Questions that need better answers: the Universe has no center
As part of a new project to rekindle my love of basic physics and challenge myself, I asked my Twitter followers to send me questions that they felt were never adequately answered, or were usually answered with the same pat explanation that was not intellectually satisfying. I was then sent so many questions that I had to close replies to the thread in order to make answering them possible. I am gradually working my way through them, and this is the first of a series of posts that will attempt to answer these questions in a more satisfying way. I plan on working my way through this list for free, and then have it form the basis for a larger, ongoing project where I take on some of what I see as limitations of balancing accessible popsci explanations with practical pedagogical examples.
EPISODE ONE: THE UNIVERSE HAS NO CENTER
Replies:
@AnhHLe2702: What does the universe expand into?
@MikeRutland2: The explanation for the expansion of the universe having no origin and inflation being faster than c
Expansion doesn’t have a single origin so much as the whole of space-time is expanding together. This is usually a problem that is introduced by how diagrams are shown in books, how we conceptualize surfaces based on our daily experience, and also our own human perception of what ‘expansion’ means.
The most common analogy is usually the balloon. Draw some dots on a balloon, and inflate it. The distance between the dots over the surface of the balloon increases. This is the origin of the misconception that the expansion of spacetime (the surface of the balloon) has a centre.
When people look at this demo, they see the solid sphere - the balloon surface and the air inside it, surrounded by the air outside of it. When we don’t think about it too deeply and accept that ‘well, the Universe doesn’t have a centre like the balloon does' the analogy does OK, but they quickly fall apart.
When I use the analogy, most of the audience happily accepts them, but anyone with a passing knowledge of physics quickly interrogates me for more detail, which they rightfully should.
Technically, when we use the analogy we should only talk about the balloon’s surface as a (limited, 2D) representation of spacetime.
Personally I always struggled with spheres. All the spheres I encountered in my life are 3D objects. However, mathematically a sphere is not a 3D object - it is a 2D surface embedded in a third dimension. So when we use the balloon - which everyone sees as a 3D object - we are primed to see the third dimension because having a third dimension is critical for humans to interact with the world. What we should be focussing on is only the surface of the balloon (a 2D object). In this 2D analogy, only the surface of the balloon exists. For anyone struggling with this concept Flatland is an excellent book to build the intuition.
Explanation
The best way to imagine the expansion of the Universe, at least in my mind, is to imagine a 2D infinite sheet with grid lines drawn in it, intersecting at grid points - an infinite sheet of paper from a math workbook. Remember there is no depth in this representation - you can only exist in the 2D plane defined by the infinite sheet. Asking ‘but what about the third dimension’ is redundant, because there is none in this case - we have defined our analogy to be 2D only.
If the sheet is infinite, it has no centre.
Expansion is the lengthening of the distance between all the grid points on the sheet (stretched uniformly, at the same rate, in both x and y directions). The size of each square on the sheet then increases (and every square increases at the same rate), thus there is no centre to the expansion.
You can then extend this into a third dimension by turning all your squares into cubes (infinitely, up and down) and then the volume of every element cube in your 3D grid is then increasing uniformly at the same rate.
In this analogy, you can imagine the rate at which the grid is being stretched as varying as a function of time. And right at the very beginning of time, all of the grid existed (still infinite), it was just that the grid points are infinitesimally close together (so the grid is still infinite, and there is still no centre!).
As for expansion being faster than the speed of light, changing the grid spacing is not actually transmitting any information, so you are permitted to increase the spacing as fast as you please as the grid points are only to act as a guide for us, they have no physical property. Only objects that move from grid point to grid point have a speed limit.
If anything is still unclear - I encourage feedback! You can contact me via Twitter (@fipanther)