#### [SOLVED] Misused physics analogies

By Kostya

Have you noticed that many questions and misconceptions in physics arise due to misuse of analogies, which were invented to "explain in simple words" some physical phenomena?

For example there is a "stretching rubber band" analogy for Hubble expansion of the Universe, which make people ask about the "tension" of this rubber band or speculating about "cutting a hole" in it.

I'm pretty sure that there are a lot of such misuses. Do you have any remarkable examples of these (together with a proper treatment n of course)?

#### @Pulsar 2014-01-03 00:05:11

An analogy that I really hate is Newtonian cosmology. You'll find it in many courses on cosmology as an introduction to the Friedmann equations and the expansion of the universe. The idea is that you consider an object on a sphere with radius $r$ and average density $\rho$. The specific energy of this object is then $$U = T + V = \frac{1}{2}\dot{r}^2 - \frac{4\pi G}{3}\rho r^2,$$ which can be rewritten in the form $$\left(\frac{\dot{r}}{r}\right)^2 = \frac{8\pi G}{3}\rho - \frac{kc^2}{r^2},$$ and lo and behold, this looks just like the Friedmann equation (without dark energy). This little exercise often confuses students; it reinforces the misconception that galaxies are moving through space, away from a central point; it only makes it harder to stamp out this idea with the full machinery of GR. Just because the Newtonian equation has the same form, that doesn't make it a good introduction to cosmology.

#### @Selene Routley 2015-11-08 12:36:19

I actually haven't seen FLRW introduced like this. Your example reminds me of the coincidence that this article explains or the fact that by setting the Newtonian escape velocity to $c$ will get the GR expression for the Schwarzschild radius, even though the two descriptions are worlds apart. I must say the existence of co-incidences like these is a bit unsettling and shows how misleading "correct predictions" can be: your example is a good one, illustrating this salutary warning

#### @Pulsar 2015-11-10 19:22:56

@WetSavannaAnimalakaRodVance I've seen it a few times, unfortunately, including a course that I took when I was a student. Susskind also uses it in his 'theoretical minimum' cosmology lecture, and it only confuses the students.

#### @yayu 2011-08-22 11:07:26

The worst analogy I have seen is that of general relativity where they show a curved sheet and how a ball revolves due to the curvature.

As far as I remember, I have seen this at two places:

1. The movie "Einstein and Eddington" where Arthur Eddington explains Einstein's theory to his housemaid
2. Carl Sagan in his celebrated video series.

#### @Oscar Cunningham 2015-09-09 22:04:44

This criticism doesn't really hold water. Everybody understands that on the length scale of a rubber sheet gravity just pulls things downwards. So they do understand gravity well enough to understand the analogy. Likewise, the "solar system" model of the atom isn't perfect, but the problem with it isn't that the solar system is made of atoms.

#### @benrg 2019-02-03 10:39:24

The rubber sheet model is accurate if you take the sheet to be a graph of the Newtonian gravitational potential. It's entirely wrong (not just inaccurate) to interpret it as an embedded slice of spacetime. See this answer.

#### @Arjang 2011-01-19 21:04:22

The problem in the rubber band analogy is not the analogy itself but the object that it uses becomes the focus. If instead of using a rubber band they used computer graphics with emphasis on galaxies further away accelerating faster then nobody would think of tension of the band.

The attention should be given only to the position of dots on the band and their relative motion from each other. But if the ether theory was being thought rubber band could have been considered as the ether!

#### @Noldorin 2011-01-19 12:40:34

The "solar system" analogy of the atomic nucleus and electrons is certainly a very misleading one, in many ways. Unfortunately, this is all too often the model taught until late high school or early undergraduate level.

The Bohr model, or more usually the fuller quantum mechanical description, is of course required to do any useful physics. The shell model can sometimes be sufficient for some chemistry, though it is often not justified properly.