/sci/ - Science & Math

>>9321992
It doesnt. Only things in space curve.
It also doesn't curve into anything. There is no need for higher dimensions.

>>9321992
It doesn't really curve into anything, its geometry is reciprocative to the local fields

>>9322010
How do you explain the orbital discrepancy of mercury then?

>>9321992
curvature is an intrinsic property. a manifold doesn't curve "into" something. it (its riemannian metric) -is- curved.

>>9322010
shut up honestly

>>9321992
intredesting

is it spacetime or space that curve. there's light bending implying that something curves but how can you tell which is curving. gonna ask my prof thanks brodie

>>9322044
but how, how can something be called curved if you aren't comparing it to something that isn't curved? what's the reference? what is curvature?

>>9321992
Some people think it curves into the time dimension.

>>9322074
>what is curvature?
that's the important question. it's not very easy to define, you need some understanding of differential geometry, and then you can read any book on Riemannian Geometry (e.g. do carmo) to understand it properly.

that said, the idea is closely related to this result: https://en.wikipedia.org/wiki/Theorema_Egregium.. curvature can be defined and calculated just by measuring angles and distances on a surface, which does not depend on the space where the surface is embedded (or if it's embedded in anything at all)

>>9322081
no one thinks that, fuck off idiot

>>9322086
Suck a cock, Fuckhead. ;)

>>9322086
>>9322087
ebin :^)

>>9322084
Yes, and we can draw hills and mountains with topological maps on a flat surface, so there's no reason to think they really have height.

>>9322097
what do you mean? homeomorphisms don't preserve curvature, you need an isometry to do that. e.g. a sphere is locally homeomorphic (diffeomorphic even) to R^2, which is flat, but a sphere is not flat.

>>9321992
I think of space as having a varying refractive index.

>>9322106
I think >>9322097 meant topographic maps.

is spacetime embedded in a bigger manifold

>>9321992
You're confusing "intrinsic" and "extrinsic" curvature.
A section of a sphere is curved.
A flat sheet of paper isn't, even if you curl it into a cylinder and tape the ends together.
The difference is whether the inhabitants of the space (or paper sheet) find the triangles they draw always have vertices adding to 180 degrees.

Your triangles don't have to be solid. A beam of light reflected from a mirror to a second mirror and then back to the source will do. Do the experiment on Earth and the deviation from 180 is too small to measure.
Do it near the Sun and the angles are a little off.
Do it near a black hole or neutron star and the error is substantial!

>>9322091
I wonder if that kid ever did manage to berry that dick.
Must be fucking old by now.

>>9323772
But doesnt that just mean triangle dont have to sum up 180? That seems less insane than curving space.

>>9324976
the 'straight lines' between the corners are 'curved' as a result of (or resulting in) angles not summing to 180

You could also ask "why is space non-curved?"
You make assumptions

>>9325046
Because space is a backdrop for fields to extend into

>>9325055
what does that even mean?

>>9322017
please do elaborate, this is an area I have expertise in and I have no idea what you're talking about
inert pair effect?
lanthanide contraction?
why mercury is liquid in room temp?

>>9325064
I think Anon means Mercury, the planet, not mercury, the metal.

>>9325064

>>9321992
don't worry lol it's just some random metric lmao it's only math dude xD
>mfw I actually aswered that in a midterm
>needless to say got 0 points in that question and teacher was a bit pissed off.

>>9325064
>this is an area I have expertise in and I have no idea what you're talking about
What?
Mercury goes around the sun so fast that we couldn't accurately describe it's orbit until Einstein and relativity.

>>9321992
>what can it curve into?
One or several higher spatial dimension. It's very easy, take a string (1 dimensional object). You can have it straight (no curvature) so it only expands in one dimension. But you can also knot it an than it is curved when you look at it in 3D space. Some being that is trapped inside the string/tube still only has 1 spatial dimension, it can only backward or forward.

>>9321992
It doesn't curve, our perception if it curves. Fantasy points don't move, just the pieces.

>>9322044
literally the only correct answer in the thread, right down to the shut the fuck up

>>9326509
>>9326512
SHUT THE FUCK UP

>>9321992
> curves into time
lol, terribly vague

Is one dimension of time possible?

In this thread... people with advanced knowledge of math and physics demonstrate social and emotional retardation and personality disorders.

You know in your heart these guys aren't going to reproduce...

>>9327121
>he didnt put all his stats into INT and WIS
yeah okay brainlet

>>9327121
>can't understand simplest concepts of differential geometry
>b..b..but at least I am going to reproduce! Yeah!
You sure showed us.

>>9326509
Stop. Anyone who hasn't studied differential geometry, please just stop because you're not gonna get it right. I mean it.

It curves around widomakers FAT ASS

>>9325227
lol

>>9322074
You don't need a ruler at the ready to know that a fucking baseball's surface isn't the same

>>9321992
With enough energy concentrated into an area it can form what we NOW know as a black hole.

>>9323772
>You're confusing "intrinsic" and "extrinsic" curvature.
Not op but pls elaborate, this seems interesting.
How is a cylinder different to a sphere besides the fact that the circle is curved in all directions while the cylinder also has one straight dimension?

>>9323772
>a flat sheet of paper once curved does not have a curve
This is retarded, I think you need to reexamine basic logic. By YOUR logic a sphere that is unfolded and made flat, would still be curved and not flat. This makes no sense, as does your paper example. Like, this is basic geometry dude.

>>9328231
Ever tried flattening a sphere then? It won't work unless you start cutting something somewhere.