# Universal Misconceptions #4: You don't expand

Okay, let’s tackle one more of these common misconceptions about the universe. The first three are here, here, and here.

Today I’d like to dispel a few myths about local expansion. Put simply. while the universe expands on large scale:

• Your atoms do not expand
• You do not expand (insert dumb fat joke here)
• The sun, earth, and solar system do not expand
• The Milky Way does not expand
• Our local group of galaxies (including the Milky Way, Andromeda, and about 30 or so others) does not expand

In other words, anything that has a high enough density to be bound by its own local gravitational field (or on the very smallest scales, electromagnetic field) isn’t part of the universal expansion.

That’s a statement of fact, but you still may wonder why that’s the case. In order to solve for this, it might be helpful to write down an equation, give a quote, and show a picture, all of the same thing.

First, the equation:
$G_{mu nu}=8pi T_{mu nu}$
What we have here is the Einstein field equation. It looks innocuous enough, but in reality, it’s actually 16 equations, and that term on the left, in particular, has a lot of math buried underneath it.

What does it mean? Here’s where the quote comes in, from the great general relativist, John Archibald Wheeler:

Space tells matter how to move, and matter tells space how to curve.

Einstein’s field equations are essentially the second part of Wheeler’s description. The right-hand side of the field equations are known as the stress-energy tensor, and they contain a description of all of the stuff in a particular region of space and how it’s moving around. The left-hand side describes the curvature of time and space.

Or perhaps a picture from the good folks at Encyclopedia Britannica will help:

Rubber sheets again. Massive bodies distort the local gravitational field. However, and here’s the important thing, if you take a global view, all of those local bumps and wiggles (galaxies) average out.

Let’s try another analogy, this time using the electromagnetic and nuclear forces. Suppose you stretch a rubber band. You know that the band is made of molecules, and that the molecules must, on average, get further apart from one another as you stretch the band. But look deeper and you’ll see the molecules are made of atoms and the vast, vast majority of the mass of the atoms (about 99.95% or more) are in the nuclei. The nuclei couldn’t care less that you’re stretching the rubber band. Double, triple, quadruple the length of the band, and the protons and neutrons in the nuclei won’t budge one bit because of it.

The point (going back to the cosmological scales) is that the solutions to the expanding universe are based on averaging over relatively large scales of space. On scales of a few hundred million light years, the universe appears to be relatively smooth, and so the cosmic expansion behaves just like you understand it. On scales smaller than that, gravity is controlled by local perturbations, which means no expansion.

Not even a little bit.

-Dave

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### 2 Responses to Universal Misconceptions #4: You don't expand

1. josh k-sky says:

Local perturbations, you say? Could you discuss briefly that of Uranus?

2. will says:

pardon what may be a silly question, but in the above scenario, wouldn’t the combined matter of the newly birthed universe be bound by its own density and gravitational field (or at least, after the application of the higgs field and everything has mass) and stop the universe from ever expanding past that point?

or is that what did happen, and it stopped the inflationary period from … inflating too much?