What do people mean when they say “space is flat?”

[BadgerBadger92]

TL;DR Summary

I’ve heard a lot of people that say this

Please excuse my ignorance

I hear some people say that space is flat. What exactly do they mean by this?

 

[PeterDonis]

I hear some people say

Where? Please give a reference.

What exactly do they mean by this?

It's impossible to tell without knowing the context, which means we need a specific reference.

For one thing, since you posted this in the relativity forum, "space" is not the same as "spacetime", and "space" being flat is something different from spacetime being flat.

As a general matter, "flat" when referring to a metric space means that the Riemann curvature tensor derived from the metric is zero.

 

[BadgerBadger92]

Where? Please give a reference.


It's impossible to tell without knowing the context, which means we need a specific reference.

For one thing, since you posted this in the relativity forum, "space" is not the same as "spacetime", and "space" being flat is something different from spacetime being flat.

As a general matter, "flat" when referring to a metric space means that the Riemann curvature tensor derived from the metric is zero.

Well my “source” isn’t reliable, it was Facebook where people were telling me space is flat, which I never heard before so I decided to ask you guys for a clear answer. Luckily I’m starting school at a local community college.

 

[Nugatory]

TL;DR Summary: I’ve heard a lot of people that say this

Please excuse my ignorance

I hear some people say that space is flat. What exactly do they mean by this?

Be aware that “space is flat” and “spacetime is flat” are different things.

But with that caveat, “space is flat” can be understood to mean that space behaves as expected from Euclidean geometry: the Pythagorean theorem works, parallel lines never intersect, the interior angles of triangles add to 180 degrees, all the axioms you learned and all the theorems you proved in high-school geometry class apply.

 

[Hornbein]

It means that if you send out two parallel laser beams through empty space they will stay parallel forever. They won't converge or diverge. Maybe it would have been better to call this straight space.

 

[Ibix]

I hear some people say that space is flat. What exactly do they mean by this?

The problem here is lack of context. Who are those people (professors, students, some random blokes?)and what were they talking about (cosmology, maths, undergrad physics homework?)? And are you sure they said space and not spacetime?

On the assumption that it was a couple of non-technical people talking about pop science, they're probably talking about cosmology. The equations describing the large scale structure of the universe are the Friedman equations. They allow three different types of solution, usually called "closed", "flat" and "open", referring to the geometry of the "obvious" set of spatial slices. Our universe is either flat or a lot bigger than the part we can see, so big we can't detect the curvature of space.

 

[Ibix]

It means that if you send out two parallel laser beams through empty space they will stay parallel forever. They won't converge or diverge. Maybe it would have been better to call this straight space.

Note that this isn't true (at least, not without caveats) in the "space is flat" cosmological solution, because spacetime is not flat (nor empty). This kind of thing is why context is important, @BadgerBadger92.

 

[Vanadium 50]

[quote[What do people mean when they say “space is flat?”[/quote]

When you asked your Facebook friends what they mean, what did they say?

 

[PeterDonis]

my “source” isn’t reliable, it was Facebook

Which, as you admit, is not a good source. And certainly does not provide any kind of useful context.

Given that, we have answered your question as best we can. Thread closed.