energy from the electron. Hence the electron looses permanently energy. As a consequence it approaches an orbit nearer to the nucelus and finally rushes into the nucleus.

Summing up: The model of spinning electrons is inconsistent and cannot serve to explain the phenomena.

Historically this was a great problem in the beginning of the 20th century. The solution came up with quantum mechanics (Bohr, Heisenberg, Pauli, Dirac). That's quite a different theory. Its enhancement as quantum electrodynamics is one of the best theories we have today.

In general, chemistry works fine with quantum mechanics, see e.g. Pauling, Linus: General Chemistry 1970. One can actually compute the ionization energy, see Chap. 5.2 "Excitation and Ionization Energies".

Note. No other theory allows to compute these values. Hence your example does not illustrate the fact that different theories explain the same phenomenon.

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    This is all (as far as I understand these things) true, but I don't see how it answers the question. Commented Jan 31, 2016 at 4:55
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    @David Richerby I added the note to indicate that the OP bases the question on a wrong assumption. The chemistry from the OP is only explained and computable by quantum mechanics, not by any different theory.
    – Jo Wehler
    Commented Jan 31, 2016 at 6:55

You have discovered a basic principle of theory: Make your theory only as complicated as it is necesssary to explain the phenomena you want to explain. It is also known as Occam's Razor.

It results in models. Models are analogous, simplifying: They basically say that things would work like something else in some aspects (the simpifying part), but in another sense different. That is why a model must contain the actual explanation by analogon as well as a commentary for the differences. See the last chapters of Empiricism and the Philosophy of Mind by Wilfried Sellars, where he uses this picture.

Coming to the problem of electrons: The circular-path model, as you call it, has been used to explain two phenomena: 1) Atoms are not solid 2) They have a massive, positive core and small, negative charges around it with a really big deal of nothing in between. That is the problem Ernest Rutherford had been confronted with. What is more obvious than using a model that looks like the sun and its planets?

For understanding some phenomena, this model is enough. And it has one striking feature: It is easy. Why using a more complicated model for explaining phenomena that become perfectly understandable using this one?

I think Rutherford knew very well that his theory was flawed, as Maxwell's equation were about 50 years old back then, but nevertheless the success of models also depends on how well they can induce/use familiar pictures as mere illustrations. The model could intuitively explain a whole lot of things and others not.

So the question is not if the model is wrong (every model is to some extend, see below), but whether it is able to convey a picture that makes it easier to grasp an idea of how atoms may look like if we could look at them, considering the empirical data/phenomena we look at. What Sellars calls the commentary part of the model would have to include that the atom is not just a planetary system with an electric field instead of a gravitational one (reasons provided by @JoWehler). It would have to state in which respects the powerful picture is a false one.

Now, if you wanted to explain more phenomena, you would have to develop a more complicated model, which explains all of them (@JoWehler's answer talks about this). But the more complicated, the more abstract and harder to understand it will become, up to the point of being essentially useless for illustrative/explanatory purposes. If you want to explain something, using something nobody understands does not do the job.

I think your teacher is rightfully only using this easy model. Because explaining it in the more modern models would involve higher mathematics and a really high level of abstraction and knowledge. It would not use a nice picture everybody knows as illustration. The most advanced models involve equations that aren't fully understood by more than a handful people worldwide and cannot be visualised very well. It is coherent with the phenomena/data (or so they say), but it cannot explain anything but to a handful of people.

And now the point behind all this: Even the latest complicated, scientific, sophisticated model is still...just a model. It basically says "Insofar as we can measure and interpret the data (up to now), what we call atoms behaves like the variables in this equation the solutions of which look like this in the case of hydrogen" and the like.

It is how we are able to make sense out of what we see and measure. It is not what it actually and finally is and 'looks' like without question. This would not even be a scientific theory, see Popper's falsifiability. And models by definition have to be more crude than the theory behind them, otherwise they could not fulfil their illustrative/explanatory function.

  • What about that the Rutherford model - like any model from classical physics - is inconsistent, because it contradicts Maxwell's electrodynamics?
    – Jo Wehler
    Commented Jan 30, 2016 at 21:27
  • That is the commentary part of the model. I actually think that Rutherford himself was perfectly clear that the electrons do not actually move in circles around the nucleus. But that is what models are for. Economic models are so simple that it hurts (linear models ftw), but nevertheless they explain basic mechanics. The problem of modern science is the hybris of thinking that they are actually describing reality and not making models.
    – Philip Klöcking
    Commented Jan 30, 2016 at 21:31
  • @What do you mean by "commentary part" of a model? - Though, a model, which is inconsistent in itself, seems misleading. But of course, a model does not need to represent every feature from the domain of investigation.
    – Jo Wehler
    Commented Jan 30, 2016 at 21:40

This is a concern I have with how science is taught these days. Good for you for being frustrated by it!

Electrons move how electrons move. That's all we can really say (and even then, we have to question whether electrons exist at all). However, science has been able to construct models of how the universe functions, including those which involve electrons spinning around. These models are valued because they are "consistent" with the observed behavior of our universe. As best as we can tell, there are things that we call electrons, and they orbit the nucleus in some ways. Are we positive this model is "true?" No. Are we confident enough in its predictive abilities to hang several multi-billion dollar industries on the assumptions that its predictions are useful, yes. We have mounds of experimental evidence which suggests this is an effective way of thinking about the world.

Now it should be reasonable to assume that there can be many models for the same behavior. There may be a model of an electron whizzing around in a circular orbit, and there may be a model of a quantum fuzz of electron probabilities (which is likely the "latest theory" your teacher mentions). Both may be consistent with much of the data we have collected over the years, but the latter model would be consistent with some of the more extreme cases, where we really stretched the theories to their limits.

If you are not operating in a region where you're stressing the theories to the limit, both theories are consistent with the universe to the fidelity you are concerned with. It may be very easy to demonstrate some phenomenon with the orbiting electron which requires advanced mathematics to demonstrate using the more advanced model. So long as all of the effects you are concerned with remain in the region where the two models are consistent, you can get away with using the simpler one. If you enter the regions where they start to differ (such as semiconductor physics), you will find that the two models give you different results, but only one of them is consistent with the experimental data. A skilled scientist knows when they can get away with using a simpler model, and when they have to move up to the more complicated one.

As an example, take the Coriolis effect. In theory the "most correct" model of how the macroscopic world works is General Relativity (GR), so we would theoretically need to use GR equations to show the Coriolis effect. However, we know that GR and Newtonian physics are "consistent" at small velocities (read: small fractions of the speed of light). Thus instead, we can show the math behind the Coriolis effect using the much simpler Newtonian physics. If we were ever to explore the Coriolis effect on particles traveling at a significant fraction of the speed of light, we would find we need to use the far more complicated GR models to accurately show what happens.


We observe things in science and postulate possibilities to explain them. Multiple theories can be developed to explain the same phenomenon, but when other observations are made, some theories will be proven false.

To provide a clear example, I will use a mathematical example. Consider the observation 2 ? 2 = 4. We might postulate that the question mark represents + (addition) or * (multiplication). With only this observation, it appears that either theory is valid, because we know that 2 + 2 = 4 and 2 * 2 = 4.

To complete the example, we might make another observation that 3 ? 3 = 9. Now we can see that + no longer explains the phenomenon and we might say * is the "correct" theory, at least until we find more observations, because further observations might invalidate our existing theories and force us to develop new ones.

Hence it is possible given our limited number of observations at a certain time that multiple theories might simultaneously explain them, until future observations allow us to narrow down which theories are correct (and indeed much of physics attempts to disprove or prove certain theories through experiments that give us new observations).


Imagine you're in a train and it stops in the middle of nowhere for no apparent reason. You can formulate different explanations: maybe the engine broke, maybe a tree fell on the tracks, or maybe they're waiting for another train to cross. If you stay inside the wagon you have no choice but observe by the window if one explanation works better than the other (are there lots of trees around? Is the weather stormy? Did you hear a noise in the engine before the train stopped?). Even if there are strong indicators in favor of one hypothesis you cannot exclude the others (maybe it's stormy and there are lots of trees around, but the fact is that the engine broke). You cannot exclude that there's another explanation you didn't imagine either.

It's pretty much the same for electrons, except for the fact that we're dealing with a type of phenomena rather than a single event: we can observe some manifestations but there are different possible explanations, and all we can do is test our hypothesis through various observations to see which one fits best. At some point we can be confident that our theory is right but there is always room for alternative theories.


Just as in mathematics, different axiomatic systems can prove some common theorems, in physics you can have different theories (I don't like to use the word "theory" here, as it has a very specific meaning that's not the one I'm using, so please forgive this) that explain the same phenomenon, it's not problematic at all. Assume you want to explain why apples fall. Then Newton's theory of gravitation works perfectly fine, and any reasonable measuring you can make will confirm Newton's theory. However, Einstein's general relativity works fine as well (although the calculations will be harder). These two may not be the best example, as some experiments can show that Einstein's theory is more reliable than Newton's, but going from this to theories that have almost the same results (such as the different interpretations of quantum mechanics) shouldn't be too hard.

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