Strange Posted January 18, 2015 Posted January 18, 2015 But it was never space-time equals 0 or 1...its been mass and energy...i have mentioned space-time being empty...but is there anyway to define space-time values without regarding matter and energy? If there is zero mass and zero energy, I would say that space-time is empty of mass and energy, and to give it any value at that point seems strange...but i am still grasping... I don't know what it means to give space-time "a value". Can you give the tin in your example "a value"? No, you can describe its shape, volume, colour of the label, etc. You can say the contents are zero beans (but the volume is still not zero). I'm not sure if you are just expressing yourself in a fuzzy way, or if you haven't got your idea clear in your head ... (the two often go hand in hand, in my experience)
JohnSSM Posted January 18, 2015 Author Posted January 18, 2015 (edited) You are trying to understand something that I think requires several years of postgraduate study. Asking ad-hoc questions on a forum and reading a few articles is not going to get you up to speed quickly. This is just what we learn in school: 3 different dimensions at right angles to each other - space divided up into cubic grid. Yep...I do agree with that...this is a long and graduating study... Gotcha...thats what I thought euclidean space was till i started reading about it...ha This little gif helped me move forward with understanding Minkowski space and the manifold light cone... http://commons.wikimedia.org/wiki/File:Lorentz_transform_of_world_line.gif Lorentz transformations occur in Minkowski space and gallilean transformations happen in euclidean space? http://commons.wikimedia.org/wiki/File:Galilean_transform_of_world_line.gif Comparing those 2 diagrams was an eye opener... I doubt ill have years to study this stuff to get it like yall got it...let me stay and ask questions anyway...and anytime I make a statement, just pretend its a question... I don't know what it means to give space-time "a value". Can you give the tin in your example "a value"? No, you can describe its shape, volume, colour of the label, etc. You can say the contents are zero beans (but the volume is still not zero). I'm not sure if you are just expressing yourself in a fuzzy way, or if you haven't got your idea clear in your head ... (the two often go hand in hand, in my experience) The properties of the can could become its values in any sense you wanted to express...my point is spacetime without energy or mass would have nothing to give it properties to define any values...alas...we can forget the tin can...ha... I should go back in this topic and find quotes from yall saying the opposite of what youre saying now...if someone suggested that space-time had vacuum energy, my thoery would still be alive...so maybe it is...the gluon field...its all about the gluon field... Id also like to add that space-time really seem to be defined best by a polar coordinate system...the poles are essentially the lightcones in minkowski space...seems totally apparent... Did anyone see my depiction of an object moving through minkowski space? https://www.facebook.com/photo.php?fbid=1523336581288210&set=a.1399707273651142.1073741829.100008356482793&type=1&theater Can anyone see it without a facebook account? Edited January 18, 2015 by JohnSSM
ajb Posted January 18, 2015 Posted January 18, 2015 (edited) Im still trying hard to take in Minkowski space.. Still trying to grasp what vectors, scalars and tensors are...im pretty lost on the subject right now I dont really understand Euclidean space either... The first place to start is to make sure you understand [math]\mathbb{R}^{n}[/math] as a set and then as a vector space over [math]\mathbb{R}[/math]. Then you should then also get to grips with the standard inner product on [math]\mathbb{R}^{n}[/math]. From there you should also look at the relation between [math]\mathbb{R}^{n}[/math] and the affine space [math]E^{n}[/math] (equipped with the norm induced from the standard inner product). Once you have the basics here have a look at quadratic forms and their symmetries. After that you should have an idea of Minkowski space-time. Most of the above I covered in a one semester course on linear algebra, but we did not cover symmetries of quadratic forms or specifically Minkowski space-time. Edited January 18, 2015 by ajb
JohnSSM Posted January 18, 2015 Author Posted January 18, 2015 IS the manifold in minkowski space where the equations account for time in 3d space? the fourth dimension is why we need a manifold at all?
ajb Posted January 18, 2015 Posted January 18, 2015 (edited) Lorentz transformations occur in Minkowski space and gallilean transformations happen in euclidean space? Not quite, the Galliean transformations occur on 'Newtonian space-time'. Also they do not correspond to the Euclidean group of 4 dimensional Euclidean space. Edited January 18, 2015 by ajb
JohnSSM Posted January 18, 2015 Author Posted January 18, 2015 I don't know what it means to give space-time "a value". Can you give the tin in your example "a value"? No, you can describe its shape, volume, colour of the label, etc. You can say the contents are zero beans (but the volume is still not zero). I'm not sure if you are just expressing yourself in a fuzzy way, or if you haven't got your idea clear in your head ... (the two often go hand in hand, in my experience) Its fuzzy cuz i cant get over this hurdle..."empty space-time can still have energy or mass"...my lil brain keeps tellin me that it wouldnt be empty if it "had" energy or mass....is is so hard to understand that confusion? ha
ajb Posted January 18, 2015 Posted January 18, 2015 IS the manifold in minkowski space where the equations account for time in 3d space? the fourth dimension is why we need a manifold at all? Minkowski space-time has the structure of a smooth manifold, it is just [math]\mathbb{R}^{4}[/math] (considered as a smooth manifold). Importantly this manifold comes with a pseudo-Riemannian metric, that is a way of defining distances. Thinking of the vector space structure here, this is just a quadratic form.
JohnSSM Posted January 18, 2015 Author Posted January 18, 2015 If we can just define empty as "no mass and no energy" then, if spacetime DOES have mass and energy when it is empty, what accounts for it?
ajb Posted January 18, 2015 Posted January 18, 2015 Its fuzzy cuz i cant get over this hurdle..."empty space-time can still have energy or mass"...my lil brain keeps tellin me that it wouldnt be empty if it "had" energy or mass....is is so hard to understand that confusion? ha Empty means 'empty' of fields and particles apart from the gravitational field. The gravitational field does not contribute to the energy-momentum tensor in Einstein's equations.
JohnSSM Posted January 18, 2015 Author Posted January 18, 2015 Vector space structure... i thought i understood that...every volume of mass contains 4 vectors that account for it's "internal pressures" in terms of energy and time, and when you "average" or "consider all together", you get a tensor for that volume...and that tensor info is what GR geometry uses to figure the space-time and associated vectors within it.... Empty means 'empty' of fields and particles apart from the gravitational field. The gravitational field does not contribute to the energy-momentum tensor in Einstein's equations. I never imagined a gravitational field without something to create gravity...akin to imagining an electromagnetic field without electromagnetic influences...the only field I knew to have vacuum energy was the gluon field... Ok...this is the vacuum energy that Strange or Mordred has discussed earlier....the ole virtual particle in and out theory...To put it lightly, this vacuum energy is not that well understood... Its supposed to be fuzzy!
ajb Posted January 18, 2015 Posted January 18, 2015 (edited) Vector space structure... i thought i understood that...every volume of mass contains 4 vectors that account for it's "internal pressures" in terms of energy and time, and when you "average" or "consider all together", you get a tensor for that volume...and that tensor info is what GR geometry uses to figure the space-time and associated vectors within it.... I just meant that you can think of [math]\mathbb{R}^{n}[/math] as a vector space, that is we can add elements of this set together, and multiply them by a real number and remain in that set, and we have some natural compatibility conditions. You can do the same with Minkowski space-time as it can be considered as a vector space, but now we have a quadratic form "the space-time interval". You can also think of Minkowski space-time as a smooth manifold with a pseudo-Riemannian metric. This is in fact the better way to think of it. Vector field now now sections of the tangent bundle of Minkowski space-time. This is the better way to think as it allows us to pass to curved space-times. The important thing with vector fields on manifolds is that when you write them in component form, using some coordinate system they have a very nice linear transformation law when changing coordinates. Tensors have something very similar that looks like the transformation laws for vectors multiplied together. It is a very nice law, and allows us to write the rules of physics in a very nice way that does not fundamentally depend on the coordinate choices. Or rather we have nice rules when we do change coordinates. That is why physics, and not just GR makes use of tensors and tensor-like objects. They all transforms in nice ways when we change the coordinate systems. Edited January 18, 2015 by ajb
JohnSSM Posted January 18, 2015 Author Posted January 18, 2015 Quantum field theory is wacky...i dont even want to go there yet... I just meant that you can think of [math]\mathbb{R}^{n}[/math] as a vector space, that is we can add elements of this set together, and multiply them by a real number and remain in that set, and we have some natural compatibility conditions. You can do the same with Minkowski space-time as it can be considered as a vector space, but now we have a quadratic form "the space-time interval".You can also think of Minkowski space-time as a smooth manifold with a pseudo-Riemannian metric. This is in fact the better way to think of it. Vector field now now sections of the tangent bundle of Minkowski space-time. This is the better way to think as it allows us to pass to curved space-times.The important thing with vector fields on manifolds is that when you write them in component form, using some coordinate system they have a very nice linear transformation law when changing coordinates. Tensors have something very similar that looks like the transformation laws for vectors multiplied together. It is a very nice law, and allows us to write the rules of physics in a very nice way that does not fundamentally depend on the coordinate choices. Or rather we have nice rules when we do change coordinates.That is why physics, and not just GR makes use of tensors and tensor-like objects. They all transforms in nice ways when we change the coordinate systems. Where do you get the values from an object to determine its four vectors? where is that info? what is that info made up of? momentum? spin? relative motions? compression and distribution of mass?
ajb Posted January 18, 2015 Posted January 18, 2015 Quantum field theory is wacky...i dont even want to go there yet... It too makes use of vectors and tensors in various ways. First the classical theory will make use of these objects, fields are sections of fibre bundles over space-time. Then quantisation is a mix of methods to associate with this classical field a Fock space; which is a direct sum of the tensor powers (symmetrised and/or antisymmetrised) of a Hilbert space. All this is linear algebra.
JohnSSM Posted January 18, 2015 Author Posted January 18, 2015 Im just gonna stick with GR for the moment...or maybe years...
ajb Posted January 18, 2015 Posted January 18, 2015 Where do you get the values from an object to determine its four vectors? where is that info? what is that info made up of? momentum? spin? relative motions? It seems to be a metatheorem of physics that all the information about a system is contained in a Lagrangian. You can then extract the properties of an objects from that. Well, I don't think that this metatheorem is strictly true, when we have dissipative forces for example you need to add more to the theory and there are examples of equations of motion with no known Lagrangian. So maybe the metatheorem only holds for fundamental theories, anyway the Lagrangian is the usual starting place.
swansont Posted January 18, 2015 Posted January 18, 2015 I do agree...and the equation needs terms doesnt it? But it was never space-time equals 0 or 1... No? I use an equals sign...is this not math? IF spacetime is empty then mass value = 0 if mass value=0 then spacetime value=0 So, Empty spacetime = 0 Never? 1
JohnSSM Posted January 18, 2015 Author Posted January 18, 2015 No? Never? Yes...never....even in that example anyone can see its energy im talking about....and if they cant, its their problem...there is no space-time mass equivalence...energy mass equivalence,,,i would think I wouldnt have to explain that to guys like you...sheesh tee hee
Strange Posted January 18, 2015 Posted January 18, 2015 even in that example anyone can see its energy im talking about.... Sorry, not a mind-reader. When you say "spacetime value=0" or "Empty spacetime = 0" then I have to assume you mean "spacetime [value]=0". Because if you had meant energy = 0 then I assume you would have written "energy = 0". and if they cant, its their problem... I beg to differ. If you are unclear or ambiguous, then it is your fault, not ours.
JohnSSM Posted January 18, 2015 Author Posted January 18, 2015 Sorry, not a mind-reader. When you say "spacetime value=0" or "Empty spacetime = 0" then I have to assume you mean "spacetime [value]=0". Because if you had meant energy = 0 then I assume you would have written "energy = 0". I beg to differ. If you are unclear or ambiguous, then it is your fault, not ours. Yknow what they say about assuming... I do really wish I woulda made it clear that I was referring to the energy and mass of spacetime...not just spacetime and mass...I was kinda stealing the language from the "infinity hypothetis" in speculations...i do apologize Can I ask someone to use GR to figure for 2 masses in space and what effects these masses have on the shape of spacetime? Where does one begin? What info needs to be gathered to do the equations?
swansont Posted January 19, 2015 Posted January 19, 2015 .I was kinda stealing the language from the "infinity hypothetis" in speculations Cribbing from speculations is generally a poor strategy. It's there for a reason.
JohnSSM Posted January 19, 2015 Author Posted January 19, 2015 Cribbing from speculations is generally a poor strategy. It's there for a reason. So you really create atomic clock technology? Sounds an amazing gig... The only reason i was even referring to that topic was "I cant believe you all let this guy get away with this"...It seemed like nonsense that you let someone else get away with, and my feelings were hurt...twasnt my idea to give empty space time a value, and then also conclude that the value of mass and energy would match it...
Mordred Posted January 19, 2015 Posted January 19, 2015 Lets put it this way your learning far more due to your listening and applying what we explain. Some posters no Matter how you correct or teach them never learn and ignore anything that conflicts with their ideas. Even when the idea is utter nonsense Speaking of studying. I'm not sure I posted this excellent aid for you. It's extremely handy though math heavy http://www.blau.itp.unibe.ch/newlecturesGR.pdf"Lecture Notes on General Relativity" Matthias Blau it's a little over 900 pages but it covers numerous metrics used in GR 1
ajb Posted January 19, 2015 Posted January 19, 2015 Can I ask someone to use GR to figure for 2 masses in space and what effects these masses have on the shape of spacetime? You want an exact solution for two non-rotating spherically symmetric bodies? I don't think that an exact solution exists. People study the two body problem via various approximations or use numerical methods.
JohnSSM Posted January 19, 2015 Author Posted January 19, 2015 Lets put it this way your learning far more due to your listening and applying what we explain. Some posters no Matter how you correct or teach them never learn and ignore anything that conflicts with their ideas. Even when the idea is utter nonsense Speaking of studying. I'm not sure I posted this excellent aid for you. It's extremely handy though math heavy http://www.blau.itp.unibe.ch/newlecturesGR.pdf"Lecture Notes on General Relativity" Matthias Blau it's a little over 900 pages but it covers numerous metrics used in GR The truth is more important to me than my ideas...I just want to understand...and I have picked up huge amounts of knowledge since hanging around here with you stubborn folk You want an exact solution for two non-rotating spherically symmetric bodies? I don't think that an exact solution exists. People study the two body problem via various approximations or use numerical methods. The question "how did they ever prove this math" comes to mind... Right now, im mostly interested in understanding how to figure the four vectors of "an object"...and then how to find the tensor solution which "combines" them... What is the raw data from mass that is used to figure GR? Dont you need to know the volume and mass? and also, how it is distributed throughout the object? If it has momentum, spin...dont all these factors effect the shape of space? I suppose id be happy to see GR solve the spacetime surrounding any object with NO other influences from other objects...a single object solution...The process of what data is needed and to see it plugged into equations... Found this awesome page of info... http://en.wikipedia.org/wiki/Exact_solutions_in_general_relativity Physics is like politics...if everyday people knew all the shit going on, they wouldnt believe it...and usually they dont...
ajb Posted January 19, 2015 Posted January 19, 2015 I suppose id be happy to see GR solve the spacetime surrounding any object with NO other influences from other objects...a single object solution...The process of what data is needed and to see it plugged into equations... The first non-trivial solution is the Schwarzschild metric. It describes the space-time around a spherically symmetric, non-rotating body. You should look into how it is derived.
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