I think what he's saying is that the universe is a ball, or flat space with a boundary. It's clearly not a sphere because a sphere obviously has curvature. I'm going to chalk this up as another example of Farsight misunderstanding the lingo. I'll respond to the rest when it's not 1 am.
So you think our understanding of general relativity has not moved on since Einstein, despite continual study for over 100 years?! Einstein was certainly a remarkable physicist, but he wasn't that remarkable. All theories are better understood by subsequent physicists than by the guy who proposed them - that's just natural. Case in point, Maxwell originally wrote the equations that bare his name in terms of quaternions. Nowadays we have the much more elegant and powerful vector calculus formalism and I doubt most modern day physicists would even recognise them in their original form. And as I was saying, Einstein's understanding has now been superseded by a better understanding of GR. The maths of GR is exactly the maths of curved space, but physically it's hard to visualise curved 4 dimensional space so it's not much of a stretch to think about what is properly called curvature as some sort of "density" of space, especially in the case of something like the Schwarzschild solution. This is simply wrong, and I'm getting fed up of repeating it - FR & W found solutions to GR with the assumption that spacetime was both homogeneous and isotropic and they found that all of their solutions (even the 'flat' one) have non zero curvature. You're the one that wants to say that if the spatial sections of a space are flat then the curvature is zero (wrong, as shown by the flat FRW universe). Despite the fact I'm not a cosmologist, I am familiar with basic cosmology. Now it looks like you have forgotten that making a change of coordinates doesn't affect curvature so my response to this is "so what." The universe either expands and time ticks at a constant rate or it is static and the rate of flow of time (ugh) depends on your position. It's not removing curvature, it's making a choice about where you want your curvature to come from - space or time. You can go further and make the approximation that the size of the universe now is at a much larger scale than the expansion of the universe. While this is true now, it certainly was not true for inflation during which the universe expanded exponentially, multiplying it's size many times. PS You didn't reply to post 14
A change of coordinates will not change the curvature of space-time but it will change the curvature of the spatial part because the division between space and time in space-time is coordinate dependent. As commented on, often people doing differential geometry refer to the entire manifold they work on as a 'space', even when that manifold is space-time. If you don't know this then it might seem that a lot of books and papers say that properties of the spatial part of space-time doesn't change with a change of coordinates but that isn't what they mean. Again, you're failing to grasp subtleties because you haven't looked at the details. Something being isotropic doesn't mean its flat nor does it mean its a sphere and in fact those two things are mutually exclusive, a sphere is not flat. Isotropic means rotational invariance, which a flat 2d plane has despite it not being spherical. You can put a 1d sphere (a circle) into that space and still have isotropy with respect to the point in the plane which is the centre of the circle. Isotropy in the 3 spatial dimensions of space-time means you can plonk a 2d sphere down somewhere and you have rotational invariance but that isn't the same as having isotropy on the sphere itself. Isotropy on the sphere would mean picking a point on that sphere and rotating the sphere about that point in such a way that the tangent space (as embedded in the 3d parent space) is taken to itself. Since I know you don't know what a tangent space is a simple way of viewing that would be rotating the sphere about an axis through its centre (as viewed in the parent space) and the point you picked. This will give SO(2) isotropy as the sphere is 2 dimensional while the parent space has SO(3) isotropy. No doubt you'll whine that this is all mathematical and its okay to ignore it but its not, its a formal way of describing the properties of multi-dimensional systems and its an explicit demonstration your attempts to work by your intuition fail. And Newton believed in alchemy so should we stop teaching chemistry to students? I love the irony of you telling people to read ArXiv when you ignore it when people tell you to read a 1st year beginners guide to pretty much every area of physics you open your mouth about. Is that as far as you got? The same can most definitely said about you. Do you own a calendar? When you've read anything about GR which isn't pop science perhaps you can tell people what GR says but until then at least have the decency not to pretend you understand it, particularly when talking to people who demonstrable do. So we should pay attention to Wikipedia but you don't have to pay attention to the sum total of general relativity textbooks, papers and courses because you just know what they say, despite not having read any of them? Tell me Farsight, if you don't read any GR (or much of anything else beyond A level science) why do you think you know what it says? If you don't have any understanding of the workings how do you know what they say? Please specify precisely what it would, hypothetically, take to convince you you might be wrong on this stuff? Its just that papers, textbooks, lecture notes, experiments and direct conversation with professional physicists hasn't worked so either you have standards of evidence beyond even the most stringent reputable journal or you simply will not listen. I doubt its the former, since you failed to meet their requirements in regards to your own work. That leaves the latter, which means you aren't interested in truth or honest discussion or anything like that, you simply want to try to con people into thinking you're not useless at physics. The fact you engage in a long list of crank identifying behaviours and yet try to profess you're interested in science is pretty worrying.
Your language has changed. I tried out some of your old personality. Pretty good in the right circumstances. Yeah you are "are" the hero type for sure
Sorry guys, this thread slipped off my radar and I forgot about it. And I've been busy. I really did mean space. I'm very particular about the distinction between space and space-time. I don't misunderstand this. I'm saying the space within the universe is flat, and the universe is spherical. I note http://en.wikipedia.org/wiki/Sphere and "In higher mathematics, a careful distinction is made between the sphere (a two-dimensional spherical surface embedded in three-dimensional Euclidean space) and the ball (the three-dimensional shape consisting of a sphere and its interior)". So if you'd prefer to say it's a ball rather than a sphere that's fine by me. We've been here before. You're dismissing Einstein. You don't understand it better than him. And what a mistake that was. The vector approach says what it does, not what it is. It throws away the curved space. Aaaagh! Curved space isn't the same as curved spacetime! Yes, interpreting curved spacetime as inhomogeneous space is easy, as per Inhomogeneous Vacuum: An Alternative Interpretation of Curved Spacetime . A light beam veers like a car veers when it encounters mud at the side of the road. Please look it up. Read what it says: The FLRW metric starts with the assumption of homogeneity and isotropy of space. Space, not spacetime. No, that's uniform curvature. Elliptical, Euclidean, and Hyperbolic. And guess what, in Euclidean space that uniform curvature is uniformly zero. Space is flat, light rays go straight as a die. Tell me how Euclidean space is curved. We've already said we'll set aside the expansion of the universe. We're talking about the universe as it is now, not how it's evolved. And right now, the universe is flat. WMAP says it's flat, why do you cling to curvature in the face of the evidence and simple logic? And dismiss Einstein to boot. Let's come back to inflation. I'll take a look.
The time "direction" is an abstract thing. We see space and motion through it. We don't see time flowing in some direction. The metric isn't something real that's "out there". It's a mathematical artefact associated with measurement. Space is out there. Change your motion through it and your measurements change. Inhomogeneous space affects your motion, and your measurments change again. Einstein wasn't wrong, and nor am I. There is no gravity in homogeneous spaced. Don't listen to AN. He attempts to spoil discussions. They don't contradict my claim. You're in denial, prometheus. That's a rubbish anwer. It convinces nobody. It's a solid elastic sphere, and it's compressed. Stressed. Like a stress-ball when you let it go. It expands. Dismissal, just like you dismissed Einstein. Don't you get it yet? When you dismissed Einstein, you dismissed GR. You're clutching at straws and trying to hide behind a mathematical smokescreen because you've lost this argument. Read the quote again: This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that 'empty space' in its physical relation is neither homogeneous nor isotropic". Now look up the FLRW metric as per my previous post. The FLRW metric starts with the assumption of homogeneity and isotropy of space. Space, not spacetime. Understand the difference, and that veering car. The road is straight, the surface has a gradient in mud depth, the tyre tracks are curved.
Just who do you think believes you Farsight? Do you think no one else can read the forum for themselves and see how you avoid direct questions and honest offers of discussion? I cannot spoil a discussion with you since you refuse to have one with me. You want people to fawn over your 'work' (as evidenced by, for instance, the Facebook page related to it started by members of your own family) but when someone puts forth serious, sound arguments against some part of it you don't want to talk about it. To be a good scientist it is a necessary requirement that you listen to criticism. If you don't accept it, you have to explain why, else you're just sticking your fingers in your ears. You claim various people on this forum are 'scared' by your work yet you're the one running from honest offers of discussion. Wrong. You're conflating the views of one person with a scientific discipline. Einstein contributed a lot to many areas but in none of them is his word 'law'. He was wrong about a lot of things, as every scientist ever has been. The fact science can say "This bit of Einstein's work was wrong" without also saying "Thus we toss out all of his work" is a plus for science. As soon as you canonise someone, anyone, you go from science to dogma. Considering you're always whining about how there's entrenched dogma in the current research community your endless attempts to canonise Einstein are all the more humorous. But then I suspect its partly because of something else you said : It wouldn't surprise me in the slightest if this betrays a subconcious association you have between yourself and Einstein. You clearly want to be hailed as 'the new Einstein' and your repeated "He and I are right, you're wrong!" hints at it further. The fact you haven't even read a single textbook by him or can even work through the methodologies he used to derive his quantitative predictions suggests you're not a little deluded. Your 'work' doesn't lead to Einstein's, you just want it to. I guess string theory necessarily leads to Einstein's work is just another sharp stick in your eye Please Register or Log in to view the hidden image! When you have the intellectual honesty to a frank discussion on your 'work' let me know.
You keep dumping this article on us as if the title alone is supposed to prove something. Before I delve into it, here's a question: have you checked that this article actually supports your position? For example, do the authors claim they've shown a general equivalence between curved spacetime and inhomogenous space, or does it hold only under certain restricted conditions? Misrepresentation. Nobody is "dismissing Einstein". Everyone is dismissing your interpretation of Einstein. Nope, what we call "general relativity" today is a theory based on the principle of general covariance and the Einstein field equation: \(R_{\mu\nu} \,-\, \frac{1}{2}R g_{\mu\nu} \,=\, 8 \pi G T_{\mu\nu} \,.\)In this theory, curvature of space-time is not synonymous with inhomogeneity of space, as shown by the FRW solutions. We generally credit Einstein with the discovery of this theory. This theory has been shown to be consistent with a variety of experimental observations over the last century, so if this enormously successful theory was not Einstein's, and Einstein was talking about some other theory at the Leyden address about gravity being inhomogenous space, could you tell us whose theory it was so we can give credit to the person who did formulate it? You've got this really bizarre idea that if the theory we call "general relativity" today wasn't the one Einstein proposed, we should blindly go with what Einstein said rather than the theory that's actually got all the evidence backing it. No, he's pointing out a detail in the math, which Einstein himself stated, that contradicts your position. Calling that "clutching at straws" is disingenuous, especially when your best response: just amounts to repeating yourself and doesn't resolve the conflict. Einstein said "...compelling us to describe its state by ten functions (the gravitation potentials gμν)", and only metrics in four dimensional spaces have ten components. This isn't going to go away; you have to deal with it. Why did Einstein speak of "ten" components and not some other number? You say that every time someone confronts you with math. This excuse is really getting rather old. There is nothing opaque about the argument prometheus put in front of you. It is a clear, direct, succinct argument that you have failed to address, despite several opportunities now. Why did Einstein speak of ten components? It's a simple question. Can you give a straight answer?
The curvature of space (as opposed to spacetime, if you really want me to make the distinction explicit) is not something that is invariant. As I said before, I can make a coordinate change and the curvature of spacetime is invariant, but the curvature of the spatial subsection is not invariant. In both physics and maths words that you may throw around with a slightly fuzzy meaning in common parlance actually have a very specific meaning, a good case in point being the difference between a ball and a sphere. What you are saying is that your view of the universe is that it is a ball, the surface of which is an expanding sphere. If you're going to propose things in science you at least need to learn the scientific lingo - it's there to stop this type of confusion. So you're saying that our understanding of gravity hasn't moved on, despite some of the smartest people on the planet studying it for over 100 years? Really? Huh?! They are the same equations, written in a more elegant and useful way. Anything the old formulation of the equations contain will be captured in the vector calculus formalism, with the bonus that they are a lot easier to work with. Furthermore, the generalisation to curved space (and spacetime) is very easy. Flat space: \(\partial_\nu F^{\mu \nu} = 0\\ \partial_\nu \epsilon^{\mu \nu \rho \sigma} F_{\rho \sigma} = 0\) Curved space: \(\frac{1}{\sqrt{-g} }\partial_\nu\left( \sqrt{-g} g^{\alpha \mu} g^{\beta \nu} F_{\alpha \beta} \right)= 0\\ \frac{1}{\sqrt{-g} }\partial_\nu\left( \sqrt{-g} g^{\alpha \mu} g^{\beta \nu} \epsilon_{\alpha \beta \rho \sigma} F^{\rho \sigma} \right)= 0 \) The fact that this paper is published in Chinese physics letters means my hopes are not high, but I will read it if I get some time. Whatever. The point is that the curvature of all of the solutions are non zero. I have no idea how you arrived at the conclusion that one of the FRW solutions is Euclidean. Since the signature of the FRW metric is Lorenzian there is no way that a solution can be Euclidean unless you make the replacement \(t \to i \tau\) so you're measuring time in units of \(i\), not real numbers. As I said before, the flat FRW solution still has non zero curvature. Work it out if you don't believe me. Umm... go on then. We certainly see the curvature of space(time) affect the passage of time, and that is captured by the coefficients of the terms containing a \(dt\) in the metric. The time direction is the opposite of abstract - the passage of time is about the most fundamental concept in physics. The metric is nothing more than Pythagoras' theorem, yes, and one may change the metric by changing coordinates. I certainly agree with that. A fundamental property of space is curvature, which you calculate from the metric because to measure distances you need to know about the curvature of the space, or if you like the gravitational fields. The curvature is an invariant quantity, which means you can't change it by doing coordinate transformations on the metric. In that sense, the curvature of the space is something that is truly real. You are quite simply wrong. There are many many counter examples already cited in this thread. In my experience AN knows what he's talking about and isn't shy about explaining things. That's very good for people that want to learn, but bad for people that want to foist their uneducated opinion on others. I can see why you don't like him. What exactly was your claim? Wasn't it that you could account for the perceived expansion of the universe as a time dilation effect? The CMB begs to differ. It's actually a very good answer. You claim there was no yardstick and I countered by giving 4 examples of yardsticks. Anyone not convinced by that is clearly not keeping up. That type of expansion is essentially the same. There is an imbalance of forces that causes the structure to expand. In the case of the stress ball it's some complicated repulsive force caused by the foam, and in the case of the balloon it's the pressure. It's quite obvious to me, and probably to anyone reading this thread that you don't understand GR in the original Einstein sense and in the modern sense (which is actually not all that different anyway). I'd better understand GR because my job depends on it - I use GR every day of my working life and so far I've managed OK. As Pryzk says, you're going to have to face up to this sooner or later. What exactly are the 10 functions that Einstein refers to?
To make things easy for farsight, the only way for a rank 2 tensor like the metric to have 10 independent components is for it to be symmetric in 4 dimensions or for it to be antisymmetric in 5 dimensions.
Yes, the paper supports my position. It includes this: "The strong similarity between Eqs. (3) and (5) indicates again that an inhomogeneous vacuum may be the physical reality of the curved spacetime. From these two equations and the boundary conditions at infinity, the refractive index of this inhomogeneous vacuum can be derived as follows... Equations (6) and (7) provide a general method for finding the vacuum refractive index profile of a static spherically symmetric gravitational field, where the coefficients A(R) and B(R) can be obtained from the Schwarzschild solutions.... And remember that Einstein supports my position too. And Newton. And the scientific evidence - atomic clocks go slower in a region where gravitational potential is low. Not because of "curved spacetime", but because they employ electromagnetic phenomena. They're essentially light clocks. The clocks go slower because the light goes slower, because the vacuum impedance of space there is different to what it is at altitude. So my position is rock solid. What have you got to counter it with? Dishonesty? See what prometheus said here. That's a "We know better than Einstein, we can safely ignore Einstein" if ever I heard it. And he actually called Einstein an idiot, see this post. Dismissal? What you call "general relativity" today doesn't have to bother itself with what Einstein actually said? A retreat to your textbook? Einstein didn't talk about the curvature of space-time. He talked about the curvilinear motion of light, and the equations of motion. And the FLRW metric starts with the assumption of homogeneity and isotropy of space. Einstein said a gravitational field is inhomogeneous space. It isn't some magical mysterious action-at-a-distance. There are no gravitons. Things fall down because of the space they're in. Make space homogeneous and there's no gravitational field. Then things don't fall down. And if they don't fall down, if they don't follow curved paths and instead carry on straight as a die, because space is flat like WMAP says, where's your curved spacetime now? In the expanding universe? When at all times space is flat? Wild accusations? It was Einstein's theory. It's consistent with experiment, as documented at http://arxiv.org/abs/gr-qc/0510072. I'm the one rooting for Einstein here, you're the guys dismissing him and calling him an idiot. Ad hominem abuse? Just read what Einstein said, don't throw "bizarre" mud in an attempt to avoid doing so. Disingenousness? It doesn't contradict my position at all. Distraction? Yes, distraction. You've totally evaded the salient points of my position and now you're attempting to discredit my argument by demanding something irrelevant. Einstein spoke of ten components because he referred to a fluid, see section 19 of The Foundation of the General Theory of Relativity. He gave what is in essence a fluid solution. In general it requires ten functions to specify a fluid. Doubtless there will now follow a pointless off-topic diatribe intended to bury this thread and attempt to conceal the fact that I've won this argument hands down. Like I said, my position is solid as a rock. You've got nothing to touch it.
Blandishments like this just won't wash, prometheus. You're wrong, and you still don't know the difference between curved space and curved spacetime. What are you going to do if you're in a region of curved space? So curved that it's closed? Change coordinates and hop your way out like mathematical magic? No chance. Yep. Get real. There's no confusion, just an attempt at cheap point scoring by playing the Hiumpty Dumpty card. Yes. Your understanding of gravity is different to Einstein's, but you cling to your textbook teaching so much that you won't even read what he said. They certainly aren't the same equations. They're written in a different formalism remember? You should try reading the original Maxwell sometime. Watch my lips: you don't understand the difference between them. You won't. You're in denial. You'll find a reason not to read it, and justify it with some lame excuse. Really? So the curvature of Euclidean space is non-zero? Run that by me again. Flannel. You should read more: Please Register or Log in to view the hidden image! See that picture above? It isn't curved space. The space is flat. Homogeneous. No overall gravity. And guess what? The universe expanded even when it was very dense. Time doesn't pass. Godel and Einstein worked it all out in 1949, see this. The passage of time is just a figure of speech. The direction of time is an abstraction. It makes as much sense as assigning a direction to all the motion in the universe, or the direction in which energy does work. No, the Lorentz factor is derived from Pythagoras' theorem. The metric is "what you measure". It isn't something real that's out there. Nor are coordinates. You change what you measure by moving, or by moving to a place where space is different. Stop right there. Space is fundamental, energy is fundamental. The metric isn't. It's an artefact of measurement, not "the fabric of space and time". Wrong again. To measure distance you use the motion of light. The curvature of space-time is the gravitational field. That's a region where the speed of light varies. Hence light follows a curvilinear path. Einstein said all this, repeatedly. The curvature of space is something that is truly real. But it isn't what a gravitational field is. A gravitational field is a curvature of space-time, and it's high time somebody else chimed in to correct you on this. Now think about what I've been saying. What you've been taught gets cause and effect back to front. Light curves when it moves through inhomogeneous space. It follows a curvilinear path. You'd probably say it's moving through curved spacetime, but that's wrong. Nothing moves through spacetime. There is no motion through spacetime. Think it through. I'm not wrong prometheus. And there aren't "many counter examples already cited in this thread". If you could demonstrate why I was wrong you'd have done it by now instead of trying to bore me to death with a monster post full of ducking and diving. He's dishonest. He won't admit it when I'm right and he won't pick you up when you're wrong, because that would be backing me up too. The guy's a thread wrecker and a serial abuser, a typical string-theory troll who patrols boards like this playing thought-police. I can account for inflation as a time-dilation effect. There's a parallel between the expanding universe and coming out of a gravity well. It's really simple once the penny drops. No it wasn't. Your yardsticks change, but you can't tell. Just get a stress-ball. Squeeze it in your fist. Then let go. It's a much better analogy for the expanding universe than the balloon. I'm the one who does understand it in the original Einstein sense. Read this to appreciate the difference between that and the modern interpretation. You don't understand GR. If you did you wouldn't be getting confused about curved space and curved spacetime. What does your job entail by the way? See above. Pryzk's got nothing.
That's actually impossible, again by a simple counting argument: the gravitational field is specified by ten functions, while a refractive index is only one function. Now part of the metric is just a matter of how you pick your coordinate system, but even accounting for that you're still left with about six parameters after fixing the coordinate system, and you can't interpret six parameters as just one parameter. It's only going to be possible if the authors restrict their attention to special cases. If you check the paper this is indeed what you find. For example near the end of the first page: Landau and Lifshitz have derived from the general relativity Fermat’s principle for the propagation of light in a static gravitational field as \(\delta \int g_{00}^{-1/2} dl = 0\)In other words, it only works for a particular class of gravitational fields that don't vary in time. The Eq. (3) referred to in your quote also looks like it's only valid for the Schwarzschild solution, and the authors themselves say: A(R) and B(R) come from a static and spherically symmetric metric of the standard form Finally, and most obviously, they only consider light. What about massive particles that don't travel along light-like geodesics? In order for the analogy to hold in general they'd have to show that they could predict the motion of matter as well using the same refractive index they do for light. Learn to check the fine print when reading scientific papers. That the authors were limiting their attention to static, spherically symmetric gravitational fields is even mentioned in the text you quoted above: Equations (6) and (7) provide a general method for finding the vacuum refractive index profile of a static spherically symmetric gravitational field, where the coefficients A(R) and B(R) can be obtained from the Schwarzschild solutionsyet apparently you didn't notice. Little details like these will bite you if you don't look out for them. So, if you're claiming that the behaviour of light in static, spherically symmetric gravitational fields is analogous to the behaviour of light in a refractive medium then fine. But if you want to claim that space-time curvature is analogous to inhomogenous space in GR then you're on your own: your paper only shows that the analogy works in a special case. Misrepresentation again. prometheus was speaking much more generally than the quote we were talking about, in saying that later generations of physicists developed a better understanding of the theory of general relativity than Einstein had. That's not really dismissing Einstein so much as building on his work. Related to this, in physics we're not required to just accept everything Einstein says. This does not mean we are "dismissing Einstein" when we don't accept your quote: This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that 'empty space' in its physical relation is neither homogeneous nor isotropicthe way you'd have us read it. It is merely pointing out a second flaw in your argument. Your argument relies on two assumptions: that a) Einstein meant that the way you claim he did, and b) we're required to accept what Einstein says. As it happens, we think you're wrong about a), so we don't even need to worry about disagreeing with Einstein in this case. Blasphemy! No, why should it? If you think that by some historical mixup the theory of gravity we've been testing the last hundred years wasn't Einstein's theory, then the priority should go to the theory with the evidence, and not to Einstein just because he's Einstein. No, a famous counter-example to your position. One you still haven't adequately addressed. (emphasis added). I thought you cared about the distinction between space and space-time? The spatial section being flat doesn't imply that the space-time curvature is zero. Then why is there even a debate? Take another look at the equation I posted above: \(R_{\mu\nu} \,-\, \frac{1}{2} R g_{\mu\nu} \,=\, 8 \pi G T_{\mu\nu} \;.\)On the left hand side, \(R_{\mu\nu}\) and \(R\) are respectively the Ricci curvature tensor and Ricci scalar. Both are measures of space-time curvature. On the right hand side, \(T_{\mu\nu}\) is the stress-energy tensor, which is non-zero in the presence of matter. So if there's matter present, the RHS of the equation is non-zero, which implies that the LHS of the equation is non-zero, which is only possible if the space-time curvature is non-zero. In other words, according to the Einstein field equation, if there's matter there, you must have space-time curvature, no matter how homogenous the matter distribution is. Now here's the kicker: you've just told me this is Einstein's theory. So if you deny this obvious implication of the Einstein field equation, it is you who is "dismissing Einstein" here. No, an ad hominem is an attack on the person making an argument rather than the argument itself. "Bizarre" was directed at the idea, not at you. Technically I suppose you could accuse me of making an appeal to ridicule for calling the idea "bizarre" without explaining what was wrong with it, though I'd have thought that should be obvious to anyone who even wants to pretend they're doing science. Incidentally, you're not in a good position to be complaining about "ad hominem abuse". Any time you accuse someone who disagrees with you of being narrow-minded, dogmatic, thinking like a creationist, etc. you are making an ad hominem attack. When you accused me of making a "retreat to [my] textbook" above, you were employing an ad hominem instead of addressing the point I was making. You claim Einstein was talking about space and specifically not space-time. Einstein, in the same sentence, says that we need to describe "space" with ten functions \(g_{\mu\nu}\). The metric only has ten components in four dimensional spaces. How does this not contradict your position? Your "salient points" are an attempt at an argument from authority, a paper you only read at a superficial level, and a belief that any qualitative explanation you give for why light bends is automatically correct and the only allowable explanation. No, he referred to \(g_{\mu\nu}\) - the metric. And it's in your own quote: he was talking about "space", not the matter in space, which is often modelled as a fluid. These "ten functions" are, again, the ten components of a symmetric tensor in space-time. Specifically, the ten functions referred to on your wiki page are the ten components of the fluid's stress-energy tensor. I've actually [POST=2689668]already explained this[/POST] to you. But since, as I said, Einstein was talking about the metric in that sentence, this is no more relevant than the fact Einstein had ten fingers. Only if you set superficial standards for yourself and ignore everyone else's criticisms. By those standards, sure, you've "won". But in a rational debate, you don't get to dismiss something as "off-topic" or "irrelevant" just because it's inconvenient for your position.
Er he just gave an example of a difference between the curvature of space and the curvature of space-time. Incidentally, since I mentioned the appeal to ridicule in my last post, this: is a perfect example of that particular rhetorical device.
Bloody hell you've got a paranoid take on things. How is 3 postgrads/PhDs replying to you trying to conceal this thread? We reply point by point to your posts. You refuse to reply to me, not the other way around. And what evidence do you have your position is solid as a rock? Every single person, everyone, who has studied relativity at university level who has discussed your 'work' with you has failed to support you, be they string theorist postgrads through to Nobel Prize winning journal editors. The fact you're stuck arguing your work on forums, because it got laughed out of journal review, shows that the reality of your situation is the complete opposite of what you think it is. How many times have I offered to have an honest discussion with you? One where I'd be banned for a month if I were dishonest or didn't answer direct relevant questions? How many times have I tried to discuss things you bring up, like curvature or the difference between a mathematical axiom and a physical postulate? You whine about suppression yet you refuse to engage in a discussion when the ground rules are you can't be dishonest or duck out of it. Says a lot. Is 4 different from 2+2? They are written in different ways. Your lack of understanding of mathematical formalism is hindering you, again. Besides, the original way Maxwell wrote down his equations was using quaternions. I don't for a second think you understand quaternionic algebra. I'm not even convinced you could go well on an A Level maths exam. Got anything other than baseless assertions? Kind of hypocritical since you complain such things exist in the mainstream. A space-time can have Euclidean spatial components and yet have non-zero curvature. Part of your issue is you don't realise that often 'space' refers to 'space-time', since in the more mathematical approaches the underlying manifold is just called 'space', regardless of whether it refers to space, time, space-time, phase space, gauge fields etc. You should take your own advice and read a little. Well, you should read proper books, not pop science books bought from WHSmiths. Your pictures show the spatial component, not the entire space-time. If you understood even the most basic geometry relevant to relativity, rather than working by pictures you see on Wiki, you'd know that the Minkowski space-time is flat yet non-Euclidean. It's spatial component is Euclidean but it's more than just space. The FRW metric has a similar property, you can consider the curvature of its spatial component, which is precisely what the K in the metric represents, but that doesn't mean the space-time as a whole has the same curvature. Yet another one of the subtle results in relativity people get to understand by doing it. Both Prom and I have work in precisely this sort of stuff, curvatures and structures of part of a space-time. And unlike you we passed peer review. So you're not wrong, just multiple counter examples and mistakes you've made have been provided in this and other threads, your work has been rejected from every journal you've submitted it to, you couldn't get it published, you can't provide a single model of any phenomenon, you make no quantitative testable predictions and even on forums you are laughed at. I guess this is like your "I'm not a crank", despite a lengthy list to the contrary. A list you never did reply to, from that 'rock solid' position of yours. Please provide specific examples where you have demonstrated I've been incorrect and I haven't admitted it. That's why I offer, repeatedly, to start a new thread with you and I where we're both constrained only to reply to the topic at hand, with no insults allowed. I'm offering to discuss your work with you, along with topics like curvature, in dedicated threads where if I am rude I get a suspension. The reason we're not doing that right now is you. You don't want to be put in a position where you're forced to answer direct questions under pain of suspension, because you know you can't stand up to scrutiny. The reason you consider me a 'thread wrecker' is I have no problem pointing out your repeated lies. You whine about string theory, throwing out comments I must have corrected you on half a dozen times over the space of years. You complain there's a conspiracy of silence yet also complain I keep replying to your posts! Yes, yes, I ask you to provide a single working model of any real world phenomenon and suddenly I'm the thought police. In 1984 the thought police didn't offer to have a public discussion on the matter of disagreement, they just made you an unperson (I'm assuming you've read 1984). The refusal or restriction of public discussion is a sign of a lack of support for ones position, hence why regimes like that in 1984 avoid it. I'm offering it to you, on topics you brought up, rather than topics I might have found more interesting. And the 'string theorist' attempt at an insult is getting a little old. I've commented on it in this thread already and I commented on it here too, after you tried it again. It would seem the people who studied string theory have managed to get further in science than you have. Now all you have left is throwing hollow insults are us from your 'rock solid' position of vanity publishing and journal rejections Please Register or Log in to view the hidden image!
I'm afraid that isn't how it's reading, Farsight. I asked you in another thread: I would very much like you to try to convince us why there is no conflict between your interpretation of Einstein's words and his reference to ten functions in the metric tensor. If the posts in this thread are attempts to do so then you've well and truly failed, at least from this scientist's point of view.
Your simple counting argument is no argument at all. Einstein referred to Huygens in his foundation paper, he talks about matter conditioning the surrounding space, we employ a graded refractive index for black hole "analogies", and light bends in a gravitational field. We call this gravitational lensing. The details of how much it bends where, and how being at some location alters your measurements, does not render this paper or Einstein's own words "impossible". This is a straw-man argument. Nobody's talking about a single parameter. Come off it przyk. Let's find a planet and throw rocks at it. Can you see that gravitational field varying in time? No. The special case is a simple case, and it works. It’s valid for the Schwarzschild solution and that's enough to show the principle. Particularly since the infinite time dilation at an event horizon means that as far as you and I are concerned, a black hole is static. It takes infinite time as measured by us to turn round once. So it isn't rotating. That’s easy. We make electrons and positrons via pair production, electrons have spin angular momentum and magnetic dipole moment and can be diffracted. So you take the sphere of light approach, simplify it to a ring, then to a square. Only the horizontals bend, hence matter is affected half as much as light. Thin gruel here. The paper supports my position. Good. Now we're getting somewhere. Now go back and read what Einstein said about inhomgeneous space and how die Ausbreitungs-geschwindigkeit des Lichtes mit dem Orte variiert. I’m not on my own. Other people have said this sort of thing. And I’m with Einstein. The guy who prometheus dismisses, and called an idiot. You’re the one doing the misrepresenting. Prometheus made his opinion of Einstein perfectly clear. Einstein said what he said. Oh come on, pryzk, I'm with Einstein. You're not. I’ve addressed it enough. We’ve been through this. We said we’ll set the expansion of the universe aside. Space being flat means the universe is either infinite, or it has some kind of boundary. Go read The Foundation of The General Theory of Relativity and show me where Einstein talks about spacetime curvature. Then read http://arxiv.org/pdf/physics/0204044, then come back to me with an argument that holds water. This is imprecise. Einstein made a distinction between ponderable matter and matter, and said The energy of a gravitational field shall act gravitatively like any other form of energy. So think in terms of energy rather than just energy tied up as matter. When you smooth out the energy uniformly, light doesn’t bend. Think this one through. You have space with a uniform energy density, and you send a beam of light through it. Does the light bend? If so, does it curve downwards? Or up? Or to the left, or right, or some combination of the above? No. The space is homogeneous, there are no differences in any plane to make the light curve. There's no gravitational field present. It isn't just energy that results in gravity, it's a variation above the background level. I’m quoting the guy. You're the one saying "he didn't mean that" and inserting a different meaning. You started it. Don't do it. A four-dimensional "space" that includes time is a mathematical space that you can't move through. We describe the metrical qualitites of space, so we aren't describing space so much as motion through it, measured in terms of distance and time. My argument quotes Einstein, but it's evidential too. I've referred to the Shapiro delay, the GPS clock adjustment, and parallel-mirror light clocks. Light moves through space, and it moves at different speeds at different locations. And it bends because there's a gradient in the space it's moving through. It doesn't move through spacetime. It doesn't bend because it's moving through curved spacetime. Like I said, that's the effect, not the cause. He said these confer upon space its metrical qualities. You continue to talk of "the metric" instead of space and how you measure motion through it. I think you should examine this. I've won, przyk. By any standards.
Clearly not the scientific standard held to by any journal, as they all rejected you. Every single journal you submitted your work to rejected you. Do those journals count as a scientific standard? If so they you've failed to meet said standard. If not then its silly you tell people to read papers on ArXiv or by Einstein, since you dismiss the authority of papers due to lack of scientific standards. What about the standard of making predictions? You keep claiming string theory predicts nothing (repeatedly ignoring my correction of this misconception you have) yet when I ask you to provide a single working testable model derived by your work you can't provide one. Yet another standard you've failed to meet. What about honest open discussion? I repeatedly offer you a platform to discuss things relevant to your work, a platform where I am penalised if I behave dishonestly. You refuse, yet simultaneously complain there's a conspiracy of silence to keep you down. Its quite the opposite, I'd like to see you do a talk at a reputable university physics department, in front of people whose physics ability you can't dismiss as you try to with Ben and myself (and others). In fact, provided it was not too out of the way I'd even take a day off work to travel to see that talk. Why? Because I think you'd crash and burn so hard it'd be comedy gold. While I can't speak for them definitely I'm sure one or two others here or who know of you would be of a similar view. I wouldn't want to try to help you sort out such a talk, I wouldn't in all honesty be able to vouch for you as a worthy speaker but if you can ever sort it out yourself please let me know in plenty of time and I'll make every effort to be in the audience. Hell, if you could sort out recording it (seminars at the Isaac Newton Institute or at DAMTP are regularly filmed) then all the better. Seriously, I'd very much like such a film to be available to as many people as possible, as (I imagine) do you. You want it because you think you'll convince people of your genius. I want it because I think you'll convince people of precisely the opposite.
How many refractive indices are used to describe the "inhomogenous vacuum" in the paper? This is silly. Do you think that planets leave their gravitational fields behind as they orbit the sun? Haven't you heard of binary pulsars? We have to be able to account for non-static gravitational fields in any model that's supposed to be representative of nature. No, this is a hasty generalization - a logical fallacy. You have given me no good reason to believe this result generalises beyond the special case the authors have considered, and I've given you at least a few reasons to believe it won't. What are you talking about? The whole Schwarzschild solution is static. The point you're missing is that the Schwarzschild solution is only the correct solution if you're assuming the gravitational field is static and spherically symmetric. It is not a general solution. It is a special case. If the matter creating the gravitational field is not static or not spherically symmetric, the Schwarzschild solution does not apply. Sorry, but this sounds like hand-waving. And even if I did accept that massive particles could be described as bound light states - which I don't - this behaviour is not predicted by the action principle the authors used (they just treat light as a massless point particle), so this would be another hasty generalisation. If I agreed with you, then I'd have to conclude the authors used an over-simplistic model for light, and their result still doesn't necessarily generalise beyond that. He said: This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that 'empty space' in its physical relation is neither homogeneous nor isotropic ...This is just saying space is inhomogenous (which is true). It's not saying that gravity is inhomogenous space or that inhomogenous space is equivalent to curvature in space-time. I've already given this as my interpretation of what Einstein was saying. Do you remember your response? You said "No problem". ([POST=2670533]here[/POST].) So you can't continue to use this quote as evidence for your position. As Guest put it, "Because that's how I interpret this sentence" does not constitute evidence. Even if you are, what does that get you beyond an argument from authority? If Einstein said 1 + 1 = 3 would you expect us to believe it? Where? We have homogenous but curved cosmological models that are solutions to general relativity. On what basis are you dismissing them? Where did I agree to that? What does this have to do with spatial curvature being different from space-time curvature? Why don't you just tell me what \(R_{\mu\nu}\) and \(R\) represent, if not curvature? This doesn't change anything: if there's energy there, there's curvature according to the EFE, no matter how homogenously it is distributed. What, specifically, do you mean by light "bending"? As prometheus has already pointed out, this is not a good test for the presence of a gravitational field simply because the concept of "straight line" is not invariant. For example, there's a coordinate system called the Kruskal chart in which light follows straight line trajectories in the vicinity of a black hole, despite the fact there's clearly a gravitational field there. At the opposite extreme, you can get light to apparently bend even in the absence of gravity, just by accelerating or rotating on the spot. Started what? I do not make a habit of routinely accusing people of being like creationists, or imply that they're mindlessly repeating textbooks or defending a 'special interest' just because they disagree with me. Even if I do throw in the occasional ad hominem (pretty infrequently nowadays), I only do so only after having repeatedly explained why the recipient's position is bogus, and never as a substitute for that. You, on the other hand, just implied I was mindlessly repeating a textbook (an ad hominem), and you did that instead of addressing the existence of the FRW solutions. How does this in any way resolve the conflict it is supposed to be replying to? I'm not asking for your personal take on space-time or what the metric is. I'm confronting you with what Einstein said about them. I wouldn't say space-time was described by ten metric components anyway because the metric components are also partly a matter of which coordinate system you feel like expressing things in. But we're not discussing what you or I think. We're discussing what Einstein said. Why did Einstein say there were ten \(g_{\mu\nu}\)s? This is all quantitative evidence for the modern theory of general relativity, which you claim isn't faithful to Einstein. Where does anyone show, quantitatively, that "gravity is inhomogenous space" theory can account for all this evidence? Not if your aim was to convince others of your position by scientific standards. If you were just trying to convince yourself then that's too easy: you just have to cherry pick what Einstein said and turn a blind eye to the FRW solutions if you want to do that.
I have just noticed that when someone mentioned the FRW metric Farsight said "Retreating into your textbook", as if making reference to previous peoples work isn't a valid argument, yet his entire argument boils down to "Einstein said...". Yet another example of your hypocrisy Farsight. You dismiss references when they prove you wrong but treat them !s gospel when it suits your purpose. Looks like you fail by yet another standard.
