Because Stephan Hawking said so, that's why. Deal with it.
Can Anyone Answer These Black Hole Problems?
- Thread starter A-wal
- Start date
Why is it.
Whenever I ask a simple physics question, no-one can answer it?
Whenever I ask a simple physics question, no-one can answer it?
Not yet. Oh, yes I do it's called special relativity. Gravity is the same but in reverse so the equations just need to be, er, turned round.
Oh dear.
Alphanumeric is going to tear you to pieces.
Comments like this:
make it impossible to take you seriously.
The only ones you are convincing is yourself and the willfully ignorant.
and this:
make it impossible to take you seriously.
The only ones you are convincing is yourself and the willfully ignorant.
No offence but I hope you weren't being entirely serious. Never believe anything just because someone you don't know says it, especially a physicist. Make them explain it. It's their job to make you understand. If they can't then it's their deficiency, not yours. Never let them make you think that it's your fault. If they understand it then they'll be able to explain it in a way that you understand. Obviously some people just aren't capable of understanding some things but the vast majority are capable of understanding everything the physicists do. Most of them just don't want people to know that.
One reason is because physicists really hate direct questions.
Because everything is causally connected, or more accurately there's a causal connection that links everything, it's not that everything is causally connected to everything else. That's what light cones are, they show the connections. For information to be destroyed it would have to leave the universe, which is obviously impossible. That's why physicists have to fudge black hole dynamics and can't even come to a consensus on how the behave.
Yea because that worked really well last time he tried it. I'd love to see him try again, but I'd like it even more if I could have a sensible conversation with him and the other physicists here.
The top comment was an open admission that I don't understand the equation side of the maths, I've never really tried, but I have no trouble understanding how the mathematical relationships work in relativity. The other one is perfectly accurate. An object can use energy or mass to accelerate. Mass creates an inwards curvature of space-time that pulls objects together. Energy creates an outwards curvature of space-time that pushes objects apart. Gravity is so weak because of the E=mc^2 ratio. The strength of acceleration due to gravity times the speed of light squared is equal to the strength of acceleration due to energy.
Yes I do understand the maths. There's a big difference between maths and equations. I haven't tried to do it using equations because I don't see the point. If it's total crank nonsense then tell me what's wrong about this: "An object can use energy or mass to accelerate. Mass creates an inwards curvature of space-time that pulls objects together. Energy creates an outwards curvature of space-time that pushes objects apart. Gravity is so weak because of the E=mc^2 ratio. The strength of acceleration due to gravity times the speed of light squared is equal to the strength of acceleration due to energy." Try to refute it by offering a counter argument. If all you can do is say that it's wrong then you're just a troll.
This is simply wrong.
It is sad that you only present one equation in your whole conversation and completely misunderstand what it means!
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None taken, I don't really believe a lot of the stuff in the black hole wars myself. Last time I talked about it on these forums it became a heated discussion that I don't know anything about it, even when I got some of the things directly from what has been going on in the black hole wars. I wonder if they even knew enough about it to even be able to correctly pick out what I did or did not really know about it. The discussion went nowhere fast. So that was the best answer I have, even though it is not a good one. A lot of the time, I think the problem is that they have taken conservation laws too far. I think they should be more like guidelines, not the cause of interactions themselves. Then again I think if an observer could measure his own time dialation in an accelerating frame the actual physics inside of a black hole could be much different than what is currently prescribed.
That's a completely hollow statement. Why is it wrong?
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. Actually I've used two equations.
Yea I know exactly what you mean. People love to try to belittle others just for asking questions on these kinds of forums. You should take that as a sign that you're making them very uncomfortable by asking the right kinds of questions. You can either ignore it and try to rise above it or you can do what I do and have some fun with it by making these kinds of people look stupid. Just make sure you don't get wound up by it. That's exactly what they want.
There is a way to work out the time dilation and length contraction experienced when accelerated by gravity. Tidal force. I mentioned last night, you must have missed it. Tidal force is the proper acceleration (acceleration that's felt rather than coordinate acceleration in case you didn't know) when an object is accelerated by mass because the two are equivalent. Mass curves space-time inwards, pulling objects together, energy curves space-time outwards, pushing objects apart, or you can view as accelerating objects in flat space-time.
Right back at you. Mass attracts, so to massives objects would be drawn towards each other. If they are coverted into energy then other massive objects would be moved away from the annihilation when the energy waves reaches them. Gravtitational waves pull mass in, energy waves push mass out.
Another way is doppler shifts. That is how the twin paradox is solved. Tidal Forces are not really involved there where I was placing my concern. An object that is accelerating can then detect a difference in his own doppler shifts independent of tidal forces or not having any tidal forces present.
The best descriptioon of spacetime curvature as a cause of gravity, I think was by Michio Kaku. He wrote that the force of gravity is felt because we are only trying to travel in a straight line in a higher dimension. I think he has also claimed that electromagnetism can counter the force of gravity or spacetime curvature to create an open singularity (but I have met much opposition, and haven't found anyone that agrees with this statement). But I don't think it is as simple as inwards or outwards, a magnet could attract another magnet just like one gravitational body could attract another, the poles only need to be facing in the right direction. Higher dimension are described as being unimaginable and sceintifically impossible to even visualize. Even though he has done a lot of work on writing about higher dimensions, it is still kind of inconceivable to be able to even understand what traveling in a straight line in a higher dimension even is or how that can relate to a pull of gravity. But, it can be made easier to understand with some methods he proposes about translating it into lower dimensions that is how I believe he came up with the statement.
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.
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.
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.
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.
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.
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.
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.
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). Both of them fall in a trajectory shown in Figure 5. 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.
Pity.
I'm sorry you haven't bothered to learn (or are incapable of learning) an area of science which you feel the need to mouth off about and that isn't my problem. But since you'll no doubt complain that I'm not willing to spoon feed you information which you are too lazy to find out yourself I'll explain.
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.
No, I haven't. But nice of you to again show how you don't grasp the subtleties of this.Ah now you see, if the rope has to snap then all objects get atomised as they reach the event horizon as same thing applies to any extended object because the front of it will have to rip away from the rest of it because if the rope has to snap then that's an infinite amount of energy (which is completely ridiculous btw) and the free-falling object doesn't need to be accelerating in the opposite direction for it to have to snap, and then the new front of the object will rip away from the rest of it, and so on. The rope isn't at all necessary, it's just to make it easier to visualise. You've just inadvertently asserted that the standard view that objects can cross the event horizon of a super massive black hole without being ripped to shreds is in fact completely false. I told you this was going to be fun, for me anyway. Are you having fun? I'm having fun.
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).
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.
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'.
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.
Where to start....
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.
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.
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.
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!
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).
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.
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.
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.
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?
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.
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.
I should clarify that a bit. Acceleration is just as relative as velocity so strictly speaking you can't feel acceleration. But what you can do is use an extended body with the acceleration concentrated in on end of the object, a rocket for example. You then then measure the stress on hull caused by the difference in force over the different parts of the object to work out the strength of the gravitational field you're in and get the time dilation and length contraction from that. It's the same thing that makes us feel acceleration due to energy, like our weight for example, which is concentrated on our points of contact with the ground and spreads out when we sit or lay down.
Oh, proper reply.
Cheers. It's 1:10 though, I'll reply tomorrow.
A-wal,
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.
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?
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".
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.
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.
In your model of gravity in flat spacetime, how do you account for the equivalence principle?
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?
What are ig and og? And your equation doesn't look dimensionally correct to me.
What does a cone look like in four dimensions? Are you thinking of something like a spacetime diagram and not actual geometry?
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?
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.
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?
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.
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.
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?
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".
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.
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?
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".
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.
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.
In your model of gravity in flat spacetime, how do you account for the equivalence principle?
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?
What are ig and og? And your equation doesn't look dimensionally correct to me.
What does a cone look like in four dimensions? Are you thinking of something like a spacetime diagram and not actual geometry?
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?
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.
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?
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.
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.
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?
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".
Yeah, its such a time-waster, I don't know why people want to chit-chat so much.
Sorry Alpha but I think you also replied with a wall-of-text.
Actually energy and information are the same thing in the context of black holes. Therefore, why shouldn't they be the same thing in other contexts?Capt said:
I guarantee there is no known way to store information without using energy; there is no way to dissipate (that is, erase) information without energy.
The information loss paradox (so-called) relates this equivalence--energy can't be created or destroyed, ergo neither can information.
So if you drop a computer into a black hole you will eventually recover, via the Hawking process, all the information corresponding to the "lost" computer. It's irrelevant to physics that it might take rather a long time, the thing is, it's predicted to happen since information is conserved.
I was responding point by point to a post of A-wal's. If you open a thread with a wall of text then it is bad, as you aren't replying to individual points people have made, you're just excessively monologuing.Sorry Alpha but I think you also replied with a wall-of-text.
@arfabrane
Thanks.
Possible problem.
Take the information in a book.
If you burn the book all the energy is converted to heat and light, and not lost, but the information is completely lost.
I think that with the Black Hole, the conserved energy refers to Physical Energy only.
Position, wavelength etc encoded in energy.
But why can't this energy be converted to an equivalent energy, losing the information,
just like the encoded words in a book that is burned.?
Thanks.
Possible problem.
Take the information in a book.
If you burn the book all the energy is converted to heat and light, and not lost, but the information is completely lost.
I think that with the Black Hole, the conserved energy refers to Physical Energy only.
Position, wavelength etc encoded in energy.
But why can't this energy be converted to an equivalent energy, losing the information,
just like the encoded words in a book that is burned.?
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Of course. Special relativity is the special case of flat spacetime, or absence of gravity.
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) geodesics. 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.
Second, objects can't travel faster than light in GR any more than in SR. Where did you hear otherwise?
And just where did you get that impression?
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 geodesic equation:
$$
\frac{\mathrm{D}^{2} x^{\rho}}{\mathrm{d} \lambda^{2}} \,=\, \ddot{x}^{\rho} \,+\, \Gamma^{\rho}_{\mu\nu} \dot{x}^{\mu} \dot{x}^{\nu} \,=\, 0 \,,
$$
\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}$$ which you can think of as the pseudo-forces that appear in non-inertial coordinate systems (e.g. the pseudo-gravitational "force" you feel in an accelerating coordinate system, or the centrifugal and coriolis pseudo-forces that appear in rotating coordinate systems). But trajectories following the geodesic equation have no real acceleration associated with them: the four-acceleration associated with such a trajectory is zero. Gravity doesn't cause acceleration in GR. That is one of the most basic tenets of the theory, and something has gone seriously wrong if you don't understand that.
In the context of GR, gravitational attraction simply refers to the tendency of geodesics to converge in the sort of gravitational field (i.e. curved spacetimes) typically created by matter. If you work out the possible convergence or divergence of two nearby test masses in GR, you arrive at a result called the Jacobi equation, which relates that convergence or divergence explicitly to the curvature of spacetime.
If you're going to bring up math, this (the geodesic and Jacobi equations) is the math relevant to the study of how objects behave in a gravitational field. I have no idea where you're getting this "acceleration due to energy" ($$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.
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, 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.
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.)
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.)
(Incidentally, I notice I need to correct the wording from my previous post. Where I said "The idea of the event horizon as a point in space" I was referring to the singularity and not the event horizon, of course.)
The event horizon (not the singularity) of a black hole is a light cone (or "expanding light sphere") in spacetime.
Well you tell me. You're the one having a hangup with this.
Yes they do (at least in classical GR), and no they don't.
I'm not pretending to be an expert in Hawking radiation. I'm merely pointing out that if black holes do evaporate via Hawking radiation, and the process is time-reversible, then it should be theoretically possible (if impossibly unlikely) for a white hole to form by some process of "reverse Hawking radiation".
That said, Hawking radiation as I understand it doesn't require particles to have negative mass. It's just that if matter/energy can radiate away from a black hole then conservation of energy requires the black hole to gradually evaporate away, though I'll admit I don't know anything about the details of the mechanism (and I don't know to what extent anyone does).
As I explained above, gravity is not a force, so your whole line of reasoning is nonsensical in the context of GR.