I'm confused about expansion

1. May 5, 2015

thetexan

Even though the big bang wasn't an actual explosion per se it did have the expansive characteristic of an explosion right?

At some point in time during the expansion two bodies might be x distance apart. A little farther down the timeline those same two objects would be farther from each other due to the expansion, correct? In any case, if the big bang idea is correct, we start with a very small singularity and end up with a big universe so expansion and thus distance increased during that time, correct? Or, in general, since the big bang objects have been and continue to be getting farther apart?

tex

2. May 5, 2015

Drakkith

Staff Emeritus
The only things that an explosion and the metric expansion of space have in common is that things will, on average, get further apart. But the devil's in the details. The metric expansion of space is a very, very particular type of expansion that causes all unbound objects to recede from each other over time, and this recession velocity follows a very specific linear profile that depends only on distance and the current rate of expansion. In other words, the recession velocity increases linearly with distance, with the current velocity at approximately 70 km/s per megaparsec in distance. So for every megaparsec (million parsecs, or just over 3 million light-years) an object is from us, its recession velocity increases by about 70 km/s.

An explosion does not follow this profile. Objects are thrown away from a center point, do not increase their velocity over time or distance, and measuring the relative velocity of the 'shrapnel' would not give us a law similar to Hubble's law that applies to all objects in every direction. In an explosion, objects on opposite sides of the expanding cloud of shrapnel would have the largest relative velocities, and objects on the same side would have much smaller relative velocities. This isn't what we see when we look at the sky.

On average, yes. Galaxy clusters and objects smaller than this can approach each other thanks to gravity overcoming expansion, but these pockets of bound matter are, in general, getting further apart over time.

3. May 5, 2015

Ken G

Actually explosions do give a Hubble law, since the shrapnel is thrown out at speeds that don't change over time and so the distance away is just v*t, i.e., velocity is proportional to distance. And if there was gravity from matter that was slowing the expansion, or dark energy accelerating it, a uniform explosion would still follow a Hubble law. So the Hubble law follows only from the cosmological principle, not from general relativity or the concept of a metric expansion.

However, you are still right that an explosion is not considered to be a terribly good model, only a kind of analogy. One reason is that an explosion cannot obey the cosmological principle everywhere (though it could obey it out to the distances we can actually observe), because explosions require a pressure difference inside and outside the explosion. Also, an explosion would need to give some particles speeds faster than light in order to maintain the Hubble law to the distances we see. So it's not a correct description, but it's not a terrible analogy for introductory purposes.

4. May 5, 2015

Drakkith

Staff Emeritus
I'm not following you. I'm not an expert on explosions, but I can't see how the velocity would change over distance or time.

Still not following you.

5. May 6, 2015

Ken G

Imagine a spherical spray of shrapnel, where each shard has a constant speed, but there is a full range of speeds from zero to some maximum speed c. The equation of motion for each shard is r = vt, or v = r/t, where v is the speed of that shard and t is the age since the explosion. That's a Hubble law, not only for the central point, but also for any individual shard-- as long as it cannot see the edge of the explosion.

If the density is uniform in the explosion, and we can't see the edge, we would also have a cosmological principle, in that every place would be like every other, but would evolve with age. Any flow that maintains a uniform density, i.e., has a cosmological principle, must have the distance between any two points satisfy D = a(t)*Do, where Do is the distance at a time regarded as "now". This is because if the expansion is uniform, there can only be one time-dependent function a(t) that governs the whole thing. So if we take the time derivative dD/dt, we have v = dD/dt = da/dt * Do, which is also a Hubble law. So the Hubble law just comes from the cosmological principle.

6. May 6, 2015

Drakkith

Staff Emeritus
Okay. Apparently I wasn't thinking of a large enough explosion that is also uniform.

7. May 6, 2015

Ken G

Yes, it's a pretty forced analogy, but it can be made to kind of work.

8. May 7, 2015

Drakkith

Staff Emeritus
Does the CMB still work in this analogy?

9. May 7, 2015

Ken G

Only for constant expansion, where there's basically no gravity. The "explosion" picture treats the redshifts as Doppler shifts, which isn't strictly true when there's gravity changing the expansion rate. Maybe there's a way to kind of include it as a Doppler shift effect, but the analogy gets more and more forced. Still, students usually hear about Doppler shifts in other contexts, so it can be used to motivate the CMB redshift. That was Hubble's initial mindset, after all.

10. May 7, 2015

Drakkith

Staff Emeritus
Got it. Thanks, Ken.

11. May 7, 2015

Ken G

It's one of those things where you kind of have to ask yourself if the misconceptions you promote when invoking the explosion analogy are worth the benefits of having something to talk about that is already understood to some degree! Sort of like "the 2D balloon analogy." Pedagogical choices tend to end up being rather subjective, especially in regard to difficult theories like general relativity-- some might tell a high school class the Big Bang is an explosion, but a graduate class in GR would never be told that.