Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: parakorn on 28/08/2014 17:03:11
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Every one know that Einstein was the creator of the General relativity,yes I know too, But after I have read this article http://arxiv.org/ftp/physics/papers/0204/0204044.pdf that was written by Peter M Brown who was the member here too. I also confused with this articles very much. This article said that Einstein did not create the real General relativity he didn,t think that gravity was the space time curvature but I have read many book and almost of it said that Einstein create the General relativity of space time curvature. Who can explain me and tell me that who is Peter M brown does he was the professor of any university ??
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Every one know that Einstein was the creator of the General relativity,yes I know too, But after I have read this article http://arxiv.org/ftp/physics/papers/0204/0204044.pdf that was written by Peter M Brown who was the member here too. I also confused with this articles very much. This article said that Einstein did not create the real General relativity he didn,t think that gravity was the space time curvature but I have read many book and almost of it said that Einstein create the General relativity of space time curvature. Who can explain me and tell me that who is Peter M brown does he was the professor of any university ??
Yes. Einstein created relativity. If you read otherwise then it was wrong or you misread it. If you read that someone said that Einstein showed that Einstein proved/showed that gravity is a curvature in spacetime then they're wrong. If you understand GR then all the evidence is in that article. I never claimed that Einstein didn't create GR so you read the article incorrectly.
That's not what I wrote in that article. I explained that what physicists thought Einstein said, such as gravity = spacetime curvature, was not due to him but due to someone else, namely Max Von Laue.
I'm not a professor in a university. I worked as a physicist in the public domain before I became disabled. I'm still a physicist since my mind is still working fine. I studied general relativity at MIT and when I wrote that paper I had a general relativity expert (who's also an expert in the history of general relativity), John Stachel, confirm everything that I said in that article.
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I think that I have read your article clearly, Your article try to proof that there are two version of The General relativity the Einstein version and The modern version.You try to proof that Einstein did not determine the gravity as the space time curvature. If Einstein did not determine gravity as spacetime curvature why he tried to study the Riemann Geometry that was the Geometry for non euclidean of curvature geometry.
There are many time that Einstein say that space time curvature like in http://en.wikisource.org/wiki/Relativity:_The_Special_and_General_Theory/Part_III in section 32 first sentence he say that "According to the general theory of relativity, the geometrical properties of space are not independent, but they are determined by matter." .In year 1915 in The field equation of gravitational paper he said that space time variable http://en.wikisource.org/?curid=735695 and can determine by matter and energy tensor. in this paper too http://en.wikisource.org/wiki/The_Meaning_of_Relativity/Lecture_4
Tesla criticize Einstein general relativity http://en.wikipedia.org/wiki/Nikola_Tesla he said that " I hold that space cannot be curved, for the simple reason that it can have no properties. It might as well be said that God has properties. He has not, but only attributes and these are of our own making. Of properties we can only speak when dealing with matter filling the space. To say that in the presence of large bodies space becomes curved is equivalent to stating that something can act upon nothing. I, for one, refuse to subscribe to such a view".
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I think that I have read your article clearly, Your article try to proof that there are two version of The General relativity the Einstein version and The modern version.You try to proof that Einstein did not determine the gravity as the space time curvature.
Then you read it wrong. The article only refers to the interpretation of how the term "gravitational field" is defined. Einstein defined it one way and others defined it another way. I know that's what the author means because I'm the author. Anything else is your interpretation. If you claim that I said otherwise then please post the page number and the sentence in which you claim I said it.
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...Tesla criticize Einstein general relativity http://en.wikipedia.org/wiki/Nikola_Tesla he said that " I hold that space cannot be curved..."
There's a delicious irony to that. Have a read of The role of the potentials in electromagnetism (http://www.compumag.org/jsite/images/stories/newsletter/ICS-99-06-2-Hammond.pdf) by Percy Hammond and see where he says "We conclude that the field describes the curvature that characterizes the electromagnetic interaction".
What Peter says is true. There are some differences between relativity as described by Einstein and relativity as it's taught today. I think it's something of an issue actually. It causes problems.
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I think that I have read your article clearly, Your article try to proof that there are two version of The General relativity the Einstein version and The modern version.You try to proof that Einstein did not determine the gravity as the space time curvature.
Then you read it wrong. The article only refers to the interpretation of how the term "gravitational field" is defined. Einstein defined it one way and others defined it another way. I know that's what the author means because I'm the author. Anything else is your interpretation. If you claim that I said otherwise then please post the page number and the sentence in which you claim I said it.
first page that you wrote that "Einstein identified the existence of gravity with the inertial motion of
accelerating bodies (i.e. bodies in free-fall) whereas contemporary physicists identify
the existence of gravity with space-time curvature (i.e. tidal forces). The
interpretation of gravity as a curvature in space-time is an interpretation Einstein did
not agree with"
In the fourth page that you wrote Did Einstein actually hold the view that gravity is a
curvature in space-time? At this point let us whet your appetite. No. Einstein
never said nor implied in anyway that gravity is a curvature in space-time. This
apparent disparity is a result of a change of interpretation.
In page 9 that you wrote In the year following the completion and publication of the general theory
of relativity Einstein published the review article The Foundation of the General
Theory of Relativity in 1916 3. The statement
It will be seen from these reflections that in pursuing the general theory
of relativity we shall be led to a theory of gravitation, since we are able to
“produce” a gravitational field merely by changing the system of coordinates.
identifying gravity with non-inertial systems, wholly reflects Einstein’s
interpretation of gravity, the existence of which depends on the observer’s frame
of reference.
and in the conclusion in page 22 that you wrote Einstein did not interpret gravity as a curvature of space-time, rather that
space-time curvature is a manifestation of gravity. This is the difference between
EGR and MGR
But in truth there are many time that Einstein said that gravity is the curvature of space time
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But in truth there are many time that Einstein said that gravity is the curvature of space time.
No there isn't. If you beg to differ, give a few reference where he did say that.
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But in truth there are many time that Einstein said that gravity is the curvature of space time.
No there isn't. If you beg to differ, give a few reference where he did say that.
He certainly realized that the mathematics of his theory describing gravitation also describe curvature in space-time
(http://www.nobelprize.org/nobel_prizes/physics/laureates/1921/einstein-lecture.pdf).
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But in truth there are many time that Einstein said that gravity is the curvature of space time.
No there isn't. If you beg to differ, give a few reference where he did say that.
for example http://en.wikisource.org/wiki/Relativity:_The_Special_and_General_Theory/Part_II section 23-section 27 and section 31-32
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first page that you wrote that "Einstein identified the existence of gravity with the inertial motion of accelerating bodies (i.e. bodies in free-fall) whereas contemporary physicists identify the existence of gravity with space-time curvature (i.e. tidal forces). The interpretation of gravity as a curvature in space-time is an interpretation Einstein did
not agree with"
All I see in your response is you quoting me. Quoting me is not a rebuttal to what you're quoting. And all of what you quoted is very much true. All one has to do is read Einstein’s paper in which he published GR to see that to be the case.
In the fourth page that you wrote Did Einstein actually hold the view that gravity is a curvature in space-time? At this point let us whet your appetite. No. Einstein never said nor implied in anyway that gravity is a curvature in space-time.
That's correct. But don't make the mistake of confusing that to say that matter can't curve spacetime.
This apparent disparity is a result of a change of interpretation.
That’s very much so and I showed you the statement where Einstein said it in a letter to Max Von Laue.
In page 9 that you wrote In the year following the completion and publication of the general theory of relativity Einstein published the review article The Foundation of the General Theory of Relativity in 1916 3. The statement It will be seen from these reflections that in pursuing the general theory of relativity we shall be led to a theory of gravitation, since we are able to “produce” a gravitational field merely by changing the system of coordinates. identifying gravity with non-inertial systems, wholly reflects Einstein’s interpretation of gravity, the existence of which depends on the observer’s frame
of reference.
Again all you're doing is quoting me for not apparent reason. Why this time?
That Einstein said that is easily seen in his paper which is online at http://hem.bredband.net/b153434/Works/Einstein.htm
This view is made possible for us by the teaching of experience as to the existence of a field of force, namely, the gravitational field, which possesses the remarkable property of imparting the same acceleration to all bodies. The mechanical behavior of bodies relatively to K' is the same as presents itself to experience in the case of systems which we are wont to regard as "stationary" or as "privileged." Therefore, from the physical standpoint, the assumption readily suggests itself that the systems K and K' may both with equal right be looked upon as "stationary" that is to say, they have an equal title as systems of reference for the physical description of phenomena.
It will be seen from these reflexions that in pursuing the general theory of relativity we shall be led to a theory of gravitation, since we are able to "produce" a gravitational field merely by changing the system of co-ordinates. It will also be obvious that the principle of the constancy of the velocity of light in vacuo must be modified, since we easily recognize that the path of a ray of light with respect to K' must in general be curvilinear, if with respect to K light is propagated in a straight line with a definite constant velocity.
If you knew general relativity then you’d know that spacetime curvature cannot be produced by a change in coordinates.
But in truth there are many time that Einstein said that gravity is the curvature of space time
You're quite wrong. There are absolutely no cases in which he said that. Didn’t you read my paper closely? In fact he actually spoke out against that interpretation in a letter to When Max von Laue stated as I said earlier. Von Laue sent Einstein a book on GR he was working on to be proof read. Einstein wrote back to him with the following protest
... what characterizes the existence of a gravitational field from the empirical standpoint is the non-vanishing of the components of the affine connection], not the vanishing of the [components of the Riemann tensor]. If one does not think in such intuitive (anschaulich) ways, one cannot grasp why something like curvature should have anything at all to do with gravitation. In any case, no rational person would have hit upon anything otherwise. The key to the understanding of the equality of gravitational mass and inertial mass would have been missing.
That quote is in the paper written by a GR historian and GR expert John Stachel, in
General Relativity and Gravitation Proceedings of the 11th International Conference on General Relativity and Gravitation, (Stockholm,Cambridge University Press, Jul 6-12, 1986), How Einstein Discovered General Relativity: A Historical Tale With Some Contemporary Morals, John J. Stachel
As I said, this is a fact, not a guess. John is a world renowned expert on general relativity and the most knowledgeable Einstein historian in the world. While it was I who wrote the paper, John made sure that my premises and conclusions were correct. There’s nothing wrong with my paper.
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But in truth there are many time that Einstein said that gravity is the curvature of space time.
No there isn't. If you beg to differ, give a few reference where he did say that.
for example http://en.wikisource.org/wiki/Relativity:_The_Special_and_General_Theory/Part_II section 23-section 27 and section 31-32
Those sections say no such thing. In you next post please cut and past where you think Einstein said "Gravity is a curvature in spacetime".
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But in truth there are many time that Einstein said that gravity is the curvature of space time.
No there isn't. If you beg to differ, give a few reference where he did say that.
He certainly realized that the mathematics of his theory describing gravitation also describe curvature in space-time
(http://www.nobelprize.org/nobel_prizes/physics/laureates/1921/einstein-lecture.pdf).
Absolutely true. Too many people interpret my paper to mean that Einstein said nothing about curvature. That's extremely frustrating. This newbie is seeing things in http://en.wikisource.org/wiki/Relativity:_The_Special_and_General_Theory/Part_II#Section_23_-_Behaviour_of_Clocks_and_Measuring-Rods_on_a_Rotating_Body_of_Reference which aren't even there though!!!!
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He certainly realized that the mathematics of his theory describing gravitation also describe curvature in space-time (http://www.nobelprize.org/nobel_prizes/physics/laureates/1921/einstein-lecture.pdf).
There's certainly some non-Euclidean geometry and some curvature in the mix! But when you actually read the various documents, what's missing is curved spacetime. It just isn't there. It isn't in the Nordic document. In fact Einstein talks about unifying electromagnetism and gravity and refers to "space curvature", which relates to what Percy Hammond was saying about electromagnetism.
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Curvature of any sort will only happen when the gravitational radiation is emitted from a curved surface and is a result of the geometry. An enormous flat slab would radiate a generally flat field. The geometry of the field would vary at the corners.
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Curvature of any sort will only happen when the gravitational radiation is emitted from a curved surface and is a result of the geometry. An enormous flat slab would radiate a generally flat field. The geometry of the field would vary at the corners.
That's quite incorrect. Gravitational radiation is in no way required for the presence of spacetime curvature. Where did you ever get that idea from?
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Curvature of any sort will only happen when the gravitational radiation is emitted from a curved surface and is a result of the geometry. An enormous flat slab would radiate a generally flat field. The geometry of the field would vary at the corners.
That's quite incorrect. Gravitational radiation is in no way required for the presence of spacetime curvature. Where did you ever get that idea from?
OK then Pete. What is required? This is of particular interest to me.
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OK then Pete. What is required? This is of particular interest to me.
Let's use the Newtonian description since most people are used to that terminology. Mass generates gravitational forces, right? When the distribution of matter is such that the tidal force tensor is non-zero then there are tidal forces present. That means that the gravitational force varies from one place to another. See
http://home.comcast.net/~peter.m.brown/mech/tidal_force_tensor.htm
NASA describes it here - http://spacemath.gsfc.nasa.gov/blackh/4Page33.pdf
A tidal force is a difference in the strength of gravity between two points.
Princeton describes it here - https://www.princeton.edu/~achaney/tmve/wiki100k/docs/Tidal_force.html
Wiki describes it at http://en.wikipedia.org/wiki/Tidal_force
See also - http://burro.astr.cwru.edu/Academics/Astr221/Gravity/tides.html
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OK then Pete. What is required? This is of particular interest to me.
Let's use the Newtonian description since most people are used to that terminology. Mass generates gravitational forces, right? When the distribution of matter is such that the tidal force tensor is non-zero then there are tidal forces present. That means that the gravitational force varies from one place to another. See
http://home.comcast.net/~peter.m.brown/mech/tidal_force_tensor.htm
NASA describes it here - http://spacemath.gsfc.nasa.gov/blackh/4Page33.pdf
A tidal force is a difference in the strength of gravity between two points.
Princeton describes it here - https://www.princeton.edu/~achaney/tmve/wiki100k/docs/Tidal_force.html
Wiki describes it at http://en.wikipedia.org/wiki/Tidal_force
See also - http://burro.astr.cwru.edu/Academics/Astr221/Gravity/tides.html
In order for there to be a tidal force a mass has to radiate force carriers, surely! That's the point isn't it? To get a value for g you need a force acting on a mass.
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In order for there to be a tidal force a mass has to radiate force carriers, surely!
Nope. I don't know where you get these ideas from. I don't even know what that means. What does "radiate force carriers" mean and where did you get such an idea from?
Unless you're thinking about quantum field theory where particles interact by exchanging virtual particles? If so then that'd be quantum gravity and there's no such theory as of yet. In any case that has absolutely nothing to do with gravitational radiation.
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Well quantum gravity is the ultimate goal.
http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_radiation.html
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Those virtual particles are virtual, Jeffrey. They aren't real particles. Hydrogen atoms don't twinkle, magnets don't shine, and there are no gravitons pouring out of a black hole. Have a read of Matt Strassler's article (http://profmattstrassler.com/articles-and-posts/particle-physics-basics/virtual-particles-what-are-they/). Note this bit: "The best way to approach this concept, I believe, is to forget you ever saw the word “particle” in the term. A virtual particle is not a particle at all. It refers precisely to a disturbance in a field that is not a particle at all". Virtual particles are "field quanta". It's like you divide the field up into little distorted squares, and say each one is a virtual particle.
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Those virtual particles are virtual, Jeffrey. They aren't real particles. Hydrogen atoms don't twinkle, magnets don't shine, and there are no gravitons pouring out of a black hole. Have a read of Matt Strassler's article (http://profmattstrassler.com/articles-and-posts/particle-physics-basics/virtual-particles-what-are-they/). Note this bit: "The best way to approach this concept, I believe, is to forget you ever saw the word “particle” in the term. A virtual particle is not a particle at all. It refers precisely to a disturbance in a field that is not a particle at all". Virtual particles are "field quanta". It's like you divide the field up into little distorted squares, and say each one is a virtual particle.
I went down that avenue originally not was not satisfied with the results. I will read the article though I will have to find something convincing.
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Well that was interesting. The trick is to view the standard model and the fields involved to determine exactly how we can end up with an attractive force. I had in mind 3 disturbances. That's where I went wrong. I can now make a bit more sense of the G2 gas cloud encounter.
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I'm afraid some of what you read about is just rubbish, Jeffrey. Have a google on virtual evanescent (https://www.google.co.uk/?gws_rd=ssl#q=virtual+evanescent). The reality that underlies virtual photons is the evanescent wave aka near field. Have a look at near and far field (http://en.wikipedia.org/wiki/Near_and_far_field#Quantum_field_theory_view) on Wikipedia and you can read this: "In the quantum view of electromagnetic interactions, far-field effects are manifestations of real photons, whereas near-field effects are due to a mixture of real and virtual photons". Virtual photons aren't real photons flying back and forth at c. They're just chunks of field going nowhere. In similar fashion (virtual) gravitons aren't real particles flying out of a black hole at c. They're just chunks of field going nowhere. Only people don't know how to use the quantum field theory methodology for gravity.
By the by, have a look at gluons (http://en.wikipedia.org/wiki/Gluon#Confinement) on Wikipedia. See this: "as opposed to virtual ones found in ordinary hadrons". Gluons are virtual particles too.
Anyway, we're getting off topic with this. Which is that Einstein described gravity in a certain way, but some people nowadays tend to describe it in a way that contradicts Einstein, and it's causing problems. Because if they don't understand gravity properly, they can't quantize it.
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Well quantum gravity is the ultimate goal.
http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_radiation.html
That's beside the point, Jeff. You claimed that
Curvature of any sort will only happen when the gravitational radiation is emitted from a curved surface and is a result of the geometry.
which is wrong.
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May be we had out from our first topic of this discussion so I think that we should back to our topic about Einstein and his Gravitational theory. PMB you want me to find the evidence about Einstein theory of space time curvature I will show you
my evidence
first http://en.wikisource.org/wiki/Translation:The_Field_Equations_of_Gravitation the field equation of gravitatinal of General Relativity in 1915 Einstein wrote that "I have shown in two recently published reports,[1] how one can arrive at field equations of gravitation, that are in agreement with the postulate of general relativity, i.e. which in their general form are covariant in respect to arbitrary substitutions of space-time variables".
We obtain the ten general covariant equations of the gravitational field in spaces, in which "matter" is absent, by putting
G_{im}=0 (2)
These equations can be formed in a simpler way, when one choses the reference system so that \sqrt{-g}=1. Then S_{im} vanishes due to (1b), so that one obtains instead of (2)
R_{im}=\sum\limits _{l}\frac{\partial\Gamma_{im}^{l}}{\partial x_{l}}+\sum\limits _{\rho l}\Gamma_{i\rho}^{l}\Gamma_{ml}^{\rho}=0 (3)
\sqrt{-g}=1 (3a)
Here we put
\Gamma_{im}^{l}=-\left\{ {im\atop l}\right\} (4)
which magnitudes we will denote as the "components" of the gravitational field.
If "matter" exists in the considered space, then its energy tensor appears on the right hand side of (2) or (3). We put
G_{im}=-\varkappa\left(T_{im}-\frac{1}{2}g_{im}T\right)
Second in Einstein book http://en.wikisource.org/wiki/Relativity:_The_Special_and_General_Theory/Part_III#Section_32_-_The_Structure_of_Space_According_to_the_General_Theory_of_Relativity Einstein said that " According to the general theory of relativity, the geometrical properties of space are not independent, but they are determined by matter. Thus we can draw conclusions about the geometrical structure of the universe only if we base our considerations on the state of the matter as being something that is known." That mean the curvature of space can explain by the appear of matter.
In third evidence is about Einstein field equation in The meaning of relativity paper http://en.wikisource.org/wiki/The_Meaning_of_Relativity/Lecture_4
R_{\mu\nu} - \frac{1}{2}g_{\mu\nu}R = -\kappa T_{\mu\nu}. In the left hand side show the Einstein tensor that have Ricci tensor to explain about the curvature of space and in right side show about mass and energy tensor
All of these were the evidence about matter can cause of the curvature of space time.
If you said that Einstein version of general relativity wasn't relate with space time curvature I think you are wrong but if you said that Einstein version of general relativity wasn't relate with Tidal force.I will agree with you because The tidal force conect with general relativity was the modern view of general relativity not Einstein general relativity. I haven't seen in any paper of Einstein general relativity that he write about tidal force
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I can't post the equation here who can help me please.
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There is a difference between the curvature of the trajectory and the inherent geometry of the field causing the curvature. They will both be parabolic but will differ due to the geometry of the masses involved.
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I'm afraid some of what you read about is just rubbish, Jeffrey.
Probably some of the work I am attempting is too. I am open to learning more.
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May be we had out from our first topic of this discussion so I think that we should back to our topic about Einstein and his Gravitational theory. PMB you want me to find the evidence about Einstein theory of space time curvature I will show you
my evidence ..
You can't merely toss out a page of text and say "This is where Einstein said this is true". You have to post the exact sentence and what about that sentence makes you correct and me wrong. Watch. That's what I'll do with your "evidence"
Einstein wrote
Here we put
\Gamma_{im}^{l}=-\left\{ {im\atop l}\right\} (4)
which magnitudes we will denote as the "components" of the gravitational field.
which is exactly what my paper says. Here's an example of a gravitational field which has flat spacetime but for which the "components" of the gravitational field are not zero - http://home.comcast.net/~peter.m.brown/gr/uniform_force.htm
I gave that example in my paper but you ignored it. Why did you ignore it?
All of these were the evidence about matter can cause of the curvature of space.
Just as I though. You're not reading what I'm posting carefully enough. In reply #3 I wrote
The article only refers to the interpretation of how the term "gravitational field" is defined.
I never anywhere claimed that gravity can't curve spacetime. And we've been talking about this in many posts. Do you not understand the difference between a gravitational field with and without tidal forces in it? The gravitational field around the earth has tidal forces while a uniform gravitational field such as though found in this page
http://home.comcast.net/~peter.m.brown/gr/grav_cavity.htm has zero tidal forces inside the cavity illustrated in the diagram.
If you said that Einstein version of general relativity wasn't relate with space time curvature I think you are wrong ...
I never said such a thing.
I haven't seen in any paper of Einstein general relativity that he write about tidal force
He didn't use the term but it's there in principle. The Riemann tensor in GR is merely the relativistic version of the tidal force tensor from Newtonian gravity. Tidal forces and spacetime curvature are merely two ways of saying the same thing.
See Black Holes and Time Warps by Kip Thorne page 111. After the author discusses the crossing of two paths of falling objects the author writes
Thus, Einstein and Newton, with their very different viewpoints on the nature of space and time, give different names to the agent that causes the crossing. Einstein calls it spacetime curvature; Newton called it tidal gravity. But there is just one agent acting. Therefore, spacetime curvature and tidal gravity must be precisely the same thing, expressed in different languages.
I don't see how you could have missed that since its prominently written on page 3 in the Introduction.
It's quite clear to me that you didn't read my paper very carefully at all.
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OK may be I didn't understand your paper or I didn't read your article clearly.May be you can to simplify about the different between Einstein General Relativity and Modern General Relativity in the easy word for me. Sorry for I didn't read your article clearly and sorry if this reply disturb you. Thank you
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OK may be I didn't understand your paper or I didn't read your article clearly.May be you can to simplify about the different between Einstein General Relativity and Modern General Relativity in the easy word for me. Sorry for I didn't read your article clearly and sorry if this reply disturb you. Thank you
Okay. Thanks. And I'd like to compliment you on being able to notice that you might have made a mistake and then be able to correct it and then move on. That's one of the cherished traits in physics that I admire in a person who's discussing physics. [:)]
Einstein defined gravity such that it's locally equivalent to an accelerating frame of reference. The weak equivalence principle states that at uniform gravitational field is equivalent to a uniformly accelerating frame of reference.
If you're in a flat spacetime then, regardless of what frame of reference (system of coordinates) you're using the Riemann tensor will be zero. There is no gravitational field in this frame. Now transform to a uniformly accelerating frame of reference. In that frame there is a uniform gravitational field. If you read page 9 in my paper you'll see this
In the year following the completion and publication of the general theory of relativity Einstein published the review article The Foundation of the General Theory of Relativity in 1916. The statement
"It will be seen from these reflections that in pursuing the general theory of relativity we shall be led to a theory of gravitation, since we are able to “produce” a gravitational field merely by changing the system of coordinates."
Others didn't like this notion since it seemed too odd for people to grasp. I.e. How can you create a gravitational field merely by changing to an accelerating frame of reference. Since they knew that there's no kind of accelerating frame of reference that will mimic tidal gradients (which is dictated by spacetime curvature) they decided to think of a "real" gravitational field as being determined the presence of spacetime curvature. However that has a lot of problems because even some experts will claim that the gravitational force is replaced by spacetime curvature since one has nothing to do with the other in some instances, e.g. like the uniform gravitational field. I've seen most people not understand that a uniform gravitational field has no spacetime curvature because they think of gravity as being spacetime curvature and where ever there's a gravitational force there's spacetime curvature, which is wrong. I saw a guy publish a paper in the American Journal of Physics claim that a uniform gravitational field (which is flat - by definition) claim to have proved that it's curved. He made an error in his assumption of what the proper acceleration should be of a particle. Since he got a curved spacetime it should have told him that it was the wrong answer but since he assumed that gravitational fields have spacetime curvature then he made no mistake. See how these problems can arise because of not using Einstein's definition? His definition is how we think of gravity.
Einstein didn't like all that stuff about curvature. That's why he wrote that letter to Max Von Laue saying
... what characterizes the existence of a gravitational field from the empirical standpoint is the non-vanishing of the components of the affine connection], not the vanishing of the [components of the Riemann tensor]. If one does
not think in such intuitive (anschaulich) ways, one cannot grasp why something like curvature should have anything at all to do with gravitation. In any case, no rational person would have hit upon anything otherwise. The key to the understanding of the equality of gravitational mass and inertial mass would have been missing.
Make sense now? [:)]
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Perhaps I could back that up with a simplified version? Parakorn, have a look at the depiction of gravitational potential (http://en.wikipedia.org/wiki/Gravitational_potential):
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fupload.wikimedia.org%2Fwikipedia%2Fcommons%2Fthumb%2Fd%2Fd9%2FGravityPotential.jpg%2F300px-GravityPotential.jpg&hash=848f35613bf74f8f41fe54b2817d5567)
The curvature you can see in the depiction relates to the Riemann curvature tensor (http://en.wikipedia.org/wiki/Riemann_curvature_tensor). But things don't actually fall down because of this. The force of gravity is denoted by the degree of slope, the first derivative of potential. The tidal force or Riemann curvature tensor is denoted by the change in slope, the second derivative of potential.
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Perhaps I could back that up with a simplified version? Parakorn, have a look at the depiction of gravitational potential (http://en.wikipedia.org/wiki/Gravitational_potential):
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fupload.wikimedia.org%2Fwikipedia%2Fcommons%2Fthumb%2Fd%2Fd9%2FGravityPotential.jpg%2F300px-GravityPotential.jpg&hash=848f35613bf74f8f41fe54b2817d5567)
The curvature you can see in the depiction relates to the Riemann curvature tensor (http://en.wikipedia.org/wiki/Riemann_curvature_tensor). But things don't actually fall down because of this. The force of gravity is denoted by the degree of slope, the first derivative of potential. The tidal force or Riemann curvature tensor is denoted by the change in slope, the second derivative of potential.
And of course acceleration is curved in Minkowsi diagrams and shows curvature but unlike gravitation and free-fall a force IS felt.
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And of course acceleration is curved in Minkowsi diagrams and shows curvature ...
What do you mean by "shows curvature"? Suppose you're in a uniformly accelerating frame in flat spacetime. There's acceleration but no curvature. So how does what you say apply in that case?
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Jeffrey, imagine you're standing on a big flat board. You roll a bowling ball across it, and it goes straight. There's no curvature. But now imagine I tilt the big flat board. Now when you roll the bowling ball across it, it curves because of the slope. However the board isn't curved, it's still flat, but it's tilted. Spacetime is like the board, the path of light is like the path of the bowling ball.
Once you've got that just think of the board as being tilted and curved, like something in a skateboard park.
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Jeffrey, imagine you're standing on a big flat board. You roll a bowling ball across it, and it goes straight. There's no curvature. But now imagine I tilt the big flat board. Now when you roll the bowling ball across it, it curves because of the slope. However the board isn't curved, it's still flat, but it's tilted. Spacetime is like the board, the path of light is like the path of the bowling ball.
Once you've got that just think of the board as being tilted and curved, like something in a skateboard park.
That is a wonderful analogy John! [:)]
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Thanks Pete. It can be difficult to find a way to make it sound simple.
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Thanks Pete. It can be difficult to find a way to make it sound simple.
Your welcome. Back in the late 90's I came up with the same analogy myself. I set it aside because I'm not 100% sure that there aren't any problems with that analogy. But I still thing its a wonderful one. I just don't use it myself at this point in time.
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And of course acceleration is curved in Minkowsi diagrams and shows curvature ...
What do you mean by "shows curvature"? Suppose you're in a uniformly accelerating frame in flat spacetime. There's acceleration but no curvature. So how does what you say apply in that case?
Have you ever plotted acceleration on a Minkowski diagram?
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Think of a row of horse drawn wagons but instead of horses we have attached ropes. In one situation the ropes are only attached to the furthest wagon and when we pull it it moves independently of the others. Eventually it will touch the wagon in front and ultimately all the wagons will touch and we can pull them all. This compresses the wagons and we can say a force is felt. Now consider that we have ropes attached to all the wagons and can pull them at exactly the same time. Since no compression occurs we can liken this to gravity. Think of it like every particle in a falling mass moving in unison.
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And of course acceleration is curved in Minkowsi diagrams and shows curvature ...
What do you mean by "shows curvature"? Suppose you're in a uniformly accelerating frame in flat spacetime. There's acceleration but no curvature. So how does what you say apply in that case?
Have you ever plotted acceleration on a Minkowski diagram?
There are two ways to address that. What are you referring to when you use the term "Minkowski diagram"? Typically that refers to spacetime diagrams for inertial frames of reference. When you plot an acceleration on such a diagram like I have in figure one here http://home.comcast.net/~peter.m.brown/sr/uniform_accel.htm then that's a particle moving under a force, not in free fall and having nothing to do with gravity.
However if you have in mind a spacetime diagram of a frame of reference which is accelerating uniformly and plotting the position of a particle in free-fall then that will be a curved trajectory. However the use of the term "Curvature" here refers to the worldline and not the spacetime. The spacetime is still flat. Have you been confusing the curvature of world-lines and the curvature of spacetime all this time, have you?
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And of course acceleration is curved in Minkowsi diagrams and shows curvature ...
What do you mean by "shows curvature"? Suppose you're in a uniformly accelerating frame in flat spacetime. There's acceleration but no curvature. So how does what you say apply in that case?
Have you ever plotted acceleration on a Minkowski diagram?
There are two ways to address that. What are you referring to when you use the term "Minkowski diagram"? Typically that refers to spacetime diagrams for inertial frames of reference. When you plot an acceleration on such a diagram like I have in figure one here http://home.comcast.net/~peter.m.brown/sr/uniform_accel.htm then that's a particle moving under a force, not in free fall and having nothing to do with gravity.
However if you have in mind a spacetime diagram of a frame of reference which is accelerating uniformly and plotting the position of a particle in free-fall then that will be a curved trajectory. However the use of the term "Curvature" here refers to the worldline and not the spacetime. The spacetime is still flat. Have you been confusing the curvature of world-lines and the curvature of spacetime all this time, have you?
No
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We can make acceleration linear by a varying scale on the SPACE and TIME axes. How is that confusing world lines with spacetime. Or are you just trying to make me look inept? Are you?
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A fter I have come back to read the article again and again many time. In my understanding from the article are There are two version of General relativity once is einstein version and another was modern version. In Einstein version there are 2 type of gravitational field 1. uniform gravitational field that can conclude that gravitaty is the same as acceleration that we can create gravitational by changing of the coordinate there is no curvature of space time in this type of gravitational field. 2. Permanent Gravitatinal field is the space time curvature that is the same thing with tidal force. In modern view physicist confuse in 2 type of the field and conclude that uniform gravitational field is the same thing with curvature of space time.That wrong interpretation. Does I read it correctly or not ???
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A fter I have come back to read the article again and again many time. In my understanding from the article are There are two version of General relativity once is einstein version and another was modern version. In Einstein version there are 2 type of gravitational field 1. uniform gravitational field that can conclude that gravitaty is the same as acceleration that we can create gravitational by changing of the coordinate there is no curvature of space time in this type of gravitational field. 2. Permanent Gravitatinal field is the space time curvature that is the same thing with tidal force. In modern view physicist confuse in 2 type of the field and conclude that uniform gravitational field is the same thing with curvature of space time.That wrong interpretation. Does I read it correctly or not ???
I'm so glad to see that you've got it now. It warms my heart to see that I was able to get through to someone. Thanks for your diligence! :)
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A fter I have come back to read the article again and again many time. In my understanding from the article are There are two version of General relativity once is einstein version and another was modern version. In Einstein version there are 2 type of gravitational field 1. uniform gravitational field that can conclude that gravitaty is the same as acceleration that we can create gravitational by changing of the coordinate there is no curvature of space time in this type of gravitational field. 2. Permanent Gravitatinal field is the space time curvature that is the same thing with tidal force. In modern view physicist confuse in 2 type of the field and conclude that uniform gravitational field is the same thing with curvature of space time.That wrong interpretation. Does I read it correctly or not ???
I'm so glad to see that you've got it now. It warms my heart to see that I was able to get through to someone. Thanks for your diligence! :)
Thank you [:)]