The Infinite Sea (WIP)
This is a work in progress.
The Infinite Sea is novel model for teaching cosmology. Despite its simplicity, it represents the real universe with richness.
Curriculum notes:
We offer the following metaphors-
Infinite Sea : the Universe.
It's the same everywhere, looks the same in every direction. Homogeneity and isotropy of space
It is Sparse
boat : galaxy
flotilla : galaxy cluster
the sea expanding : cosmological expansion
the expansion happens at the "water drop" level.
a field suppressing expansion : this is Gravity, though not the everyday attractive gravity. This is an effect of gravity predicted by General Relativity: Expansion of space only happens in "flat" space not curved by mass & energy. We introduce this characteristic of gravity *first*, intentionally inverting the everyday precedence.
flotilla stays together, not via being roped together. but because the sea around it literally does not engage in expansion.
different measurement of expansion : the hubble tension
common zero-velocity rest frame - CMB rest frame.
Other boats are adrift also - expansion is not via propulsion, but by being carried by the expansion of the sea itself
Peculiar velocity vs recession velocity
To come:
given an expansion rate, our protagonist will attempt to calculate the age of their universe, but will quickly be confronted with a problem. a purely geometric expansion simply goes back infinitely in time, getting ever tinier and tinier. Modern cosmology hit this issue also, resulting in theories of inflation, expansion etc.
Liberties taken - while these do "break physics" in the every day sense, it is service of the overall storytelling, and they do not harm the essential concepts of the model.
instant communication - breaks FTL. Language, common agreement on units, etc.
magically can measure expansion of water, distance to other boats
no treatment or recognition of "mundane" gravity, pulling one down.
You are at sea. It goes on forever as best you can tell, in every direction. Welcome to the infinite sea.
Your boat floats for a long, long time. The sea looks the same everywhere. No start, no end, no middle. There isn’t a saltier region, nor warmer or colder spots . If you wanted to meet a friend out in the sea, you wouldn’t know how to give directions.
Not that you’re alone.
You see other boats dotting the sea. Some near, some far. Watching carefully over time, you notice they’re all moving away from you. But strangely, their sails aren’t full - they aren’t moving away by any propulsion. They are just as stationary in their local water as you are in yours. The sea itself seems to grow, everywhere, spreading all the boats apart.
You closely study the water and learn: The water itself grows. You measure that it expands about 10% each day.
A boat with red sails is 2 km from you. In a week it’s 4 km. Its speed averaged about 2km/7 days. You spy a boat 15km away; 7 days later it is 30km away; it covered 15 km in 7 days.
The farther away, the faster it’s moving from you - because there’s more water between you to expand. But you are stationary. You intuit that the other boats also might feel that they are stationary, and central. You can’t see any particular winds pushing them - they appear as adrift as you.
Did i mention your flotilla? You have company. Not only do distant boats dot your view, you have close neighbors. These boats float along near you, close enough you can make out their rigging styles.
You study the water again. You’re perplexed. You know that all water expands, carrying everything apart. But your flotilla is not stretching apart. The water between you and the closest boats is not expanding! Why not? You make a new discovery: Water won’t expand near boats. The growth only happens where there are no boats around. It’s like the water is skittish, and only grown where it is calm and far from your activity. Maybe boats give off an anti-expansion-field or something. By careful measure, you find the suppression is greater - expansion rate is least - close to your flotilla. Looking far in the distance, you discern that the sea expands most in the spots farthest from any boats.
You decide to check out that catamaran in your flotilla. You fire up the outboard and motor toward them. You notice the rush of water along your hull. Hmm. You contemplate - i observed motion between me and distant objects before. But it didn’t feel like i was moving. But now i can tell i’m moving relative to the sea - it’s flowing past. We’ll call that my “peculiar velocity”. You observe distant flotillas more carefully, and now see them shuffling amongst each other - they have peculiar velocities relative to each other like your flotilla, which combines with their ‘expansion velocity’.
You might not be able to tell a friend how to find you in this infinite sea. It has no absolute frame of reference - for locations, but you realize, there is a common frame of reference for velocity. We could all agree on whether we were moving or at rest relative to the sea. We could also state in absolute terms how fast we’re moving relative to the sea.
Provided the sea is the same everywhere. We sure hope it is, because if the sea’s rest frame isn’t the same everywhere, then we’re going to have an extra hard time putting this all together.
If everything is drifting apart now, then in the past it was closer. The farther back in the past, the closer it must have been. If the expansion rate has always been the same, then can we calculate when this sea began?
Perhaps we can solve for when we and the red boat were in the same place. It’s 2km away today.
How many days ago was it zero?
2km / 1.1^T = 0
hmm.
this doesn’t work.
All we get is everything in the sea getting closer and closer, going back infinitely in time.
Clearly, if this sea had a beginning, then some other mechanisms got us to where we are now, aside from what we currently observe.
Mysterious.
Your radio crackles… “hello out there. Anyone listening?”
You answer “Hello! I’m here. I’m in a boat on an ocean”
“Me too.”
“Which boat are you?”
“I’m the one with the rooster weather vane on my mast” they say.
You scan all around you.
“I don’t see you. You must be far away. Where are you?”
Alien:“… um, compared to what?. It feels like I’m just right in the middle”
“Me too. It looks the same in every direction.”