I didn't say there was. I was merely offering suggestions on how best to facilitate discussions. Walls of text are an anathema to such things.
Maybe I should have just posted the questions and left it at that.
Unless you have a formal model of black holes you wish to put forth and which is viable phenomenologically I don't see how you can make any such assertions if they run counter to general relativity.
Because I believe that velocities can't add to together to produce a velocity of the speed of relative to other objects as GR describes them doing when an object reaches an event horizon. Instead I think that velocities add together in the same way that SR describes an object accelerating towards the speed of light relative to another object and no amount of proper time can ever be enough to reach an event horizon because of length contraction and time dilation.
There always appears, to the distant observer, that the in falling person still has the opportunity to turn around but the person falling in will not experience that. He has a finite amount of time before he crosses the event horizon and is unable to escape.
It becomes a direct contradiction the moment the falling object can't turn back. Different observers can disagree at what time something happens but never on whether something does or doesn't happen. If it never happens from one observers point of view then it can never happen from any observers point of view.
As you admit, there is no universal notion of time so when you make statements like "at no time can...." then it has to be qualified by whose point of view that is. Your statement does not apply to the person falling into the black hole.
Use the black holes frame of reference. They don't last forever. I don't think they evaporate, I think they have a contracted horizon horizon because I don't think they're real objects as such, they're just the visual effects of singularities, but that's not important for this. The point is that they get smaller over time. If no object can reach the event horizon from the perspective of a more distant object then at no time in the black holes life can any object reach its event horizon. If the more distant object waits until the black hole is almost gone then still, no object would have reached it. The event horizon contracting by whatever means means that it happens quicker the closer the observer is because of length contract and time dilation. Right on the horizon it would be rushing away at the speed of light so it could never be caught even if an object accelerates towards it.
And your experience is....? There is never 100% consensus in any area of science, that is part of its power, but the overwhelming consensus among those who consider black holes a real phenomenon that their dynamics are described, at least on non-quantum scales, by general relativity or something extremely close to it.
I think that too. I think SR describes it.
So again, you need to qualify where you're getting this information, from whose perspective is that (except this time it is actual people not hypothetical observers). In general relativity the event horizon is fixed (for a given mass, charge and angular momentum), particularly from the point of view of the distant observer, whose point of view you were so adamant about in the previous quote. For someone falling into the black hole it is possible to pick a set of coordinates which falls with them and which would thus have the black hole moving up to meet them, including the event horizon. It may well be in such (or not too different) coordinates it is possible to view the event horizon as moving at light speed, rushing past the in falling person but this is a coordinate dependent construct and only makes sense in the infinitesimally small region around the in falling person, therefore precluding you from making statements about a global property of the black hole such as its event horizon radius.
More than one physicist on physicsforums.com a few years ago when I was first learning this. If free-fall is inertial like GR claims then the event horizon can easily be viewed as expanding at the speed of light locally. I don't think free-fall is inertial though and I don't think the event horizon would be expanding in that scenario. It would be contracting at the speed of light locally so that it could never be reached. The event horizon and the singularity at the centre are the same physical object viewed from different distances.
This is an example of how it is important to grasp details, coordinate dependent statements are often mistaken by people who don't know any of the mathematics as universally applicable. For example, there is no barrier at the event horizon, there is no "You cannot mathematically describe passing this!!" obstruction, the fact a term in the metric goes infinite is an artefact of the choice of coordinates. Pick your coordinate properly and the event horizon doesn't cause things to go to infinity. Too many people read a pop science summary of the Schwarzchild metric, hear about this coordinate singularity and think it is physical. A coordinate singularity can be removed by restructuring the mathematics, a physical singularity (such as the one in the centre of the black hole) cannot be removed in such a way. An alternative example would be computing the Ricci curvature on the event horizon, it is zero.
That's cheating! By changing the mathematical construct like that when it doesn't suit you is contradicting yourself! You should never need to use more than one coordinate system to describe an object fully. If you want to use multiple coordinate systems then you should be able make a smooth transition between them if they don't contradict each other. How would you create a smooth transition between a coordinate system in which an object reaches an event horizon and one which it never can? The Schwarzschild coordinates do describe it perfectly, the whole thing. The event horizon becomes the singularity at zero distance.
Let's call them A and B. A and B start at the same place and at rest relative to the black hole. A starts to fall in at some point in time, say t=0, while B waits some non-zero time before doing likewise (call it t=T). A and B will fall along those sorts of trajectory except B's will start from a position slightly above the start of A's because it is later in time. The figure also shows how their light cones tip over as they fall. Notice that when the trajectory crosses the event horizon is it not horizontal, that happens when it hits the singularity at r=0.
This is important because B is observing A by the light A emits. As the light cones tip over the photon paths are such that they require more time to move outwards by some set amount. This contributes to the fact B sees A move slower and slower. So what happens when B's trajectory crosses the event horizon? Well he'll be able to observe the light A emitted when A crosses the event horizon. Suppose A was wearing a watch. When A crossed the event horizon he looked at his watch and saw it read t=X so it took X amount of time, from A's point of view, to get to the event horizon. B reaches the event horizon and sees the light emitted by A's watch at that moment in time, he sees A's watch reading t=X. He looks at his watch and it will say t=X+T. Is A still at the event horizon? Have they met?
No. This follows from the fact the trajectories at r=2M do not intersect, that what it means for A and B to be at the same location. B sees light emitted by A when he was at the event horizon, light which the event horizon has been 'holding' and which B can only see when he is also at the event horizon (since the photons cannot move in any path with increasing r) but A is not there, his trajectory has taken him further into the black hole.
From the point of view of a distant observer A and B will seem to be getting closer and closer, their watches also getting closer and closer in their time readings. The longer the observer waits the closer the images of A and B get. But this is all via photon communication, the observer is seeing light emitted by A and B as they move along their paths. They will see all the people who have ever fallen into the black hole still slowly falling towards the event horizon, edging ever closer to the horizon and one another, but from the point of view of the people falling into the black hole it is a different matter. This is the difference between $$\frac{dr}{dt}$$ and $$\frac{dr}{d\tau}$$ (see section 2.6 of that pdf). The former goes to zero at the event horizon, ie a distance observer sees the in falling person stop, while the latter doesn't go to zero, the in falling person always seems themselves falling further.
Right, this is huge gaping hole in the theory. When B reaches the event horizon it will have to observe A as still at the horizon. If A has actually crossed the horizon at the time that B reaches it then objects can reach an event horizon from the perspective of more distant objects. If A hasn't reach the event horizon before B reaches it then all objects have to reach it at the exact same time. You simply can't have it both ways. You're claiming the former. The light is only getting slowed because of length contraction and time dilation which would apply equally to the object itself. It can't overtake its own light as you're claiming it to do.
Like it or not, that statement means that you think that in one moment a finite amount of energy is enough to pull an object away, but the very next moment all the energy of a trillion universes isn't. Do you deny this? If the answer is no then the real pity is that you could believe that it's possible that no amount of one force would ever be enough to overpower a finite amount of another. If the answer is yes then what gives?
As I've said and as you can find in any introductory book on general relativity (or just on Google!) the infalling person will cross the event horizon in finite time from their point of view. If it takes X units of time for A to see himself cross the event horizon then if he waits till time X+d for any d>0 he'll be unable to escape. But what about a distant observer, call him C. C watches A fall and get slower and slower. C can wait time X, 2X, 10X $$10^{100}X$$ and A will always seem to be above the event horizon. After some time Y C decides "I'm going to save A!" and so ties a rope to a very powerful rocket and blasts the rocket, call it R, at A, hoping that if the rocket gets to A before A crosses the event horizon then C can save A.
As the rocket approaches the black hole C will see its clock tick slower. Conversely R will see A's watch begin to tick slightly faster and thus move towards the event horizon faster than C sees. This is the whole $$\frac{dr}{dt}$$ vs $$\frac{dr}{d\tau}$$ thing again. As R catches up with A their individual $$d\tau$$ measures begin to get closer and closer. Likewise with the B person mentioned above. In the case of B because he falls in exactly the same manner as A, via gravity only, the same time passes. I haven't crunched the algebra (its 11.55pm and I've spent the day a boring as hell conference) but it is possible, for certain Y, X and acceleration profiles, for the rocket to catch up with A and hand him the rope. However, if R catches up to A and A's watch reads later than X then they are already inside the event horizon.
The watch will never reach time X. It's exactly equivalent to objects using rockets to accelerate. Why wouldn't it be? Three objects, A B and C. All three start off as inertial and at rest relative to each other. Object A starts to accelerate and continuously increases its acceleration at a consistently ever increasing rate. Object B does the exact same thing but a few seconds later. To start with A will be gradually pulling away from B and at a faster rate over time from all three objects perspectives, but not quite at the same rate as their difference in acceleration would suggest from B and Cs perspective because of length contraction and time dilation. As (as) time passes the rate of the increase in distance between A and B lessens from B and Cs perspective until the distance between them actually starts to decrease, but the distance between A and B is always increasing from As perspective. Inertial object C then accelerates at a fast enough rate to start catching up to object B and as it does it sees the distance between A and B increasing again. It overtakes B and and catches up to A and then attaches a rope and decelerates it until its inertial with a finite amount of force. This is exactly how the Schwarzschild coordinate system describes gravitational acceleration and to switching to a set of coordinates where object A reaches the speed of light from it's own perspective but not from B and Cs is exactly what you're doing when you switch to a false coordinate system that shows an object reaching an event horizon from it's own perspective.
The whole "You can cross an event horizon without dying but eventually you'll have your feet pulled from your head" thing is to do with tidal forces. It is possible to quantify the tidal forces an object experiences and in yet another counter intuitive result the larger the black hole the weaker the tidal forces on an extended object at the event horizon. Given a sufficiently strong tidal force any object can be pulled apart. This is manifested in astrophysics by the Roche limit for planets or moons. Too close to the thing they orbit and tidal forces break them up. Once inside a black hole you can only fall further and the tidal forces get stronger and eventually kill you in a way known as 'spaghettification' (for obvious reasons).
Tidal force being weaker around the event horizons of more massive black holes is not counterintuitive at all. Event horizons accelerate objects to a relative velocity of the speed of light (or they would if they were reachable) and the more massive the black hole, the more noticeable it's gravitational effects are at a distance, so it will produce a gentler acceleration curve towards the speed of light.
None of that makes any reference to how an extended object is actually held together, it is just considering two points some small distance apart and asking what forces they experience and how their distance varies (ie it increases till any object would be pulled apart, regardless of tensile strength). In reality materials are formed from atoms, held together via the exchange of virtual photons between electrons and nuclei. If two electrons cannot communicate then they cannot form a bond. Therefore if had two electrons just above the event horizon and you let one go then it would fall into the event horizon and all the remaining one would see is the fading image of the electron slowly inching its way towards the event horizon. Yes, this means the residual effects can still interact, the held electron still experiences some electromagnetic interactions but not the same as normal. The in falling electron only released so much energy and momentum via the photon mediated exchange, whose effects on the held electron will then be spread out over an eternity.
You said that the rope would snap. That means that it have to keep snapping as the parts that reach the event horizon are accelerated to the speed of light relative to the parts that haven't reached it yet. The tidal force of any mass black hole has to reach infinity at the event horizon. It's no different to G-force.
As I just explained in regards to A,B and R, if the held electron is then released and falls into the black hole it will 'catch up' with additional photon interactions which the black hole has been keeping locked up and so there will be further interactions. If the two electrons were separated slightly but otherwise allows to fall together then there would be more interactions, the further in electron receiving photon interactions from the one further out and the one further out 'catching up' to the photons left by the one further in. Since the tidal forces will eventually over power the electromagnetic bonds and pull them apart the end result is unchanged. But this is only if you're constantly falling, one electron always chasing the 'wake' of the other. Inside the black hole it is impossible not to fall, regardless of engine capabilities. However, for the example of one side of the rope held by a distance rocket there isn't this 'catch up' interaction, the rope on the outside can only see a capped finite amount of interaction from the rope which was 'lowered in'.
Then it has to always be possible for the more distant object to pull the closer one away. How could the one further out catch up to one further in one the closer one will always be accelerating at a greater rate than the further one?
So what I said didn't contradict the result it is possible for hypothetical objects to survive inside an event horizon. I'm well aware of that, as numerous threads on this forum will attest to. Rather the subtitles were lost on you.
The mathematical trickery and misdirection (what you call subtleties) were not lost on me. I noticed instantly. I've seen them before.
How about basic concepts in general relativity. Space-time is a 4 dimensional 'arena' within which events lie. An object which exists for some period of time will sweep out a 'world line', essentially its path as a function of time. If something is a single point in space-time it means that to all observers in all coordinates it exists for a single instant at a single point location. A Schwarzchild black hole's singularity is zero dimensional in space, it occupies only a single point in space. This can be seen from its very construction as a solution to the Einstein field equations, its mass distribution is just $$\rho(\mathbf{x},t) = M \delta(\mathbf{x})$$, ie a point mass at some location (which these coordinates call the origin). This mass distribution is time independent, it exists for all t and doesn't change. Therefore it sweeps out a worldline in the (to be overly technical because I can be) pseudo-Riemannian manifold (M,g) where g is the Schwarzchild metric and M is 4 dimensional. It is not localised in time because it would then require $$\rho(\mathbf{x},t) = M\delta(\mathbf{x})\delta(t)$$, which means everyone would only see it exist for an instant. This is obviously not consistent with the Einstein field equations because there would be no energy conservation.
You can't use the assertions of GR as evidence of its own validity, you have to justify them.
For someone working in particular coordinates or moving in a particular way it may well be the coordinate coefficients of $$dt$$ go singular but that doesn't mean the manifold is altered. Coordinates are abstract constructs, they have no physical meaning any more than English and French do. They are descriptive methods. Changing coordinates does not alter the manifold, only describe it in a new way. The Schwarzchild solution has a mass distribution whereby any space-like surface (which is as close to the notion of 'now' as GR gets) intersects the singularity's worldline once and only once. If the black hole was instantaneous in time then it would mean someone watching the relevant part of space would see the black hole appear and then disappear in an instant. Obviously that isn't the case.
Yes I know what coordinate systems are, and you can't change reality by switching systems as you say, but that's exactly what you're trying to do when you switch between Scharszchild coordinate and a coordinate system that allows objects to reach an event horizon. You may claim that the Scharzschild coordinates don't cover the entire manifold, so it's not actually changing. I'm claiming that they do. I wish I could prove mathematically that they have to.
As for 'within a unified space-time structure' this is another example of you not understanding something so you dismiss it. A valid GR construct is one which solves the Einstein Field Equations. These lead to the 4 types of black holes in 3+1 dimensions but if you consider a space-time with say 4+1 dimensions or even 9+1 dimensions then the additional freedom allows for many other kinds of spaces which possess a singularity. A singularity is somewhere where a Lorentz scalar dependent upon the metric goes singular. For example, the Ricci scalar or some combination of the Riemann tensor such as $$R_{abcd}R^{abcd}$$. In the case of the Schwarzchild black hole we have $$R_{abcd}R^{abcd} = \frac{48\pi^{2}}{r^{6}}$$ (if memory serves), which is finite at r=2M but infinite at r=0. Similarly $$R=0$$ everywhere but r=0, where it is infinite. For more elaborate constructs, such as wrapped black branes in string theory or disk black holes in 4+1 dimensional space-time, you can have them form all kinds of funny shapes but the common defining property is their curvature scalars go infinite on them but nowhere else.
Yes, they're singular on them but nowhere else. That's why black holes occupy a non-zero amount of space-time at the event horizon as the Shwarzschild coordinates show.
And how about 4d hyperspheres. Clearly you don't know what a hypersphere is. An n-sphere of radius R (n=1 is a circle, n=2 is a spherical 'skin', like the surface of the Earth, n>2 are often labelled 'hyper') is defined as the loci $$\mathbf{x}\cdot\mathbf{x} = R^{2}$$ for $$\mathbf{x} \in \mathbb{R}^{n+1}$$. The metric corresponding to this shape can be computed easily via a metric pull back on a parametrisation of this space. Since I'm certain you haven't got a clue what that means I'll do an example. A 1-sphere is a circle, $$x^{2}+y^{2} = R^{2}$$. We can parametrise it using an angle $$\theta$$, $$x = R\sin\theta \equiv \xi_{1}$$ and $$y = R\cos \theta \equiv \xi_{2}$$. The metric on the circle $$h_{ab}$$ is defined by $$h_{ab} = \partial_{a}\xi_{i}\partial_{b}\xi_{j}\delta_{ij} = \partial_{a}\xi_{i}\partial_{b}\xi_{i}$$. In this case we only have $$h_{\theta\theta}$$ and so $$h_{\theta\theta} = \partial_{\theta}x\partial_{\theta}x + \partial_{\theta}y\partial_{\theta}y = R^{2}\left( \cos^{2}\theta + \sin^{2}\theta) = R^{2}$$ and so we have a line element on the circle being $$ds^{2} = h_{\theta\theta}d\theta^{2} = R^{2}d\theta^{2}$$ which becomes $$ds = Rd\theta$$, which is precisely the equation for the arc length of a circle!
They become singular in space and time at the event horizon, making them perfectly spherical in four dimensions from any distance. That's a hypersphere! Why do you think that time works differently to space?
Now this generalises to higher dimensions but the n=2 case is particularly of note because you get $$d\Omega_{2} = d\theta^{2} + \sin^{2}\theta d\phi^{2}$$ (for $$\theta,\phi$$ latitude and longitude). This is exactly the term which appears in the Schwarzchild metric, $$ds^{2} = f(r)dt^{2} + f(r)^{-1}dr^{2} + r^{2}d\Omega_{2}$$. The Schwarzchild metric has spherical symmetry and thus it has the spherical metric contribution from those 2 directions. However, the space-time is not a 4-sphere, it is actually equivalent to $$\mathbbR^{4}$$ in topological structure, just has a different metric. The singularity itself is a point in space, which is a form of ball, not a sphere (these are different concepts in topology, which you would know if you'd any maths knowledge).
Like I said previously, the notion of an object localised in time as well as space is well studied in the literature, they are instantons. They are, by definition, localised in time but they can be spatially extended, yet another generalisation beyond the most basic of black hole concepts (the Schwarzchild one).
That makes no sense! If they can be extended in space then they can by extended in time. If you move to a frame where length gets contracted then time gets dilated by exactly the same amount. Obviously the same is true in reverse.
Time and again you show you are unfamiliar with what relativity actually says or what science has to say or even relevant mathematics. You asked if I have any experimental evidence it isn't localised in time. Well we do observe black holes and since they exist for more than a single instant yes, we do have such experimental evidence. And even if we didn't it is a shifting of the burden of proof. GR is the model by which we describe black holes. If you wish to put forth a notion counter to it in regards to black holes you have to provide your own model which leads to such a conclusion, else you're just making random assertions. The structure of a 4-sphere is well examined in the literature, we know what it would look like if GR implied such a thing. Hell, the 5-sphere version is used in the gravity/gauge holographic duality where stacks of 3 dimensional black (hole) branes are used to construct a space-time which has a 5-sphere structure in it (the rest being AdS-5), they are of considerable interest to people who do this sort of stuff for a living. As such your assertion about what the Schwarzchild metric is saying is false. If you're working within the bounds of GR then you're wrong. If you're working outside the bounds of GR then you need to show you have your own working model of black holes capable of formally describing hypersphere structures in gravitational systems, else you're just telling us your unjustified random opinion. Since you obviously lack the knowledge and capability to construct such a thing yourself I conclude we're just getting you uninformed opinion on things you don't have any understanding of.
I'm not unfamiliar with what your version of relativity says. I just don't agree. Everyone here is well aware of complete lack of credentials so I can only assume that your repeated efforts to point out this fact are a sign of desperation. No one's going to forget, you don't need to keep saying it. Of course black holes exist for an extended length of time from distance, in the same way the exist over an extended length of space from a distance. I am putting forward my own model.
You didn't ask questions, you made assertions. And does it look like I'm running away from you? You have made it obvious you have no working familiarity with any of these areas of physics, you have little or no mathematical knowledge (which is the language GR is written in) and you are not above making baseless uninformed assertions about things you have no experience of. As the length of this post attests to, you have plenty of problems to discuss without having to go through all 9 of your nonsense.
Eight. The nonsense claims aren't coming from my direction. My version of it is the one that actually makes sense. Yours is all over the place needing multiple and contradictory coordinate systems to cover the entire manifold. Mine's simple. Objects can't reach the speed of light relative to other objects but space-time can? In the hopefully not too distant future people are going to look back at that view and laugh, and wonder how qualified people could ever have believed that made any sense. Shall I just add 'how is this possible?' to the end of each paragraph? I know you're trying to avoid the Rindler horizon. That's okay. I can do this with one hand tied behind my back. It makes it more a challenge.
I've shown, at great length, I have a working understanding of this. You call it 'nonsensical physics' yet you obviously cannot do it, have no experience of it and have no problem pretending the contrary. I'm sorry you don't grasp it but that isn't a reason to dismiss it.
I don't pretend to the contrary at all. In what sense? It's not that I don't grasp it. I don't grasp the equations. I get the model and it's really silly.
And me pointing out you're obviously unfamiliar with the subject matter is relevant to the discussion. If I called your mother's parentage into question then it would be an irrelevant personal attack. Instead I'm showing, at great length, how you're mistaken about a great many things. It is a demonstrated fact you are not very well informed on this subject. You obviously don't like being told that, you obviously liked all the praise heaped on you on other forums where you've posted this nonsense. Now that I think about it were you expected similar responses here? Were you expecting us to praise you and complement your supposed brilliant knowledge and explaining abilities? Perhaps you were expecting the opposite response to the one you got?
No not at all. Criticisms give me a chance to strengthen my case. Praise doesn't. I wanted responses like this one, which is nothing like your other one. This it great because it gives me the chance to explain why I see it the way I do.
Sorry, some of us actually give a shit about science and as a result bothered to learn some of it before going on forums to discuss it. Of course there is nothing wrong with not knowing it, provided one is self aware and makes an effort to remedy that. You don't seem to want to acknowledge that applied to you.
Rearrange these words to form a sentence: pot, the, calling, kettle, black, the. I care about the truth every bit as much as you do. That's why I'm doing this. I don't think GR is true, at least not the way it's described. It should be equivalent to SR.
Just so we can all gauge your level of knowledge perhaps you'd like to tell us how much science you've actually done. High school only? Degree? PhD? Researcher? Likewise for mathematics, how far down the educational path have you gotten? How much hands on experience doing the quantitative stuff in relativity do you have? Even if you didn't go to university to do physics or maths do you think you could pass university exams on them? If you're just a layperson where have you gotten what little knowledge you have? Pop science books? Magazines? Internet? Fox "Sun goes up, Sun goes down, never a miscommunication!" news? The inside of a cereal box? If you are able to converse on the level of say a graduate then it would greatly streamline any discussion as then you could stop with the entirely wordy arm waving and instead show us the mathematical derivation of various claims of yours, seeing as several people here can converse about GR on that level (or beyond). I await your responses.
High school science and maths. I turned up 24 hours late for science my exam though. I got a D in maths despite coming joint fourth in the year in the mocks. I was high.
An object falling into a black hole will do so in a finite proper time. Once it passes the event horizon in its own frame, it can never escape.
As seen by an external observer, the object never reaches the horizon, but that doesn't mean it could possibly come away from the hole at any time.
If you have anything that disputes this, please feel free to post it.
There always appears, to the distant observer, that the in falling person still has the opportunity to turn around but the person falling in will not experience that. He has a finite amount of time before he crosses the event horizon and is unable to escape.
It sounds like you've read a few pop-science descriptions, and haven't actually looked at an introductory textbook on general relativity. Is that correct?
That's if you use a coordinate system where the falling object is at rest.
No. As seen by an external observer, objects appear to move slower and slower as they approach the horizon. Objects that start ahead remain ahead, but the space between them decreases over time - slowly. They never reach the horizon, so there's no "meeting".
Exactly, that's my whole point. If they were able to reach the horizon then they would HAVE to meet!
You haven't given us any reason to suppose that it is possible to pull an object across the event horizon from inside the black hole to the outside. If you have any actual argument why this is possible, other than your own say-so, please post it.
:bugeye: That's not what I'm saying at all. I'm saying that it's always possible for a more distant object to pull a closer object away because the closer object can never reach the event horizon from the more distant objects perspective. It's never too late, ever!
There's no problem with objects crossing the event horizon from the outside to the inside. Tidal forces at the horizon of a large hole may be quite reasonable. But no force can hold an object together stationary and straddling the horizon.
So a finite amount of one force can over power any amount of another? That's stupid and ridiculous!
In your model of gravity in flat spacetime, how do you account for the equivalence principle?
Are you referring to the fact that free-fall is supposed to be equivalent to being inertial? It isn't. Free-fall is acceleration. Tidal force is equivalent to G-force. If you're referring to the fact that a gravitationally accelerated frame is equivalent to a non-gravitationally accelerated frame then I completely agree, and take it one step further by making them equivalent to more than just the first order. They're completely equivalent! I'm my model of gravity the equivalence principle is used properly.
Also, if you have it, please post your derivation in flat spacetime of the anomalous precession of Mercury's orbit. Or, if such a derivation is available elsewhere on the web, please provide a link. Alternatively, you might like to post a derivation of the deflection angle of light by massive objects. Why does that happen at all in flat spacetime, by the way?
It didn't mean it's easy to prove. I would suggest that it might be easier to turn the equations from conventional acceleration into a outward curving space-time structure first, then see exactly what's required to turn them back and do the same thing with in inward curvature of space-time. That's the best you're going to get at the moment I'm afraid, and I don't have the first clue how to actually do that. Light follows curved paths in the presence of acceleration in flat space-time. It follows straight paths from it's own perspective in the presence of curvature in curved space-time.
What are ig and og? And your equation doesn't look dimensionally correct to me.
Mass and energy. It's not my equation.
What does a cone look like in four dimensions? Are you thinking of something like a spacetime diagram and not actual geometry?
No I'm thinking of a four dimensional object that has three dimensions of equal length and one longer. It looks like a cone.
I'm not quite sure in what sense you claim that space and time are "equivalent". Could you please explain in a bit more detail? And why, if they are equivalent, does the time component of the spacetime interval have the opposite sign to the spatial components?
Because length contraction and time dilation are equivalent. It's because you're using a base frame where inertial objects are at rest in space travelling through time at the speed of light.
How long does it take a black hole to collapse? What happens to its mass as it collapses? Take the black hole at the centre of our galaxy as an example, if you like.
It takes no time at all from its own perspective. It takes longer the further away it's viewed from. This is purely down to length contraction and time dilation. It makes less difference if you move away by the same distance the further away you are.
In Hawking radiation, no particles are created inside the horizon. The idea is that one of a pair falls into the hole, while the other escapes. Since energy must be conserved and one real particle has been created, the question becomes: where did that energy come from? If not from the hole, then where?
Oh I see.
I look forward to seeing your demonstration of this claim of exact equivalence. Einstein couldn't make it work, but who knows? Maybe you can.
Is that supposed to discourage me? I don't care what other people have failed to do.
The thing is: nature really doesn't care what you think is or is not ridiculous. It will do what it does, whether or not you approve.
Well then it has some nerve.
Do you believe the inflationary model of the big bang? If not, how do you solve problems like the horizon problem? And if you do, how does it work without superluminal expansion of spacetime?
No I don't believe in the big bang at all. I think the universe has a curved surface and as we look across it it makes objects appear redshifted. The further away we look, the more of a curved surface we're looking across and the more redshifted they become. I think the universe is spherical in all four dimensions. Every object is at the centre from its own perspective with a horizon the same distance away from it in all directions. Travel in a straight line in any direction and you end up where you started. This applies to time as well and there's no paradox because there's no way to get information through a singularity, although it wouldn't be a singularity if you were there. From the perspective of anyone there the time we're in now would like like a singularity.
You've made this claim many times throughout your posts. Time to show us the money.
Please show us how we can derive at least one major result such as precession of the orbit or the bending of light, from your flat space-time model. Note that I want a quantitative derivation here, not just a "word slap".
You know I can't so what's the point of asking. I freely admit I haven't got a clue when it comes to equations. So what? They're just a form of expression. I use words. If I can express myself clearly enough to communicate my thoughts then what's the problem? I know it makes things a bit more difficult in some ways, but in others it's good. It forces me to really think about what's happening in real rather than abstract terms. I construct logical models in my head. That's what's allowed me to see the problems with how black holes are described.
Sorry Alpha but I think you also replied with a wall-of-text.
Don't discourage him. That's exactly what I'm after. It's why I'm here.
Of course. Special relativity is the special case of flat spacetime, or absence of gravity.
Yes I know that. It shouldn't be though.
This looks like a mangled retelling of something you might have read somewhere but didn't understand. First of all, in an invariant sense, gravity doesn't accelerate anything in GR. In GR, test particles in a gravitational field follow (time-like). These are the closest analogue in curved spaces to straight lines in flat spaces, and saying that test particles follow geodesics is simply GR's analogue of Newton's first law.
Yes I know that too but an object accelerated by gravity is the equivalent to an object accelerated by energy, not an inertial object. G-force and tidal force are equivalent.
Second, objects can't travel faster than light in GR any more than in SR. Where did you hear otherwise?
Objects are accelerated to a relative velocity of the speed of light when they reach an event horizon.
And just where did you get that impression?
Common sense.
Seriously,
where are you getting this stuff from? Like I explained above, and in my previous post, test masses in a gravitational field follow trajectories governed by the:
$$
\frac{\mathrm{D}^{2} x^{\rho}}{\mathrm{d} \lambda^{2}} \,=\, \ddot{x}^{\rho} \,+\, \Gamma^{\rho}_{\mu\nu} \dot{x}^{\mu} \dot{x}^{\nu} \,=\, 0 \,,
$$
which like I said is just GR's version of Newton's first law (which says that acceleration $$\bar{a}$$ is zero when the net force $$\bar{F}$$ is zero) expressed in terms of an arbitrary coordinate system. The closest thing in that equation to a force are the Christoffel symbols $$\Gamma^{\rho}_{\mu\nu}$$ which you can think of as the pseudo-forces that appear in non-inertial coordinate systems (e.g. the pseudo-gravitational "force" you feel in an accelerating coordinate system, or the centrifugal and coriolis pseudo-forces that appear in rotating coordinate systems). But trajectories following the geodesic equation have no real acceleration associated with them: the four-acceleration associated with such a trajectory is zero. Gravity doesn't cause acceleration in GR. That is one of the most basic tenets of the theory, and something has gone seriously wrong if you don't understand that.
I do understand that, and I understand why it's wrong.
In the context of GR, gravitational attraction simply refers to the tendency of geodesics to converge in the sort of gravitational field (i.e. curved spacetimes) typically created by matter. If you work out the possible convergence or divergence of two nearby test masses in GR, you arrive at a result called the Jacobi equation, which relates that convergence or divergence explicitly to the curvature of spacetime.
Yes, in GR objects aren't accelerated as such. It's an acceleration of space-time I suppose. It's very stupid.
If you're going to bring up math, this (the geodesic and Jacobi equations) is the math relevant to the study of how objects behave in a gravitational field. I have no idea where you're getting this "acceleration due to energy" ($$E = mc^{2}$$ is simply the rest energy of a mass, and has no particular connection with acceleration) or "acceleration due to gravity" (gravity in GR doesn't cause acceleration, as measured by the four-acceleration) stuff from.
Energy can accelerate an object and so can mass. They are equivalent.
Yes. That's the point. If you have a friend that starts falling toward a black hole, then they do cross the event horizon at some point and there will be a definite, finite, time after which it would be hopeless for you to try to "rescue" your friend. You just never see your friend cross the event horizon, for the simple reason that information about your friend crossing the horizon stays trapped on the horizon and can never reach you.
No that's not right even according to GR. It's always possible to pull an object away and they never reach the event horizon from any external objects perspective.
No, as long as you're outside the event horizon of a black hole, all the matter that ever fell into it is still in your past light cone and can causally influence you. The event horizon itself is a region in your causal present and future and can exert no influence on you.
So you're saying that the majority of the mass of a black come from matter around it and not from the singularity. I don't think that's the standard view.
The hint's in the name: "eternal". The white hole never formed. It simply existed from the beginning of time. (I'm not claiming such objects actually exist, just that GR theoretically allows them and there's an answer for them too.)
That clue didn't escape me. I was making a sarcastic point, that obviously escaped you.
You claimed the singularity was a "singular point in time as well as space". It's not. It actually appears more as a spacelike hypersurface - i.e. you can roughly think of it as a point in time, but extended in space. (I say "appears" because that's the way it looks on Kruskal-type charts. In reality I'm not sure the question of the "shape" of a singularity is well defined because the tool we'd use to analyse that -- the metric -- blows up there.)
I don't see why or how its length in time would be any different from its length in the other three dimensions.
The event horizon (not the singularity) of a black hole is a light cone (or "expanding light sphere") in spacetime.
Yep, but they're spheres in four dimensions as well. Time behaves no differently to space. Look at length contraction and time dilation. It's what makes them hyperspheres.
Well you tell me. You're the one having a hangup with this.
White holes can't even form according to GR, they can just exist. They're an extremely poor and desperate attempt to explain why black holes contradict the fact that gravity is still an attractive force if the arrow of time is reversed.
Yes they do (at least in classical GR), and no they don't.
They don't last forever because the event horizon is contracting at the speed of light because it's just an affect of the singularity and not a real physical object.
As I explained above, gravity is not a force, so your whole line of reasoning is nonsensical in the context of GR.
I know. I don't agree with how GR describes gravity. Not a force? Seriously?
You replied: why it is wrong?
Well, lets look at the equation you quoted: $$ E=mc^2$$
This equation shows the mass to energy equivalence. This means that if you were to convert a certain amount of matter to energy this is the amount of energy you would get from it. So if there is a 1 kg mass it will cause a slight curvature of space (gravity). If we convert all of that 1 kg of mass to energy (somehow) that will give us $$8.99 x 10^{16}J$$. That energy will cause the same curvature of space (gravity) that the 1 kg of mass caused. It will cause the same curvature of space, not an "outwards curvature of space-time".
Energy pushes objects apart. Mass pulls them together. If mass is converted into energy it will accelerate objects away from the source *c^2 more than the mass accelerates them towards the source.
Your reply was: What is sad is that you instantly reject something because you haven't seen it used that way before. Just because I'm using it in a way that you're unfamiliar with doesn't make it wrong.
$$ E=mc^2$$ is the mass to energy equivalence. It has nothing to do with gravity. The only relationship to gravity is that the equation shows how much energy is in a given amount of matter. You are demonstrating a misunderstanding of some basic stuff.
No, you're just taking what I'm saying out of context. You're just parroting back the standard view at me as if I don't know it.
@A-Wal
Mass creates an inwards curvature of space-time that pulls objects together. Energy creates an outwards curvature of space-time that pushes objects apart.
I like the sound of that.
If it isn't true, it should be.
I know, and that should be enough, but no. I have to show them that it's true.
It isn't
You'll have to convince God to change physics, good luck, he is stubborn as hell.
Fine arguments there. It just isn't, okay!
Firstly, hello A-wal and welcome to the forums.
Thankyou.
I hope you will receive the following in the way it is intended. There are many, many people who spend a lot of their time on Internet forums proclaiming to have a deep understanding of some theory of physics without needing to bother with any of the details of said theory (i.e. the mathematics). You'll find many such characters on this very forum. I would urge you not to join their ranks.
There is an exceptionally easy way to separate yourself from these people and that is to simpy learn and understand some of the details. Then, when people ask what you mean by "just turn the equations around" you'll be able to articulate your thoughts in precise manner and give a meaningful response. I'm not suggesting that the details are easy to understand, but I imagine you think you're up to the intellectual challenge. Show us this is the case!
The alternative is that you join the group of nutters I mentioned earlier. If this is the case, then you can follow in their footsteps: You can continue to insist that you know what you're talking about, forever, but never actually learn anything; You can continue to patch up other peoples' vague analogies and hope that your interpretation acurately reflects the theory you're trying to talk about; You can tell us all that black holes can't exist in GR because you don't understand what coordinates are; You can pay to publish a book full of your ramblings and insist that it will change the world of physics (and then it doesn't).
If you want people to take you seriously, try to separate yourself from this group of people.
Cheers for the advice. I do understand coordinate systems, and when they contradict each other. I'm not sure how I'll do with the maths. I think I'll really struggle to start with because that's just not how I like to think, but hopefully I'll get to point where it will just click. That's what happened when I learned how to script.
Therefore, I also offer A-wal some advice: accept the truth because you understand it, not because you read it.
Thanks, but that's the whole reason why I don't just accept what I'm being told.
