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Thread: stress energy tensor

  1. #1 stress energy tensor 
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    Someone emailed me the following statement that does not make sense to me.

    "The Einstein theory is an example of a non-linear theory in which the stress energy tensor vanishes in a mass zero zone."

    Is there any evidence of nonlinearity? How can the tress energy tensor vanish near a mass when the field does not vanish?


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    I think the point of that statement is that spacetime is flat (four dimensionally speaking) without mass to distort it.


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  4. #3 Re: stress energy tensor 
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    Quote Originally Posted by Sanford
    Someone emailed me the following statement that does not make sense to me.

    "The Einstein theory is an example of a non-linear theory in which the stress energy tensor vanishes in a mass zero zone."

    Is there any evidence of nonlinearity? How can the tress energy tensor vanish near a mass when the field does not vanish?
    I'm not entirely sure how your last senetence relates to what you were emailed.

    With regards to what you were emailed, if the stress-energy tensor they are referring to is the stress energy tensor of the source, then they are correct. In mass free zones it is customary to set the stress-energy tensor of the source equal to zero.

    As for your final sentence, the stress-energy tensor doesn't vanish when it's near the source, it vanishes far away.

    The final part of your sentence is a good question. Why does the field not vanish even though the source vanishes? This is due to the fact that the field propagates out from the source as a gravitational wave. So even though the source term is zero at our position, the field still reaches us.

    This wiki link will help you to understand linearised theory.

    http://en.wikipedia.org/wiki/Gravita...ve#Mathematics

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  5. #4 Re: stress energy tensor 
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    Quote Originally Posted by Sanford
    Someone emailed me the following statement that does not make sense to me.

    "The Einstein theory is an example of a non-linear theory in which the stress energy tensor vanishes in a mass zero zone."

    Is there any evidence of nonlinearity? How can the tress energy tensor vanish near a mass when the field does not vanish?
    The Einstein field equations (essentially the equations of motion in general relativity) happen to be non-linear partial differential equations. That is what people mean when they say it is a "non-linear" theory.
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  6. #5 Re: stress energy tensor 
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    Quote Originally Posted by sox
    Quote Originally Posted by Sanford
    Someone emailed me the following statement that does not make sense to me.

    "The Einstein theory is an example of a non-linear theory in which the stress energy tensor vanishes in a mass zero zone."

    Is there any evidence of nonlinearity? How can the tress energy tensor vanish near a mass when the field does not vanish?
    I'm not entirely sure how your last senetence relates to what you were emailed.

    With regards to what you were emailed, if the stress-energy tensor they are referring to is the stress energy tensor of the source, then they are correct. In mass free zones it is customary to set the stress-energy tensor of the source equal to zero.

    As for your final sentence, the stress-energy tensor doesn't vanish when it's near the source, it vanishes far away.

    The final part of your sentence is a good question. Why does the field not vanish even though the source vanishes? This is due to the fact that the field propagates out from the source as a gravitational wave. So even though the source term is zero at our position, the field still reaches us.

    This wiki link will help you to understand linearised theory.

    http://en.wikipedia.org/wiki/Gravita...ve#Mathematics
    Your comment about gravitational waves is wrong. We are discussing a static situation. Since you are wrong mentioning waves, your entire comment is wrong.

    Again, I'll clarify. A satellite is attracted to the earth and the sun. As it moves to a position where the sun and earth are lined up, so that the gravitational field is strongest, it will then be attracted to this strong field location, in addition to the attraction to the earth and the sun. Weinberg discussed this in his 1972 book on gravitation. Understanding this, now read my original comment and discuss it.
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  7. #6 Re: stress energy tensor 
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    Quote Originally Posted by Sanford
    Quote Originally Posted by sox
    Quote Originally Posted by Sanford
    Someone emailed me the following statement that does not make sense to me.

    "The Einstein theory is an example of a non-linear theory in which the stress energy tensor vanishes in a mass zero zone."

    Is there any evidence of nonlinearity? How can the tress energy tensor vanish near a mass when the field does not vanish?
    I'm not entirely sure how your last senetence relates to what you were emailed.

    With regards to what you were emailed, if the stress-energy tensor they are referring to is the stress energy tensor of the source, then they are correct. In mass free zones it is customary to set the stress-energy tensor of the source equal to zero.

    As for your final sentence, the stress-energy tensor doesn't vanish when it's near the source, it vanishes far away.

    The final part of your sentence is a good question. Why does the field not vanish even though the source vanishes? This is due to the fact that the field propagates out from the source as a gravitational wave. So even though the source term is zero at our position, the field still reaches us.

    This wiki link will help you to understand linearised theory.

    http://en.wikipedia.org/wiki/Gravita...ve#Mathematics
    Your comment about gravitational waves is wrong. We are discussing a static situation. Since you are wrong mentioning waves, your entire comment is wrong.
    Is it? If so then I apologise, though perhaps you could point out to me where I've gone wrong.

    Quote Originally Posted by Sanford
    Again, I'll clarify. A satellite is attracted to the earth and the sun. As it moves to a position where the sun and earth are lined up, so that the gravitational field is strongest, it will then be attracted to this strong field location, in addition to the attraction to the earth and the sun. Weinberg discussed this in his 1972 book on gravitation.
    Your original post gave none of this information so you are not clarifying anything "again".

    Quote Originally Posted by Sanford
    Understanding this, now read my original comment and discuss it.
    Therw are two things I shall say to this. 1) There is no point as according to you I'm wrong. 2) Telling someone to do something is never a good way to get help. But perhaps if you can explain my errors I shall try and help you with your ponderings.

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  8. #7 stress energy tensor 
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    Okay, very simple.
    We have a static situation. We therefore are not discussing waves.

    The force of gravity is due to mass and the energy of the grav. field. If so, then the curvature tensor is not zero in the empty space where there is no mass, for the force acts there.

    Something in Weinberg's book does not make sense. I wrote to him, and his answers do not make sense.
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  9. #8  
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    The field manifests itself as the curvature of space.

    Assume the sun and the earth are point sources with the sun located at (1,0,0), the satellite at (40,0,0) and the earth at (80,0,0).

    If the sun and earth are point sources then the mass is confined to their coordinates. But the field cgenerated by each extends way beyond their locations.

    So even if their is no source between the satellite and one of the sources, there can still exist a field there.

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  10. #9  
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    There original statement wasn't that the curvature was zero when there was no mass there, it was when there was no mass anywhere near there. Big difference. In fact, in the real world, the curvature would never be zero anywhere since there's always mass somewhere. There are places where it comes arbitrarily close though.
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  11. #10  
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    @ MagiMaster - Are you talking to me or Sanford?

    I can't see anything about that in the original post.

    All I can see is this:
    Quote Originally Posted by Sanford
    Someone emailed me the following statement that does not make sense to me.

    "The Einstein theory is an example of a non-linear theory in which the stress energy tensor vanishes in a mass zero zone."

    Is there any evidence of nonlinearity? How can the tress energy tensor vanish near a mass when the field does not vanish?

    __________________________________________________ _____________
    "Happy is the man who can recognise in the work of To-day a connected portion of the work of life, and an embodiment of the work of Eternity. The foundations of his confidence are unchangeable, for he has been made a partaker of Infinity." - James Clerk Maxwell
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  12. #11 field 
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    Let's not get confused. There is a field between masses. Now is a mass attracted to the field just as a mass is attracted to a mass? How can we verify this? After we clarify this, we'll go to the other points I made.
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  13. #12  
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    Yeah, I was talking to Sanford.

    @Sanford, mass is attracted to mass because of the field. Your question makes it sound like the two things are separate even though you can't really have one without the other (baring very exotic situations).
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  14. #13 mass is attracted to mass 
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    Quote Originally Posted by MagiMaster
    Yeah, I was talking to Sanford.

    @Sanford, mass is attracted to mass because of the field. Your question makes it sound like the two things are separate even though you can't really have one without the other (baring very exotic situations).
    Well, the things are indeed separate, according to Weinberg. Please read his 1972 book and then discuss it. It is a waste of time for us to discuss things before you do your necessary reading.
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  15. #14  
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    Perhaps YOU should go and read a different book on general relativity instead of being rude to people who have taken their time to help you?

    Also how can we read the book? Is it online? Not everyone will own it or have acess to it through a library.

    Honestly, the lack of manners is apalling...

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  16. #15  
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    @Sanford, My library catalog has this to say when I searched Weinberg:
    Entries
    535 Found
    Narrowing it down by year there are still 8 books, though I can assume that you're talking about Steven Weinberg's Gravitation and Cosmology book, which is currently checked out by someone else.

    Anyway, can you briefly summarize how you can separate a mass from its gravitational field or vice versa?

    Edit: Also, your original question was related to the quote:
    "The Einstein theory is an example of a non-linear theory in which the stress energy tensor vanishes in a mass zero zone."

    In this case it's referring to a (rather large) zone with no mass anywhere in it. In that case, can you still say there'd be a gravitational field?
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  17. #16 text 
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    Gravitation and Cosmology

    Read this around p. 150. Weinberg has two assumptions to derive GR. One is nonlinearity, meaning that a mass is attracted to the grav. field. The second is that the trace of the curvature tensor vanishes in a mass free zone. It seems to me that the second assumption contradicts the first. I can send you some papers. First beg, borrow, or whatever the book.
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  18. #17  
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    You appear to be confusing a lot of things. I can tell this much without reading the book (which is checked out for at least another month).

    Anyway, those two assumptions do not lead to any contradictions. The first refers to a situation with mass, the second without. Where's the contradiction?
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  19. #18 read the book 
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    Get back to me next month after you read the book, and we'll talk.
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  20. #19  
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    Sorry. I'm not going to go out of my way to find this book. There's no garauntee it'll be back this year since people can just keep rechecking it if they need to.

    Anyway, care to answer my previous question?
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  21. #20  
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    Quote Originally Posted by MagiMaster
    Sorry. I'm not going to go out of my way to find this book. There's no garauntee it'll be back this year since people can just keep rechecking it if they need to.

    Anyway, care to answer my previous question?
    Don't bother. The book (which I own) is being badly misquoted and misrepresented. There is not a lot of point in carrying out this discussion. Even Sanford's characterization of "nonlinearity" is so far off the mark as to be irreparable.
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    Quote Originally Posted by DrRocket
    Quote Originally Posted by MagiMaster
    Sorry. I'm not going to go out of my way to find this book. There's no garauntee it'll be back this year since people can just keep rechecking it if they need to.

    Anyway, care to answer my previous question?
    Don't bother. The book (which I own) is being badly misquoted and misrepresented. There is not a lot of point in carrying out this discussion. Even Sanford's characterization of "nonlinearity" is so far off the mark as to be irreparable.
    Okay, then you explain the basic assumption of GR as Weinberg puts it. Explain in your words what Weinberg means by nonlinarity. If you cannot explain it, you do not understand it.
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  23. #22  
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    Quote Originally Posted by Sanford
    Quote Originally Posted by DrRocket
    Quote Originally Posted by MagiMaster
    Sorry. I'm not going to go out of my way to find this book. There's no garauntee it'll be back this year since people can just keep rechecking it if they need to.

    Anyway, care to answer my previous question?
    Don't bother. The book (which I own) is being badly misquoted and misrepresented. There is not a lot of point in carrying out this discussion. Even Sanford's characterization of "nonlinearity" is so far off the mark as to be irreparable.
    Okay, then you explain the basic assumption of GR as Weinberg puts it. Explain in your words what Weinberg means by nonlinarity. If you cannot explain it, you do not understand it.
    You are most certainly not the judge of what I do or do not understand.

    I understand quite well that I have no desire to waste my time with you, sonny.

    Read the damn book. Weinberg is pretty clear.

    non-linear = not linear

    Weinberg merely points out that since gravity interacts with itself, whereas photons do not, that the Einstein field equations should be expected to be non-linear.
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  24. #23 Gravity interacts with itself 
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    Okay, can you give me a specific concrete example? Let me try. Satellite attracted to earth and sun. The satellite moves to a point where the earth and sun are lined up, where the gravitational field is strongest. As the satellite approaches this point, there are three forces acting on the satellite: the field due to the sun, the field due to the earth, and the field due to the gravity at this strong point.

    Is this correct? Is this what Weinberg meant? If not, please give me a concrete example.
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  25. #24 Re: Gravity interacts with itself 
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    Quote Originally Posted by Sanford
    Okay, can you give me a specific concrete example? Let me try. Satellite attracted to earth and sun. The satellite moves to a point where the earth and sun are lined up, where the gravitational field is strongest. As the satellite approaches this point, there are three forces acting on the satellite: the field due to the sun, the field due to the earth, and the field due to the gravity at this strong point.

    Is this correct? Is this what Weinberg meant? If not, please give me a concrete example.
    Your question is monstroulsy mis-framed. It falls under what Pauli had in mind when he said, "That's not right. It's not even wrong."

    Wenberg is attempting to motivate the form of the Einstein field equations, not solve the three-body problem, which is already too hard in the Newtonian model.

    You are clearly trying to read a book that is WAY over your head. If the word "non-linear" is as unfamiliar as it obviously is to you, then you need to drop back quite a way and understand calculus, linear algebra and ordinary differential equations before you take on the differential geometry and non-linear partial differential equations of general relativity.

    There is no point to continuing this discussion.
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  26. #25 Re: Gravity interacts with itself 
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    Quote Originally Posted by DrRocket
    Quote Originally Posted by Sanford
    Okay, can you give me a specific concrete example? Let me try. Satellite attracted to earth and sun. The satellite moves to a point where the earth and sun are lined up, where the gravitational field is strongest. As the satellite approaches this point, there are three forces acting on the satellite: the field due to the sun, the field due to the earth, and the field due to the gravity at this strong point.

    Is this correct? Is this what Weinberg meant? If not, please give me a concrete example.
    Wenberg is attempting to motivate the form of the Einstein field equations, not solve the three-body problem, which is already too hard in the Newtonian model.
    I said if you do not like my three-body example, give your own. Give an example to clarify Weinberg, instead of talking nonsense about Pauli and how you do not want to continue the discussion. If you understand the book, you should be able to give examples. Do your professors give examples of what they say in class? If not, they are not doing their job and you are not doing your job as a student which is to understand and question.

    Okay, wise guy, you say you understand Weinstein. Then clarify with an example.
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  27. #26 Re: Gravity interacts with itself 
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    Quote Originally Posted by Sanford
    Do your professors give examples of what they say in class? If not, they are not doing their job and you are not doing your job as a student which is to understand and question.
    Sonny, I don't have professors. I have been my own professor for quite a while -- since receiving my Ph.D. quite a few years ago.

    So, don't lecture me, particulalry when it is abundantly clear that you don't know what you are talking about. Go learn enough background material to understand an answer when it is given to you. That is what understanding and questioning is all about. Learn the material yourself, the hard way, with work and expenditure of intellectual capital.

    But before you try to answer questions, you need to learn enough to frame a question intelligently. You have not done that yet.

    Weinberg is abundantly clear in the section of the book that is giving you trouble. I explained to you what he is tryiing to do. You just don't get it. You clearly lack the background to get it. Stop your whining and go get the background.
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  28. #27 Re: Gravity interacts with itself 
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    Quote Originally Posted by DrRocket
    Quote Originally Posted by Sanford
    Do your professors give examples of what they say in class? If not, they are not doing their job and you are not doing your job as a student which is to understand and question.
    Sonny, I don't have professors. I have been my own professor for quite a while -- since receiving my Ph.D. quite a few years ago.

    So, don't lecture me, particulalry when it is abundantly clear that you don't know what you are talking about. Go learn enough background material to understand an answer when it is given to you. That is what understanding and questioning is all about. Learn the material yourself, the hard way, with work and expenditure of intellectual capital.

    But before you try to answer questions, you need to learn enough to frame a question intelligently. You have not done that yet.

    Weinberg is abundantly clear in the section of the book that is giving you trouble. I explained to you what he is tryiing to do. You just don't get it. You clearly lack the background to get it. Stop your whining and go get the background.
    Okay, prof. I'll shut up. Weinberg is clear. No specific numerical example is needed. He has spoken, and we mortals must try to understand and accept. I guess I do not know how to frame a question. I just want an example, but this is too hard to explain. I have to learn the material myself, and do not need your help in getting examples. You guys are incapable of giving specific examples. You just think in the air.

    Are you all theoreticians? Have any of you given thought to devising an experiment to verify Weinberg's two assumptions? Or do just shut up and accept the words of the wise man?
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  29. #28 Re: text 
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    Quote Originally Posted by Sanford
    Gravitation and Cosmology

    Read this around p. 150. Weinberg has two assumptions to derive GR. One is nonlinearity, meaning that a mass is attracted to the grav. field. The second is that the trace of the curvature tensor vanishes in a mass free zone. It seems to me that the second assumption contradicts the first. I can send you some papers. First beg, borrow, or whatever the book.
    If Weinberg's two assumptions are "GR is nonlinear" and "the trace of the curvature tensor vanishes in a mass free zone", then the conclusions you've drawn from those assumptions are what doesn't make sense.

    BTW, what do you think the word nonlinear means?
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  30. #29 Re: Gravity interacts with itself 
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    Quote Originally Posted by Sanford
    Are you all theoreticians? Have any of you given thought to devising an experiment to verify Weinberg's two assumptions? Or do just shut up and accept the words of the wise man?
    Are you really that dumb ?

    Of course there have been experiments to verify general relativity. Many of them. That is how physics works. Nobody accepts a model unless and until it has made experimentally verifiable predictions. Without those predictions nobody would be reading Weinberg's book, and in fact he would not have written it.
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  31. #30 Re: Gravity interacts with itself 
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    Quote Originally Posted by DrRocket
    Quote Originally Posted by Sanford
    Are you all theoreticians? Have any of you given thought to devising an experiment to verify Weinberg's two assumptions? Or do just shut up and accept the words of the wise man?
    Are you really that dumb ?

    Of course there have been experiments to verify general relativity. Many of them. That is how physics works. Nobody accepts a model unless and until it has made experimentally verifiable predictions. Without those predictions nobody would be reading Weinberg's book, and in fact he would not have written it.
    Sorry, there have been no experiments to directly verify the two assumptions Weinberg's book. Jaroslav Hynecek has published an alternative theory which does not agree with Weinberg's assumptions, but does agree with the various tests, such as the orbit of Mercury, bending of starlight near the sun, etc. If a physicist makes a statement, this must be verified.

    Again, devise a thought experiment to verify these assumptions. You beat around the bush, you scream and yell, but you do not reply to my challenge.
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  32. #31 Re: Gravity interacts with itself 
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    Quote Originally Posted by Sanford

    Sorry, there have been no experiments to directly verify the two assumptions Weinberg's book. Jaroslav Hynecek has published an alternative theory which does not agree with Weinberg's assumptions, but does agree with the various tests, such as the orbit of Mercury, bending of starlight near the sun, etc. If a physicist makes a statement, this must be verified.

    Again, devise a thought experiment to verify these assumptions. You beat around the bush, you scream and yell, but you do not reply to my challenge.
    You miss the point entirely and you are becoming rather irksome. I have no idea who Jaroslav Hynecek is, nor do I care. If he has alternate theory to general reltivity, then let it be tested. If he has alternate approach to the pedagody associated with the teaching of general relativity, then that is fine but nobody really cares.

    Ok I did a little "google" on Jaroslav Hynecek. He appears to me to be a nut. Are you he ?

    http://en.scientificcommons.org/52142692

    We are done.
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    I have Googled Jaroslav Hynecek and found this little snippet, relating to this forum.

    http://thescienceforum.com/viewtopic.php?p=242253

    It seems it does not take too long, to get published, on the net.
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  34. #33 Re: Gravity interacts with itself 
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    Quote Originally Posted by DrRocket
    Quote Originally Posted by Sanford

    Sorry, there have been no experiments to directly verify the two assumptions Weinberg's book. Jaroslav Hynecek has published an alternative theory which does not agree with Weinberg's assumptions, but does agree with the various tests, such as the orbit of Mercury, bending of starlight near the sun, etc. If a physicist makes a statement, this must be verified.

    Again, devise a thought experiment to verify these assumptions. You beat around the bush, you scream and yell, but you do not reply to my challenge.
    You miss the point entirely and you are becoming rather irksome. I have no idea who Jaroslav Hynecek is, nor do I care. If he has alternate theory to general reltivity, then let it be tested. If he has alternate approach to the pedagody associated with the teaching of general relativity, then that is fine but nobody really cares.

    Ok I did a little "google" on Jaroslav Hynecek. He appears to me to be a nut. Are you he ?

    http://en.scientificcommons.org/52142692

    We are done.
    I am not Hynecek. Have you read his papers? Why do you argue like politicians rather than like physicists? You use words meaningless in physics, like "irksome", "nor do i care".

    Hynecek published papers presenting his theory, along with results that agree with observations. Hynecek gets better agreement than Weinberg. I can email you his papers if you send me your email addresses.

    I ask a simple question that you do not answer. Give thought experiments which verify Weinberg's assumptions directly.
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  35. #34  
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    If there's any weight to what this Hynecek person is proposing, then he should publish it in a peer-reviewed journal.

    The name "Jaroslav Hynecek" does not even show up on the arXiv server. That's pretty strong evidence that he is not affiliated with any university and that he does not know any physicists who are interested in his work and willing to vouche for him.

    And note, there's nothing particularly prestigeous about posting a paper on arXiv. The spectrum of quality of arXiv papers ranges from very good to very poor.

    My advice, if you are a physics student, is to avoid wasting your time on this person.
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  36. #35 Four Tests of Gravitational Theory 
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    Physics Essays is a peer reviewed journal. Here are a few papers.

    Physics Essays volume 20, number 2, 2007
    313
    New Space-Time Metric, Four Tests of Gravitational Theory, and Newton’s Law of Gravitation, Jaroslav Hynecek

    PHYSICS ESSAYS 22, 2, 2009
    New space-time metrics for symmetric spaces, Jaroslav Hynecek

    "In the previously published article,1 the new space-time
    metric for the centrally gravitating body was derived and
    compared for agreement with the formulas of general relativity
    theory, GRT. The predictions of the new metric were
    also compared with observations and it was found that the
    new formulas provide more accurate descriptions that are in
    principle testable and distinguishable from the predictions of
    the GRT formulas. The derivation was based on the introduction
    of a new concept of the physical space-time that remains
    Minkowski flat when the gravity is added. For completeness,
    the derivation is briefly repeated here with some simplifications
    and clarifications."

    PHYSICS ESSAYS 22, 4, 2009
    Basic assumptions and black holes, Sanford Aranoff
    From the abstract:
    The statement “an observer crossing the event horizon and losing all contact with the rest of the universe is part of physics” is a counterexample to the proper understanding of theories. Statements incorrectly based on theories may be obstacles to the advance of science. One needs to understand the philosophical underpinnings of science, and how one can tease out the hidden assumptions of a theory.
    2009 Physics Essays Publication. DOI: 10.4006/1.3241135
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