jssamp said:
I can't be the only person to ever have this thought so I am hoping one of you star gazers can tell me what I am missing. I understand Hubble's theory and the idea of space itself expanding. My question is this. If we know the universe is expanding because of the redshift and the farther away we look, the more red the spectra are shifted, doesn't that mean in the past, expansion was greater. Since the more distant light sources are older? Where do we conclude that expansion is accelerating because more distant galaxies were moving away faster when their light started towards us. Is it just the accepted conjecture or did I miss something. Seems to me the universe was expanding faster then and is slowing now. TBH I really can't base any conclusion about current expansion based on observations of what happened 10 billion years ago.
The fact that red-shift increases with distance, in of itself, just tells us that the universe is expanding and gives us no clue as to whether that expansion rate has increased or decreased over time.
Let's first look at what we would see in an universe that expands at a constant rate. We'll use an imaginary universe where the expansion constant is 100 km/sec per
light-year. Two stars 1 light year apart will being moving apart at 100 km/sec. If we had three stars, spaced 1 light year apart in a line, star 2 would be moving at 100 km/sec with respect to star 1, star 3 would be moving and 100 km/sec with respect to star 2 and thus star 3 is moving at 200 km/sec with respect to star 1. Every light-year between stars adds another 100 km/sec to the recession speed.
So let's say that we measure a star to be 10 light-years away. we would measure its red-shift to give a velocity of 1000 km/sec. Off course we realize that this info is 10 years out of date. So that means that by at the time we make the measurement, that star is actually further than 10 light-years away. So what it tells us is that when that star was 10 light-years away, it was moving away at 1000 km/sec. In turn, if we see a star 30 light years away and measure its red-shift, and get a recession speed of 3000 km/sec, we know that 30 years ago, that star was 30 light years away and receding at 3000 km/sec. That matches the constant we gave above of 100 km/sec per light year and means that this universe was expanding at the same rate 30 years ago as it was 10 years ago, (or now).
To determine that the expansion rate has changed over time, we need to see a difference in the speed to distance constant as we look at further stars. For example, if we were to measure a 1000 km/sec recession in that 10 light-year star and a 3010km/sec recession in the 30 light-year star, That means that 10 years ago the expansion rate was 100 km/sec per light year, but 30 years ago it was ~100.33 km/sec per light year, and the expansion rate of our universe had slowed during the intervening 20 yrs.
Conversely, if that we measured a 2990 km/sec speed for that 30 light-year star, then we have to conclude that the expansion rate had increased over the 20 yrs.
So basically, if you plot red-shift/recession speed vs distance:
With a constant rate expansion, you get a straight line with red-shift increasing with distance.
With a decreasing expansion rate you get a curve that deviates from that straight line in one direction.
With an increasing expansion rate you get a curve that deviates in the other direction.
In all of these cases, you see an increasing red-shift with increasing distance with an expanding universe, it is how red-shift changes with distance that distinguishes between the three cases. The fact that the universe was expanding was noted in 1929, but it wasn't until 1998 that the measurements that indicated that accelerating nature of this expansion were made.
