What is the meaning of "Spacetime Curvature"?

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Offline Pmb

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What is the meaning of "Spacetime Curvature"?
« on: 04/07/2013 01:42:11 »
I'm curious as to what the average Joe thinks when he hears the term spacetime curvture. What did think when you heard of it the first time. By this I mean what did the concept bring to mind when you first learned about it? If you've studied it for some time now then what do you think it means now as compared to when you first started learning it?

My impression is that many people believe that spacetime curvature refers to the curving of a worldline in spacetime caused by a gravitational field. Am I close? I, of course, know what it means. I just want to know if people have the right idea about it. It seems to me that when people think of spacetime curvature and the phrase gravity is a curvature in spacetime that they think that the gravitational field we all know and love and have grown up in and live with all of our lives are the same thing.

What do you think? And than you for your thoughts in advance. :)
« Last Edit: 04/07/2013 22:50:37 by chris »

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Offline galaxysim

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Re: The Meaning of "Spacetime Curvature"
« Reply #1 on: 04/07/2013 02:09:01 »
from my experience on other forums....and my oft quoted phrase 'cant count or wont count ? '  im pretty sure the 90% and perhaps 95%+ of the populace suffer brain implosion the moment things go beyond their tangible experience


You have to have what i call the maths gene AND an ability to carry out thought experiments AND a good instinct for self checking your progress.

Most lay peoples knowledge comes from opinion, rather than an internal matchstick pyramid of knowledge that they have painstakingly built from the ground up....this is why 'does not compute' is a common theme. Its very easy to get confused if you don't have the guardrails of science based education.

The mindset required to 'get laid and paid' is of a very different architecture to that of the scientific method. Thus if your new to science it can take some time to wrap your head around what might be a relatively straight forward scientific concept...this is of course frustrating for all parties in the discussion....people are impatient and the human mind tends to over simplify in when facing complexity.

A long winded reply to your OP

I think very few peoples understanding of Spacetime Curvature goes beyond ye olde cannon ball and rubber mat
http://en.wikipedia.org/wiki/Spacetime

 Joe Average meets the train in a tunnel paradox....paradox wins every time.



@Pmb says your a physicist ? curious what field ? casual or pro

....Mine is AI and general science Astronomy to zoology






« Last Edit: 04/07/2013 02:29:35 by galaxysim »

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Offline Pmb

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Re: The Meaning of "Spacetime Curvature"
« Reply #2 on: 04/07/2013 20:57:32 »
Quote from: galaxysim
A long winded reply to your OP

I think very few peoples understanding of Spacetime Curvature goes beyond ye olde cannon ball and rubber mat
http://en.wikipedia.org/wiki/Spacetime
That doesnít tell me what they think it is though. For example; take a look at the uniform gravitational field inside a spherical cavity that was hollowed out from a spherical homogenous distribution of matter. The center of the cavity is offset from the center of the sphere.

http://home.comcast.net/~peter.m.brown/gr/grav_cavity.htm

Is the spacetime associated with the gravitational field inside the cavity curved? Hint: The field inside the cavity is uniform, i.e. the tidal force tensor is zero. If you donít know what that tensor is then please see

http://home.comcast.net/~peter.m.brown/mech/tidal_force_tensor.htm

Quote from: lean bean
Is this leading up to affine connections?
Not really but thanks for asking. Iím not sure whether the connection coefficients are geometric objects or not.

Quote from: lean bean
I was surprised to read Edwin Taylor say of John wheeler non-use of tensors.
Yeah. I know that about Edwin. I can never talk to him about anything to do with tensors. I think that after a while he developed a phobia about them. The same thing happened to me with the multiplication table. Lol!

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Offline yor_on

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Re: The Meaning of "Spacetime Curvature"
« Reply #3 on: 04/07/2013 21:05:54 »
The way matter moves seems to be the best answer there, but it also connects to what you define as a universe, and its dimensions. As for a space without gravity? Can you get both? Defining it as the way matter moves, and also draw 'boundaries', as a ball shaped 'universe'. What defines that 'ball', a 'flat space'? The universe we have seem to 'stretch out', but if we use the 'ball' as our referee, the first thing to question should be. What defines that 'ball'? mass-'energy'? Matter? Gravity? Depending on choice, as for example me expecting gravity being the metric defining a 'shape', one then have to define what this stretched out universe is defined by, gravity too? If that is so, what is a 'flat space'?
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Re: The Meaning of "Spacetime Curvature"
« Reply #4 on: 04/07/2013 21:11:40 »
You didn't answer my question. There are only three possible responses to my question

Is the spacetime corresponding to the gravitationa field inside the cavity curved?

(1) Yes
(2) No
(3) I don't know

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Offline yor_on

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Re: The Meaning of "Spacetime Curvature"
« Reply #5 on: 04/07/2013 21:23:43 »
How about a fifth?
5. it depends on the distribution of matter, and also from 'where' you define it, as well as what scale you use :)

You make hard questions Pete. You yourself has pointed out that you can transform away gravity, by 'free falling'. That's why I haven't found any better approximation for it than a 'preferred direction'. But 'free falling' and a 'flat space' is still questions unanswered to me, wondering what defines a universe. If gravity defines a shape, and have a infinite reach, then it shouldn't matter what 'shape' we define a universe to, should it? And whatever is meant by a 'flat space' it still must contain that metric, as I think for now, to exist.
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Offline yor_on

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Re: The Meaning of "Spacetime Curvature"
« Reply #6 on: 04/07/2013 21:47:51 »
Ahh sorry, I was still stuck on your first there.  The Meaning of "Spacetime Curvature"  . As for the later, I would assume the space to be 'flat' and so 'non curved', but still containing a gravitational metric. And no, I don't think a space need to be curved as long as we have matter defining gravity. But it seems that some define a 'flat space' as something not using the metric of gravity? And that one is weird to me.
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Offline Pmb

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Re: The Meaning of "Spacetime Curvature"
« Reply #7 on: 04/07/2013 22:33:09 »
Ahh sorry, I was still stuck on your first there.  The Meaning of "Spacetime Curvature"  . As for the later, I would assume the space to be 'flat' and so 'non curved', but still containing a gravitational metric. And no, I don't think a space need to be curved as long as we have matter defining gravity. But it seems that some define a 'flat space' as something not using the metric of gravity? And that one is weird to me.
Do you understand that spacetime curvature is merely a fancy name for tidal force?

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Offline Bill S

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #8 on: 04/07/2013 23:16:23 »
Quote
Do you understand that spacetime curvature is merely a fancy name for tidal force?

No;  but I would like to!

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Offline Pmb

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #9 on: 04/07/2013 23:30:55 »
Quote from: Bill S
No;  but I would like to!
Okay. It will help me if I knew where you are with math, Newtonian mechanics, gravity, tensors etc. I.e. can you follow these two pages
http://home.comcast.net/~peter.m.brown/mech/tidal_force_tensor.htm
http://home.comcast.net/~peter.m.brown/gr/geodesic_deviation.htm

See if you can find the subject in Taylor and Wheeler's new version of Exploring Black Holes at http://exploringblackholes.com/
« Last Edit: 04/07/2013 23:33:52 by Pmb »

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #10 on: 05/07/2013 00:04:08 »
Quote from: galaxysim
I think very few peoples understanding of Spacetime Curvature goes beyond ye olde cannon ball and rubber mat
http://en.wikipedia.org/wiki/Spacetime
Strangely enough those diagrams are really embedding diagrams and weren't supposed to represent spacetime curvature unfortunately it didn't work out that way.

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #11 on: 05/07/2013 11:00:23 »
Sure. everything defining a direction is 'gravity' Pete, and it's no 'force' either, as I get it. And all this about gravitomagnetic forces is just confusing to me, it splits gravity into two parts as I get it. One part of it being some 'component' making you anchored to earth (analogue to electricity) the other treating tidal forces (magnetic part), suggesting you can see it as some sort of electromagnetism. You can't have it as a force, as far as I see it's just a preferred direction. And we're all following geodesics. A force is what intrudes on a geodesic in this case, breaking it.
=

Who 'invented' gravitomagnetism btw? I just can't make me believe it was Einstein that created that slogan, someone clever did it, and it has caught on, but it don't fit Einsteins thoughts, to me that is.
« Last Edit: 05/07/2013 11:07:06 by yor_on »
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Re: What is the meaning of "Spacetime Curvature"?
« Reply #12 on: 05/07/2013 11:25:36 »
Ahh, think I found him?

http://en.wikipedia.org/wiki/Gravitoelectromagnetism

"The analogy and equations differing only by some small factors were first published in 1893, before general relativity, by Oliver Heaviside as a separate theory expanding Newton's law."

http://en.wikipedia.org/wiki/Oliver_Heaviside

On the other hand, this was before GR, so some must have reused it, banking into skulls using equations for electromagnetism, as presumed of a idea of all 'forces' coming from one origin, at some temperature for example (regime / symmetry breaks). If fits a Higg explanation, possibly? But I still don't see it fit Einsteins GR?
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Re: What is the meaning of "Spacetime Curvature"?
« Reply #13 on: 05/07/2013 18:15:27 »
Sure. everything defining a direction is 'gravity' Pete, and it's no 'force' either, as I get it.
Not according to Einstein. GR states gravity is an inertial force rather than a 4-force like the Lorentz force.

For more on inertial forces and how some physicists percieve them as being "real" please see the web page I created on this subject at
http://home.comcast.net/~peter.m.brown/gr/inertial_force.htm0

For example please see the quote on that page from Introducing Einstein's Relativity, by Ray D'Inverno, Oxord/Clarendon Press, (1992) page 122
Quote
Notice that all inertial forces have the mass as a constant of proportionality in them. The status of inertial forces is again a controversial one. One school of thought describes them as apparent or fictitious which arise in non-inertial frames of reference (and which can be eliminated mathematically by putting the terms back on the right hand side). We shall adopt the attitude that if you judge them by their effects then they are very real forces. [Author gives examples]
Other quotes are like that.

Here's what Einstein said about this point

From an article in the February 17, 1921 issue of Nature by Albert Einstein
Quote
Can gravitation and inertia be identical? This question leads directly to the General Theory of Relativity. Is it not possible for me to regard the earth as free from rotation, if I conceive of the centrifugal force, which acts on all bodies at rest relatively to the earth, as being a "real" gravitational field of gravitation, or part of such a field? If this idea can be carried out, then we shall have proved in very truth the identity of gravitation and inertia. For the same property which is regarded as inertia from the point of view of a system not taking part of the rotation can be interpreted as gravitation when considered with respect to a system that shares this rotation. According to Newton, this interpretation is impossible, because in Newton's theory there is no "real" field of the "Coriolis-field" type. But perhaps Newton's law of field could be replaced by another that fits in with the field which holds with respect to a "rotating" system of co-ordinates? My conviction of the identity of inertial and gravitational mass aroused within me the feeling of absolute confidence in the correctness of this interpretation.



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Re: What is the meaning of "Spacetime Curvature"?
« Reply #14 on: 05/07/2013 18:17:17 »
Sure. everything defining a direction is 'gravity' Pete, and it's no 'force' either, as I get it.
Everything? The electric field defines a direction. Are you saying that the electric field is a gravitational field?

Anyway, not according to Einstein (and me) it's not. GR states gravity is an inertial force rather than a 4-force like the Lorentz force.

For more on inertial forces and how some physicists percieve them as being "real" please see the web page I created on this subject at
http://home.comcast.net/~peter.m.brown/gr/inertial_force.htm

For example please see the quote on that page from Introducing Einstein's Relativity, by Ray D'Inverno, Oxord/Clarendon Press, (1992) page 122
Quote
Notice that all inertial forces have the mass as a constant of proportionality in them. The status of inertial forces is again a controversial one. One school of thought describes them as apparent or fictitious which arise in non-inertial frames of reference (and which can be eliminated mathematically by putting the terms back on the right hand side). We shall adopt the attitude that if you judge them by their effects then they are very real forces. [Author gives examples]
Other quotes are like that.

Here's what Einstein said about this point

From an article in the February 17, 1921 issue of Nature by Albert Einstein
Quote
Can gravitation and inertia be identical? This question leads directly to the General Theory of Relativity. Is it not possible for me to regard the earth as free from rotation, if I conceive of the centrifugal force, which acts on all bodies at rest relatively to the earth, as being a "real" gravitational field of gravitation, or part of such a field? If this idea can be carried out, then we shall have proved in very truth the identity of gravitation and inertia. For the same property which is regarded as inertia from the point of view of a system not taking part of the rotation can be interpreted as gravitation when considered with respect to a system that shares this rotation. According to Newton, this interpretation is impossible, because in Newton's theory there is no "real" field of the "Coriolis-field" type. But perhaps Newton's law of field could be replaced by another that fits in with the field which holds with respect to a "rotating" system of co-ordinates? My conviction of the identity of inertial and gravitational mass aroused within me the feeling of absolute confidence in the correctness of this interpretation.


« Last Edit: 05/07/2013 19:35:56 by Pmb »

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Offline niebieskieucho

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #15 on: 06/07/2013 00:18:14 »
I'm curious as to what the average Joe thinks when he hears the term spacetime curvture. What did think when you heard of it the first time. By this I mean what did the concept bring to mind when you first learned about it? If you've studied it for some time now then what do you think it means now as compared to when you first started learning it?
It's a double rubbish. Spacetime is a sick idea. It's just space that has nothing to do with time (of what BTW?), as time spontaneously does not exist. As to the second rubbish, i.e. alleged curvature of space, it's simply impossible. Space does not undergo deflection, is indestructible, does not expand, is of the same volume as it was before origin of matter.
Quote
My impression is that many people believe that spacetime curvature refers to the curving of a worldline in spacetime caused by a gravitational field. Am I close? I, of course, know what it means. I just want to know if people have the right idea about it. It seems to me that when people think of spacetime curvature and the phrase gravity is a curvature in spacetime that they think that the gravitational field we all know and love and have grown up in and live with all of our lives are the same thing.

What do you think? And than you for your thoughts in advance. :)
The only curvature of space I can accept is due to spherical shape of the (finite) universe. But this is its natural shape.
Those who claim that understood Relativity, automatically claim that understood nonsense

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #16 on: 06/07/2013 00:54:51 »
Quote from: niebieskieucho
It's a double rubbish. Spacetime is a sick idea. It's just space that has nothing to do with time (of what BTW?), as time spontaneously does not exist.
From these comments its clear that you donít know what spacetime is. Please learn about these things before you make another attempt at commenting on them. I.e. please study what spacetime is. I created the following for this purpose
http://home.comcast.net/~peter.m.brown/sr/spacetime.htm

Whether spacetime is curved or not is not up for debate. Itís an observable fact. Itís a measurable phenomena. But until you learn what it really is as opposed to what you think it is (which youíve proven that what you think it is is wrong) you wonít be able to understand that very simple fact. If you had chosen to first learn about the subject that youíre criticizing then you wouldnít have made these mistakes. I showed you where to read about it online. Please do so before you make another attempt to argue that itís wrong.

Quote from: niebieskieucho
As to the second rubbish, i.e. alleged curvature of space, it's simply impossible. Space does not undergo deflection, is indestructible, does not expand, is of the same volume as it was before origin of matter.
These comments also tell me that you donít know what space curvature is. You incorrectly assumed that it meant that space is deflected. It doesnít. It has to do with the measured distance between various points in space. The amount of deflection of star light by the sun is a measure by how much space is altered by the sunís gravitational field.


Quote from: niebieskieucho
My impression is that many people believe that spacetime curvature refers to the curving of a worldline in spacetime caused by a gravitational field. Am I close?
No. Youíre way off. A charged particle moving in flat spacetime in an electric field will have a worldline that curves. That in no way shape or form means that the spacetime is curved.

If the particleís worldline is a geodesic (i.e. the 4-force on it is zero Ė only inertial forces are acting on it) and it curves then all that tells you is that youíre observing the motion of the particle from a non-inertial frame of reference. Spacetime curvature pertains to the divergence of two geodesics which start out parallel and deviate. See
http://home.comcast.net/~peter.m.brown/gr/geodesic_deviation.htm

Quote from: niebieskieucho
The only curvature of space I can accept is due to spherical shape of the (finite) universe.
Then why not choose to learn about it and learn what it really means as opposed to what you think it means.

If you really want to learn what spacetime curvature is then read Exploring Black Holes at http://exploringblackholes.com/

Or read
http://home.comcast.net/~peter.m.brown/sr/sr.htm
http://home.comcast.net/~peter.m.brown/gr/gr.htm

I know itís a lot but nobody said that learning about spacetime curvature could be easy to learn.

Unless you really donít want to learn it?


I'm sorry if I come across as being rude to you. I don't mean to be. I simply get irritated when people claim that things are wrong when it's also clear that they've never learned what it is in the first place.
« Last Edit: 06/07/2013 00:58:27 by Pmb »

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Offline yor_on

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #17 on: 06/07/2013 01:10:54 »
"The electric field defines a direction. Are you saying that the electric field is a gravitational field?"

No, I was talking about what you discussed, 'gravity', but there are several descriptions to it. gluing a name to it, as gravitomagnetism, doesn't catch it for me though. I think I prefer it as a direction so far :)
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Re: What is the meaning of "Spacetime Curvature"?
« Reply #18 on: 06/07/2013 01:51:48 »
"The electric field defines a direction. Are you saying that the electric field is a gravitational field?"

No, I was talking about what you discussed, 'gravity', but there are several descriptions to it. gluing a name to it, as gravitomagnetism, doesn't catch it for me though. I think I prefer it as a direction so far :)
Gravitomagnetism refers to a specific gravitational effect. It's about a velocity dependant gravitational force just like the magnetic force is velocity dependant. The direction of the gravitational force depends on the direction of the velocity of the particle. So what direction are you talking about?

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #19 on: 06/07/2013 01:55:21 »
Fictitious force is a very nice description of it Pete. As you can transform it away by a free fall. If I assume that all matter in the universe has a preferred direction (geodesic) in where no forces act on it, then I suppose this should be 'gravity'. And that should be a preferred direction to me, or 'SpaceTime curvature'. Even though uniform motion is a relative motion, we still can use fixed stars, CBR, etc to define a direction for it. But if I go strictly by what 'relative motion' state, that you can redefine any (uniform) motion by just changing a reference frame? Then I'm not sure how to describe the 'direction' of matter, because you need a 'motion' to have a direction. And that one is intuitively weird to me, and in some way more correct, although I can prove motion just by introducing more uniformly moving objects in a 'system' and so be able to define different speeds relative those objects. If I can find that, then motion should exist, as I think for now :)
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Re: What is the meaning of "Spacetime Curvature"?
« Reply #20 on: 06/07/2013 02:11:16 »
Maybe one could turn it around and state that as I feel a gravity, standing on earth, then that too must be a proof for a preferred direction, or geodesic, existing. And if matter tells space how to 'bend', and space tells matter how to 'move' then we all are in a geodesic, having a preferred direction, defined by all matter in a universe, or locally defined (earth) if one want, defined by the matter close to me. But if gravity has a infinite reach the first statement should be more correct I think?
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Re: What is the meaning of "Spacetime Curvature"?
« Reply #21 on: 06/07/2013 02:46:14 »
Fictitious force is a very nice description of it Pete. As you can transform it away by a free fall.
Here's the problem with that. It has given the false impression that such a field cannot be caused by matter, which is false. People think that if it's fictitious then it can't be caused by a gravitational source. That's what happens when you label things as fictitious. You can call it what you like. I prefer to call it real because it is real. You can't tell the difference. Calling it fictitious because you can transform it away is like saying that an electric field is fake because you can transform that away too.

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #22 on: 06/07/2013 09:45:27 »
Fictitious force is a very nice description of it Pete. As you can transform it away by a free fall.

Here's the problem with that. It has given the false impression that such a field  cannot be caused by matter, which is false. People think that if it's fictitious then it can't be caused by a gravitational source. That's what happens when you label things as fictitious. You can call it what you like. I prefer to call it real because it is real. You can't tell the difference.

Pete
 What do you mean by field here "It has given the false impression that such a field cannot be caused by matter, which is false.''

Are you saying...the region of altered spacetime in the vicinity of mass is real, but locally it can be transferred away?
 To make it clearer for me, and if it helps others, is this field you refer to Newton's gravitational force of attraction or a region of altered spacetime? Evidence of this altered region of spacetime being accelerations and the converging together of test particles (originally on parallel paths) as they move towards the centre of mass of a planet?
« Last Edit: 06/07/2013 16:55:45 by lean bean »

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #23 on: 06/07/2013 17:12:00 »
Quote from: lean bean
Pete
 What do you mean by field here "It has given the false impression that such a field cannot be caused by matter, which is false.''
Iíve been discussing general relativity with people for over a decade now. It seems that people think of spacetime curvature as being what we normally think of as a gravitational field (i.e. things fall when we drop them at a rate which is independent of their mass). However that is not the case. But people have come to expect that when there is a body falling from the gravitational acceleration caused by a planet it is due to spacetime curvature (Riemman tensor) when actually itís due to whatís called the affine connection. Since people have the wrong idea about it Iíve found that in almost all circumstances people have expected spacetime curvature where there shouldnít be any. The example I always use is the uniform gravitational field. Such a field is actually defined as having no spacetime curvature yet since people are always associating spacetime curvature with gravity they also expect there to be spacetime curvature in a uniform gravitational field. And Iím not talking about the layman. Iím talking about experts. This occurred in the American Journal of Physics as well as in Gravitation by Misner, Thorne and Wheeler (MTW). In the case of MTW they wrongly assert that gravitational redshift implies spacetime curvature, which it doesnít. In fact the very first calculation of gravitational redshift, by Einstein of course, used flat spacetime!

Quote from: lean bean
Are you saying...the region of altered spacetime in the vicinity of mass is real, but locally it can be transferred away?
Not just locally but in a finite region of spacetime. The term local means a small region. The region need not be small when the field is a uniform gravitational field. However the equivalence principle states that the gravitational field (the affine connection) can always be transformed away whereas spacetime curvature cannot.

Quote from: lean bean
To make it clearer for me, and if it helps others, is this field you refer to Newton's gravitational force of attraction or a region of altered spacetime?
You seem to be indicating that there is a difference between Newton and GR in this area and there isnít. The area of physics where Newton differs from Einstein is not the gravitational force, because that also exists in GR (see http://home.comcast.net/~peter.m.brown/gr/grav_force.htm). Its in the area of the field e equations and the fact that Newtonís gravitational field acts instantaneously with no delay in propagation time between a change in the distribution of matter to a change in the gravitational field.

Quote from: lean bean
Evidence of this altered region of spacetime being accelerations and the converging together of test particles (originally on parallel paths) as they move towards the centre of mass of a planet?
That exact same thing happens in Newtonian physics too you know?

Quote from: lean bean
Am I wasting my time asking direct questions of you? :)
I'm sorry but I don't understand this question. Why would it be a waste of time? Donít you think I'm capable of answer your questions?

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Offline galaxysim

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #24 on: 06/07/2013 20:08:54 »
ref What do you think? And than you for your thoughts in advance. :)

I think you should make the effort to make a series of video shorts, or at the very lest build up a link of video shorts you can send people off to watch. Assuming your mission is education of the many ?

pages of text and diagrams is not only dry but a poor communication medium...it might suit some people in some circumstances but people tend not to posses the mindset of a low grade bank clerk...which is what you would have to have to enjoy wading through reams of dry text and line drawings

Far too many intellectuals have poor multi media and communication skills
Thus much of that knowledge remains buried in books or the halls of academia

The mind that can understand deeply is often hampered by the inability to communicate widely

We are much like ants, and the intrinsic complexity of the universe and our finite brain capacity means overspecialization has its downsides.

Sagan, Feynman & Neil deGrasse Tyson the exception rather than the rule....i think thats a great shame for all of us

Dr. Neil DeGrasse Tyson: A fascinatingly disturbing thought
http://www.youtube.com/watch?v=KeJoVeKSsyA

Dawkins & Tyson on Intelligent Aliens
http://www.youtube.com/watch?v=qikjljlbTQw


communication the other half of the 'lack of wisdom problem'



« Last Edit: 06/07/2013 20:34:32 by galaxysim »

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lean bean

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #25 on: 06/07/2013 21:18:21 »
You seem to be indicating that there is a difference between Newton and GR in this area and there isnít.
There is a difference between the Newton and Einstein when it comes to field.
Newton is action at a distance with force of attraction, wheeler says moving orders are from local spacetime right where the partical is. Read on for Newton quote and wheeler.

Why do people like E. Taylor and J. Wheeler give  ''These notes supplement Chapter 3 of EBH (Exploring Black Holes by Taylor and Wheeler).''

Quote
It seems astonishing that a result from special relativity carries over directly to general relativity without modification. The key is that, in the paradigm of general relativity, free-fall motion arises not from acceleration but from the effects of spacetime curvature. As we will see, the appearance of acceleration arises naturally from extremal paths in a curved spacetime.
We say ďappearance of acceleration" because ordinary acceleration depends on the motion of one's reference frame. In an inertial reference frame in Newtonian gravity, a body moves at a constant velocity if no forces act on it. In Newtonian theory, an inertial reference frame can be extended over all of spacetime. But we have already argued in the first set of notes that there are no global inertial reference frames in curved spacetime. Consequently the notion of acceleration is ambiguous! Acceleration depends on frame, and if there are no preferred frames, there is no preferred concept of acceleration.
Pick the pdf titled ĎHow Gravitational Forces arise from Curvatureí
From http://ocw.mit.edu/courses/physics/8-224-exploring-black-holes-general-relativity-astrophysics-spring-2003/assignments/

So, above quote as Taylor and co  saying the appearance of acceleration arises naturally from extremal paths in a curved spacetime.
-------
 Newton is force and attraction...
Hereís a quote from Newtonís ''Philosophiś Naturalis Principia Mathematicaíí

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For by the propositions mathematically demonstrated in the first books, we there derive from the celestial phenomena, the forces of gravity with which bodies tend to the sun and several planets.
Please donít ask me to link to thatÖitís in google books and the page just doesnít present itself when I link to it.

Also.
In the book EBH you have Taylor and Wheeler sayingÖ
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In Newtonian theory this effect is ascribed to gravitational force acting at a distance from a massive body. According to Einstein a particle gets its moving orders locally, from the geometry of spacetime right where it is.

So there is the difference between the Newton and Einstein.

So, Newton has a force of attraction and Wheeler saying itís local spacetime geometry giving the moving orders. In fact, wheeler says elsewhere itís the local spacetime metric and maximum aging of rocks wristwatch that  selects the geodesic path through spacetime

Now this is the nub...
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I'm sorry but I don't understand this question. Why would it be a waste of time? Donít you think I'm capable of answer your questions?
Itís hard to answer that without it seeming personal, I have read articles of people  mis-understanding GR even though they may be able to Ďdo the mathí, because of that Iím very suspect of most things on the web, especially forums. I know you wrote the glossary of the first book, but I seem to be getting different understandings of GR from the bookís authors and you??
And I have to say this, I'm rubbish at math, so have to rely on acknowledged Ďexpertsí. Donít get down pete, Itís my own defence against the web. I try to use university research sites and acknowledged Ďexpertsí own sites for info. Trying to avoid a bun fight here.
« Last Edit: 06/07/2013 21:23:11 by lean bean »

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #26 on: 06/07/2013 21:52:47 »
Quote from: lean bean
And I have to say this, I'm rubbish at math, so have to rely on acknowledged ‘experts’. Don’t get down pete, It’s my own defence against the web. I try to use university research sites and acknowledged ‘experts’ own sites for info. Trying to avoid a bun fight here.
Let me make something very clear to you LB. I respect you, plain and simple. If you have something to say to me then Iíll listen and that includes criticism from you. Iím man enough and confident enough in myself to believe that we can work through our differences so that we can either get to a point where I can help you understand something or you can help me understand something. Iím man enough to admit when Iím wrong my good man. :)

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #27 on: 07/07/2013 08:53:43 »
There are so many complications and paradoxes it is not easy for ANYONE to wrap there head round.

Which is why a series of video shorts would be the best method of communication.


« Last Edit: 07/07/2013 08:55:59 by galaxysim »

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Offline niebieskieucho

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #28 on: 07/07/2013 10:03:51 »
Quote from: niebieskieucho
It's a double rubbish. Spacetime is a sick idea. It's just space that has nothing to do with time (of what BTW?), as time spontaneously does not exist.

From these comments its clear that you donít know what spacetime is. Please learn about these things before you make another attempt at commenting on them. I.e. please study what spacetime is. I created the following for this purpose
http://home.comcast.net/~peter.m.brown/sr/spacetime.htm
You are living in an antiquated, hermetic world of ďofficialĒ science that stuck to their myths cherished for over a century and is deaf for a down to earth physics offered by number of independent scientists and researchers. Well, I'll have to use the same arguments in the discussion because there are produced the same counterarguments. Please note that those who claim that understood relativity automatically admit that understood nonsense. Thank you for the links but it's wild goose chase. Do you really think that I do not know ďscientificĒ explanation of spacetime? Sorry, I cannot treat it seriously. Minkowski talked about time as if it were an independent physical entity. May I in turn submit you my article about time. I would be grateful for your kind leaning over it, and letting me know if you find anything that seems to you untrue. 
http://www.eioba.com/a/33e7/why-time-cannot-dilate
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Whether spacetime is curved or not is not up for debate. Itís an observable fact. Itís a measurable phenomena.
Nonsense. Nothing of the kind.
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But until you learn what it really is as opposed to what you think it is (which youíve proven that what you think it is is wrong) you wonít be able to understand that very simple fact.
Among other things, I did it by the above article. There is no scientific proof to support what you claim.
Quote
If you had chosen to first learn about the subject that youíre criticizing then you wouldnít have made these mistakes. I showed you where to read about it online. Please do so before you make another attempt to argue that itís wrong.
You have referred to material that is nothing new to me.
Quote
Quote from: niebieskieucho
As to the second rubbish, i.e. alleged curvature of space, it's simply impossible. Space does not undergo deflection, is indestructible, does not expand, is of the same volume as it was before origin of matter.
These comments also tell me that you donít know what space curvature is. You incorrectly assumed that it meant that space is deflected. It doesnít.
Really? So, I'll have to remind you artistic vision of the (allegedly) curved spacetime in the vicinity of massive bodies (something like a trampoline):
http://cosmicshipmedia.net/spacetime/Spacetime_curvature.png
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It has to do with the measured distance between various points in space. The amount of deflection of star light by the sun is a measure by how much space is altered by the sunís gravitational field.
No way! Nothing can influence on deflection of space. Which are you talking about is just contents of space. Beam of light can be curved, but not space.
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My impression is that many people believe that spacetime curvature refers to the curving of a worldline in spacetime caused by a gravitational field. Am I close?
I don't know what others think. I do not accept spacetime or its alleged curvature (see the image above).
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No. Youíre way off. A charged particle moving in flat spacetime in an electric field will have a worldline that curves. That in no way shape or form means that the spacetime is curved.
I do not honour spacetime. Space is a physical reality whereas time does not autonomously exist, moreover, it's an abstraction as it is mathematical notation. Please try to couple for example 1 hour with space. Could you? It doesn't matter whether it is electric field or any object or particle. Any of them is in constant motion or is timing, thus time is property of matter but not space. Nevertheless, nobody hit upon the idea to call it mattertime.
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If the particleís worldline is a geodesic (i.e. the 4-force on it is zero Ė only inertial forces are acting on it) and it curves then all that tells you is that youíre observing the motion of the particle from a non-inertial frame of reference. Spacetime curvature pertains to the divergence of two geodesics which start out parallel and deviate. See
http://home.comcast.net/~peter.m.brown/gr/geodesic_deviation.htm
If you say spacetime you by this talk about non-existent entity. I do not honour spacetime. Matter is matter. It doesn't mean if it is some object or particle. They undergo the same laws of nature.
Quote
Quote from: niebieskieucho
The only curvature of space I can accept is due to spherical shape of the (finite) universe.
Then why not choose to learn about it and learn what it really means as opposed to what you think it means.
I know what is said in this question. Let's quote Wikipedia, http://en.wikipedia.org/wiki/Spacetime
Nonsense follows nonsense. I could make a list of them but it can't afford to spend hours to do it.
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If you really want to learn what spacetime curvature is then read Exploring Black Holes at http://exploringblackholes.com/
There is no spacetime. Spacetime is absurdity. Black Holes are contained in the universal space and they cannot curve it. All they can do it's absorption of spatial contents.
Quote

Or read
http://home.comcast.net/~peter.m.brown/sr/sr.htm
http://home.comcast.net/~peter.m.brown/gr/gr.ht
You are recommending false theory as such one is Relativity.
Quote
I know itís a lot but nobody said that learning about spacetime curvature could be easy to learn.
Unless you really donít want to learn it?
I like learning, but not scientific rubbish Ė no offence. To let you know my point of view on space, kindly see my article: http://www.eioba.com/a/3dm8/how-to-comprehend-space
My quality is lack of faults and my fault, is nothing but qualities :)
In addition, I trace - unfortunately - scientific absurdities :(
Quote
I'm sorry if I come across as being rude to you. I don't mean to be.
Not at all. You weren't.
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I simply get irritated when people claim that things are wrong when it's also clear that they've never learned what it is in the first place.
Maybe some do so. But I am aware enough what I am talking about.
Those who claim that understood Relativity, automatically claim that understood nonsense

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #29 on: 07/07/2013 10:39:08 »
Quote from: lean bean
It’s hard to answer that without it seeming personal, I have read articles of people  mis-understanding GR even though they may be able to ‘do the math’, because of that I’m very suspect of most things on the web, especially forums. I know you wrote the glossary of the first book, but I seem to be getting different understandings of GR from the book’s authors and you??
This part is absolutely true. The authors and I see things a bit different. However that doesn't make things wrong by any means. I see things the way that Einstein did and they see things the way that Wheeler did, which is consistent with the way that Max Von Laue saw things. My viewpoint is consistent with the way that John Stachel, Professor Emeretus at Boston University sees things which is also the way Einstein saw things.

Einstein saw the existance of a gravitational field in terms of the non-vanishing of the affine connection whereas myself, Einstein and Dr. Stachel see the non-vanishing of the gravitational field as the non-vanishing of the components of the affine connection.

Note: Dr. Stachel was the editor of the previous editor of the Einstein Papers Project.

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #30 on: 08/07/2013 15:43:16 »
First of all. "I think you should make the effort to make a series of video shorts, or at the very lest build up a link of video shorts you can send people off to watch."

No GS.

Never liked that. The difference between TNS and some u-tube movie, is that you can think for yourself, we're not stuffing 'food down your mouth', you are free to argue your ideas and questions, even refuse it :)

As for " Assuming your mission is education of the many ?" I think Pete want to share what he find to be the essence of Relativity, and as long as he accept that there will be arguing, (it always is, btw:) I think the journey will be worth it, for all of us.
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Re: What is the meaning of "Spacetime Curvature"?
« Reply #31 on: 08/07/2013 15:51:32 »
And Pete "The example I always use is the uniform gravitational field. Such a field is actually defined as having no spacetime curvature yet since people are always associating spacetime curvature with gravity they also expect there to be spacetime curvature in a uniform gravitational field."

Then you say "Einstein saw the existance of a gravitational field in terms of the non-vanishing of the affine connection ...

...whereas myself, Einstein and Dr. Stachel see the non-vanishing of the gravitational field as the non-vanishing of the components of the affine connection."

So, 'affine connection'? And what do you mean by the above?

My very own view is that a metric must be there, but it doesn't need to 'curve' for a observer. Although it 'must' be there to make sense, to a lot of things, as a 'closed universe' for example, like that ball shaped one.
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Re: What is the meaning of "Spacetime Curvature"?
« Reply #32 on: 10/07/2013 13:49:09 »
Quote from: yor_on
So, 'affine connection'? And what do you mean by the above?
Take a look at the page I created for the uniform gravitational field at
http://home.comcast.net/~peter.m.brown/gr/uniform_force.htm

The capital gamma's in Eq. (5) are the affine connection, aka the connection coefficients. They are also referred to as the Christofell symboks.

Please readhttp://www2.warwick.ac.uk/fac/sci/physics/current/teach/module_home/px436/notes/lecture9.pdf

I will too so that we're on the same page.

Wish me luck or say a prayer for me today folks, depending on your theological bent. This morning is the morning that I finally have cataract surgery for my left eye. Then I'll see just like a real person does again. :)
« Last Edit: 10/07/2013 13:52:23 by Pmb »

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lean bean

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #33 on: 10/07/2013 17:36:08 »
Wish me luck or say a prayer for me today folks, depending on your theological bent. This morning is the morning that I finally have cataract surgery for my left eye.
Best of luck pete...no gravitational lens jokes please :) :)

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #34 on: 11/07/2013 13:23:05 »
Wish me luck or say a prayer for me today folks, depending on your theological bent. This morning is the morning that I finally have cataract surgery for my left eye.
Best of luck pete...no gravitational lens jokes please :) :)

Thanks buddy. All went well. I didn't even have to have an eye patch over the eye after suergery. I was sitting waiting for them to take me into surgery and then they told me it wsa all over. That freaks me out to no end. Lol!!

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #35 on: 11/07/2013 22:48:38 »
Quote from: niebieskieucho
You are living in an antiquated, hermetic world of ďofficialĒ science that stuck to their myths cherished for over a century and is deaf for a down to earth physics offered by number of independent scientists and researchers.
In this forum we see quite a few people who donít have any real understanding of science, never mind physics, that youíve demonstrated such a large lack in. We donít waste our time with people claim to know everything but whose posts demonstrate that they actually know nothing. Had you chosen to learn relativity and what the terminology means then youíve have learned that the term curvature when applied to spacetime is used as an analogy and not used erroneously as you have obviously done and to be taken as a literal meaning. And this is all already explained quite clearly to anyone and everyone who wants to know it. But youíve chosen not to learn the truth since you ignored http://exploringblackholes.com/

Anyone whoís studied general relativity and actually knows what theyíre talking about knows this as one of the most basic of all truths of physics. However since youíve instead chosen to take this as an opportunity to criticize general relativity rather than to learn it youíre going to remain ignorant. That this is the case is apparent from your choice to ignore the online text on GR by Bertschinger, Taylor and Wheeler which explains that curvature is a term used as an analogy just goes to show how little youíre willing to learn.

Good lord! Itís amazing on how much youíve droned on about things you have absolutely no idea what they are. On this forum we only spend time talking to people who actually want to learn and either know what theyíre talking about or ware willing to learn about it.

Iíve cut the rest since its of no worth to anyone.

In a way I feel sad for you. But not that sad since you could learn but have chosen not to.


Come on folks! Why do we allow trash to be posted in this forum by people who have absolutely no idea about what they're talking about? I mean this is just a little too overboard for my taste.

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #36 on: 14/07/2013 16:49:29 »
Hope it worked out for you Pete, with the operation and all. As you forgot to link Einsteinís gravitational field. which gives a more digestible introduction (for us laymen) to your thoughts, I took upon me the liberty of linking it .

As for people not trusting relativity.
Well, everyone has his own ideas. That's why we discuss, and as they say, 'don't get mad, get even'.
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Re: What is the meaning of "Spacetime Curvature"?
« Reply #37 on: 16/07/2013 00:21:09 »
Hope it worked out for you Pete, with the operation and all. As you forgot to link Einstein’s gravitational field. which gives a more digestible introduction (for us laymen) to your thoughts, I took upon me the liberty of linking it .
Thank you my friend. How do you like thar article by the way?

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #38 on: 16/07/2013 00:36:28 »
I enjoyed it. It was very readable, and I agree to that a earths gravitational field is there, even when I am in a 'free fall', if we by that refer to tidal forces? Although it seem to clash with the idea of a geodesic to me, as a geodesic, per definition and as I read it, exist everywhere you have a free fall, and a geodesic should be without 'gravity'?
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Re: What is the meaning of "Spacetime Curvature"?
« Reply #39 on: 16/07/2013 00:56:44 »
Then again, you have this example with a uniform gravitational field that you would be welcome to expand on, preferably without mathematics, :)

You say " This expression gives the local acceleration of an object whose velocity is v. Observers at different positions z in the field system will not measure the same local value of acceleration. Not only will the objectís acceleration depend of position but also on velocity. This is contrary to what one would normally assume for a uniform gravitational field. "

If it is a uniform field, me reading that as it should have a same value at all positions, then what gives those, lets say two, observers different accelerations? You give their initial velocity (uniform) as one reason, the other being where they are positioned in it. Can you find a way to define it without mathematics?
=

I am assuming that the observers are identical to each other, preferably able to be defined as being 'at rest' with each other, although at different positions.   

(Eh, better add that I totally agree on that gravity should be everywhere, no matter how one define the space, as flat or not.)
« Last Edit: 16/07/2013 01:20:12 by yor_on »
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Re: What is the meaning of "Spacetime Curvature"?
« Reply #40 on: 16/07/2013 01:36:21 »
It's tricky Pete, rereading it I confuse myself :) I want to put it into my own terms, and then I would say that gravity is observer dependent. Then again, I'm always wanting to define it locally. when I say that I agree to that 'gravity must exist everywhere' I'm using what I call a 'global definition', as opposite to a local, it makes it clearer for me defining it such, a local definition of a geodesic versus one where I speak about a whole 'SpaceTime's' gravity.

You write "Einstein did not interpret gravity as a curvature of space-time, rather that space-time curvature is a manifestation of gravity." giving me a feeling that you then may consider it a 'force' defining a SpaceTime. That would then be from what I call a 'global definition', not local.

Alternatively I could read it as a statement that something is needed to create gravity, mass (energy), and so define a SpaceTime. And it is true that the elevator example only can be used ignoring tidal forces, as you otherwise would be able to differ between the 'gravity' you find in a uniformly constantly accelerating rocket, relative on Earth. And so restrict the equivalence principle.

The question then becomes what one consider tidal forces as? Myself I think of it as 'gravity' too and so consider it irrelevant for a wider definition of the equivalence between gravity, and a uniform constant acceleration? Either there is a equivalence, as I think now :) and then this exception (tidal forces) is something solvable, or we have a situation in where Earths gravity, as it involve tidal forces, can't be applicable to a uniform constant acceleration of that elevator.

I guess I'm using it in its wider sense, if I now would try to define it.
=

If a geodesic is something without 'forces' acting on it, in a free fall finding no gravity acting on you, no friction or resistance retarding your uniform motion, then that should include tidal forces? If I exclude tidal forces from that definition, I come to a definition in where I have to assume that this ultimately will retard my uniform motion, as I think. But I have to admit that I found geodesics to be one of the most difficult assumptions to make, as from my 'global definition' gravity and tidal forces exist everywhere matter is. And if we then include the way binary stars act gravitationally, as well as other tidal forces, then there is a 'friction' to a geodesic too. And all mass have a gravity acting on them, even in a geodesic, the gravity created by its own mass though.

I've been thinking about it actually, now and then, wondering if there is some better definition I can make, the one I'm leaning too is one in where a geodesic will be defined by gravity, including tidal forces, and it won't matter if matter 'spagettifies' under its influence. The directions 'they' take, under and after, such a event should still be geodesics, to make sense for me. So you might be able to see it as 'straight lines', without resistance, although for the poor bast* getting split :), as well as for any other observers, might want to define a 'force' to it.
=

But that is what I call a global definition. From a local point of view a ideal geodesic must be free from 'friction', in a constant uniform motion (or uniform gravitational acceleration as it comes down to the same. No 'local gravity'), to fit the idea I have of it.
==

If you look at

"Can gravitation and inertia be identical?  This question leads directly to the General Theory of Relativity.  Is it not possible for me to regard the earth as free from rotation, if I conceive of the centrifugal force, which acts on all bodies at rest relatively to the earth, as being a "real" gravitational field of gravitation, or part of such a field?  If this idea can be carried out, then we shall have proved in very truth the identity of gravitation and inertia. For the same property which is regarded as inertia from the point of view of a system not taking part of the rotation can be interpreted as gravitation when considered with respect to a system that shares this rotation.

According to Newton, this interpretation is impossible, because in Newton's theory there is no "real" field of the "Coriolis-field" type.  But perhaps Newton's law of field could be replaced by another that fits in with the field which holds with respect to a "rotating" system of co-ordinates?  My conviction of the identity of inertial and gravitational mass aroused within me the feeling of absolute confidence in the correctness of this interpretation."

then I feel I have gotten the idea right :) That's how I think of 'tidal forces'.
« Last Edit: 16/07/2013 03:38:59 by yor_on »
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Re: What is the meaning of "Spacetime Curvature"?
« Reply #41 on: 16/07/2013 15:04:39 »
"I've been thinking about it actually, now and then, wondering if there is some better definition I can make, the one I'm leaning too is one in where a geodesic will be defined by gravity, including tidal forces, and it won't matter if matter 'spagettifies' under its influence. The directions 'they' take, under and after, such a event should still be geodesics, to make sense for me. So you might be able to see it as 'straight lines', without resistance, although for the poor bast* getting split :), as well as for any other observers, might want to define a 'force' to it."

That one has to do, for me that is, with what a 'frame of reference' can be 'minimized' too. I assume that locally a 'frame of reference' can be defined to some scale, stopping at Planck scale. and if one look at a 'spagettifiezation' from a very local perspective then each particle will find its own geodesic. On the other hand you need a acceleration to 'split' those particles from each other, as there is a force binding particle to particle. so I'm of two minds you might say, the acceleration happening is not a geodesic, but what you had and what you get after should still be a geodesic. But geodesics are a very difficult idea to encompass, as it should be definable from 'test particles' but as you gather those into pieces of matter it seems to become a lot more complicated to me.
=

It also depends on how you define something being 'at rest' with each other. In a piece of matter, is its particles 'at rest' with each other? That depends on how I would like to define a 'frame of reference' does it not? From a view in where you have a decided minimized scale to what a 'frame of reference' might be, only test particles make sense, and they better be 'point like' to make me happy. On the other hand we have something being 'at rest' with each other in a uniform motion, and from that we can also find some defining it as you also can be 'at rest' in a acceleration, equivalent to some other accelerating object in a equivalent space. Thats also why I find your definition of two objects in a uniform gravity (field), presenting us with different definitions so interesting. I'm assuming them to be uniformly moving though, for this.
« Last Edit: 16/07/2013 15:24:56 by yor_on »
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Re: What is the meaning of "Spacetime Curvature"?
« Reply #42 on: 16/07/2013 15:41:26 »
Let us put it this way. Assume that you have a test particle passing a event horizon, it being 'indivisible' for this (point like). should I define it as it undergoing a acceleration meeting tidal forces, or should I define it as a 'straightest path' in a 'bent/distorted' SpaceTime?
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Re: What is the meaning of "Spacetime Curvature"?
« Reply #43 on: 17/07/2013 01:41:50 »
yor_on - I'm unble to follow your posts. They're too confusing for me. For some bizzare reason you keep changing the background color and you posts multilple posts one after another. Why do you do this?

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #44 on: 17/07/2013 01:52:09 »
I'm curious about something. Do you folks understand that by the term "curvature" as it's used in "spacetime curvature" refers to what's known as intrinsic curvature? E.g. the surface of a sphere has intrinsic curvature but that of a cylinder extrinsic curvature.

See
http://mathworld.wolfram.com/ExtrinsicCurvature.html
http://mathworld.wolfram.com/IntrinsicCurvature.html

Einstein also used the term curvature to refer to acceleration as well, e.g. in his text Relativity: The Special and General theory
« Last Edit: 17/07/2013 01:55:07 by Pmb »

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #45 on: 18/07/2013 17:00:09 »
I do not change the background colors?
Could it be your browser?

And yeah, I definitely wrote too much there :)
But I got two questions. The one about you using, if I got it right that is, equivalent observers, in a uniform gravitational field, finding them to have different accelerations. How would you go about describing it without the mathematics?

And the one about a 'test particle' meeting tidal forces, as passing some event horizon. It's about how one would define that particle? To have a acceleration at some point, or following a geodesic at all times? I think I read somewhere that Einstein defined it as long you don't find forces acting (free fall) on you, you're in a geodesic?
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Re: What is the meaning of "Spacetime Curvature"?
« Reply #46 on: 18/07/2013 17:28:28 »
Quote from: yor_on
And yeah, I definitely wrote too much there :)
If you don't mind me making a suggestion than you might want to consider shortening your post to more readable lengths. When a post is too long you read I skip over it no matter how much I'm interested in what the writer has to say. And I am interested in what you have to say. You have a reasonably good understanding of general relativity. I'd like to help you make it better. But I will not read multiple posts each of which is too long to begin with. I recommend that you try to shorten what you want to say and say it in fewer words. I.e. be more efficient in what you're writing. Think of this forum as you would a journal. In a journal article you only have so much space to get across what you want to and editors want you to say what you have to say using as little words as possible.

Also don't write posts one after each other. If there's something you want to add to your post and someone hasn't posted after you last one then use the edit function and edit that last post to say everything you want to in what would have been the next post. I've had this discussion with many other posters. We all want to hear what you have to say. We're just not going to spend what little time we have on the internet reading such long posts. Okay? Take all Iíve said here as a compliment, not as a criticism, okay my friend?

Quote from: yor_on
But I got two questions. The one about you using, if I got it right that is, equivalent observers, in a uniform gravitational field, finding them to have different accelerations. How would you go about describing it without the mathematics?
The equivalence of a uniform gravitational field and a uniformly accelerating frame of reference means that you cannot tell whether youíre in a uniformly accelerating frame of reference or a uniform gravitational field merely by observing nature, i.e. all particle experimental outcomes will be the same regardless of which frame of reference that youíre in. Toss a ball in a vacuum. Then the trajectory will be exactly the same in each frame and depend only on the initial conditions. Experiments in electromagnetism will be the same regardless of which frame youíre in. Etc.

Quote from: yor_on
And the one about a 'test particle' meeting tidal forces, as passing some event horizon.
Where did I say anything about such a thing?

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #47 on: 18/07/2013 17:56:32 »
No problem Pete :)

How do you think of a intrinsic curvature? As a way to describe a space without referring to a embedding? If that is correct, how would you describe the space we and Earth traverse? It's a very interesting subject, but seems very tricky mathematically. As I get it it is a way to describe a curvature without referring to what the curvature may exist in?

Or, possibly giving you a same value/description no matter how you embed it, dimension-wise?
=

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. A intrinsic curvature would then be measuring the interior angles of a triangle, but on a ball, finding it to give you more than 180 degrees (as the triangles 'legs' bends over the ball). So telling you that you have a 'curved space'. Gaussian curvature. And all as I get it.

The first is a Euclidean 'flat' geometry. The one we use to define a triangle, and the one you can define by scaling the universe down to a 'locally flat space'. The other is a closer representation of our 'SpaceTime' as I get it. If our SpaceTime has a 'overall' curvature, taking you back to the point of origin without you ever deviating from a 'straight' path, you now should have defined both a extrinsic as well as intrinsic shape to our universe. But if you only are able to define intrinsic properties, what is the universe's shape? And does it need to have one?

Shape of the Universe. You might also say that it depends on if we got the Big Bang right, and so the homogeneous and isotropic universe we want
.

But the point still is that a intrinsic curvature does not have to relate to any shape at all as I get it, it's a intrinsic property we define, we can't place us outside our universe to find which way it is shaped, if it now is, in any special way. And all as I get it Pete :)
« Last Edit: 18/07/2013 20:56:22 by yor_on »
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Re: What is the meaning of "Spacetime Curvature"?
« Reply #48 on: 18/07/2013 18:10:27 »
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?
« Last Edit: 18/07/2013 19:33:08 by yor_on »
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Re: What is the meaning of "Spacetime Curvature"?
« Reply #49 on: 19/07/2013 16:43:39 »
Quote from: yor_on
How do you think of a intrinsic curvature?
Itrinsic curvature is curvature that can be measured by observers who only have the ability to make measurements within the surface and they find that in their space geodesic which start out parallel do not remain parallel. E.g. the surface of a cylinder has zero intrinsic curvature.

See
http://mathworld.wolfram.com/IntrinsicCurvature.html
http://mathworld.wolfram.com/ExtrinsicCurvature.html

Quote from: yor_on
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

Gaussian curvature - Please note that Gaussian curvature is not defined for spaces of dimension other than two. So it can't be defined for spacetime, which has four dimensions.

Euclidean geometry is defined by the metric by the way so you need to be careful when using this term. E.g. even in a flat spacetime with no curvature the spacetime still can't be considered Euclidean unless the metric is defined in the same way it is in regular geometry, i.e. as

ds2 = (cdt)2 + dz2 + dy2 + dz2

If time is imaginary then this metric can be used in flat spacetime. Some authors still use imaginary time, e.g. Richard Mould does in his text Basic Relativity.

The way you used the term is not the correct way.