JohnSSM Posted January 10, 2015 Author Share Posted January 10, 2015 Here I of course meant test particle. I still dont understand why one needs a a test particle to say anything about gravity... Link to comment Share on other sites More sharing options...
ajb Posted January 10, 2015 Share Posted January 10, 2015 Wait a second here...why does anyone have to test for GR if it is expected to be 100 percent reliable equations? Is this basically when youre using GR to prove some other unknown? IS there anything other than the equations of general relativity that effect gravity? It is nature that decides if GR works well or not. Thus we need to test it and keep looking for possible situations for which GR could fail and then hopefully the experimental data will give us some clue as to a more complete theory of gravity. Link to comment Share on other sites More sharing options...
JohnSSM Posted January 10, 2015 Author Share Posted January 10, 2015 It is nature that decides if GR works well or not. Thus we need to test it and keep looking for possible situations for which GR could fail and then hopefully the experimental data will give us some clue as to a more complete theory of gravity. GR could fail? I proposed that very early on...and now im a believer...and you pull this on me? LOL... Its my reality now...i aint budgin one bit till i see math that contradicts it...or someone really good with math tells me that math contradicts it... And until then, anyone who is even testing for it is wasting their time... Link to comment Share on other sites More sharing options...
ajb Posted January 10, 2015 Share Posted January 10, 2015 I still dont understand why one needs a a test particle to say anything about gravity... You don't need test particles, but they are a very useful way of probing things. Just in the same way you use test particle in electromagnetic theory; for example you may want to know how an electron is deflected in an magnetic field, the simplest thing to do is assume that the EM field that the electron generates is small and can safely be neglected. In the same way, typically it will be okay to think of a planet as a test particle in the gravitational field of its star. Link to comment Share on other sites More sharing options...
JohnSSM Posted January 10, 2015 Author Share Posted January 10, 2015 The sama paradox I was in! Link to comment Share on other sites More sharing options...
ajb Posted January 10, 2015 Share Posted January 10, 2015 Its my reality now...i aint budgin one bit till i see math that contradicts it...or someone really good with math tells me that math contradicts it... And until then, anyone who is even testing for it is wasting their time... For example, we have theories that use higher curvature terms, but so far there is no evidence that they are needed in nature. It would be great to find some evidence of these extra terms as they can be motivated by string theory. Link to comment Share on other sites More sharing options...
JohnSSM Posted January 10, 2015 Author Share Posted January 10, 2015 You don't need test particles, but they are a very useful way of probing things. Just in the same way you use test particle in electromagnetic theory; for example you may want to know how an electron is deflected in an magnetic field, the simplest thing to do is assume that the EM field that the electron generates is small and can safely be neglected. In the same way, typically it will be okay to think of a planet as a test particle in the gravitational field of its star. I get it...im just mentioning that I found out today that each little bit of mass effects GR in its own individual way...so you can measure the effects of GR in one mass...and like i said...in terms of reality, everything in the universe is one mass and has one collective vector with energy...the tensor of the universe? Say im standing on the earth...whe you measure earths gravity, my own will be a part of that product...when i jump 10 feet from the earth,...my gravity is still part of the product...when i get 5 million miles away, my own gravity is still part of the product...depending on whether or not you now include me or dont include me in earths gravitational product is weather I effect it or not...no amount of space between us (space is only the product of vectors and energies) will make us mutually exclusive of the others gravity...nothing can if we exist in the same universe... You can use one half of the earth as a test particle for the other half...you dont have to rip earth apart to do that.... Link to comment Share on other sites More sharing options...
ajb Posted January 10, 2015 Share Posted January 10, 2015 I don't quite follow your 'vector with energy'. Are you talking about the energy-momentum tensor? Link to comment Share on other sites More sharing options...
JohnSSM Posted January 10, 2015 Author Share Posted January 10, 2015 Beyond all that i do see the reason for a test particle...like a little feather in the wind...to see whats happening to the wind I don't quite follow your 'vector with energy'. Are you talking about the energy-momentum tensor? Yes...I think so Link to comment Share on other sites More sharing options...
ajb Posted January 10, 2015 Share Posted January 10, 2015 Beyond all that i do see the reason for a test particle...like a little feather in the wind...to see whats happening to the wind. That is not a bad analogy. Another one could be using smoke in wind tunnels when studying air flow over objects. You trace out the air flow while minimally disturbing it. Link to comment Share on other sites More sharing options...
JohnSSM Posted January 10, 2015 Author Share Posted January 10, 2015 That is not a bad analogy. Another one could be using smoke in wind tunnels when studying air flow over objects. You trace out the air flow while minimally disturbing it. Would you, at some point, take a moment to look at something i wrote earlier? I really wanted a couple opinions on it and its fun stuff... Link to comment Share on other sites More sharing options...
ajb Posted January 10, 2015 Share Posted January 10, 2015 Would you, at some point, take a moment to look at something i wrote earlier? I really wanted a couple opinions on it and its fun stuff... What is the post number? Link to comment Share on other sites More sharing options...
JohnSSM Posted January 10, 2015 Author Share Posted January 10, 2015 What Im trying to establish in my head is that mass effects spacetime, due to its own propeties (vector and energy), and from the vectors of other mass in its relative vicinity... Its tied to another point that was discussed...If you brought a magnet into a room with no EMF, then the only EMF in the room would be sourced by the magnet...when you heat the magnet, it loses it's magnetic properties and the field IT created is now gone...If we couldnt get a room free of EMF, could we at least distinguish the EMF created by the magnet itself to run the same experiment?...I know heat would not disable the entire EMF from the room, but it would disable the EMF created by the magnet... Replace EMF with space-time, and replace Magnet with mass...then youd replace heat with gravity... If you brought a mass into a room with no space_time, then the only space-time in the room would be sourced by the mass...when you add gravity to the mass, it loses it's mass-like properties and the field (space-time) it created is now gone...If we couldnt get a room free of gravity, could we at least distinguish the gravity created by our mass from the rest of gravity created from other mass to run the same experiment?...I know gravity would not disable the entire space-time from the room, but it would disable the space-time created by the mass we entered with... Now just replace gravity with compression...You can also replace space-time with geomtery or even GR What is the post number? 236...but i did a quote above Can i apply enough external vectors and energies to make the vectors and energies of a much less energetic object obsolete in the mix? sure, it may add to the total, but now instead of being 10 percent of its own influence, its .00000001 % of its own influence...obsolete basically, if the sun gets close enough to the earth, the moon is going to leave our orbit... IN deep space, i dont know how little gravity can exist...but if you were floating in a region of 99 percent uncurved space, you would mostly only be under the influence of your own vectors and energies...and how could you ever get out without waiting for the 1 percent of gravitational influence to bring you close enough to something before it started to slowly speed up? worse than a black hole death? maybe Link to comment Share on other sites More sharing options...
ajb Posted January 10, 2015 Share Posted January 10, 2015 If we couldnt get a room free of EMF, could we at least distinguish the EMF created by the magnet itself to run the same experiment?... You can more-or-less do this. A bar magnet on your desk would do. Just clear it of any other magnets and ferrous materials and you will be okay. You can map the magnetic field in a 2d plane easily using iron filings, I think others have suggested this to you. The only problem is that the Earth has a background magnetic field. However, compared to your bar magnet this is weak and over the time scales of your experiment it is constant. You may need to take it into account with very precise measurements, but not for what we are talking about here. If you brought a mass into a room with no space_time, then the only space-time in the room would be sourced by the mass You should not think of space-time as being generated by mass or energy. Nor should you think of gravity as space-time. Gravity is the local geometry, loosely the local shape of space-time. It depends on how you actually want to describe this, but typically one takes the metric to be the gravitational field... just note that there are other ways you can describe the gravitational degrees of freedom. The metric is a tensor that describes what we mean by 'lengths', from it you can construct various tensors that describe mathematically what 'curvature' means. In fact, you should do a little experiment. Take a ball and mark three distinct points on it. Take a pen or something similar and place it at one of the points. Then move the pen along the surface of the ball without changing the direction the pen is pointing, i.e. don't twist it yourself just follow the surface of the ball. Now pass through the other point and back to where you started. If you have done this correctly, the pen should be pointing in a different direction as compared to its initial direction. This angular difference is the curvature. What you have done is formed a closed path and parallel transported a vector along it. The difference between the vector that you started with and the final vector is measured by the Riemann curvature tensor. You now have to do some more work in general but the idea is the same. You need to define a notion of parallel transport, and the fundamental theorem of differential geometry says you can always cook-up a unique notion from the metric. You look at parallel transport of vectors round a loop and this gives you the curvature. Now, try the exercise with a cylinder (say an empty toilet paper tube). ...If we couldnt get a room free of gravity, could we at least distinguish the gravity created by our mass from the rest of gravity created from other mass to run the same experiment?...I know gravity would not disable the entire space-time from the room, but it would disable the space-time created by the mass we entered with... We kind of have the opposite problem here as compared to the magnet case. Although the force of gravity is relatively weak, the Earth is very heavy compared to objects in our room. It would be very difficult to measure the gravitational field between to objects in our room. However, it can be done. Look up the Cavendish experiment. I am sure there are some modern versions of this. As our masses are light, we are okay to use the Newtonian limit. There are exact solutions to the Einstein field equations for a pair of static spherical objects. I am not familiar with details here, but I know such solutions are known. 1 Link to comment Share on other sites More sharing options...
JohnSSM Posted January 10, 2015 Author Share Posted January 10, 2015 You can more-or-less do this. A bar magnet on your desk would do. Just clear it of any other magnets and ferrous materials and you will be okay. You can map the magnetic field in a 2d plane easily using iron filings, I think others have suggested this to you. The only problem is that the Earth has a background magnetic field. However, compared to your bar magnet this is weak and over the time scales of your experiment it is constant. You may need to take it into account with very precise measurements, but not for what we are talking about here. You should not think of space-time as being generated by mass or energy. Nor should you think of gravity as space-time. Gravity is the local geometry, loosely the local shape of space-time. It depends on how you actually want to describe this, but typically one takes the metric to be the gravitational field... just note that there are other ways you can describe the gravitational degrees of freedom. The metric is a tensor that describes what we mean by 'lengths', from it you can construct various tensors that describe mathematically what 'curvature' means. In fact, you should do a little experiment. Take a ball and mark three distinct points on it. Take a pen or something similar and place it at one of the points. Then move the pen along the surface of the ball without changing the direction the pen is pointing, i.e. don't twist it yourself just follow the surface of the ball. Now pass through the other point and back to where you started. If you have done this correctly, the pen should be pointing in a different direction as compared to its initial direction. This angular difference is the curvature. What you have done is formed a closed path and parallel transported a vector along it. The difference between the vector that you started with and the final vector is measured by the Riemann curvature tensor. You now have to do some more work in general but the idea is the same. You need to define a notion of parallel transport, and the fundamental theorem of differential geometry says you can always cook-up a unique notion from the metric. You look at parallel transport of vectors round a loop and this gives you the curvature. Now, try the exercise with a cylinder (say an empty toilet paper tube). We kind of have the opposite problem here as compared to the magnet case. Although the force of gravity is relatively weak, the Earth is very heavy compared to objects in our room. It would be very difficult to measure the gravitational field between to objects in our room. However, it can be done. Look up the Cavendish experiment. I am sure there are some modern versions of this. As our masses are light, we are okay to use the Newtonian limit. There are exact solutions to the Einstein field equations for a pair of static spherical objects. I am not familiar with details here, but I know such solutions are known. Im not trying to do these experiments...ha...Im making a correlation between Electromagnetic fields, Magnets and heat to Space-time geometry, mass and gravity.... I said that spacetime geometry is created by the vectors at their energy levels, of mass...Or...Mass contains energy with a vector...arent these 2 properties of each mass what general relativity uses to compute the spacetime they occupy? I know there are existing vector forces effecting spacetime cuvature as well, (they are outside forces of gravity, other mass with vector energies of their own) but general relativity figures it all for us...IT takes into account, our own, applies it to what is there allready and changes it accordingly...and then it can in turn, effect what used to be our old vector and energy level..its changes again and changes all the vectors and energy levels in its relative proximity...this is the interaction of changing geometries...isnt it? Link to comment Share on other sites More sharing options...
ajb Posted January 10, 2015 Share Posted January 10, 2015 I said that spacetime geometry is created by the vectors at their energy levels, of mass...Or...Mass contains energy with a vector...arent these 2 properties of each mass what general relativity uses to compute the spacetime they occupy? I am not really sure what you are asking. The source of gravity is energy-momentum, as shown in the field equations that have been posted in this thread earlier. Link to comment Share on other sites More sharing options...
JohnSSM Posted January 10, 2015 Author Share Posted January 10, 2015 (edited) Yes...energy-momentum...it does have a vector, right? a vector would be the direction of force...cant figure out geometry without some directions! It not only has a vector of direction (which way are forces moving me?) it also has a vector of momentum (am i losing or gaining momentum)...you need all that info to create a coordinate system and thats all you need brotha! That info is what GR uses to come up with the geometry of spacetime...or ,the curves of spacetime...did i leave out an influence? Edited January 10, 2015 by JohnSSM Link to comment Share on other sites More sharing options...
Strange Posted January 10, 2015 Share Posted January 10, 2015 I do understand that these foljks used GR to figure these solutions...the question` then becomes, could the circumstance of their presuppositions ever exist? Whether they could exist is not the point. The point was that space-time (a construct of GR) exists in models (based on GR) with no mass or energy. This is why one's intuition is not reliable on these things. 1 Link to comment Share on other sites More sharing options...
JohnSSM Posted January 10, 2015 Author Share Posted January 10, 2015 (edited) Whether they could exist is not the point. The point was that space-time (a construct of GR) exists in models (based on GR) with no mass or energy. This is why one's intuition is not reliable on these things. Strange...my point WAS, could they exist?...not how it would look if they did exist...cause if something cant exist, theres really no reason to look any farther... Without merging GR and QM, we will never KNOW what might exist first...which is why they moved that forum topic to speculations too... How many times have I heard that curved spacetime is the geometrical results of the masses within it...and i was like...no...its foam being compressed...they were like...you dont need the foam...its all done in geometrical eqautions...that is where the curves are made and found...but only after you apply some mass... If some mass has some energy in a certain vector...or someone is pushing me at a house,..youre gonna have to apply the fact that i just recieved energy from a certain direction to create the space time that i move into...and the distance between me and the house apparently shrinks no matter what direction and energy i had before being pushed...energy applied in that vector is going to influence my movements in that directions...but im not moving...the energy was applied to me and now space-time changes shape and form... But it changes shape and form because I took on more energy...in a certain vector...it couldnt change spacetime accurately without both bits of info... if there were no mass to create a change in vector or energy, why would there be a coordinate system created by anything....it has no input...no impetus for creation...there is no info...none...why do you need space to store no info? you dont Edited January 10, 2015 by JohnSSM Link to comment Share on other sites More sharing options...
ajb Posted January 10, 2015 Share Posted January 10, 2015 Yes...energy-momentum...it does have a vector, right? It is a tensor and you can of course construct vectors from that. a vector would be the direction of force...cant figure out geometry without some directions! What force? You mean something like the stress or pressure? (i.e. some of the components of the energy-momentum tensor) It not only has a vector of direction (which way are forces moving me?) it also has a vector of momentum (am i losing or gaining momentum)...you need all that info to create a coordinate system Okay, you have a 4-momentum vector for a test particle. and thats all you need brotha! That info is what GR uses to come up with the geometry of spacetime...or ,the curves of spacetime...did i leave out an influence? All you need is a source and that is energy-momentum. Well in fact you don't need a source to have interesting geometry, there are plenty of vacuum solutions. Link to comment Share on other sites More sharing options...
JohnSSM Posted January 10, 2015 Author Share Posted January 10, 2015 (edited) It is a tensor and you can of course construct vectors from that. What force? You mean something like the stress or pressure? (i.e. some of the components of the energy-momentum tensor) Okay, you have a 4-momentum vector for a test particle. All you need is a source and that is energy-momentum. Well in fact you don't need a source to have interesting geometry, there are plenty of vacuum solutions. \ Definition of Vector " a quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another." Tensor " a mathematical object analogous to but more general than a vector, represented by an array of components that are functions of the coordinates of a space." I ADD THIS...an array of components that are functions of space are vectors... Yes...a four momentum vector makes good sense... That bit about four vectors of momentum is definitely making me think I should have known that...it is intuitive In my mind, all those vectors combined (source of gravity from itself and other objects)...they each effect a direction and time influence... But i knew every object has four dimensions of force being applied to it...i might have called it 3...is the 4th accounting for time and the other 3 space? Edited January 10, 2015 by JohnSSM Link to comment Share on other sites More sharing options...
ajb Posted January 10, 2015 Share Posted January 10, 2015 (edited) Definition of Vector " a quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another." It is true that at every point on the manifold we can think like that, the space then the tangent space at that point. In general relativity and more generally differential geometry we need vector fields, which is a smooth assignment of a vector from each tangent space for all points. You should try the experiment I suggested with the ball and the pen. In what sense is the pen on or in the ball? Really, the best you can say is that we can attach a pen to each point. The notion of parallel transport, which in out 2d case is just don't twist or rotate the pen as we move it point to point, allows us to connect vectors in different spaces. This is why we call the mathematical gadget that allows us to construct parallel transport a 'connection'. Anyway, this definition is not quite right for the modern meaning of a vector. Tensor "a mathematical object analogous to but more general than a vector, represented by an array of components that are functions of the coordinates of a space." Again here we should be thinking of tensor fields, but that is no problem. Okay, the array has some nice properties when you change coordinate systems, which should be specified in this definition. (You are using the old school, but very useful notion of a 'geometric object'. The modern language would be a section of a natural bundle.) Edited January 10, 2015 by ajb Link to comment Share on other sites More sharing options...
JohnSSM Posted January 10, 2015 Author Share Posted January 10, 2015 Yes...Im being forced to read about MONDs now...and scalar fields and tensor vector scalar gravity...What an incredibly good time it is to express and confirm and re-evaluate and realize and unlearn and move forward...its friday night...i wouldnt have chosen another way to spend it...crashin...thanks for the discussion Link to comment Share on other sites More sharing options...
ajb Posted January 10, 2015 Share Posted January 10, 2015 Yes...Im being forced to read about MONDs now...and scalar fields and tensor vector scalar gravity... Tensors and tensor-like objects (densities, sections of affine bundles, etc ) are all the bread and butter of physics. Link to comment Share on other sites More sharing options...
JohnSSM Posted January 10, 2015 Author Share Posted January 10, 2015 ps...i shall attempt the experiment and see what i see...i didnt feel like holding torches under magnets, or compressing mass into a black hole that then interupts the spacetime continuum...but i got a pencil and ball right here brotha Newtonian gravity didnt need tensors, did it? Doesnt the swartzman prophecy tell us that compressed mass is what interupts spacetime and causes a black hole? Link to comment Share on other sites More sharing options...
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