# Q & A: measuring time after Big Bang

Q:
Lots of accounts of the early universe say things like "in the first second after the big bang..." This sounds to me like absolute time, which I understand was thrown out with special relativity. So, when someone says "in the first second after the big bang," which frame of reference are they measuring that second?
- Paul (age 30)
Los Angeles, CA, USA
A:
Ordinarily people use the co-moving frame. That is the frame in which the coordinates track the average motion over a large sphere around itself.  That means that if you look at a collection of nearby objects, their spatial coordinate typically doesn't change in time.  In that frame the momentum density in the stress-energy tensor is on average zero in each vicinity. The way that this coordinate frame describes the increasing distances over time is via the metric scale factor.

This frame has the nice property that at t=1sec each point has material of the same age, as measured by itself. Each spot will have progressed, for example, equally far on the path toward nuclear equilibrium.

Mike W.

(published on 04/29/2012)

## Follow-Up #1: What is a co-moving frame?

Q:
I don't totally understand what you mean. Are you saying the proper frame inside of which is the entire universe? In the first few seconds/minutes/hours after the big bang, not everything was co-moving, right? I'm confused. Also, while the universe was still opaque, was everything moving at the same speed?
- Paul (age 30)
Los Angeles, CA, USA
A:
General Relativity gives us a wide range of choices about what space-time coordinates to assign to different events. There's no definite fact about which events are simultaneous, for example, but rather a wide set of choices about how to draw same-time-sheets through the event space. As I understood it, your original question was about what sort of choice people usually make for those sheets when they're describing cosmology.

Let me start with your new questions. You ask "was everything moving at the same speed?" That question is meaningless. Any object with any rest mass can be assigned a velocity of zero, and then the rest of the coordinates stitched together around that. You can end up assigning any velocity up to the speed of light in any direction to any object, depending on your choice of coordinate frames.

The phrase "co-moving" does not describe the behavior of the objects. The overall picture of the Big Bang is that, picking a typical lump of stuff to call "stationary", distant stuff will be moving away from it at a roughly constant speed. On top of that overall picture, there are of course all sorts of local motions as things whizz around each other.

Instead by "co-moving" what we mean is that in assigning a time coordinate to some event we pick the time that a clock which traveled along with the average of the things in the neighborhood of that event would read. As I mentioned, the advantage of this choice is that if we look at all the events at time, say, one year post-Bang, they all look like the stuff there is the same age. For other coordinate choices the things at "one year" look like different ages, depending on their locations.

There's a Wikipedia article that describes these coordinates more completely, but in somewhat technical language.

Mike W.

(published on 05/02/2012)