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Author Topic: What is the meaning of "Spacetime Curvature"?  (Read 11828 times)

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 isn’t.
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).''

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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 “appearance 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 ‘How Gravitational Forces arise from Curvature’
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...
Here’s a quote from Newton’s ''Philosophić Naturalis Principia Mathematica’’

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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 don’t ask me to link to that…it’s in google books and the page just doesn’t present itself when I link to it.

Also.
In the book EBH you have Taylor and Wheeler saying…
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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 it’s local spacetime geometry giving the moving orders. In fact, wheeler says elsewhere it’s 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? Don’t you think I'm capable of answer your questions?
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??
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.
« Last Edit: 06/07/2013 21:23:11 by lean bean »
 

Offline Pmb

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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 I’ll listen and that includes criticism from you. I’m 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. I’m man enough to admit when I’m wrong my good man. :)
 

Offline galaxysim

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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 »
 

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 don’t 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 [nofollow]
You are living in an antiquated, hermetic world of “official” 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 “scientific” 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 [nofollow]
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Whether spacetime is curved or not is not up for debate. It’s an observable fact. It’s 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 you’ve proven that what you think it is is wrong) you won’t 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.
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If you had chosen to first learn about the subject that you’re criticizing then you wouldn’t have made these mistakes. I showed you where to read about it online. Please do so before you make another attempt to argue that it’s wrong.
You have referred to material that is nothing new to me.
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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 don’t know what space curvature is. You incorrectly assumed that it meant that space is deflected. It doesn’t.
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 [nofollow]
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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 sun’s 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. You’re 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 particle’s worldline is a geodesic (i.e. the 4-force on it is zero – only inertial forces are acting on it) and it curves then all that tells you is that you’re 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 [nofollow]
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.
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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 [nofollow]
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/ [nofollow]
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.
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Or read
http://home.comcast.net/~peter.m.brown/sr/sr.htm [nofollow]
http://home.comcast.net/~peter.m.brown/gr/gr.ht [nofollow]
You are recommending false theory as such one is Relativity.
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I know it’s a lot but nobody said that learning about spacetime curvature could be easy to learn.
Unless you really don’t want to learn it?
I like learning, but not scientific rubbish – 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 [nofollow]
My quality is lack of faults and my fault, is nothing but qualities :)
In addition, I trace - unfortunately - scientific absurdities :(
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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.
 

Offline Pmb

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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.
 

Offline yor_on

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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.
 

Offline yor_on

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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 »
 

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 “official” 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 don’t have any real understanding of science, never mind physics, that you’ve demonstrated such a large lack in. We don’t 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 you’ve 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 you’ve chosen not to learn the truth since you ignored http://exploringblackholes.com/

Anyone who’s studied general relativity and actually knows what they’re talking about knows this as one of the most basic of all truths of physics. However since you’ve instead chosen to take this as an opportunity to criticize general relativity rather than to learn it you’re 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 you’re willing to learn.

Good lord! It’s amazing on how much you’ve 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 they’re talking about or ware willing to learn about it.

I’ve 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.
 

Offline yor_on

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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 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 .

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?
 

Offline yor_on

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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'?
 

Offline yor_on

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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 object’s 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 »
 

Offline 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 »
 

Offline 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 »
 

Offline 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 »
 

Offline yor_on

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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 I’ve 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 you’re 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 you’re 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 you’re 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?
 

Offline yor_on

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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 »
 

Offline 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.
 

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Re: What is the meaning of "Spacetime Curvature"?
« Reply #49 on: 19/07/2013 16:43:39 »

 

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