So what's this mysterious "real-solution criterion"? Oppenheimer interpreting the Schwarzchild solution a particular way, decades before the Kruskal chart was even discovered, is not an objective "criterion". As opposed to what, a fake universe? That's not an answer. Who measures that it takes "forever" and how do they make that measurement? No, in general relativity, time is not just "accumulated local motion". You having a particular philosophy about time doesn't make it fact and doesn't prove anything about general relativity which models time completely differently. False analogy. Carpets by definition don't have negative length. There is no analogous criterion in general relativity that you can use against the Kruskal chart. I specifically asked and you failed to give one. Just because some mathematical problems have unphysical solutions doesn't mean you can dismiss anything you like with that excuse. There is absolutely nothing unphysical about the Kruskal solution. Here's the Schwarzschild metric (in units where G = c = 1): \( \mathrm{d}s^{2} \,=\, - \bigl(1 - \frac{2M}{r}\bigr) \mathrm{d}t^{2} \,+\, \bigl(1 - \frac{2M}{r}\bigr)^{-1} \mathrm{d}r^{2} \,+\, r^{2} \mathrm{d}\Omega^{2} \,. \)What's \(\bigl(1 - \frac{2M}{r}\bigr)^{-1}\) when \(r = 2M\)? Another non-answer. How do you measure that light is going slower in one place than in another? You don't even know what you're talking about here. The Ricci scalar is a physical quantity in the sense that it is a Lorentz scalar. It is completely invariant under coordinate transformations. That's the fundamental difference between the coordinate singularity on the event horizon and the true gravitational singularity at r = 0. We know there's a "true" singularity there, that no coordinate transformation can ever eliminate, because the coordinate-independent Ricci scalar blows up there. It's not like you can just sweep away any infinity by magic, you know. By contrast, there are no coordinate-independent quantities that blow up on the event horizon. Only coordinate-dependent quantities blow up there in the Schwarzschild chart. Incidentally, the Ricci scalar isn't just a real physical quantity in the sense of it being coordinate independent, and it has little, if anything, directly to do with time. The Ricci scalar is a contraction of the Ricci curvature tensor, which in general has a physical interpretation related to volume deformation in curved spaces (eg. the volume of a ball of radius r in a curved 3 dimensional space is no longer necessarily \(\frac{4}{3} \pi r^{3}\), and it's possible to relate the volume deformation to the Ricci tensor). The Ricci tensor itself is a contraction of the Riemann curvature tensor. That quantity tells you whether you're in a flat spacetime or not (ie. it tells you when you can map the whole of spacetime with an inertial coordinate system). It also tells you the deviation between infinitesimally separated worldlines, via the Jacobi equation, so you can think of the Riemann tensor as a measure of tidal forces. Not just because you say so, and so far that's what all your arguments boil down to. Clocks measure time. If all clocks and all physical processes go slower by the same factor then, for all practical purposes, time goes slower. There's really no point in making a distinction between the two.
It isn't mysterious, it’s just taking a reality check and asking yourself if the solution represents something that can actually exist. The negative carpet is the simple case, where you say lengths aren’t negative because length is a scalar and negative distances don’t exist. Re Schwarzchild/Kruskal the issue lies with an infinite t. To decide whether we're dealing with a real solution one has to examine what does t actually represent? and to do that you have to examine what does a clock clock up? An observer some distance away from the black hole is doing the measuring with his local clock, but he can’t actually take a measurement that takes forever. It’s all rather gedanken anyway, because we’ve never actually been to a black hole. But we can compare those very accurate optical clocks and see that the lower clock is running slower than the upper clock. We extrapolate this to the black-hole scenario to say the lower clock is subject to infinite time dilation as compared to the upper clock at an "infinite" distance. So from the POV of the upper clock it isn’t running any more. Adopting Kruskal-Szekeres coordinates is an attempt to do away with the infinity and take the POV of the lower clock. But it misses the significance of what does a clock clock up? and fails to see that clocks clock up motion, and that the infinite time dilation is actually zero motion. It isn’t something I invented. Take a look at Presentism, Aristotle, and a A World without Time, and more importantly at what a clock actually does. A clock doesn’t measure “the passage of time”. My "philosophy" about time isn’t so much some philosophy as a hard-nosed evidential view. I thought I’d given you enough with the infinite peak on the Schwarzschild chart. You just can’t get past it because it the top of it is infinitely high and represents the end of time. I’m not challenging it for nothing. I’m challenging it because it attempts to sweep the infinite coordinate time under the carpet. It’s rather like an inverted version of Zeno’s paradox. Stop right there. That c=1 is axiomatic. If you’ve got a light clock that isn’t running, what you’ve actually got is a c=0. When you imagine yourself at that clock’s POV you’re saying that 0/0 =1, which is wrong. It’s “indeterminate”. A poster called Twiffy was talking about this a week or two ago. He's a mathematician specialising in topological quantum field theory. Zero. Or maybe that should be indeterminate, like we've got a poisoned well. You take two identical synchronised optical clocks, put one in one place and the other in the other, and you leave them for a while. Lie them flat to avoid radial length contraction and leave them for a long while to diminish the effect of travel. Then you retrieve the clocks and compare their readings. The one with the lower reading has been in the place where light goes slower. It's that simple. You could do the same with tape reels. You’re sweeping away the Schwarzschild singularity with magic and saying it isn’t true when it is. I'm flipping the infinity into the zero it really is. Have a read about gravastars, but note that I say a black hole is a black hole even without the central singularity. The 0/0 has rather blown up. Noted. I have some issues wrt space v spacetime, and with tidal forces which takes us back to inhomogeneous space, but I have to go I’m afraid. I’ll get back to you on this and your other points when I can. But for now: time doesn't "go" at all, things move.
I can't bite my tongue anymore, so because this seems to come up all the time with people who don't have much experience with relativity, we should have a go at laying this coordinate chart thing to rest. I won't use mathematics because the root cause of the problem is that people don't understand the mathematics. So here we go: Think of coordinates as a language. Just as you use words from a language to describe things around you, mathematicians and physicists use coordinate charts to describe properties of spacetime. If you use two different languages to describe some physical object, the change of language does not alter the characteristics of the object you're describing. Exactly the same is true of coordinate charts. The Schwarzschild "language" doesn't have the appropriate words to describe spacetime at the event horizon, so we are forced to use another language. One possible option is Kruskal's "language", which is slightly more complicated than Schwarzschild's but it has the bonus that you can describe all of spacetime with it. This is made all the more obvious if you do actual calculations in GR. If you actually compute proper times for observers, you will find that no matter what coordinate chart you use, you get the same answer. If we go back to our language analogy, we see this is entirely expected. Call someone stupid in Chinese or Bulgarian, it conveys the same meaning, just different words. With regards bad coordinate charts (or "languages"): the English language doesn't have a word for Schadenfreude -- but you'd be thought a fool if you suggested the lack of an English word meant nobody takes pleasure from other people's misfortune. So, when thinking about coordinate charts in GR, laypeople have two options: a) Bring in the language analogy for personal understanding and ask those who are experienced with GR when more is needed. b) Learn GR, do computations for some physics and find that coordinate charts don't change your answers. Then relay this back to the definition of a coordinate chart and to see why this was obviously going to be the case. Invariably, with no exceptions, it is those who cannot do the latter who have the problem understanding general relativity and in particular, the coordinate singularity of the Schwarzschild chart.
And how do you tell that? You still aren't giving any criteria. Literally, all you've got are these metrics: \( \begin{align} \mathrm{d}s^{2} \,&=\, - \bigl(1 - \frac{2M}{r}\bigr) \mathrm{d}t^{2} \,+\, \bigl(1 - \frac{2M}{r}\bigr)^{-1} \mathrm{d}r^{2} \,+\, r^{2} \mathrm{d}\Omega^{2} \,, \\ \mathrm{d}s^{2} \,&=\, f^{2} \bigl( - \mathrm{d}v^{2} \,+\, \mathrm{d}u^{2} \bigr) \,+\, r^{2} \mathrm{d}\Omega^{2} \,. \end{align} \)All GR has to say about these two metrics is that they're both solutions to the Einstein field equation and that in both cases accumulated proper time is given by the integral of \(\mathrm{d}\tau = \sqrt{-g_{\mu\nu} \mathrm{d}x^{\mu} \mathrm{d}x^{\nu}\) along a given curve. That's all you've got. So from there, on what basis other than arbitrary whim are you calling the first solution "physical" and the second "unphysical"? So why are you calling the one with the infinite t "physical" and dismissing the one where everything is well behaved as "unphysical"? How? Sure, the person falling toward the black hole can have a clock and the observer some distance away can have a clock, but how do they compare them? How does the distant observer tell that the infalling person's clock is frozen compared to theirs? That's the problem I'm getting at here: you're implicitly assuming that there's a well-defined notion of simultaneity in GR that lets you say that one person's clock reads something when - ie. at the same time as - the other person's clock reads something else, and in GR there isn't one. Simultaneity is already relative in special relativity. It isn't well defined at all in GR over significant distances in curved spacetimes. No, you seem to have completely missed my point: I told you that the Kruskal metric was a solution to the Einstein field equation independently of the Schwarzschild solution. Given that, on what basis are you dismissing it as unphysical? Let's say for argument's sake the Schwarzschild metric had never been discovered, and we only knew about the Kruskal metric. What would be your argument against it then? No, try again. If you need a refresher, \(x^{-1} = \frac{1}{x}\). So what's \(\frac{1}{1 - \frac{2M}{r}}\) for \(r \rightarrow 2M\)? Why should this have anything to do with the speed of light? In SR if an observer moves close to the speed of light, SR predicts that all their clocks will also go slower. Does that mean the speed of light is slower for a fast moving observer? You've got no reason to presuppose it's "true" in the first place. It's easy to invent coordinate systems for which trajectories shoot off to infinity and come back again just like in the Schwarzschild chart. (Eg. you can do something like starting in a Euclidean coordinate system and then doing \(x \rightarrow 1/x\). Then any trajectory passing through the origin shoots off to infinity in the new coordinate.) There are no steps taken in the derivation of the Schwarzschild solution to ensure we don't end up with such a pathological chart. It's not like when we derive a metric we can say "I want t to represent this and r to represent that" in advance, like you do in highschool problems. GR just spits out a metric expression that has both the physical significance of the coordinates and the geometry of spacetime encoded in it, and there's no reason one derivation shouldn't produce a metric with infinities in it just because the coordinates turn out to be pathological.
I find this totally funny, only about four (4) month prior Farsight was arguing against "Black Holes" claiming that they don't exist. I could provide the proof in various posts, and on other websites, but it is not worth my time and energy. Now, all of a sudden you are now defending "Black Holes" like you are some expert on "Black Holes." What inspired your magical switch and new acceptance of "Black Holes" And what is even funnier, is that you are ignoring the Schwarzschild Metric, which everyone talks about and reaching to understand the Kruskal-Szekeres coordinates. My suggestion is first comprehend the Schwarzschild Metric, before tackling something more complicated like Adopting Kruskal-Szekeres coordinates. Do you even know why Kruskal was successful in providing a "Black Hole" solution? Of course you don't. So I will help you. And once you have this as understanding, you can claim that you understood it all along. A Black Hole is a symmetric object, meaning that a sphere, ellipsoid, ellipse, and circle are all conic sections that are symmetric. And using this geometry and the Schwarzschild solution yields infinities at the surface of the "Black Hole" Event Horizon. So Kruskal, knowing that he needs symmetric geometry, first considered the parabolic geometry, but this conic section is asymmetric. But once he considered the hyperbolic geometry of the conic section, this provides the answer. Why? Because the hyperbolic geometry is symmetric and provides a "diretrix" and is offset from the center where you can define a open curve and not a closed curve. Now back to your newly acceptance of the existence of the "Black Hole." It is ok to evolve in your understanding, once you learn a new thing; this is natural. It is just the way that you are going about it. In the bible, Paul the Apostle killed thousands of Christians who believed in Jesus Christ. Then one day as he was traveling along the Damascus road, Jesus Christ met with him and converted him. Once he was converted, this confused people. Everyone knew that just months ago he was killing people that spoke of Jesus. But he admitted that he learned some new information and had changed his mind. And in his subsequent writings he would state that he once believed one way, but then later his mind was changed. Paul was an honest man, stating and admitting that he had a change of mind; he never tried to hide the fact that he once felt vehemently against something that he now accepts. You, who are not honest, would never do such a thing. What inspired your new conversion for black hole acceptance??
You don't understand general relativity any more than Farsight does! You've even been daft enough to document your complete lack of understanding in the self-published book of jokes "Super Principia Mathematica".
Przyk, Sockpuppet 2 of 23 Sorry, I believe that you are correct, and I am ok with your time equation. I forgot that you like to use natural units where (c = 1). The form of your equation is therefore ok!
You are a smart guy! Treat it as a physics problem and solve it!!Please Register or Log in to view the hidden image!
As Magneto accused me of having sock accounts under the names of you, Guest, Tach and someone else beginning with T I changed the bit of text under my name to read 1 of 23. Basically anyone who disagrees with Magneto he thinks is me in disguise. Never mind said people have argued with one another, corrected one another, registered at different times, go into different parts of the forums, it's all a massive conspiracy. He's not the first crank who has claimed I've got half a dozen (or more!) accounts. Cranks seem struggle to accept that multiple people can disagree with them, that it must be impossible for more than one person to form similar negative views of them thus it's all one person. What Magneto (and other cranks who've made similar accusations) fail to realise is that I don't need multiple accounts to nail their crap to the wall, I do it well enough with just this account. You write lots of very good posts and if you were a sock puppet of mine I'd just use this account so that this account gets the credit, rather than spreading it between two accounts. Magneto needs to realise that his misunderstandings and mistakes are so basic that anyone who didn't sleep through physics class can see them and there's more than one such person on these forums.
Ah, OK. I was just wondering whether Magneto really believed the accusations he was making or if he was just making it all up. Well not all of them, but even there they don't really grasp that we can disagree with them all independently of each other. I can't count the number of times someone here has accused me of "establishment thinking" in some form or other, just because everyone else with any level of education in physics reacts the same way.
Stupid conspiracy to try to convince people that reality matters. Please Register or Log in to view the hidden image!
No, don't think of coordinates as a language. And don't think of spacetime as something that has properties. It's an abstract mathematical "space". Space has properties, such as vacuum permittivity and permeability that can be combined as impedance. Those properties vary from place to place, and as a result our measurements of distance and time vary. Our measurements also vary with our motion, and we employ a coordinate system, something else that's abstract, to represent those measurements. See above. Spacetime isn't something physical that's there at the event horizon. Space is. You really don't have a clue about this do you? Typical mathematician pretending he understands physics when he doesn't. It's doggerel, used to describe a never-never-land that only exists beyond the end of time. Like the rest of your silly condescending post. Do bite your tongue in future. When you try to contribute to the physics you merely embarrass yourself. Best stick to sniping and playing the troll.
Edit: Thanks to rpenner. He pointed out that I should link to the abstract page on arXiv: http://arxiv.org/abs/1106.3542 Read this: http://arxiv.org/PS_cache/arxiv/pdf/1106/1106.3542v1.pdf Is Eternal Inflation Eternal ? L. Mersini-Houghton∗ Department of Physics and Astrononmy, UNC-Chapel Hill, NC, 27599-3255, USA and, CITA, University of Toronto, Canada (Dated: June 20, 2011) In this paper we explore the relationship between the existence of eternal inflation and the initial conditions leading to inflation. We demonstrate that past and future completion of inflation is related, in that past-incomplete inflation can not be future eternal. Bubble universes nucleating close to the initial conditions hypersurface have the largest Lorentz boosts and experience the highest anisotropy. Consequently, their probability to collide upon formation is one. Thus instead of continuing eternally inflation ends soon after it starts. The difficulty in actualizing eternal inflation originates from the breaking of two underlying symmetries: Lorentz invariance and the general covariance of the theory which lead to an inconsistency of Einstein equations. Eternal inflation may not be eternal. PACS numbers: 98.80.Qc, 11.25.Wx Read it all at the link above and let me know if she has any credibility.
You haven't got a metric, a metric an abstract thing associated with your measurements, and at the event horizon you're stopped. You aren't measuring anything. You've totally ignored in units where G = c = 1 and my response saying it's a c=0. That curve is abstract, this is no arbitrary whim, the scientific evidence clocks backs me up, as does Einstein. Because it isn't really an infinite t, it's a zero c. Everything to do with black holes is a little gedanken. We've never actually been to one. We know already that clocks at different elevations here on earth run at different rates. In the black hole case we lower an observer on a rope down to just above the event horizon, wait for a long time, then pull him back up. This isn't quite the same as the infalling observer, but it ought to be close enough for you. It doesn't matter what there is or isn't "in GR". When I've talked about simultaneity it's been based on light-path lengths in a gravity-free situation, and collisions. When you introduce gravity the collissions are more important, in that two observers need to be in the same place to be sure that an event is simultaneous. Hence you pull up the guy on the rope and bring him back to the ship, and he's swearing blind that he's been down there for an hour instead of six months. Repeat with a longer rope and you see the pattern. His time dilation is tending towards infinity, his clock rate is tending to zero. You should try to get away from "in curved spacetimes" thinking and think instead of your observers carrying light clocks in inhomogeneous space. It makes things simpler. It does a hop skip and a jump over the end of time. I showed you that chart, the peak was lopped off and swept under the carpet. The same. There is no metric when you can't make any measurements because both you and your clock are stopped. Sorry, my mistake, infinity. Yes and no. If he's carrying a parallel-mirror light clock wherein each "tick" is the light reflecting off a mirror, his tick rate reduces as his speed increases. However he's subject to an immersive scale change, and measures the local speed of light to be the same old value. Take this to the limit however, and when his speed is c there are no more ticks, and he doesn't measure anything. It's an invention. There's no getting past that infinity. You can't get past the end of time.
Special relativity has three equations; one each for mass, distance and time. Most of the reference ambiguity appears because we ignore the mass variable of SR, thereby allowing us to violate the SR energy balance. It does not matter what mirage you think you see, if you apply the SR energy balance, you can separate mermaids from manatee. I understand that this mind abstraction helps the young mind learn to do mental gymnastics. But eventually we need to show them how to tell mirage from real. The three SR equations all used together mean, if there is time dilation and distance contraction occurring in reality (manatee and not mermaid), we need energy that will appear as relativistic mass. If that energy is not there, it is only a mirage; mermaid effect. Let me give an example. Let us start with three references instead of two. This makes the mirage trick harder to do and easier to see. We start with three rockets. We add sufficient energy to one of the rockets to increase its velocity to V. The other two rockets remain stationary. We know the energy balance, but will not tell the ship captains, but will allow them to play the mirage games by ignorring the relativistic mass and energy balance, using the assumption there no preferred reference since all is relative. The moving captain sees two references in relative motion, even though we know we only used half the energy needed to do that. The total amount of time dilation and distance contraction, in his reference, is more than the energy used. But he is convinced he sees the mermaid since an energy balance is not part of his equation. The two stationary reference each see one moving and one stationary references. These two references see the proper energy balance but can't fully agree who is moving. If we told them the energy balance, the magic goes away. The magical premise, that there is no preferred reference or all references are relative, implies an energy balance is not important. In the above, the energy balance tells us which is the preferred reference with enough energy. But since it is all relative, to our captains, the mermaid effect could become the rule; campaign effect.
you violate ? you sure about it? or are you having another one of your hallucinogenic-induced trances?
