Notices
Results 1 to 24 of 24

Thread: Intrinsic Curvature in GR

  1. #1 Intrinsic Curvature in GR 
    Member
    Join Date
    Feb 2013
    Posts
    30
    As I have learned intrinsic curvature can be shown on 2 D surfaces


    The spacetime model ,however is 3D+1

    How ,broadly speaking is curvature assessed in that context?Are 2D surfaces within the 4D manifold drawn locally and used to make this assessment?

    Are vectors"walked around" these surfaces?
    Reply With Quote  
     

  2. #2  
    Senior Member
    Join Date
    Sep 2017
    Posts
    127
    Quote Originally Posted by geordief View Post
    As I have learned intrinsic curvature can be shown on 2 D surfaces


    The spacetime model ,however is 3D+1

    How ,broadly speaking is curvature assessed in that context?Are 2D surfaces within the 4D manifold drawn locally and used to make this assessment?

    Are vectors"walked around" these surfaces?
    Neither. The spacetime itself (4D) is what is curved. In the presence of gravitating mass. You will need to learn differential geometry in order to understand how.
    Reply With Quote  
     

  3. #3  
    Member
    Join Date
    Feb 2013
    Posts
    30
    Quote Originally Posted by AndrewC View Post
    Neither. The spacetime itself (4D) is what is curved. In the presence of gravitating mass. You will need to learn differential geometry in order to understand how.
    Is not the curvature of space-time the "sum" of (1) the curvature along increasing time and (2) the curvature along the increasing spatial axes?


    When those increments are viewed geometrically (eg x,dx :y,dy: z,dz: t ,dt) does not geometric object created by those 8 apexes have "sides" that can be called "surfaces" and doesn't each of these surfaces deform in the presence of mass-energy?

    Does that geometric object conform to the spacetime distance relationship* so that its time component(s?) change by different rates than the spatial components?

    *s^2 =r^2 -[ct]^2

    EDIT: your link doesn't show the geometry graphically ,does it?
    Reply With Quote  
     

  4. #4  
    Senior Member
    Join Date
    Sep 2017
    Posts
    127
    Quote Originally Posted by geordief View Post
    Is not the curvature of space-time the "sum" of (1) the curvature along increasing time and (2) the curvature along the increasing spatial axes?
    No, it is not the "sum". You need to stop making guesses and you need to take a class. There is no shortcut.



    EDIT: your link doesn't show the geometry graphically ,does it?
    It doesn't because there isn't. You need to take a class, there are no shortcuts.
    Reply With Quote  
     

  5. #5  
    Member
    Join Date
    Feb 2013
    Posts
    30
    I put sum in quotes as I did not expect their contributions to "add"

    Are you saying to total spacetime curvature is not composed of its temporal and spatial parts?
    "It doesn't because there isn't" is not clear to me.

    They don't exist at all or just on that page?
    Reply With Quote  
     

  6. #6  
    Senior Member
    Join Date
    Sep 2017
    Posts
    127
    Quote Originally Posted by geordief View Post
    I put sum in quotes as I did not expect their contributions to "add"
    You need to take a class and you need to stop trying to take shortcuts.

    Are you saying to total spacetime curvature is not composed of its temporal and spatial parts?
    I have never said that. I only pointed out that things cannot be dumbed down at the level you want them dumbed down.
    Reply With Quote  
     

  7. #7  
    Member
    Join Date
    Feb 2013
    Posts
    30
    So you are apparently saying that the spatial curvature and the temporal curvature do combine to give the total space-time curvature.

    Are these components calculated separately ?
    Reply With Quote  
     

  8. #8  
    Senior Member
    Join Date
    Sep 2017
    Posts
    127
    Quote Originally Posted by geordief View Post
    So you are apparently saying that the spatial curvature and the temporal curvature do combine to give the total space-time curvature.

    Are these components calculated separately ?
    No, they are not "separate". The Einstein Field Equations are a set of coupled , non-linear differential equations.
    Reply With Quote  
     

  9. #9  
    Member
    Join Date
    Feb 2013
    Posts
    30
    But there are separate values for temporal curvature and spatial curvature.
    Do these values have to be calculated out of the EFE or can they be arrived at individually in a more direct way?
    Reply With Quote  
     

  10. #10  
    Senior Member
    Join Date
    Sep 2017
    Posts
    127
    Quote Originally Posted by geordief View Post
    But there are separate values for temporal curvature and spatial curvature.
    No.
    Do these values have to be calculated out of the EFE or can they be arrived at individually in a more direct way?
    No and no.
    One can MEASURE spacetime curvature INDIRECTLY, though a very complicated consequence, the geodetic effect.
    Reply With Quote  
     

  11. #11  
    Member
    Join Date
    Feb 2013
    Posts
    30
    So why is it that gravity in gravity wells) is described as being more a result of the curvature of time than the curvature of space? (Pretty sure I heard that)
    Reply With Quote  
     

  12. #12  
    Senior Member
    Join Date
    Sep 2017
    Posts
    127
    Quote Originally Posted by geordief View Post
    So why is it that time dilation (caused by gravity wells) is described as being more a result of the curvature of time than the curvature of space? (Pretty sure I heard that)
    No serious book would claim that, it is definitely false for the GPS. You need to stop trolling me and enroll in a class.
    Reply With Quote  
     

  13. #13  
    Member
    Join Date
    Feb 2013
    Posts
    30
    See I edited my post as I misspoke.Is that a better question?
    Reply With Quote  
     

  14. #14  
    Senior Member
    Join Date
    Sep 2017
    Posts
    127
    Quote Originally Posted by geordief View Post
    See I edited my post as I misspoke.Is that a better question?
    Your edited post is just as false. You can't learn physics from internet soundbites. The time dilation falls out the solution of the EFEs. This needs to take into consideration difference in gravitational potential and difference in terms of both radial and tangential speed between two different clocks.
    Reply With Quote  
     

  15. #15  
    Member
    Join Date
    Feb 2013
    Posts
    30
    In my edited post (you answered so quickly I had not enough time to correct it ) I don't refer to time dilation but the curvature of spacetime due to gravity.

    I have heard that this is more due to temporal effects than spatial effects

    Does that make sense? Is it true?

    I don't want to take up your time too much
    We can come back to it tomorrow perhaps
    Reply With Quote  
     

  16. #16  
    Senior Member
    Join Date
    Sep 2017
    Posts
    127
    Quote Originally Posted by geordief View Post
    In my edited post (you answered so quickly I had not enough time to correct it ) I don't refer to time dilation but the curvature of spacetime due to gravity.

    I have heard that this is more due to temporal effects than spatial effects

    Does that make sense? Is it true?

    I don't want to take up your time too much
    We can come back to it tomorrow perhaps
    In the case of geodetic effect, the time dilation contributes twice as much as the rotational effects. This is true for the case of the geodetic effect ONLY. See here for exact calculations. The language of physics is math, you need to be able to converse in that language, not in soundbites picked up from the internet. For example, the above is not true in the case of frame-dragging, another effect of spacetine curvature.
    Reply With Quote  
     

  17. #17  
    Member
    Join Date
    Feb 2013
    Posts
    30
    Quote Originally Posted by AndrewC View Post
    In the case of geodetic effect, the time dilation contributes twice as much as the rotational effects. This is true for the case of the geodetic effect ONLY. See here for exact calculations. The language of physics is math, you need to be able to converse in that language, not in soundbites picked up from the internet. For example, the above is not true in the case of frame-dragging, another effect of spacetine curvature.
    I would like to return to the OP if that is OK. I will give a different answer to your first reply and perhaps you might give an answer to it (I think I am conceding you main point I think)
    Reply With Quote  
     

  18. #18  
    Member
    Join Date
    Feb 2013
    Posts
    30
    Quote Originally Posted by AndrewC View Post
    Neither. The spacetime itself (4D) is what is curved. In the presence of gravitating mass. You will need to learn differential geometry in order to understand how.
    So are there 2D surfaces in spacetime which are used in the process of showing overall 3D+1 intrinsic curvature due to the presence of mass-energy? (say a surface with dimensions of [ct] and [x])

    Can we say the spacetime curvature along the x-axis is quantitively different from that along the y- and z-axes?
    Reply With Quote  
     

  19. #19  
    Senior Member
    Join Date
    Sep 2017
    Posts
    127
    Quote Originally Posted by geordief View Post
    So are there 2D surfaces in spacetime which can display intrinsic curvature owing to the presence of mass-energy? (say a surface with dimensions of [ct] and [x])
    This is not what GR is saying. Why do you persist?
    Reply With Quote  
     

  20. #20  
    Member
    Join Date
    Feb 2013
    Posts
    30
    Why do you jump down my throat ?Do you ever leave your device.?This is twice you have answered me so quickly before I have corrected my post(see above -again.)

    This is like the spider and the fly.

    I edited it to "So are there 2D surfaces in spacetime which are used in the process of showing overall 3D+1 intrinsic curvature due to the presence of mass-energy? (say a surface with dimensions of [ct] and [x])"
    Reply With Quote  
     

  21. #21  
    Senior Member
    Join Date
    Sep 2017
    Posts
    127
    Quote Originally Posted by geordief View Post

    Can we say the spacetime curvature along the x-axis is quantitively different from that along the y- and z-axes?
    Yes, so what? Every time I correct your misconceptions you change your post. Every time I answer your ill posed questions you move the goalposts claiming "I didn't ask A, I asked B". Where are you going with that? Why do you refuse to take a class?
    Reply With Quote  
     

  22. #22  
    Member
    Join Date
    Feb 2013
    Posts
    30
    Why don't you just answer my last underlined question?(I have conceded one or two mistakes in your favour)
    In case you forgot this is my OP and I have posed my question in order to learn.

    Let me be the judge of "so what?".If it reinforces my understanding it is helpful to me (if apparently irritating to you)

    Regardless of your attitude I appreciate the answers you have given me.They are very helpful
    Reply With Quote  
     

  23. #23  
    Senior Member
    Join Date
    Sep 2017
    Posts
    127
    Quote Originally Posted by geordief View Post
    Why do you jump down my throat ?Do you ever leave your device.?This is twice you have answered me so quickly before I have corrected my post(see above -again.)

    This is like the spider and the fly.

    I edited it to "So are there 2D surfaces in spacetime which are used in the process of showing overall 3D+1 intrinsic curvature due to the presence of mass-energy? (say a surface with dimensions of [ct] and [x])"
    A "2D surface with dimensions of [ct] and [x]" is a Minkowski PLANE. As such, it has ZERO curvature. So, you don't want to take a class. Why?
    Reply With Quote  
     

  24. #24  
    Member
    Join Date
    Feb 2013
    Posts
    30
    Quote Originally Posted by AndrewC View Post
    A "2D surface with dimensions of [ct] and [x]" is a Minkowski PLANE. As such, it has ZERO curvature. So, you don't want to take a class. Why?
    Really none of your business but since you have asked for the fifth or sixth time I am a poor and obtuse learner with blind spots that can impede my thinking.

    I neither have the time nor the opportunity to take classes and would struggle to keep up I sure.

    In my twenties this would have been easier but now(if contemplatable) it would be an all consuming commitment which would be foolish for me to undertake .


    .....So a flat plane it is.Are these ([ct],[x]) flat planes ,if small enough joined together to form a curved surface in a region of spacetime?

    Are they linked together in a "parallel transport" way?


    EDIT:thanks for answering that last readjusted question .I realize I have no claim on your time or patience,.
    Last edited by geordief; 01-10-2018 at 04:41 PM.
    Reply With Quote  
     

Posting Permissions
  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •