Curvature is the result of inhomogeneity. Inhomogeneous space causes the curvilinear motion we label as curved spacetime. There is no evidence that shows otherwise, and I'm referring you to Einstein and other material here. I'm not just making this up. LOL, fair enough. Oh come on. What he said is crystal clear: recognition of the fact that 'empty space' in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials gμν)..." And it isn't exclusively my interpretation. Read that inhomogeneous vacuum paper. Other people think like this too. OK, I'll cut you some slack and say that the space-time was a typo. Now let's look at your interpretation afresh: I read this as Einstein saying we'd have to learn to view space as being endowed with physical properties, and accept that it could be inhomogenous and anisotropic in those properties. No problem. That in itself was a new idea at the time. It wasn't totally new. Einstein is talking about an "aether" here. It isn't quite the same as saying gravity *is* inhomogenous space. But it is the same as saying a that a region of space where we find a gravitational field is a region of inhomogeneous space. In any case, the definitive statement of what GR is and isn't are the principle of general covariance (the mathematical formulation of the equivalence principle) and the Einstein field equation. There's nothing in the Einstein field equation that equates curvature to inhomogeneity. This isn't your interpretation of what Einstein was saying, this is your given reason for disregarding it. Read them. You'll learn something. Mathematics does not take precedence over physics. Did you know how Einstein predicted the perihelion advance of Mercury? He used a version of Paul Gerber’s 1902 equation. You are retreating behind mathematics przyk. Look: I don't mean to be offensive here, but that's the sort of attitude we see from young-earth creationists. They persuade themselves that they don't need to examine anything that challenges their belief. Look up Morton's Demon and Feynman's first principle. I do understand your position. That's why I give my time to address it, like I'm doing now. I'm the one offering the rational debate here. If you don't want to engage in discussion of this very simple point, then that's your choice.
You asked why I assert the universe is open - well it turns out I was mixing up the standard model of cosmology and a newer measurement from the CMB. The measurements of the density of the universe show that we are within a small percentage of the critical value for a flat universe, assuming there is no cosmological constant. Measurements of the CMB shows there is a cosmological constant (or a new form of stuff we don't understand called dark energy, but the effect is the same). The universes expansion is accelerating (observational fact), and according to the measurements we are asymptotically approaching a de Sitter, not a flat universe. de Sitter is in the open class of FRW solutions. Conclusion: AFAIK the universe is believed to be open (specifically, de Sitter) with the most modern measurements. But the universe seems to evolve according to some mathematical rules. We are trying to figure those rules out and understand them. That's what I said. Spherical coordinates aren't real?! Tell that to the Earth which seems to be quite happily existing in a rotating frame of reference. The truth is, of course, that any one coordinate system is just as valid and real as any other. My point is well taken : The "straight line motion" of light or any other object is not a good test of curvature. Hey, I'm the one publishing papers that are acknowledged as being worthwhile research by my peers. I rather like it here. Please Register or Log in to view the hidden image! Serious question: If in GR inhomogeneity causes curvature, what causes the curvature in de Sitter, FRW solutions, AdS, etc.? Do me a favour please, I'm not up with all those clever science words you use, can you just use simple, everyday language? Thanks. That's not what happened. Gerber's work was either an ad hoc model if we're being charitable or wrong and scientifically fraudulent if we aren't. The perihelion problem was well known a long time before GR, and lot's of people tried and failed to explain it. Let's be charitable and say that Gerber's formula was derived from the experimental data in order to quantify our ignorance. What Einstein did was to explain why the perihelion of orbits precesses, and to compute the amount of precession independently of any measurements. In any case, it's an exercise given to undergrads to use GR to calculate the precession of perihelion of an elliptical orbit. You aren't plugging into a 1902 formula anywhere. Let's have a rational debate. Start by answering my questions in this post. I genuinely want to improve my understanding of GR. If you think that's what Einstein said then there are three options: You misunderstood Einstein, Einstein was wrong or Einstein was giving a dumbed down talk for idiots. I suspect number 1 is most likely (hey, don't sweat it, this is Einstein we're talking about) but number 2/3 is not impossible. Einstein got a lot of stuff about physics wrong. Quite spectacularly, stupidly and comically wrong in fact. That would be a first.
Which of the following are not statements of fact : * Written a pet 'theory' claiming to explain large sections of physics which you've never studied. * Claimed to be more of an expert in electromagnetism than pretty much anyone in the world * Claims your work is worth a Nobel Prize * Spammed a great many forums with your pet theory * Made claims about how your work would be taught in schools in the not too distant future, as well as killing string theory * Failed to provide a single working model of any phenomenon in the real world, despite being asked many times over the space of years. * Don't know the different between a mathematical axiom and a physical postulate * Submitted to many journals and been rejected for publication by all reputable ones * Spent your own money on vanity publishing your work * Spent your own money taking adverts out in physics magazines for said vanity published book. * Made a television appearance on ... whatever the hell that show was, which covers other topics like alien abductions, 9/11 being an inside job and other bat shit crazy stuff. Is it abuse to state those facts? The only thing which might be considered abuse is my comment about the TV show, not you. And any mention of opinion in that list is me stating your opinion of yourself, opinions you've made clear many times (as the list of your posts Ben links to in the thread przyk linked to shows. If you're not a crank then perhaps you could explain why said list of facts are not evidence to the contrary. I know its hard for you to grasp but some of us don't just parrot science, we understand it (at least parts of it). You made claims about abstract concepts, which are clearly and precisely refuted. The fact you made incorrect claims about something sufficiently simple to be covered in basic textbooks doesn't mean that they don't count. It is not the case that the simpler and more well known the things you get wrong the more you can ignore any corrections, quite the opposite. Yet you just said : Any time you'd like to actually respond to specific points I and other have raised please do so. In fact if you wish I (or yourself) could start an alpha rules thread on curvature in differential geometry and relativity and we could go through the specifics. I share an office with a guy whose PhD was in differential geometry, so he can help with anything I might not be entirely familiar with. And to show I'm serious I'll agree to the condition that if I violate an alpha rule in said thread then I can be suspended for a month but only on the condition that you agree to the same condition and that both of us respond to direct relevant questions when asked and show intellectual honesty. We can go into the ground rules in more detail if you wish. I think people like BenTheMan and JamesR are sufficiently good at judging such things as to abide by their views. What do you say? You complain all I do is throw vitriol and the kitchen sink, now I'm putting myself in a position where I get blocked from the forum if I'm deemed to do that but only if you put yourself in the same position. I have nothing to hide and nothing to fear. Do you? So despite your supposedly undeniable logic and evidence and reason and an effort to do all the tedious stuff of getting your 'work' into the format whereby it would be judged only on its scientific merits you don't want to expose more of your *cough* 'genius' to the scientific community? You have all the answers and someone to help present them and you're unwilling to submit to a journal your 'genius'? Why, its almost like you know you're full of shit.
So how do you explain the existence of homogenous but curved solutions to GR? We're back to square one here. They contradict your position: inhomogeneity is not synonymous with curvature in GR. You still haven't explained on what basis you're dismissing them. You gave an analogy but you didn't justify it at all. Why are such solutions analogous to negative length carpets? That's not a response. You have a single example of a universe that happens to be both flat and homogenous, and you are claiming this is evidence the two are synonymous. That's a sweeping generalisation. How do you justify that? And, apparently, even more people don't. So you'll need to base your case on something other than popular vote (which I would hope you don't think is a valid argument anyway). It wasn't a typo. I understand the distinction between space and space-time and I think space-time makes more sense in the context I used it, based on my understanding of relativity. I'm allowing you to put in "space" because I don't want to pursue that particular argument here. Same for something you said earlier too: I don't have anything a priori against solutions that contain closed time-like curves. I'm not endorsing them, but I'm not prepared to dismiss them out of hand either. They're something I'd want to give some careful consideration to some time, which I haven't yet had the opportunity to do. But I know anything remotely related to the possibility of time travel is a bit of a minefield topic with you and I really don't want to get into that here and now. So you agree then? That's at least a valid interpretation of what Einstein said? It was new by contrast with Newtonian gravity, in which space is perfectly homogenous and has no properties. And even if it wasn't entirely new, it is important enough to GR to be worth some emphasis. No it isn't. Hell, if we read literally what Einstein said: "...the recognition of the fact that 'empty space' in its physical relation is neither homogeneous nor isotropic..."it sounds like he's claiming space isn't homogenous, period. There's no claim this is equivalent to curvature. Overall, that's one really vague citation you've found. Yes. I would assume that's obvious and never said otherwise, and I have been more explicit about this elsewhere (the bits about how I think the equations should take precedence over anyone's words, and so on). Why did you quote it as part of my interpretation of Einstein in the first place? If there's been some misunderstanding then I'll clear it right here: the math vs. words bits are my own opinions. I am not attributing them to Einstein. I didn't say that. And I am not choosing mathematics at the expense of physics or suggesting that you should. I am saying that mathematically formulated physics takes precedence over verbiage. The mathematics of general relativity has actually been tested in various gravity and GR experiments. The same can't be said for "gravity is inhomogenous space" theory, unless you can show it is a valid interpretation of the math (thereby leveraging the experimental support that the math conveniently summarises). That is the point I am making. Your own link has Einstein himself disavowing this: The experts are not only in agreement that Gerber’s derivation is wrong through and through, but the formula cannot be obtained as a consequence of the main assumption made by Gerber. Mr. Gerber’s work is therefore completely useless, an unsuccessful and erroneous theoretical attempt. I maintain that the theory of general relativity has provided the first real explanation of the perihelion motion of Mercury. I have not mentioned the work by Gerber originally, because I did not know it when I wrote my work on the perihelion motion of Mercury; even if I had been aware of it, I would not have had any reason to mention it.I don't know about you, but I'd say that's pretty damning. More to the point: why did you even bring this up at all? Suppose Einstein did use Gerber's equation. How would that challenge the point I'm making just above? If I was saying we should go with the math just because it's math then this would be a fair criticism. But I'm not, so it isn't. I'm putting importance on the math because it's what all the various GR and gravity experiments have actually tested. You have a single vague quote by Einstein that only you interpret the way you do, and an observation that alone can't prove the sweeping generalisation you are making. I also don't mean to be offensive, but your case isn't exactly watertight, you know. No, you don't. You appear to have read it as something like "mathematics takes precedence over physics". If you're tempted to paraphrase my position that way, then no, you don't understand it. You still haven't addressed the main points I have against you. You again basically just played your "it's just abstract math" card. I can't have a rational debate with someone who keeps responding like that.
It isn't, Acitnoids. Have a look at gravitational potential on wikipedia. There's an image rather like an upturned hat. It depicts the gravitational potential of the earth. At the bottom there's a region where there's no slope. That's where the void I mentioned is. In a void at the centre of the earth, you float around. No. Agreed. A void doesn't exist at the centre of all massive objects. But if there was such a void, you'd be in homogeneous space at that location. You wouldn't feel any gravity. You wouldn't fall down. Don't forget the important distinction between space and space-time. When space is inhomogeneous, the result is the curvilinear motion we label as curved space-time. Light bends, and things fall down. When this doesn't happen, the space isn't inhomogeneous. Yes, like a flat beach might have ripples in the sand. No problem. Yes, it is old news. And yes, Einstein had some problems with cosmology. People say that if he'd had the courage of his convictions, he might have predicted the expanding universe.
That's another way of putting it. This is getting to the heart of it. But the space-time isn't uniformly curved, it's flat. Light travels in straight lines in this region, things don't fall down. The uniform gravitational potential means there is no discernible gravitational field. The paper I referred to is important for this, see http://arxiv.org/abs/physics/0204044. A uniform gravitational field is where the gradient in gravitational potential is uniform, something like an inverted cone. A region where there is no gradient in gravitational potential is a region where there's no gravitational field at all. Hence in the "flat" universe which is homogeneous on a large scale, there's no overall gravitational field to prevent its expansion.
As ever, outraged abuse instead of civil discussion. You'll forgive me if I give my time to people who want to talk about this subject, instead of somebody who doesn't want anybody talking about it. Fair enough. We all get things wrong from time to time. Yes, the expansion of the universe is accelerating, but the universe remains homogeneous on the large scale, and hence flat. I'm afraid you've been misled Prometheus. Look at that NASA WMAP page. No problem. That's why we're here talking about this stuff. None of them are real I'm afraid. A coordinate system is just an artefact of measurement. You can't point up to the night sky and point one out. The same applies to a frame of reference. There is no other way to do it. Good. This isn't "in GR" so much as in space. An inhomogeneity in space results in the curvilinear motion motion of light. The curvature in de Sitter etc are curvatures in a hypothetical mathematical space. When you move from this back to real space, it's flat, as per the de Sitter universe I'm something of an Einstein fan, I don't mention this Gerber controversy lightly. But nevermind, it's off topic. My pleasure. And there's also the fourth option: what Einstein said was crystal clear, I understood it correctly, and he was right. See what I was saying to przyk. A light beam is affected by gravity, as we know. Not through some magical mysterious action-at-a-distance, or gravitons, but because of the space it's in. That space isn't curved. The motion through it is curved. When we see that curvilinear motion, we call it curved spacetime. But the space isn't curved, instead it's inhomogeneous.
Because the modern interpretation of GR is not faithful to Einstein's GR. I justify because I know that the electromagnetic field is curved space. This comes out of displacement current, wherein electromagnetic waves can be likened to gravitational waves. Place an electron in a region of space far away from any galaxies where we can detect no gravity and agree that space-time is demonstrably flat. It doesn't move. Thus there is no curved space at that location either. You're refusing to read a paper on grounds of popular vote. Your choice. You're wrong. Einstein said space, not spacetime. It's the swimming-pool analogy. Every morning you swim from one end to the other in a straight line. But one day in the dead of night I truck in a load of gelatine powder and tip it all down the left hand side. This starts diffusing across the breadth of the pool, imparting a viscosity gradient from left to right. The next morning when you go for your swim you're veering left. If you look back at your wake you notice it's curved. That's your curved spacetime, because the pool is the inhomogeneous space above a planet, and you're a photon. It's really simple. OK. But do note that my views on time and CTCs again derive from Einstein as per A World Without Time: The Forgotten Legacy of Godel and Einstein. Yes. But note that I replaced space-time with space. Not so. Check out Newton's Opticks, queries 20 and 21: "Doth not this aethereal medium in passing out of water, glass, crystal, and other compact and dense bodies in empty spaces, grow denser and denser by degrees, and by that means refract the rays of light not in a point, but by bending them gradually in curve lines? ...Is not this medium much rarer within the dense bodies of the Sun, stars, planets and comets, than in the empty celestial space between them? And in passing from them to great distances, doth it not grow denser and denser perpetually, and thereby cause the gravity of those great bodies towards one another, and of their parts towards the bodies; every body endeavouring to go from the denser parts of the medium towards the rarer?" Agreed. He's saying it's inhomogeneous wherever we find a gravitational field. He doesn't even mention curvature. Nor does he mention curved spacetime in The Foundation of the General Theory of Relativity. The curvature gained emphasis during the Golden Age of general relativity in the sixties. OK. I read the paragraph you gave as "your interpretation". Verbiage? I offered the paper. You make excuses and persuade yourself that you don't need to read it. I brought it up to demonstrate again that what you're taught about general relativity isn't accurate. But you are so convinced that it is, that you won't pay attention to what Einstein actually said. Mathematics is important. It isn't vague, and it isn't only me. You're kidding yourself by repeating that. Read the expletive paper. Then let's just agree to differ. But remember that Einstein and Newton are on my side, not yours.
Farsight, could you summarize what has the others upset? From what I can tell you are claiming that the universe is homogeneous on the large scale, yet inhomogeneity is equivalent to a gravitational gradient. Isn't this saying that the universe is devoid of any gravitational gradient on the large scale? It seems that once you're "outside of" the mass/energy cluster of the visible universe you would detect gravitation towards it. Or are you also postulating that mass and space are infinite?
As many people have said and I'm now going to repeat: Homogeneity does not imply flatness. Counter examples include AdS and the FRW solutions. If you don't like them because you claim "they aren't physical," then de Sitter is homogeneous, not flat and physical because in the standard model of cosmology the universe certainly underwent a de Sitter type expansion in the form of inflation. That leads me onto this: That's a pop science page. Let's try and do a little better. Here we have the original discovery of an accelerating expansion which has now been named dark energy and here is a short review about it. I know you like to phrase things in simple ways so let's think about the accelerating expansion. The most basic way of doing it is assuming there is a non zero vacuum energy, which Einstein called the cosmological constant. Since this quantity is doesn't depend on how much of it you have the universe's expansion will continue to accelerate for ever, which is pretty much what an open universe is. There are other ways to account for the accelerating expansion, like quintessence but (and I'm not an expert on this) AFAIK quintessence can lead to an open universe in the same way as a non zero vacuum energy. In fact, you can also get scenarios where eventually the gravitational repulsion can overcome the electromagnetic force and matter gets blown apart. What is a measurement? When you stand outside and look through your neighbours window while she's getting changed that's as much a measurement as what is being done at CERN or fermilab. Same applies to frames of reference. The physics doesn't depend on what coordinate system or you choose, but when you're trying to calculate things then you try and make a clever choice that makes the calculation easier. For example, when you're working out how much light is deflected by a massive body it's nice to do it in spherical coordinates where the motion of light is not in a straight line, even if there is no mass present (ie, honest to god flat space). As I've said before, you cannot measure curvature by checking if light goes in a straight line. You serious?! The straight line or otherwise motion of light is the only way to measure curvature?! What about any measurement of gravity, observations of the orbits of planets, stars and galaxies, Laser interferometry, the list goes on. Like it or not, GR describes space very well indeed, in fact, well enough for me to assert without flinching at all that GR is the way space works (at least, for large enough scales). As I said previously, the universe seems to be de Sitter and it certainly was in the past when inflation was going on. What happens with your intuition then? Einstein was great until about 1915 but after than he was an idiot. It was such a shame that he had the imagination to accept relativity but didn't have the imagination to accept quantum mechanics, which has been even more successful that GR. To be absolutely blunt, relativity wasn't the brainchild of Einstein alone. People like Lorentz, Maxwell and Poincare basically discovered relativity before Einstein but couldn't come to terms with the results. Firstly, your fourth option is inconsistent with the facts - gravity is not inhomogeneous space because gravity can and does exist in homogeneous spaces, where no gravity should exist according to your quote. I think I understand the problem you are having - it easy to visualise a curved 2 dimensional surface but it's not easy to visualise a curved 3 dimensional space, much less a 4 D one. Unfortunately, that's all you have to understand GR so instead of actually learning about it and understand it you try and come up with another "interpretation." Sadly for you, space, spacetime or whatever you want to call the 4 dimensional manifold in which you live really does have curvature in the curvature sense. Before I studied general relativity I read pop science books and articles too, and there were many times where I simply could not grasp WTF the writer was saying - it's not a good feeling. Studying GR and understanding it was a very fulfilling experience. I recommend it wholeheartedly. Just out of curiosity, have you read Einsteins original paper on GR? It's a pretty mathematical paper, in fact, it's pretty much a paper on differential geometry.
Did you even read my post? I offer to help you submit your 'work' to people whose job it is to evaluate this stuff and you turn me down. I offer to engage in a discussion with alpha rules and a penalty of voluntary suspension if broken and you turn me down. You skipped all my direct questions, all my offers, all my counters to your claims and focus on the last line. Do you think its not blindingly obvious you're just trying to come up with excuses to avoid a serious discussion because you know you aren't up to the task? Kaneda used to do the same, he'd complain I've never done anything original but when I offer to discuss my work with him in a new thread he always refused. You keep saying how I don't understand this and that and all I do is just parrot back textbooks when when I offer to demonstrate otherwise in front of everyone you run off with your tail between your legs. But I suppose that isn't unexpected... On PhysOrg before you submitted Relativity+ to journals I offered to bet you £1000 (handled via a trusted 3rd part) you'd not get your work published a reputable, including in that the offer to typeset your work appropriately for the same reason I mentioned previously. If you honestly believed your claims about being Nobel Prize worthy and you being more of an expert in various things than anyone else you'd have viewed it as free money (as you wouldn't have needed to do any further work, you'd already typed it up). Its fortunate you never took up that bet, seeing as you did indeed get rejected from all reputable journals. Its quite clear you don't want an intellectually honest discussion on your claims or work, you just want a pat on the bag and an intellectual hand job for your ego. How many years and thousands of pounds have you spent on this now? And yet you're in precisely the same position making the same sorts of claims about physics and your work which you were making in the original Relativity+ thread from 3.5 years ago. Stellar achievement.
You are basing that on a single citation - out of Einstein's entire career - that only you interpret the way you do. Besides, you've already agreed that physics is not a religion and we're not required to go along with Einstein for its own sake. Being faithful to Einstein is not a priority in physics. It is quite common for theories to become better understood over time and for their description and interpretation to change accordingly. Personally I would not be surprised if the modern interpretation of GR differs in some respects to Einstein's original views. It wouldn't be the only example of this happening, and it's just a sign that healthy scepticism and re-evaluation are constantly going on in the mainstream physics community. So I don't know why you keep repeating "You're dismissing Einstein!" as if that were some sort of crime in and of itself. This is describing the original meaning of the word "aether": as a hypothetical medium in space through which light is supposed to propagate. It isn't attributing properties to space itself. And as I said, even if the idea wasn't new, it is still central to GR and worth emphasis. Again, that is exclusively your interpretation of what Einstein said. Yes. English is notoriously vague and poorly suited to communicating subtle distinctions in physics. There is also no way of performing a quantitative test of someone's speech: it doesn't yield to experimental verification the way a mathematically formulated theory does. I've just glanced at the paper. It looks like what they're describing is subtly different from what we mean by "homogenous space". I'll try to describe the problem here, and if I've missed something (I did just glance at it after all), feel free to say so. Here's the issue: it looks like they're relating curvature of light rays to what could be called "inhomogeneity" in the metric. If you have a coordinate system in which the metric is not constant ("inhomogenous") then there will always be geodesics that follow curved trajectories in that coordinate system. And conversely, if the metric is always constant ("homogenous") in a coordinate system, then geodesics are always straight lines in that coordnate system. The problem is that an "inhomogenous" metric doesn't mean that the space it is describing is inhomogenous. As an example, consider this metric in spherical coordinates: \(\mathrm{d}s^{2} \,=\, \mathrm{d}r^{2} \,+\, \sin(r)^{2} \mathrm{d}\theta^{2} \;.\)It looks inhomogenous, right? Even if you're not comfortable manipulating metrics, you should be able to see that this one depends explicitly on r. Almost all geodesics will appear curved in these coordinates. Furthermore, if you work out the curvature associated with this metric, it's non-zero. That means that the apparent inhomogeneity of this metric isn't just a feature of the coordinate system I'm using. It's forced on you. This metric will appear inhomogenous in all coordinate systems. So, this is a space in which all possible metric expressions will look inhomogenous. Does that mean the space itself is inhomogenous? No! The example I've just given you is the metric on the surface of a sphere. There are no privileged points on the surface of a sphere: intuitively, it looks the same around every point. Ordinarily, we'd sum that up by calling the sphere homogenous. If you want to disagree here then fine. But then you're not really challenging the mainstream. The root of the disagreement is simply that you are adopting a different definition of "inhomogenous space" than the mainstream does. What isn't accurate about it? It can recover Newtonian gravity in the weak field limit and it can account for the results of a number of GR and gravity experiments that I'm sure you'll have already heard about. That's what's important in physics. If the mainstream view can do that, it's perfectly good science, whether or not it has Einstein's blessing. I am paying attention to what Einstein said. I disagree with your interpretation of it. I gave an alternative interpretation of what Einstein could have meant and you didn't have a problem with it. That was literally your response: "no problem". If different people can read the same citation and come up with different interpretations for it, it's vague. Well, with reference to what I said earlier in this post, if you are employing a definition of homogeneity according to which the sphere is inhomogenous, then yes, we're just going to have to agree to disagree..
I wouldn't say they're upset, RJ. Alphanumeric is doing his usual spoiler-tactics to disrupt civil discussion, prometheus has been somewhat impolite, but przyk has been fairly reasonable. I'd say it's something like a spectrum of disbelief, where people have difficulty in accepting something which challenges a long-held conviction. They sometimes refuse to examine the evidence, and sometimes react with hostility, especially if pride/reputation is at stake. Yes. Hence the universe is devoid of space-time curvature. I've also said it's devoid of spatial curvature because the electromagnetic field is curved space, but that's a little more contentious. No. You can't go outside space or get outside the universe. No, not at all. We don't know for sure how big the universe is. But the observable universe is said to have a diameter of 96 billion light years, and if the big bang was not a local phenomenum, I envisage the universe to be finite.
You're still confusing homogeneous physical space with a mathematical space. No problem with that. But the space in the expanding universe is still flat. We could talk about inflation separately if you wish. There are important conclusion to draw from what I've been saying here. But not exaclty. Like Acitnoids said, a flat universe can expand like this too. Again, let's talk about expansion elsewhere. It's related to inflation. Yep, I've heard about the big rip. Adopting some coordinate system doesn't alter the motion of light, prometheus. See http://www.theory.caltech.edu/people/patricia/lclens.html for easy calculation. Yes, all those measurements are valid measurements, but look at your link. You're measuring gravity, the local inhomogeneity of space that causes curvilinear motion, not curvature per se. The university of Melbourne page is not responding. It's no intuition, but it is extremely simple. Start a thread on inflation and expansion and let's talk. He was in on the ground floor of QM. He didn't accept the Copenhagen Interpretation. I know. Don't forget FitzGerald. Like where. Come on, describe it. I can visualize curved 3D space. No, I can't visualise this. Sorry, but space doesn't have curvature on a large scale. And spacetime isn't physical. We live in space, and we move through it. We repesent this in a mathematical space such as Minkowski spacetime, but we cannot move through this "block universe" spacetime. Then you really shouldn't have a problem with what Einstein said. Unless you think he's an idiot. Yes, his contribution to physics is arguably overstated and seemed to diminish from 1920, but he was no idiot. Yep. And guess what? It doesn't actually mention curved spacetime. He's giving the equations of motion, through space. Read that paper I mentioned: http://arxiv.org/abs/physics/0204044 Other posters: apologies, I have to go.
Prefix: If we are talking about general relativity, ie, the theory of gravity proposed by Einstein in 1915 and still a hugely successful theory of gravity then by all means answer my questions. If we are talking about your own theory of gravity, perhaps based on the pop science descriptions of GR that you've read but don't like for some reason then you can probably ignore most of my questions because I'm afraid I don't care about what you think is physical, I care about what is physical. Please tell me what you think the difference is. As I said, the universe underwent a period in it's history where it was de Sitter and will probably go to de Sitter again in the future. de Sitter is a curved and homogeneous solution to GR. I will put this in another thread once I'm done with this post. Are you trolling me? I said exactly that in the post you quoted: The physics doesn't depend on what coordinate system or you choose, but when you're trying to calculate things then you try and make a clever choice that makes the calculation easier. Perhaps you should stop arguing with me about things you and I agree on. This seems to be your personal interpretation of GR. The correct interpretation as developed since GR was proposed is that space is a 4 dimensional surface which can deform in the presence of matter or energy. I don't know much about the history but I can tell you that the physics of gravity as described by GR coincides exactly with the mathematics of differential geometry which describes curved surfaces in any number of dimensions. There is a dictionary between the two and what we call space in GR is a pseudo-Riemannian manifold in differential geometry, therefore if GR is right (which AFAIK it is) space has all the properties of this manifold, to wit, being able to bend and curve. I'm not there so I can't help with that. He didn't accept the results of quantum mechanics and advocated hidden variable theories over the quantum mechanics and he was wrong, as proven by Bell's inequalities. As I've said many times already, de Sitter is a counter example to your claim that homogeneous space cannot be curved. I direct you to the prefix of this post. Are we talking about GR or not? If by "seemed to diminish," you actually mean "he did no useful work at all," then yes, that's right. Make no mistake, Einstein was a great physicist, but there are others who were just as great, if not greater and should be recognised on an equal level with Einstein. For example Dirac, Feynman, Coleman, 't Hooft, Weinberg, Yang and Mills, Wilson etc etc. I believe that you are misrepresenting what Einstein thought. He certainly uses the metric tensor (which he calls the fundamental tensor in the English translation) as introduced by Minkowski and as I said, GR is mathematically differential geometry. On page 176 he begins a discussion of the Riemann tensor and he would certainly have known that the Riemann tensor is used to describe curved surfaces. Whether he used the words "curved spacetime" is irrelevant - that's what is implied by GR.
No, we're not. Just because you don't know how the maths plays a part in physics doesn't mean everyone else has your short comings. Besides, in your Relativity+ you confused mathematical axiom and physical postulate and despite me repeatedly explaining the difference and trying to engage you in discussion on it over on PhysOrg a long time ago you continued to fail at understanding the difference. As such I hardly think you're in a position to be telling others about what is maths and what is physics. The spatial components might be but the space-time is not. Changing coordinates will shuffle around which curvature components are non-zero but there will always be non-zero components. By definition of 'tensor' the curvature is identically zero in a frame if and only it is identically zero in another. Part of your issue is that homogeneous space doesn't mean homogeneous space-time, as Prom's new thread illustrates. If you have homogeneity in space-time then it must be flat but inflation is an example of a homogeneous space which changes in time and does so in a way to maintain its homogeneity. Thus time related curvature occurs and once you allow changes of coordinates (which is what tensor calculus is all about) then you can get coordinates where the spatial dependency is not homogeneous (which doesn't alter the underlying space-time itself). Space and time mix and so if you have time inhomogenity and space homogeneity in one set of coordinates you can reformulate the space to have spatial inhomogeneity and curvature associated to it. A little experience with tensors and coordinates would do you the world of good. Easy by someone else's standard but you're not competent at any of this or we wouldn't be having the 'discussion'. Of course not since they are not synonymous, If you worked No, you think it is but you are wrong in (at least) two ways. Firstly its not simple for other people, differential geometry and GR can be extremely complicated even for space-times as 'boring' as Minkowski (see Stewart - Advanced General Relativity) and secondly its obviously not simple for you as you've gotten it wrong. You over estimate both your knowledge and your capabilities. So you'll talk to Prom but not me, even when I offer to abide by rules even stricter than the alpha rules? You say I'm running scared but when I step up and say "Come on, put your physics where your mouth is" you tuck tail and run. You're all bluster with nothing to say Farsight. Are you pretending to be really thick and dishonest or is that how you really are? You've been given plenty of space-times which are homogeneous in space yet have curvature. Yes and I'm the King of Prussia. Its easy to say things which aren't true, how about you put your money where your mouth is? Its funny how hacks whine about "Don't accept what you're taught, open your mind" and then can turn around and quote mine the hell out of people they just denounced. And by funny I mean hypocritical, dishonest and stupid. Your entire 'argument' rests on interpreting out of context and without regard for other possible interpretations a single thing Einstein said almost a century again. And even if Einstein meant what you think he did that doesn't mean we automatically accept it or the converse, we don't and then we think he's an idiot. He did a lot of good things and plenty of bad but he at least understood that when someone provides a counter example to a claim then the claim is false. You seem to struggle with that. Until you open a textbook on basic GR and find out what it says so you can stop just making stuff up on what you think it says based on your reading of Wikipedia you're not in any position to tell other people to read up on the matter. Hopefully permanently. I look forward to seeing billboard advertisements and 20 minute long 'infomercials' broadcast at 3am on some back water Freeview channel you'll be making to promote your book Please Register or Log in to view the hidden image!
I offer to help you submit your 'work' to people whose job it is to evaluate this stuff and you turn me down. I offer to engage in a discussion with alpha rules and a penalty of voluntary suspension if broken and you turn me down.[/quote]Thanks but no thanks. You'll forgive me if I don't go into my reasons, which revolve around trust, sincerity, and honesty. Enough.
It isn't only me, przyk. That second paper makes it perfectly clear. You aren't demonstrating any healthy scepticism or re-evaluation. You won't examine anything that challenges your conviction... ...I stand corrected. OK. They're talking about inhomogeneous vacuum rather than an inhomogeneity in the metric. They aren't talking about an inhomogeneous mathematical space. They're talking about inhomogeneous space. They aren't talking about an inhomogenous metric. They mention the word metric only once. Here's a "fair use" quote: "The refractive index of vacuum, as a special optical medium, may be changed under the influence of gravitational matter. In fact, there has been a long history of such an idea. In 1920, Eddington[26] suggested that the light deflection in solar gravitational field can be conceived as a refraction effect of the space (actually the vacuum) in a flat spacetime. The idea was further studied by Wilson,[27] Dicke,[28] Felice,[29] and Nandi et al.[30-32]" Thanks for trying, but I rather fear you've missed the point. I and the paper are talking about physical space. When it's homogeneous, the thing we call spacetime is flat. The surface of a sphere isn't. It has a uniform curvature. For physical space to result in lightpaths demonstrating a similar uniform curvature, then that space has to be uniformly inhomogeneous. The history of what Einstein actually said. No problem with that. I'm looking at your interpretation again along with my comments: I read this as Einstein saying we'd have to learn to view space as being endowed with physical properties, and accept that it could be inhomogenous and anisotropic in those properties. No problem. It isn't quite the same as saying gravity *is* inhomogenous space. But it is the same as saying a that a region of space where we find a gravitational field is a region of inhomogeneous space. You seem to agree with what Einstein said, as I do, and yet you say you don't agree with my interpretation. I don't think we can get much further with this. OK, let's agree to differ.
We are talking about general relativity as proposed by Einstein in 1915. But you think he's an idiot and you choose to ignore what he actually said, so let's leave it at that.
Where does you needing to trust me come into it? I'm not talking about "I'll not post for 30 days", I've said in a publicly viewable thread I'll accept a suspension if I break said rules, so you can point a mod to the post (and now this one stating it again) to let them know I requested a suspension under said conditions. Or were you referring to your own sincerity and honesty, which we've yet to see anything of. Ah, did I hurt your feelings? Come off it Farsight, you once said you're amazing at arm wrestling in order to somehow intimidate Ben, you're not going to have your feelings hurt if I ask you to put up or shut up? Or if I ask you to retort my list of behaviours/actions you've done which point to you being a hack? Or if I challenge you to an honest and reasonable discussion? If my PhD was so useless and you're such an expert in physics surely the opportunity to engage in a clearly and carefully moderated discussion would be a prime opportunity for you to wipe the floor with me? Or are you not up to the task? Its just like when I offered to bet you money about your work being rejected, if you really believed the rhetoric you spew about yourself it'd have been free money but you didn't take me up on it. As usual, you fail to step up when its against someone you know you can't bullshit. Einstein didn't get a perfect understanding of GR, plenty of results were unexpected to him and found by other people. Black holes being an example. Our understanding of GR has moved on since his time, in fact the 'golden age' of general relativity was the 60s, after he'd died. Come on Farsight, if you have to sink to the level of telling Prom what he thinks about Einstein, despite him specifically saying that isn't what he thinks, then your best course of action is to just stop posting. Its funny how you simultaneously tell people the mainstream is wrong yet you're canonising a single quote of Einstein's to the point of not thinking any other interpretation could be possible and to disagree with your interpretation means people think Einstein's an idiot. We disagree with the way you have interpreted that quote, because your interpretation directly contradicts both the quantitative and qualitative results of general relativity, including work Einstein did himself. And you're not really the best person to say "You shouldn't ignore what he said" when you resolutely refuse to read anything quantitative in any area of physics. This is obviously a flawed way to go about things, as the fact your interpretation of that one thing Einstein said contradicts all the other things Einstein (and others) said on the matter yet you're unaware that (until we point it out) because you haven't read what he or others have done in GR, other than via pop science books. Until the day you have the intellectual honesty to read something other than pop science articles/books before you shout your mouth off you're just being a hypocrite when you tell others to read up on something. The fact I covered this precise point in my previous post yet you repeat the same hypocritical behaviour would suggest you have a problem with understanding what should be pretty easy for you to grasp.
