[fargolime]

If only black holes weren't illogical! [1] Any decent software developer (i.e. highly logical thinker) who knows basic info about black holes can look at the picture there to quickly see that black holes are inconsistent with the core postulate of general relativity, the equivalence principle. They're a bug! (which Einstein spent a decade trying to find, or some other way that nature could prevent black holes he thought didn't "smell right", and no that's not my blog) [2] is previous discussion showing no bona fide flaw in the argument. I've not seen anyone refute that simple picture, which should be easy if it's incorrect.

That black holes are a bug doesn't mean we can't explain observations. Gravitational redshift still exists to explain massive objects emitting no discernible light (might be only one photon every year, away from Earth).

[1] http://finbot.wordpress.com/2008/03/05/no-black-holes/

[2] https://news.ycombinator.com/item?id=4926603

[pdonis]

Here's another relevant discussion on HN that you conveniently forgot to link to, which does explain in detail the flaw in your argument (the discussion you did link to does too, but not in detail):

https://news.ycombinator.com/item?id=5233894

Click on "parent" to see the post of yours that I was responding to.

[fargolime]

You've linked to that before, but there's nothing there that refutes the blog (not my argument). If there's a flaw it should be a sentence or two of logic, not multiple paragraphs that summarize as "it's not that simple". The blog shows that inertial frames falling through a horizon are that simple (after all, the equivalence principle demands that), and Taylor and Wheeler agree there. Extraordinary evidence is not a requirement per the scientific method. "Extraordinary" is not a scientific concept.

[pdonis]

there's nothing there that refutes the blog

I understand that you don't agree that what I posted refutes the blog, but I'm not trying to convince you, and I'm not going to rehash the argument here. I'm just linking to that discussion for the record, so others reading this thread will understand that your claims and the blog's claims about black holes are not undisputed.

(not my argument).

You may not have written the blog post, but you are claiming it's correct, so it is "your" argument in the only sense that matters here. If you're not willing to own the argument when it's challenged, then you shouldn't be linking to it.

If there's a flaw it should be a sentence or two of logic, not multiple paragraphs that summarize as "it's not that simple"

That's not the summary of what I said. The summary of what I said is this: the blog post's claims about what the theory of relativity actually says are not correct. So the blog post is not refuting the actual theory of relativity; it's refuting a straw man version of the theory that the blog post's author has constructed in his own head.

Taylor and Wheeler agree there

Agree with what? That there can be an inertial frame that falls through the horizon? Yes, of course. But that does not mean Taylor and Wheeler agree with the blog post's claims about black holes. The fact that there can be an inertial frame that falls through the horizon does not mean the blog post's claims about the details of how such frames work are correct. I went into detail about what's wrong with them in the thread I linked to.

[fargolime]

What sentence in that picture's caption is wrong, or what doesn't follow from its premises? Asking for extraordinary evidence isn't a scientific thing. Valid logic is all the evidence needed.

Yes it's my argument in that way. I'll challenge a refutation or accept it, but that's difficult when the counter argument is a vague wall of text. If I were to try to summarize what you think is wrong I couldn't do it. I can't decipher your points to see how they attempt to refute any particular sentence in the blog. Please be way more clear and short and to the point, and I'll agree, or disagree with my reasoning. (For example check out Millstone's reasoning above. He/she disagrees that an inertial frame can cross the horizon. One short sentence is enough to summarize!)

> the blog post's claims about what the theory of relativity actually says are not correct

Anyone can say that; be more specific. What the blog says in that way sources from experts in relativity. Its statement of the equivalence principle, for example, is Kip Thorne's.

> Agree with what?

They agree that frame X in the blog post is validly defined and validly used in the thought experiment. Their quote in the blog makes that clear.

[pdonis]

I can't decipher your points to see how they refutes any particular sentence in the blog.

That's because the blog post itself is not very well written, and doesn't state correctly what relativity actually says.

Please be way more clear and short and to the point

I'll give it another shot below.

They agree that frame X in the blog post is validly defined and validly used in the thought experiment. Their quote in the blog makes that clear.

It does no such thing. Taylor and Wheeler do not say that the blog post's "Law J" and "Law K" are correct statements of what relativity actually says. They're not; they're not even stated precisely enough to have a definite meaning that can be compared with what relativity says.

Rather than try to go through the blog post in detail, let me try stating two simpler puzzles that bring out what seem to me to be the essential points. Here's the setting for both puzzles: an astronaut is falling through the event horizon of a black hole. Just before reaching the horizon, he launches a probe outward at escape velocity, which will be just a smidgen less than the speed of light.

Now consider the astronaut's local inertial frame (LIF) as he crosses the horizon: i.e., the origin (t = 0, x = 0) of this frame is the event at which the astronaut crosses the horizon, and the time axis of the frame is the astronaut's worldline as he falls in. According to relativity, the following are all true statements:

(1) The horizon is an outward-moving lightlike curve that passes through the frame's origin; i.e., it is the line t = x in that frame.

(2) The probe's worldline starts at t = some value just a little bit less than zero, x = 0, and moves in the positive x direction at just a bit less than the speed of light.

(3) Therefore, in this LIF, the horizon is moving outward faster than the probe.

The first puzzle is simple: if all of the above are true, how can the probe ever escape? Won't the horizon catch it? (Meaning, won't it end up below the horizon, not escaping to infinity?)

The resolution of this puzzle is equally simple: the size of the LIF is much, much smaller than the predicted distance, extrapolated from within the LIF, that it will take for the horizon to catch the probe. Therefore, within the LIF, the probe remains outside the horizon. And once we're outside the LIF, tidal gravity is not negligible, and it will "pull" the horizon down with respect to the probe, so the horizon will never catch the probe.

The calculations underlying what I just said about the size of the LIF vs. the distance required for the horizon to catch the probe are on PhysicsForums here:

http://www.physicsforums.com/showpost.php?p=4285946&postcoun...

The second puzzle is a bit more subtle. Consider the following statements, which are also true according to relativity:

(4) With respect to a global coordinate chart describing the black hole spacetime, the horizon is at a constant radial coordinate r.

(5) With respect to the same global coordinate chart, the probe's radial coordinate r is increasing.

(6) However, the distance from the probe to the horizon, in the astronaut's LIF, is decreasing, at least while the probe and horizon remain within the LIF. (This is obvious from statement #3 given earlier.)

The second puzzle then is, how can #5 and #6 be reconciled? How can the probe have increasing r when it's getting closer to the horizon, which is at constant r?

The best way I know of to see the resolution this second puzzle is to actually draw a spacetime diagram of the LIF, with curves of constant r correctly drawn. If you do that, you will see that the curves of constant r are drawn in such a way that the probe's worldline has increasing r even though its distance from the horizon, in terms of the LIF's x coordinate, decreases. I can't draw such a diagram here, but the key fact that makes this true can be seen by considering statement #4 above, combined with statement #1: the horizon is a curve of constant r, but in the LIF, it is a 45 degree line moving up and to the right! (It's the line t = x in the LIF, per #1.) A curve of constant r lying just outside the horizon will slope up and to the right, a bit more vertical than 45 degrees (which makes it timelike); whereas a curve of constant r just inside the horizon will slope up and to the right a bit more horizontal than 45 degrees (which makes it spacelike). The slope of the lines of constant r that pass through the probe's worldline, which also slopes up and to the right at almost 45 degrees (since the probe is moving outward at almost the speed of light) turn out to be sloped a little closer to 45 degrees than the probe's worldline is; so the probe ends up crossing curves with gradually increasing values of r.

[fargolime]

I do appreciate your effort. Unfortunately I only have like half an hour a day to devote to this kind of stuff. So I have to keep this short.

> the size of the LIF is much, much smaller than the predicted distance, extrapolated from within the LIF, that it will take for the horizon to catch the probe.

I'm discussing the simple picture in the blog and its caption. Not a more complex puzzle, or Laws J & K. The cloud of particles is demanded by GR to be splitting in two along the horizon, when all the particles above the horizon are let to be escaping. This "splitting in two" contradicts the equivalence principle and occurs in every arbitrarily short period of time in the life of frame X. There is always an arbitrarily short duration of time available in any LIF, so frame X's size in spacetime is not an issue.

When you talk about "global coordinate chart" and a "lightlike curve" you're being unnecessarily complex, I say. We're talking a simple inertial frame of special relativity here, plus one basic prediction of GR as it relates to the horizon, namely that everything below the horizon moves inexorably inward toward the singularity. This discussion can be much simpler than you're making it. After reading your explanation I shouldn't be left wondering which sentence in the blog is incorrect or doesn't follow from its premises.

The cloud splits in two and that's a "bug". To prove the blog wrong you need to show that the cloud doesn't split in two, that all the cloud's particles can in fact move outward in formation. Can you do that in a way that clearly shows which sentence in the picture's caption is incorrect?

[millstone]

The simplest way to show the essential physical error is via this picture, from the article: http://finbot.files.wordpress.com/2008/03/t9.png

This picture shows the event horizon as having constant position in a free-falling frame. But the event horizon accelerates in all nearby inertial frames, exactly like how the surface of the earth accelerates (towards you) in every inertial frame near the earth. So the line representing the event horizon cannot be straight: it must curve. It must be hyperbolic. That is the key feature that the article gets wrong.

> Then law J shows that a locally inertial frame relative to which the particle is at rest can’t even in principle extend below the horizon

The horizon forms a hyperbola in any such inertial frame. Because the horizon accelerates, whether a spatial point is below the horizon depends on time.

If you have a test particle moving with constant acceleration, can you reach it with a signal at some point after it leaves? In Newtonian physics you can: just send the signal fast enough. But in relativity, test particles moving with constant acceleration can be "uncatchable" even though they never reach c. See Rindler coordinates for more.

This illustrates why an outgoing test particle cannot cross the event horizon. Picture the event horizon as a hyperbola, and the test particle as an asymptote: it can never intersect it.

> a test of the laws of physics can distinguish X from an inertial frame in an idealized, gravity-free universe

Well duh. There are no inertial frames that cross the horizon. Technically any two separated points in our frame will be accelerating with respect to each other. We approximate this acceleration as zero, but this approximation can break down near the speed of light, as things tend to do.

[pdonis]

the event horizon accelerates in all nearby inertial frame

No, it doesn't. The event horizon is an outgoing null geodesic; it has zero proper acceleration. It is certainly not anything like the surface of the Earth.

The horizon forms a hyperbola in any such inertial frame

No, it doesn't. The horizon is an outgoing lightlike surface, so in any local inertial frame that contains it, it will be a straight line moving up and to the right at 45 degrees. (See my post in response to fargolime upthread for a more detailed description.)

in relativity, test particles moving with constant acceleration can be "uncatchable" even though they never reach c. See Rindler coordinates for more.

It's true that the Rindler horizon gives a good flat spacetime analogy for many key features of the event horizon of a black hole. But you appear to have things backwards: the object moving at constant acceleration is not the Rindler horizon; it is "uncatchable" by the Rindler horizon! In other words, the Rindler horizon is a light ray moving in the same direction as the accelerating object, but which never quite catches up with it (because the test object has just enough of a head start).

This illustrates why an outgoing test particle cannot cross the event horizon.

No, it doesn't. The reason an outgoing test particle inside the horizon can't cross it is simple: the horizon is moving outward at the speed of light, and nothing can go faster than light.

There are no inertial frames that cross the horizon

This is not correct; there are, just as Taylor and Wheeler say. There are plenty of wrong statements in the blog post, but this is not one of them.

[fargolime]

> This picture shows the event horizon as having constant position in a free-falling frame. But the event horizon accelerates in all nearby inertial frames

The line represents the horizon at a single moment in the life of frame X, during which it has a specific position relative to X and is not accelerating relative to X.

> If you have a test particle moving with constant acceleration, ...

The test particles are defined as freely falling. The frame X is defined as inertial. No free particle can accelerate in an inertial frame (at least not measurably), including in relativity. Check out Taylor and Wheeler's quote at the bottom of the blog post: "Keys, coins, and coffee cups continue to move in straight lines with constant speed in such a local free-float frame." According to you, those things would not move at constant speed; rather they'd be "moving with constant acceleration".

> Well duh. There are no inertial frames that cross the horizon.

This again disagrees with Taylor and Wheeler's quote. They are clear that not only can an inertial frame cross a horizon, but also that frame is "a free-float frame like any other".

I didn't respond to everything you said because it hinges on the same disagreement. Before we could get further in the discussion you would need to accept Taylor and Wheeler there, or show how I'm misunderstanding the conflict between what you said and their quote that seems to explicitly disagree with you.