The Naked Scientists

The Naked Scientists Forum

Author Topic: What is the meaning of "Spacetime Curvature"?  (Read 11881 times)

Offline Pmb

  • Neilep Level Member
  • ******
  • Posts: 1838
  • Physicist
    • View Profile
    • New England Science Constortium
Re: What is the meaning of "Spacetime Curvature"?
« Reply #50 on: 19/07/2013 16:45:47 »
Not you, it's me thinking about uniform motion, accelerations, and geodesics. I started to think about tidal forces, and wondering what it would mean if one used some particle, defined to to not be 'breakable' into smaller parts, passing a event horizon.
=

To me that 'test particle' should be in a geodesic at all times? And that matter break up under tidal forces being a measure of its particles finding new geodesics, as they get acted on by gravity, and acts. Maybe one also could see it as a question if gravity could be seen as a 'force' here?
I'm curioius yor_on. What do you think tidal forces are and how do they relate to spacetime curvature?

Request - Next time please append additional posts to your last post if nobody has posted since.
 

Offline yor_on

  • Naked Science Forum GOD!
  • *******
  • Posts: 11993
  • Thanked: 4 times
  • (Ah, yes:) *a table is always good to hide under*
    • View Profile
Re: What is the meaning of "Spacetime Curvature"?
« Reply #51 on: 20/07/2013 20:00:18 »
= quote=

"If you take a cylinder and then fold it out you get a 'plane' (a flat rectangular piece). So drawing a triangle on the outside would give you a same triangle when folded back, measuring by the triangles interior angles. That's called a extrinsic type of curvature."

That is wrong. The surface of the cylinder has zero intrinsic curvature for just the reasons you state.

== End of quote


So when they write.

"Gaussian curvature is however in fact an intrinsic property of the surface, meaning it does not depend on the particular embedding of the surface; intuitively, this means that ants living on the surface could determine the Gaussian curvature. For example, an ant living on a sphere could measure the sum of the interior angles of a triangle and determine that it was greater than 180 degrees, implying that the space it inhabited had positive curvature.

On the other hand, an ant living on a cylinder would not detect any such departure from Euclidean geometry; in particular the ant could not detect that the two surfaces have different mean curvatures (see below), which is a purely extrinsic type of curvature."

You read this is a expression describing a two dimensional surface, right? It is a tricky subject, and one I haven't used myself.

(As for 'Euclidean geometry' I was referring to the type we used, and still use in school, before we get into SpaceTime and modern physics, topology, etc, suspecting that was how Euclid thought of it too?)
==

You know, rereading it it becomes even weirder. If we take the cylinder and assume it to describe some universe it seems to state that you can have a universe shaped as a cylinder and find it to be the same shape as when 'flattened out' measuring intrinsically. And then you say, if I got you right? That this only can be true in two dimensions. So what would I find, practically, measuring the same in three?

It also assumes 'ideal surfaces' it seems? How would I be able to be to measure anything, if I was part of that 'ideal surface'? To assume a 'ant' is either to introduce a third dimension, or mixing this subject with scales. But it's not about scales at all, well, as I read it? To me it's pure mathematical concepts?

Hopefully you will have a analogue, without the mathematics, that makes sense. Because practically, and as I think, we're part of the dimensions we measure, so when we find 'space' to 'bend' we should be 'bending' too, as a integral part of  those 'dimensions'?
« Last Edit: 20/07/2013 20:41:15 by yor_on »
 

Offline yor_on

  • Naked Science Forum GOD!
  • *******
  • Posts: 11993
  • Thanked: 4 times
  • (Ah, yes:) *a table is always good to hide under*
    • View Profile
Re: What is the meaning of "Spacetime Curvature"?
« Reply #52 on: 20/07/2013 20:10:35 »
Why not answer the question Pete?
It can't be that strange?

If a 'undividable test particle' meets tidal forces, will it continuously be in a geodesic?
As for how I think of tidal forces, it's gravity, what else would it be?
=

As for relating it to a SpaceTime curvature, I better admit that I think it is 'space' myself :)
How would you define a 'ball shaped' universe as one proposition? Think Einstein used it himself to describe something having a 'straight path', still finding it ending at the origin?
« Last Edit: 20/07/2013 20:22:34 by yor_on »
 

Offline Pmb

  • Neilep Level Member
  • ******
  • Posts: 1838
  • Physicist
    • View Profile
    • New England Science Constortium
Re: What is the meaning of "Spacetime Curvature"?
« Reply #53 on: 20/07/2013 20:41:03 »
Quote from: yor_on
Why not answer the question Pete?
Which question are you referring to? I didn't realize that you asked me a question that I left unanswered. As I keep saying your posts are very confusing to me. You keep spreading them out over multiple posts and that makes things difficult for everyone here, not just me. And you know that since it's been pointed out to you on more than one occasion yet you still keep doing it.

My question to you is why not make your posts easier to understand and don't spread them out over multiple contiguous posts?
It can't be that strange?

Quote from: yor_on
If a 'undividable test particle' meets tidal forces, will it continuously be in a geodesic?
Only if it has no spin.

Quote from: yor_on
As for how I think of tidal forces, it's gravity, what else would it be?
I don't know. Some of the things I think are obvious turn out to be very different from what they really are with some people. I just want to be 100% correct that we're on the same page on this one point. Do you not wish to answer it? If not then why didn't you answer it?

Quote from: yor_on
As for relating it to a SpaceTime curvature, I better admit that I think it is 'space' myself :)
I'm trying to determine precisely what your understanding of general relativity are. If you're not going to answer the questions I ask then please state so now so that I won't waste my time asking questions that won't be answered.

The questions I answered have very straight forward responses. They're very simple to answer if you have a solid understanding of GR. Until you answer the questions I've already asked then I'm going to consider my discussion about curved spacetime with you as being over.
 

Offline yor_on

  • Naked Science Forum GOD!
  • *******
  • Posts: 11993
  • Thanked: 4 times
  • (Ah, yes:) *a table is always good to hide under*
    • View Profile
Re: What is the meaning of "Spacetime Curvature"?
« Reply #54 on: 20/07/2013 20:44:02 »
You're free to do so Pete.
 

Offline Pmb

  • Neilep Level Member
  • ******
  • Posts: 1838
  • Physicist
    • View Profile
    • New England Science Constortium
Re: What is the meaning of "Spacetime Curvature"?
« Reply #55 on: 20/07/2013 20:47:45 »
You're free to do so Pete.
As are you.

It might seem as if I'm intentionally being hard to get along with but that's not quite right. You asked me why I didn't answer your question. The reason is that the way you post and spread it all out over multiple posts is so confusing that it's hard to follow. I've explained that to you on more than one occasion so this isn't new to you. You not only didn't make any changes to your posting style to be clearer but you made no attempt to explain why you can't do so. So don't be surprised if I choose not to respond to your questions. Especially when you make no attempt to answer my questions. Nope. That's not how the world works my friend.
« Last Edit: 21/07/2013 00:51:13 by Pmb »
 

The Naked Scientists Forum

Re: What is the meaning of "Spacetime Curvature"?
« Reply #55 on: 20/07/2013 20:47:45 »

 

SMF 2.0.10 | SMF © 2015, Simple Machines
SMFAds for Free Forums
 
Login
Login with username, password and session length