If You Traveled Far Enough Through Space, Would You Return to Your Start Point? | Hacker News Reader

If You Traveled Far Enough Through Space, Would You Return to Your Start Point?

forbes.com

51 pointsrising-sky33 comments

In cosmology, there's a parameter called "curvature". If the curvature were slightly less than 1, the topology would be "closed", meaning it would be finite, and traveling in a straight line ends back where you started. This is like the surface of the Earth, but in 3 dimensions instead of 2. Triangle angles add up to greater than 180 degrees. If the curvature were equal to 1, the universe would be "flat", meaning it would be infinite and triangles would add up to 180. If the curvature were greater than 1, it would be "hyperbolic", meaning it would be infinite and triangles would add up to less than 180.

If I recall correctly, currently the best measurement of the curvature is 1 +/- .02, so it's probably flat. What's interesting is if the shape was flat and the universe were truly infinite, there would be an infinite number of perfect copies of Earth, the closest of which would be within 10^10^23 meters, as noted by Max Tegmark (source: http://space.mit.edu/home/tegmark/crazy.html)

> If the curvature were greater than 1, it would be "hyperbolic", meaning it would be infinite

There are periodic (finite-volume, homogeneous) hyperbolic spaces.

Also, I think you can have infinite-volume spaces with positive curvature if they aren't homogeneous.

>Level I: A generic prediction of cosmological inflation is an infinite ergodic universe, which contains Hubble volumes realizing all initial conditions - including an identical copy of you about 10^10^29 meters away.

Why copies? By sheer probability or some other mechanism. It indeed is crazy.

Is it possible that is the nature of the universe?

Why would an infinite universe necessarily contain infinite matter?

Think about a torus-chess-board [0]. While it is locally flat, it is finite, unbounded and you would travel back where you started. Curvature cannot give a sound argument as to whether the universe is finite or infinite.

[0] https://en.wikipedia.org/wiki/Cylinder_chess#Horizontal_Cyli...

Or the more relevant link might be https://en.wikipedia.org/wiki/Torus#Flat_torus

The better term related to curvature would be if it's bounded or unbounded.

Curvature is ofcourse the way we could time travel. Because the light of events would end up at the same place years later. And travelig faster than light would mean we could see events that will happen in the future ;)

It's also possible to have a flat universe (no curvature), where a straight line can return to the same point. An example is a torus (donut shape). You can see this by noticing that a torus can be projected onto a flat sheet (or created from one) without messing with any relative scales or angles, while the surface of a sphere cannot. (For a sphere, you need Mercator or some other projection which does not conserve an honest representation of relative sizes - e.g. Greenland vs. Africa in Mercator.)

Assuming you are in the Star Trek teleporter camp, which believes that your consciousness continues if you get destroyed somewhere and recreated somewhere else, then if the universe is infinite your consciousness might continue forever.

If the universe is infinite, with infinite matter in all possible configurations, then if you happened to be disintegrated one day, your perfect copy is already waiting for you somewhere out there.

Who knows, maybe you already died a bunch of times, but picked up somewhere else, never noticing that you left. You could still witness others dying of course. Nothing would seem out of the ordinary.

Even the surroundings of your new location in the universe would be the same as accurately as you are able to tell. Information about the planets of the solar system is part of your brain – the new location must also have those planets, otherwise you would not be identical.

> If the curvature were slightly less than 1, the topology would be "closed", meaning it would be finite, and traveling in a straight line ends back where you started.

Doesn't this require the assumption that the spacetime is embedded in a higher dimensional spacetime?

It's been a while, but IIRC there are perfectly valid topologically open cosmologies that have locally sphere-like curvatures (in other words, there's no necessary connection between curvature and topology without adding an embeddability constraint), right?

Per Brock et al, 2000, yes: the universe is shaped exactly like the Earth. If you go straight long enough, you'll end up where you were.

Do you have a link? I cannot find your reference.

https://www.youtube.com/watch?v=yGxSExvJ2L0

"The Universe is shaped exactly like the Earth, if you go straight long enough, you'll end up where you were."

Isaac Brock is the lead singer of Modest Mouse.

No.

If you could there would be a few galaxies which would be about equidistant from us along both paths. Therefore we would notice a few double copies of the same galaxies. It would be similar to standing in the middle of two mirrors. IIRC scientists have already ruled out a universe with a "radius" less than some ridiculous number (like billions of light years).

There. Just saved you a click. This is old and well know. Why is Forbes writing about it now?

>Why is Forbes writing about it now?

The general public doesn't know this, it's a very slow news week, or both.

In the case of things like this, it's as much because people have erroneous ideas left over from outdated science journalism, as it is from people just not having any information or inclination to care. (Sherlock Holmes's reaction to the information that the Earth goes around the sun.)

> Why is Forbes writing about it now?

My totally random guess is the reason why theyre writing about it now is that it might be part of PR for the First Man movie about Neil Armstrong being the first man on the moon.

Nope. Our visible universe is bounded by the expansion of space that happens at the speed of light. That means we can only see a subset of the universe at any time.

But if you travel at less than the speed of light you'd never pass that anyway

Because of expansion we'll likely never be able to travel to any of the galaxies in the universe except our local neighborhood. But it's still worth studying those galaxies from a distance to learn more about our universe.

If you traveled at the speed of light, you'd still never make it to the edge of the universe. The edge of the observable universe is moving away from us faster than the speed of light. [1]

[1] https://en.wikipedia.org/wiki/Observable_universe

So a beam of light with a head start, half-way across the universe from you, could "wrap around" and eventually reach you. But the beam of light couldn't "wrap around" and reach itself, because the universe constantly moves the goal post before light beam gets the chance?

Yes. The fact is that does it not prove or disprove the fact that our universe is wrapped around - it may be either way. The parent's point is invalid because we wouldn't be able to see the wrapped around light even if it existed.

Not only that, due to expansion, the subset is getting smaller by the second!

Expansion is not limited to the speed of light. Two points in space may be 'moving apart' faster than the speed of light because they're not moving, space is being created in-between. The more space there is in between, the faster the rate of expansion between the points.

I am not saying expansion of the universe is limited to the speed of light. I am saying the boundary of the observable universe is defined at the points where the expansion of space reaches the speed of light.

Believe it or not, everyone doesn’t know everything that everyone else knows.

> Why is Forbes writing about it now?

Why not? Look who the author is: Ethan Siegel. He has a blog (https://medium.com/starts-with-a-bang) and a podcast (https://soundcloud.com/ethan-siegel-172073460).

He basically does a Dear Abby type column based on astronomy and physics topics. He takes difficult concepts and tries to break them down into something the lay person can understand.

Quite frankly, I think he's pretty damn good at it and we should be happy Forbes is publishing his stuff for a wider audience.

Can you explain how one implies the other?

> scientists have already ruled out a universe with a "radius" less than some ridiculous number (like billions of light years)

How is billions of light years a ridiculous number? Even the observable universe is bigger than that, so the full universe could be many many times bigger.

Since you can't see past the observable universe you wouldn't be able to see the double copies.

We know from analysis of the cosmic background radiation, that the universe is at least 150 times the size of the observable universe, which puts the minimum diameter of actual universe in the range of 10 to 15 trillion light years. It could be much larger than that, however.

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