I am the first in the world

[Farsight]

Logically, it could dismissed by those grounds, but there's indeed something pretty fishy and very questionable about all this attribution to Einstein in the first place, particularly in support of Farsight's rather strong misconceptions, such as

"Your proper time is being measured on a stopped clock. Just because you're stopped too doesn't mean that nothing even slightly unusual happens. It means nothing happens".

and especially statements such as

"At the event horizon it isn't nothing unusual happens, it's nothing happens. There are no more events".

I haven't talked about Einstein that much, Vorpal. Sure I bridled at sol blithely dismissing the guy and putting himself on the wrong side of the crackpot fence, but like I said above, the scientific evidence is the most important thing here, along with some simple logic. There's nothing fishy about it.

It does not make that Einstein, who derived such results as this in collaboration with Rosen: Phys. Rev. 48, 73–77 (1935), would now suddenly take the point of view that spacetime just gets cut off at the horizon of black hole, and then suddenly advance a solution that amounts to gluing two Schwarzschild exteriors together at the horizon.

It's hard to say what Einstein might think, and it's subjective, best to stick with the scientific evidence and the logical argument.

The Einstein-Rosen "bridge" paper also reveals Einstein's motivation for it: he may have disliked the Schwarzschild interior, his main problem with it was definitely the genuine curvature singularity at the center, not the horizon itself, which, after all, the "bridge" does not get rid of it at all, and rather puts a whole universe of events beyond it.

Noted. Apologies, I've got to go. I'll get back to you later. Try to address the discussion instead of ruminating about what Einstein might have thought of it.

 

[sol invictus]

Not every physicist. Just those who thump your good book. Try emailing Steven Weinberg to see what he thinks.

I know exactly what Weinberg thinks about this, Farsight. I learned GR from his book, for one thing. He agrees completely with me.

No it isn't. I've said this and I'll say it again. Gravitational time dilation goes infinite at the event horizon, so your clock has stopped and you've stopped too. Light has stopped, so you can't measure anything, and there is no metric. Flat spacetime is irrelevant here because spacetime has gone. And you have in no way addressed the issue. The whole point of this discussion is the fallacy that a stopped clock carries on ticking. You said nothing unusual happens to observer. But everything has stopped, so nothing happens.

You still haven't been able to follow my argument. I'll try again. Flat spacetime can be written in coordinates in which there is a horizon with exactly the properties you are using, and that horizon can be put anywhere you like. If your "logic" was correct, the conclusions apply to every point in flat spacetime.

I haven't presented Einstein quotes because the scientific evidence is more important than Einstein's view.

Oh, really? Here's what you said:

You know how you get all those cranks and crackpots who know b*ggar all physics and who insist that Einstein was wrong? Well, take a look at which side of the fence you're on.

Guess what - Einstein did not agree with you about the horizon, as the quote from Vorpal makes clear. So.... which side of that fence are you on, Farsight?

As for "argument from authority", "Einstein said it so it must be true" is invalid. "Every physicist since 1960 said it, and here's the derivation they all agree on, so unless you can point out a problem with it you'll be ignored" is perfectly valid. Try to learn the difference.

 

[Vorpal]

It's hard to say what Einstein might think, and it's subjective, best to stick with the scientific evidence and the logical argument.
...
I'll get back to you later. Try to address the discussion instead of ruminating about what Einstein might have thought of it.

After insisting your views of GTR are the "original" and that you're "with Einstein", proceeding to imply that sol invictus and others are crackpots because they contradict him, it is extremely fair to examine Einstein's thoughts, as you've been invoking him to attack your opponents. And it's not subjective at all, Farsight. It's right there, hilited in the part you cut out: Einstein thinks you're dead wrong about the Schwarzschild horizon, and that your reasons are mistaken.

Not every physicist. Just those who thump your good book. Try emailing Steven Weinberg to see what he thinks.

I'm afraid Steven Weinberg disagrees with your reasoning:

But is this singularity real? We can readily calculate the four nonvanishing curvature invariants described in Section 6.7, and find that they are all perfectly well behaved at the Schwarzschild radius, although they do become singular at the origin. This suggests that the apparent Schwarzschild singularity may be only an artifact of the coordinate systems we have used.
...
However, like Aesop's fables, it is useful because it points to a moral, that what appears in one coordinate system to be a singularity may in another coordinate system have quite a different interpretation.​

from Gravitation and Cosmology, pp. 207-8. It is notable that he too bases his discussion on Kruskal's paper.

---

It isn't completely wrong. Yeah yeah, I should have said stationary observer, where his clock rate is a function of gravitational potential. But if you have that observer accelerating, his clock rate tends to zero even faster.

Yeah, that's indeed completely wrong. In the presence of gravitational field, a stationary observer is accelerated. I'm afraid you need to review the equivalence principle; you've misunderstood something very fundamental about GTR.

I'm the one who's saying it's more than just some coordinate artefact. People who swallow Kruskal-Szekeres coordinates treat the event-horizon singularity like window dressing to be disregarded.

There's a sense in which the horizon is more than (say) the Rindler one, and I briefly mentioned before, but for reasons completely different than anything you've stated. It most certainly does not behave even remotely the way you describe in any case except stationary.

Aw here we go, hiding behind inscrutable mathematics. If I say yes you sidetrack the discussion demanding that I support my claim, if I say no you say well there you go then. It isn't good enough Vorpal. Everybody can see you're ducking the argument.

It's amusing you think they're inscrutable mathematics, Farsight, because for the purely radial case I asked of you, calculating this amounts to nothing more than high-school calculus... if one is aware of the geodesic equation in the first place and what a timelike vector means. I'm assuming you're capable of basic differentiation and so will have the appropriate Christoffel symbols. Plugging them into the geodesic equation gives
[latex]\[ \frac{d^2t}{d\tau^2} = -\frac{2M/r^2}{1-2M/r}\frac{dt}{d\tau}\frac{dr}{d\tau} \][/latex]
Which can be directly integrated (with t' = dt/dτ as variable) to give
[latex]\[ \frac{dt}{d\tau} = \frac{e}{1-2M/r} \][/latex]
where e is some constant of integration. Plug that into g_μνu^μu^ν = -1 for the Schwarzschild metric, and voila:
[latex]\[ \text{const} = (e^2-1)/2 = \frac{1}{2}\dot{r}^2 - \frac{GM}{r} \][/latex]
In other words, radial freefall is exactly Newtonian in Schwarzschild r and proper time τ. And so the proper time to reach the horizon (or the r = 0) is finite. If you like, one can solve this to give the standard cycloid relations between r and τ, but it's not necessary here.

That's actually the simplified version of a more general derivation done in many GTR textbooks. A somewhat more sophisticated treatment doesn't even require the geodesic equation nor the Christoffel symbols at all, but since that's basic to GTR, anyone who knows even a little bit about GTR should be able to work it.

 

[alfa1]

steenkh,

Because of these inequalities:
I calculated the lowest number of qubits after Big Bang: min Iuniverse .
I calculated the max number of qubits, max Iuniverse if the universe will be made of photons with the 1Hz frequency.

min Iuniverse < Iuniverse < max Iuniverse

15.392 × 10^61 qubits < Iuniverse < 4.544 × 10^104 qubits

I can say:

"The Universe today is more intelligent than yesterday" Adrian Ferent

An abstract of my theory on my blog: http://adrianferent.blogspot.com/

 

[W.D.Clinger]

A map is not the territory. A chart is not the manifold.

Farsight's argument with Vorpal, sol invictus, ben m et cetera appears to involve a misunderstanding of the most basic facts of differential geometry. To understand what's going on here, it helps to understand the relationship between coordinate systems and differentiable manifolds.

(For a nice tutorial on that subject, I recommend

Jason J Sharples. Coordinate transformations and metric extension: a rebuttal to the relativistic claims of Stephen J. Crothers. Progress in Physics, 2010, Volume 1 (of the volumes for 2010), pages L1-L6. Online at http://www.ptep-online.com/index_files/2010/PP-20-L1.PDF
​

Stephen J Crothers is an advocate of Electric Universe pseudoscience who claims to have "definitive proof that black holes do not exist" and is really annoyed that so many people have found mistakes in that alleged proof.)​

By definition, an n-dimensional topological manifold is a paracompact Hausdorff space that's locally Euclidean: Every point of the space is contained within an open set that's homeomorphic to an open subset of Rⁿ.

Those homeomorphisms are called charts. Physicists generally refer to those charts as coordinate systems. As I'll explain below, the physicists' terminology is confusing, and that particular confusion may explain part of what we've seen in this thread.

By definition, a differentiable manifold consists of a topological manifold plus an atlas, which is a set of charts that cover the entire manifold and compose (in a certain way) to form sufficiently smooth diffeomorphisms.

The set of all possible charts (coordinate systems) for a manifold is called its complete atlas. The complete atlas contains infinitely many charts (coordinate systems). All of those charts are valid coordinate systems.

General relativity is a difficult subject, and there are many ways to misunderstand it. One of the more common mistakes is to treat some particular chart (coordinate system) as though it were somehow more correct than other charts (coordinate systems), and to treat the open set on which that particular chart (coordinate system) is defined as though it were the entire manifold.

With all but the simplest differentiable manifolds, there is no single chart (coordinate system) that's defined on the entire manifold. Consider, for example, the surface of the earth (which is a 2-sphere). There is no chart that covers the entire surface of the earth, because the 2-sphere is not homeomorphic to any open subset of 2-dimensional Euclidean space.

That example shows why it's confusing to refer to charts as coordinate systems. Spherical coordinates are usually thought of as a coordinate system that can deal with the entire 2-sphere, but spherical coordinates do not give us a chart that covers the entire 2-sphere because they are not bijective at the north pole: At zero inclination (90 degrees north latitude), all possible values for the azimuth (longitude) refer to the same point.

That's a simple example of a coordinate singularity. It's not a real singularity, because the vicinity of the north pole looks just like the vicinity of any other point on the 2-sphere. It's a mistake to think coordinate singularities imply any weird topology in the manifold itself. What a coordinate singularity does imply is that you'll have to switch to a different coordinate system if you want to calculate what's going on at the coordinate singularity and beyond.

With those basics in mind, let's look back at some of what's been said in this thread.

And then sol said this?

"For an external observer, yes. But for the person falling in, those time intervals are finite".

The person falling in ends up with a stopped clock. It's stopped, so his "finite" intervals take forever. So they never ever happen.

No. We're talking about two different charts here: There's the chart (coordinate system) that maps the external observer's neighborhood onto an open subset of R⁴, and there's the chart (coordinate system) that maps the infalling person's neighborhood onto an open subset of R⁴. The external observer's chart stops at the event horizon; that's a coordinate singularity. The infalling observer's chart doesn't stop at the event horizon.

The external observer's coordinate singularity at the event horizon means the external observer calculates that the infalling person's clock stops at the event horizon. That's a mere artifact of the external observer's desire to calculate within a coordinate system that makes his own neighborhood look as Euclidean as possible. If the external observer were willing to calculate using a different coordinate system, such as one that makes the infalling person's spacetime neighborhood look as Euclidean as possible, then the external observer would realize that the infalling observer's clock does not stop.

Sorry, I didn't look at it. The thing is, mathematics doesn't get this crucial point across. That's why people blithely switch to a different metric I suppose, and do that hop skip and a jump over the end of time without even noticing.

I agree that different people will disagree about where the event horizon is located. But a zero or very low speed of light is no artefact. Your coordinate system is. It isn't something real that actually exists. It's an artefact of measurement. And when all processes slow and stop, you can't measure anything. You can't see anything, and you can't even think, because all processes have stopped. So you don't have a coordinate system. Your proper time is being measured on a stopped clock. Just because you're stopped too doesn't mean that nothing even slightly unusual happens. It means nothing happens.

No. What it means is that you're trying to use a chart (coordinate system) outside the open set on which that chart is defined. That's a mistake. If you want to understand what's going on at the event horizon itself, you have to switch to a different chart (coordinate system) whose domain includes the event horizon.

At the event horizon it isn't nothing unusual happens, it's nothing happens. There are no more events. The light isn't moving any more. You can't measure space, you can't measure time, you can't see, or think, and your reference frame and coordinate system have utterly collapsed.

The highlighted part is almost correct, but not for the reason Farsight gave. The reason you can't use the external observer's chart (coordinate system) to measure space or time at the event horizon is that the event horizon lies outside the open set on which that chart (coordinate system) is defined. If you use a chart (coordinate system) whose domain includes the event horizon, you'll realize that nothing unusual happens at the event horizon.

No. I've already told you twice that the maths doesn't show you this. I've given you a good explanation, now deal with the argument instead of trying to play the inscrutable mathematics card.

Farsight is telling us untrue things about the mathematics because he doesn't understand the mathematics. Indeed, he refers to the math as "inscrutable".

The mathematics of general relativity is fairly advanced. That's why people who have little or no training in mathematics generally know better than to argue about general relativity. There are, of course, exceptions.

I've told you before, don't try hiding behind the maths, not with me.

We're not hiding behind the math. We're trying to explain the math.

It isn't. Remember what sol said: all processes slow and stop on the horizon as viewed from outside. Now imagine that you're a light wave bouncing back and forth inside his parallel-mirror light clock. At the event horizon, you stop forever.

This isn't my idea, this is the original frozen star idea, in line with Schwarzschild and Einstein. Typical textbooks do that hop skip and a jump over the Schwarzschild event-horizon singularity and write it off as a coordinate artefact, missing the whole point that when light stops you don't have any coordinates any more.

As sol invictus said, all processes appear to slow, never reaching the event horizon, as viewed from outside by an external observer who's calculating with a chart (coordinate system) that does not include the event horizon. The reason for that is simple: The external observer's chart (coordinate system) contains a coordinate singularity at the event horizon.

That coordinate singularity doesn't imply that light actually stops at the event horizon. In reality, nothing at all unusual happens as light passes through the event horizon.

If it's "straightforwardly wrong", try explaining it. Or try addressing my straightforward argument. When you can't do either, stop digging, and yield.

Farsight's argument is indeed straightforwardly wrong, because it's based on Farsight's apparent misunderstanding of the most basic definitions of differential geometry.

I'm the one who's saying it's more than just some coordinate artefact. People who swallow Kruskal-Szekeres coordinates treat the event-horizon singularity like window dressing to be disregarded.

The event-horizon singularity is a coordinate singularity. The event horizon lies outside of the open set on which the usual Schwarzschild chart (coordinate system) is defined.

That means we can't understand what happens at the event horizon without using a chart (coordinate system) other than the one Farsight insists we use. So long as Farsight insists upon using a particular mathematical formalism that becomes completely useless at the event horizon, he won't understand what happens at the event horizon and beyond.

Everybody can see you're ducking the argument. Let me take a look at the other posts, then I'll nail you to the floor. Hurry up and start backing down, because it's going to be embarrassing.

No it isn't. I've said this and I'll say it again. Gravitational time dilation goes infinite at the event horizon, so your clock has stopped and you've stopped too. Light has stopped, so you can't measure anything, and there is no metric.

No matter how many times Farsight says it, it isn't true.

Farsight is saying the well-known Schwarzschild coordinate singularity at the event horizon is a genuine spacetime singularity. He's wrong.

 

[ben m]

Farsight, I urge you to look at W.D. Clinger's math carefully.

And I urge you to notice, among other things, that this reinforces my statement that nothing you're saying is unfamiliar. Physicists have known since 1915 that it's possible to write GR metrics with coordinate singularities. We noticed the singularities, we said "hey, here are the things which are singular" and "here are the things which are not singular". We developed methods for telling the difference between a real physical singularity and a coordinate-system artifact. We developed methods for thinking about them without getting confused.

You have gotten to Version 0.1-Beta-Dev-Unstable of this. You noticed a singularity. Good for you. Einstein and Schwarzschild noticed this same singularity in 1915. You stopped with the noticing, whereas the rest of the community continued thinking about it.

Using the laws of physics, which cooperate very well with the formalities of math, the actual-working-physics-community figured out various things about this "singularity". We figured out what it looks like to various particular observers. We figured out the exhaustive group of things-it-looks-like in the exhaustive space-of-all-possible-observers. This understanding, which started coming together right away in 1915---it's not too complicated, after all---is an utterly routine aspect of every General Relativity course ever taught.

Your only response to all of that is to pretend it's a sham. I think you expect special credit for "discovering" something important about the Schwarzschild metric; when we tell you "that's not actually something important", you act as though it's a personal affront to your great discovery.

 

[alfa1]

Some fraudulent researchers might be sociopaths who don't care about the rules, but many others simply believe that they can anticipate the outcome of a research project, and see no downside to fabricating the required results to save time, or tweaking results to achieve a stronger signal. Either way, stronger action and punishments are needed to discourage such misbehaviour.
So, how can Britain highlight cases of misconduct and discourage it in future? Ultimately, the incentives probably need to come from on high, and the government could get the ball rolling by commissioning an anonymous survey on misconduct that UK researchers have witnessed and perpetrated.

Funders and universities could then work together to establish common definitions of what counts as misconduct, and how it will be punished.

http://www.nature.com/nature/journal/v481/n7381/full/481237b.html?WT.ec_id=NATURE-20120119

 

[Reality Check]

You have posted in the wrong thread, alfa1.

 

[alfa1]

Today the universe has more qubits than yesterday, from these inequalities:
I calculated the lowest number of qubits after Big Bang: min Iuniverse .
I calculated the max number of qubits, max Iuniverse if the universe will be made of photons with the 1Hz frequency.

min Iuniverse < Iuniverse < max Iuniverse

15.392 × 10^61 qubits < Iuniverse < 4.544 × 10^104 qubits

I can say:

"The Universe today is more informed than yesterday" Adrian Ferent

An abstract of my theory on my blog: http://adrianferent.blogspot.com/

 

[Reality Check]

Today the universe has more qubits than yesterday, from these inequalities:
...

alfa1m, if you have any comments relevant to the thread then I suggest that you post them rather than spamming a crank web site and displaying your ignorance of what qubits are. The universe has zero qubits except for the ones we create in quantum cumputers.

 

[alfa1]

It is good because you heard about Qubit in New Zealand

 

[Farsight]

Sorry guys, I've been pushed recently, and forgot about this thread.

Farsight, I urge you to look at W.D. Clinger's math carefully.

Will do.

And I urge you to notice, among other things, that this reinforces my statement that nothing you're saying is unfamiliar. Physicists have known since 1915 that it's possible to write GR metrics with coordinate singularities.

No problem.

We noticed the singularities, we said "hey, here are the things which are singular" and "here are the things which are not singular". We developed methods for telling the difference between a real physical singularity and a coordinate-system artifact. We developed methods for thinking about them without getting confused.

No, you didn't. You got confused.

You have gotten to Version 0.1-Beta-Dev-Unstable of this. You noticed a singularity. Good for you. Einstein and Schwarzschild noticed this same singularity in 1915. You stopped with the noticing, whereas the rest of the community continued thinking about it.

As I've said before, I'm with Einstein. You're not, and you really haven't thought about this at all. Otherwise you wouldn't be siding with a community that adopts the specious position of thinking a stopped clock carries on ticking in the frame of reference of the observer. Ben, it's nonsense. Think about it. You don't observe anything if you're travelling at c. Your proper time is absolutely non-existent. It's the same at the event horizon.

Using the laws of physics, which cooperate very well with the formalities of math, the actual-working-physics-community figured out various things about this "singularity". We figured out what it looks like to various particular observers. We figured out the exhaustive group of things-it-looks-like in the exhaustive space-of-all-possible-observers. This understanding, which started coming together right away in 1915---it's not too complicated, after all---is an utterly routine aspect of every General Relativity course ever taught.

And that utterly routine aspect of every General Relativity course ever taught is wrong. Doing a hop skip and a jump over the end of time and pretending it doesn't matter is cargo-cult pseudoscience that is a travesty of general relativity and an insult to Einstein.

Your only response to all of that is to pretend it's a sham. I think you expect special credit for "discovering" something important about the Schwarzschild metric; when we tell you "that's not actually something important", you act as though it's a personal affront to your great discovery.

I'm the one giving the carefully thought-out argument here. You're the one offering nothing in return other than "we know better". Try supporting that with some logic that counters mine. When you can't, yield. Stop digging yourself into a hole.

 

[Farsight]

I know exactly what Weinberg thinks about this, Farsight. I learned GR from his book, for one thing. He agrees completely with me.

Shall we ask him? No, let's not get bogged down by appeals to authority, let's let the argument stand on its own two feet. For the record, since I emailed Weinberg, Kevin Brown has amended his mathspages article, and now ascribes the field interpretation to nobody instead of Weinberg, and the geometrical interpretation to Einstein instead of Wheeler. It isn't the first time material I've referenced has been retrospectively altered.

You still haven't been able to follow my argument. I'll try again. Flat spacetime can be written in coordinates in which there is a horizon with exactly the properties you are using, and that horizon can be put anywhere you like. If your "logic" was correct, the conclusions apply to every point in flat spacetime.

You haven't got any argument. The spacetime around a black hole isn't flat. You can't make that go away with some coordinate transformation. And the property I'm employing is vacuum impedance, so absolute that light doesn't move and clocks don't tick. Then there isn't any spacetime any more.

Oh, really? Here's what you said:

You know how you get all those cranks and crackpots who know b*ggar all physics and who insist that Einstein was wrong? Well, take a look at which side of the fence you're on.

Guess what - Einstein did not agree with you about the horizon, as the quote from Vorpal makes clear. So.... which side of that fence are you on, Farsight?

I'm on Einstein's. What Vorpal quoted was this:

The vanishing of the coefficient of dt² i.e. (g44) for ρ = 0 results, it is true, in the consequence that the determinant g vanishes for this value; but, with the methods of writing the field equations actually adopted, this does not constitute a singularity.

It's certainly not a singularity like the mooted point-singularity in the middle of a black hole.

As for "argument from authority", "Einstein said it so it must be true" is invalid. "Every physicist since 1960 said it, and here's the derivation they all agree on, so unless you can point out a problem with it you'll be ignored" is perfectly valid. Try to learn the difference.

You said Einstein was wrong, and you've got no argument.

Next!

 

[Farsight]

After insisting your views of GTR are the "original" and that you're "with Einstein", proceeding to imply that sol invictus and others are crackpots because they contradict him, it is extremely fair to examine Einstein's thoughts, as you've been invoking him to attack your opponents. And it's not subjective at all, Farsight. It's right there, hilited in the part you cut out: Einstein thinks you're dead wrong about the Schwarzschild horizon, and that your reasons are mistaken.

What parts? That is so weak, Vorpal. Reprise the point, and this time spell it out instead of trying to get away with sleight of hand. The parts you cut out indeed. LOL.

I'm afraid Steven Weinberg disagrees with your reasoning:

But is this singularity real? We can readily calculate the four nonvanishing curvature invariants described in Section 6.7, and find that they are all perfectly well behaved at the Schwarzschild radius, although they do become singular at the origin. This suggests that the apparent Schwarzschild singularity may be only an artifact of the coordinate systems we have used.
...
However, like Aesop's fables, it is useful because it points to a moral, that what appears in one coordinate system to be a singularity may in another coordinate system have quite a different interpretation.​

from Gravitation and Cosmology, pp. 207-8. It is notable that he too bases his discussion on Kruskal's paper.

Maybe he does. We were talking about this last year, I referred to Kevin Brown's article, then emailed Weinberg about it. He got back to me saying that didn't sound right, and now Kevin Brown has removed his reference to Weinberg.

Yeah, that's indeed completely wrong. In the presence of gravitational field, a stationary observer is accelerated. I'm afraid you need to review the equivalence principle; you've misunderstood something very fundamental about GTR.

Don't try it Vorpal. I know what the priniciple of equivalence says: the freefalling observer isn't accelerated, whilst the observer on the surface of the earth is accelerated. The observer at the event horizon is like the observer at the centre of the earth. Stationary. Only his clocks are stationary too, and his nerve impulses, and his light. And above him, there's this gravitational field.

There's a sense in which the horizon is more than (say) the Rindler one, and I briefly mentioned before, but for reasons completely different than anything you've stated. It most certainly does not behave even remotely the way you describe in any case except stationary.

Oh not the Rindler horizon again. Forget it Vortpal. All you need to know is that if you were travelling at c, you don't have any proper time. It's that simple.

It's amusing you think they're inscrutable mathematics, Farsight, because for the purely radial case I asked of you, calculating this amounts to nothing more than high-school calculus... if one is aware of the geodesic equation in the first place and what a timelike vector means. I'm assuming you're capable of basic differentiation and so will have the appropriate Christoffel symbols. Plugging them into the geodesic equation gives

They're inscrutable to general readers looking at this thread wondering why nobody is dealing with this guy who's pointing out the non-constant coordinate speed of light and the infinite gravitational time dilation. They're no better than a puff of smoke and a flourish followed by a bow. How many tiomes have I got to say it: mathematics doesn't tell you that clocks clock up some kind of motion. All clocks do this. A light clock clocks up the motion of light. When we see optical clocks at different elevations lose synchronisation, we say gravitational time dilation occurs. And if that goes infinite, the lower clock has stopped. And so have you. Forever.

Which can be directly integrated (with t' = dt/dτ as variable) to give
[latex]\[ \frac{dt}{d\tau} = \frac{e}{1-2M/r} \][/latex]
where e is some constant of integration. Plug that into g_μνu^μu^ν = -1 for the Schwarzschild metric, and voila:
[latex]\[ \text{const} = (e^2-1)/2 = \frac{1}{2}\dot{r}^2 - \frac{GM}{r} \][/latex]
In other words, radial freefall is exactly Newtonian in Schwarzschild r and proper time τ. And so the proper time to reach the horizon (or the r = 0) is finite. If you like, one can solve this to give the standard cycloid relations between r and τ, but it's not necessary here.

It's a stopped clock Vorpal. All the integrating in the world isn't going to make it tick, now now, not next week, not ever. The fact that you're not ticking either won't wish it away and cancel it out. That proper time τ takes forever to happen. So it never happens at all.

That's actually the simplified version of a more general derivation done in many GTR textbooks. A somewhat more sophisticated treatment doesn't even require the geodesic equation nor the Christoffel symbols at all, but since that's basic to GTR, anyone who knows even a little bit about GTR should be able to work it.

What your good book says, is wrong. Your good book doubtless tells you that the speed of light is constant too. And yet my parallel-mirror light clocks at different elevations says it isn't:

|------------------|
|------------------|

Do we agree that gravitational time dilation at the event horizon goes infinite? If so, can we agree that the clock at that location is doing this?

|------------------|

And do we agree on the wave nature of matter? Come on Vorpal, who are you going to believe? Me and my Uncle Albert and the scientific evidence and the brutal logic? Or your good book?

 

[sol invictus]

Shall we ask him? No, let's not get bogged down by appeals to authority, let's let the argument stand on its own two feet.

That's the second time you've appealed to authority, discovered that the authority contradicts you and agrees with me, and then said something very entertaining like "let's not get bogged down by appeals to authority".

The spacetime around a black hole isn't flat.

That's true.

You can't make that go away with some coordinate transformation.

I didn't try to.

You've still utterly failed to understand my simple argument. What I've shown you is that flat spacetime - not a black hole, flat spacetime - can be written in coordinates in which there's a horizon anywhere you like, and that horizon has precisely the properties you claim demonstrate that time stops, etc. Hence, your argument is manifestly wrong.

In fact, your argument is very, very similar to the naive arguments against special relativity that students often get confused by when they first encounter it. You're picking one coordinate frame and insisting that coordinate-dependent quantities (like the coefficient of dt^2 in the metric) in that frame are the One Truth. It's called "relativity" for a reason, "Farsight".

 

[ben m]

I'm the one giving the carefully thought-out argument here. You're the one offering nothing in return other than "we know better". Try supporting that with some logic that counters mine. When you can't, yield. Stop digging yourself into a hole.

My logic is the same as Sol's, and the same as Misner-Thorne-Wheeler, and therefore the same as Schwarzschild's and Lemaitre's and Synge's and Einstein's. When I do the math, I can tell you exactly what any observer will experience on watching anyone do anything near a black hole. Your statement "a clock falling into a black hole slows to zero" is a special case; in my exact, mathematical treatment of the system, I can see when and why that case occurs; I can see when and why it doesn't occur.

You, meanwhile, are able to do one and only one thing---you have one observer, looking at one object, in one location, about whom you can make one statement. You can't change observers, you can't change targets, you can't add angular momentum. You're stalled. Therefore---especially in relativity, of all things, where changing-observers is explicitly a valid thing to do at any time----your understanding of that situation is deeply incomplete. But when anyone tries to add to your understanding, you accuse them of a "hop skip and a jump" past your one lonely equation.

It's as though you learned projectile motion, but only ever understood the "start at rest" case in which y = -1/2 g t^2. Someone tells you "yes, that's true in that case, and more generally we solve for x(t) and y(t)", and your objection is "no, I showed x = 0, you're skipping right past x=0."

 

[Reality Check]

It is good because you heard about Qubit in New Zealand

It is bad that you have never heard about Qubit where you are.

 

[Reality Check]

As I've said before, I'm with Einstein. You're not, and you really haven't thought about this at all. Otherwise you wouldn't be siding with a community that adopts the specious position of thinking a stopped clock carries on ticking in the frame of reference of the observer. Ben, it's nonsense.

Farsight, your ignorance is showing.
As several posters have stated, you are not with Einstein (for a start he is dead!).

You are lying about what the scientific community (including Einstein) has stated. If you have only one observer then either:

• The observer is traveling with the clock into the black hole and it never stops clicking or
• The observer is observing the clock falling into the black hole and the clock slows down. The clock never stops because the observer cannot observe it for an infinite length of time.

 

[Farsight]

Farsight, your ignorance is showing.
As several posters have stated, you are not with Einstein (for a start he is dead!).

I am with Einstein on this, RC. The main thing is the way the speed of light varies with gravitational potential. People will brush this off by telling you the coordinate speed of light varies with gravitational potential, but that doesn't get to the heart of it. Einstein started with the constant speed of light as a postulate in 1905 when he was doing special relativity, but in 1911 he wrote If we call the velocity of light at the origin of co-ordinates cₒ, then the velocity of light c at a place with the gravitation potential Φ will be given by the relation c = cₒ(1 + Φ/c²). That's the speed of light varying with gravitational potential. People will tell you he changed his mind, but it isn't true. In 1912 he said it again when he wrote On the other hand I am of the view that the principle of the constancy of the velocity of light can be maintained only insofar as one restricts oneself to spatio-temporal regions of constant gravitational potential. He repeated this in 1913 when he said: I arrived at the result that the velocity of light is not to be regarded as independent of the gravitational potential. Thus the principle of the constancy of the velocity of light is incompatible with the equivalence hypothesis. He says it again in 1915 with the writer of these lines is of the opinion that the theory of relativity is still in need of generalization, in the sense that the principle of the constancy of the velocity of light is to be abandoned. Then people will tell you that velocity is a vector quantity, and they won't tell you that the actual word he used was geschwindigkeit, which translates into speed, or that he referred to c, and c is a speed.

You are lying about what the scientific community (including Einstein) has stated.

I don't lie. And regardless of what Einstein said, look to the scientific evidence. You know that optical clocks lose synchronisation at different elevations, so you know that parallel-mirror light-clocks do too. Then if you say gravitational time dilation goes infinite at the event horizon, you're left with a zero speed of light at that location. It's all horribly simple.

If you have only one observer then either:

• The observer is traveling with the clock into the black hole and it never stops clicking or
• The observer is observing the clock falling into the black hole and the clock slows down. The clock never stops because the observer cannot observe it for an infinite length of time.

The observer travelling with the clock gets to a place where the speed of light is zero. So his light-clock does stop ticking, and because the speed of light goes to zero, he doesn't observe it. All electromagnetic phenomena stops, so he can't even think about it either. Saying the infalling observer doesn't notice anything different is wrong. You can't magic away a stopped clock with a stopped observer. What's right is that he doesn't notice anything. He's like the hypothetical observer travelling at c. He's blatting through the universe, frozen and oblivious, so much so that you can plot his course and put an asteroid in his way. BLAM. He doesn't observe that either.

Think this through for yourself. Don't be taken in by sophistry and evasion.

 

[Reality Check]

I am with Einstein on this, RC. The main thing is the way the speed of light varies with gravitational potential.

You are not, Farsight. You are obsessing with a single persons opinion from 1915 that is not used by the scientific community.

You are lying about what the scientific community (including Einstein) has stated. Any one who knows about GR knows about gravitational time dilation and how it acts as a clock approaches an event horizon. The clock slows down. It never stops.

You remain ignorant of relativity and the roles of observers.

The observer traveling with the clock never gets to a place where the speed of light is zero. The observer traveling with the clock

• passes through the event horizon and never notices it.
• he observes his light-clock keeps on ticking.

Saying the in-falling observer doesn't notice anything different is insanely ignorant.

An observer looking at the in-falling observer & clock will see that they never reach the event horizon. They never get to "a place where the speed of light is zero". The clock slows down. It never stops.

Work this through for yourself in GR or just read a textbook on GR. Don't be taken in by ignorance and fantasies.