Black holes

[Farsight]

The waterfall is pop-science pseudoscience, and dressing it up as hydrodynamics doesn't change that one bit. I reiterate: in no way is space moving inwards towards a black hole.

And it's not a meaningless question at all, it's the $64,000 question. If according to observers at a great distance, "the coordinate speed of light on the horizon is zero" then that's it. That's why a light beam emitted vertically from the event horizon doesn't escape. It isn't immersed in some waterfall of infalling space, it doesn't curve round back into the black hole, and it doesn't climb up to some elevation and then start falling back down.

All: I recommend that you research "frozen star", as per this [url="http://www.scientificamerican.com/article.cfm?id=frozen-stars]Scientific American article[/url]. If you were to place one of those super-accurate optical clocks at a event horizon, then it would not only tick slower than your reference clock here on Earth, it wouldn't tick at all. And choosing a different coordinate system won't make it start ticking again. Some will tell you that if you were to go to the event horizon you would see the clock ticking, but I'm afraid you won't, because you'd "stop" too.

 

[Brian-M]

I reiterate: in no way is space moving inwards towards a black hole.

Maybe it'd help if you offered a brief explanation of how gravity works according to relativity?

 

[Reality Check]

The waterfall is pop-science pseudoscience, and dressing it up as hydrodynamics doesn't change that one bit. I reiterate: in no way is space moving inwards towards a black hole.

You are actually reiterating a strawman: Relativity does not state that space moving inwards towards a black hole.

No one is saying that the waterfall analogy means that black holes are waterfalls or that waterfalls are black holes !
The analogy is that measurements can act in the same manner, i.e. there is an event horizon

A useful analogy is a river with a current that grows stronger and stronger as it approaches a waterfall. Let's say the speed of the current exceeds the speed of sound in water at some fixed distance from the waterfall. Mini-submarine probes swimming around in the river will never be able to send any sound pulses back across that line - it's a sound horizon.

 

[Reality Check]

If you were to place one of those super-accurate optical clocks at a event horizon, then it would not only tick slower than your reference clock here on Earth, it wouldn't tick at all.

The problem with your example is you are again forgetting to state who is observing the clock.
An observer on Earth will state that it is physically impossible to place one of those super-accurate optical clocks at a event horizon. All they can do is observe the clock getting closer and closer to the event horizon and so it would not only tick slower than the reference clock here on Earth, it would continue to tick.

But you could just have this as a thought experiment. Then the clock at the event horizon will never be observable. The Earth observer cannot say anything about any measurements of its ticking (as far as they are concerned the clock does not exist!).

 

[Farsight]

Maybe it'd help if you offered a brief explanation of how gravity works according to relativity?

Very briefly: light curves when the space it travels through has a non-uniform stress-energy density, and we label the result "curved spacetime". Note that light doesn't curve because it travels through curved spacetime - there's no actual motion through spacetime. You can draw worldlines in spacetime to represent the motion of light through space over time, but it doesn't move through spacetime.

You are actually reiterating a strawman: Relativity does not state that space moving inwards towards a black hole.

I know it doesn't, that's why I strongly object to the waterfall analogy. It's cargo-cult quackery, pop-science pseudoscience, etc etc.

No one is saying that the waterfall analogy means that black holes are waterfalls or that waterfalls are black holes ! The analogy is that measurements can act in the same manner, i.e. there is an event horizon

Again, it's a very misleading analogy. Sadly it featured on a BBC Horizon program last year. Note that an optical clock near the surface of a massive star runs slower than an optical clock near the surface of a minor star. But when light from both stars reaches you, it's travelling at the same speed. Think about it in the black hole context, and you'll perhaps appreciate that a better analogy would involve ice.

 

[sol invictus]

The waterfall is pop-science pseudoscience, and dressing it up as hydrodynamics doesn't change that one bit.

I know it doesn't, that's why I strongly object to the waterfall analogy. It's cargo-cult quackery, pop-science pseudoscience, etc etc.

Again, it's a very misleading analogy. Sadly it featured on a BBC Horizon program last year.

The truth is, it's an accurate analogy that captures many of the essential features of the problem.

As a perfect illustration of that, Farsight's confusions about clocks and the coordinate speed of light are completely transparent using this analogy. A "sound clock" - a device where a pulse of sound bounces back and forth between two sonically reflective surfaces, and each round trip is a "tick" of the clock's second hand - held in place at the river's sound horizon would take infinitely long to tick, because the sound can't make any progress upriver, and so never reaches the upstream reflector (if it's oriented across the current instead of up it, the sound will drift downstream past the horizon and never reflect back). So in coordinates based on such sound clocks, the coordinate speed of sound is zero at the sound horizon.

 

[Farsight]

The waterfall analogy is absolutely wrong, sol, and a travesty of relativity. Yes we can agree that sound is wavelike, and that when it's propagating through fast-moving water as you described there will indeed be a "sound horizon". But light is wavelike too, and it simply isn't propagating through fast moving space. This sonar web page shows how sound actually propagates underwater, and serves as a better basis for an analogy. The black hole equates to a region of water where the speed of sound slows to zero, and no echoes are returned.

As I was saying to RC, an optical clock near the surface of a massive star runs slower than an optical clock near the surface of a minor star. But when light from both stars reaches you, it's travelling at the same higher speed. Since the clock rates depend upon the coordinate speed of light, it's trivial to reason that the speed of a light beam increases when it's emitted vertically from the surface. The light beam doesn't slow down, it doesn't curve, and it doesn't fall back. You know full well that there is no waterfall of space at that location. Ergo it's then trivial to work out that a vertical light beam at the event horizon doesn't escape because its speed is zero.

 

[phunk]

The waterfall analogy is absolutely wrong, sol, and a travesty of relativity.

Nonsense. It's an analogy, it's not supposed to be exactly the same, it's supposed to be a different situation with something in common.

 

[sol invictus]

The waterfall analogy is absolutely wrong, sol, and a travesty of relativity.

You keep asserting that, but you seem to be incapable of providing any evidence. Here's a review of "acoustic black holes" by an expert on relativity: http://arxiv.org/abs/gr-qc/9712010. From the abstract:

The equation of motion for the velocity potential describing a sound wave is identical to that for a minimally coupled massless scalar field propagating in a (3+1)-dimensional Lorentzian geometry...This rather simple physical system is the basis underlying a deep and fruitful analogy between the black holes of Einstein gravity and supersonic fluid flows. Many results and definitions can be carried over directly from one system to another...exhibit the close relationship between the acoustic metric for the fluid flow surrounding a point sink and the Painleve-Gullstrand form of the Schwarzschild metric for a black hole.

Care to point out where the mistake is, Farsight?

 

[Farsight]

Nonsense. It's an analogy, it's not supposed to be exactly the same, it's supposed to be a different situation with something in common.

It's a nonsense analogy, phunk. Light doesn't curve because the sky is falling in. And light doesn't fail to get out of a black hole because it's sucking in space like some waterfall. Note that the physicist who featured on the Horizon program in the waterfall scene was Max Tegmark. Here's a sample of his work: http://arxiv.org/abs/0704.0646

"I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure".

 

[Farsight]

You keep asserting that, but you seem to be incapable of providing any evidence.

I've provided ample evidence previously in the form of optical clocks and the Shapiro delay. As you know the coordinate speed of light varies in a non-inertial reference frame such as the room you're in, and we can simplfy the optical clocks to parallel-mirror light clocks thus:

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The evidence is patent. There is no evidence however for the sky-falling-in waterfall scenario which is not in accord with general relativity.

Here's a review of "acoustic black holes" by an expert on relativity: http://arxiv.org/abs/gr-qc/9712010. From the abstract...

Care to point out where the mistake is, Farsight?

I'll repeat the abstract in full with comments.

It is a deceptively simple question to ask how acoustic disturbances propagate in a non-homogeneous flowing fluid.

It's even easier to ask how acoustic disturbances propagate in a non-homogeneous fluid which isn't flowing. Hence my sonar example.

This question can be answered by invoking the language of Lorentzian differential geometry: If the fluid is barotropic and inviscid, and the flow is irrotational (though possibly time dependent), then the equation of motion for the velocity potential describing a sound wave is identical to that for a minimally coupled massless scalar field propagating in a (3+1)-dimensional Lorentzian geometry.

A gravitational field has its self-energy, which has a mass equivalence, and it isn't propagating.

The acoustic metric governing the propagation of sound depends algebraically on the density, flow velocity, and local speed of sound.

Again it's simpler to omit the flow velocity and examine the acoustic metric using the density and the local speed of sound.

This rather simple physical system is the basis underlying a deep and fruitful analogy between the black holes of Einstein gravity and supersonic fluid flows.

See above. This "deep and fruitful" analogy is the wrong analogy. The right analogy would involve sound propagation in an inhomogeneous fluid, but a static fluid rather than one with a supersonic flow.

Many results and definitions can be carried over directly from one system to another. For example, I will show how to define the ergosphere, trapped regions, acoustic apparent horizon, and acoustic event horizon for a supersonic fluid flow, and will exhibit the close relationship between the acoustic metric for the fluid flow surrounding a point sink...

There simply is no spacetime flow as far as gravity is concerned, and no associated point sink.

...and the Painleve-Gullstrand form of the Schwarzschild metric for a black hole. This analysis can be used either to provide a concrete non-relativistic model for black hole physics, up to and including Hawking radiation

Painlevé-Gullstrand coordinates suffer from the same problem to Kruskal-Szekeres coordinates which we've discussed previously. See wiki and note where it says this: "The speed of the raindrop is inversely proportional to the square root of radius. At places very far away from the black hole, the speed is extremely small. As the raindrop plunges toward the black hold, the speed increases. At the event horizon, the speed has the value 1, same as the speed of light". Now look at what I was saying about light emitted from a massive star. The speed increases with radius. Hence the proposed model is not concrete, and nor I'm afraid is Hawking radiation, which is how our previous conversation got started.

or to provide a framework for attacking acoustics problems with the full power of Lorentzian differential geometry.

I have no issue with the sentence above.

 

[sol invictus]

I've provided ample evidence previously in the form of optical clocks and the Shapiro delay.

All of which hold true for sonic clocks and acoustic black holes as well. So, where's the problem?

Painlevé-Gullstrand coordinates suffer from the same problem to Kruskal-Szekeres coordinates which we've discussed previously.

You continue to fail to understand the single most basic aspect of general relativity - that its predictions are coordinate invariant. Coordinates are a human convention, and correct physical predictions can be made using any coordinate system.

Now, are you going to identify the problem with that paper? I'm not asking about the words in the abstract, I'm asking which calculation in that paper is wrong.

 

[Farsight]

Coordinates don't actually exist sol. Try to look past them at what's there, at how the light is moving. Think about what I said about light and the massive star instead of evading it.

As for the paper, you quoted part of the abstract, I quoted it all and gave my comments to point out the problem: space is not some inflowing fluid like the old luminiferous aether going down a bath plug. Surely that's enough? Surely you're not going to hide behind calculations now to try to defend this ludicrous waterfall? Come on sol, it isn't in line with relativity, I don't know why you give it the time of day. Stop digging with this one, because you're digging yourself into a hole.

 

[sol invictus]

As for the paper, you quoted part of the abstract, I quoted it all and gave my comments to point out the problem: space is not some inflowing fluid like the old luminiferous aether going down a bath plug. Surely that's enough?

Of course it's not enough. You asserted that the sonic analogue of black holes is "absolutely wrong". To support that, you simply added more assertions.

Instead, you need to either

(1) Identify a problem with the mathematics that shows that the equations governing sonic black holes are not in fact the same as those governing general relativistic black holes, or

(2) Identify a problem with the physics, namely an experiment (real or a thought experiment) which when conducted for sonic black holes gives different results than the analogous experiment conducted for real black holes.

You've done neither (1) nor (2).

This is a skeptic's forum, where you need to back up assertions with evidence. Thus far, you've failed completely.

 

[Mashuna]

Coordinates don't actually exist sol. Try to look past them at what's there, at how the light is moving. Think about what I said about light and the massive star instead of evading it.

As for the paper, you quoted part of the abstract, I quoted it all and gave my comments to point out the problem: space is not some inflowing fluid like the old luminiferous aether going down a bath plug. Surely that's enough? Surely you're not going to hide behind calculations now to try to defend this ludicrous waterfall? Come on sol, it isn't in line with relativity, I don't know why you give it the time of day. Stop digging with this one, because you're digging yourself into a hole.

I love how you use the term 'hiding behind calculations' as a pejorative here. It doesn't deflect from the fact that you hide from calculations at every opportunity.

 

[sol invictus]

I love how you use the term 'hiding behind calculations' as a pejorative here.

It's particularly entertaining considering that we're discussing physics that has never been tested by any experiment. Calculations are what we're talking about - every time Farsight refers to the "coordinate speed of light" or "experiments" with light clocks, he's referring to quantities that are calculated using the mathematics of general relativity.

One of the nice things about the sonic analogy is that the mathematics are (up to a point) identical, but one can actually do experiments with fluids and sound in the lab.

 

[Reality Check]

I know it doesn't, that's why I strongly object to the waterfall analogy. It's cargo-cult quackery, pop-science pseudoscience, etc etc.

You remain obviously ignorant of the waterfall anaolgy.
Its an anaolgy, anaolgy, etc etc.

 

[Reality Check]

Coordinates don't actually exist sol. Try to look past them at what's there, at how the light is moving.

Coordinates actually exist, Farsight. They are what observers use to measure with. But different coordintes will give different measurements.
That is the point of GR being expressed in coordinate free mathematics .


What GR shows (without coordinates) is that

• An external observer will observe a clock ticking slower and slower as it gets closer and closer to the event horizon.
• An external observer can never see a clock get to the event horizon.
• An observer with the clock will see it tick as normal as they pass through the event horizon.

 

[Almo]

Sol's analogy is a good one. Reality Check is busting out with the bullet-point lists, and we have one unconvinced person reiterating something. Looks like we have another Electric Sun thread brewing, though it has a long way to go before its magnitude is anything like that one.

 

[Farsight]

Of course it's not enough. You asserted that the sonic analogue of black holes is "absolutely wrong".

No I didn't. I gave a reference to sonar and said the flow aspect of it is wrong. And I've previously referred to The Other Meaning of Special Relativity by Robert Close who uses a sonic analogy.

To support that, you simply added more assertions. Instead, you need to either

(1) Identify a problem with the mathematics that shows that the equations governing sonic black holes are not in fact the same as those governing general relativistic black holes, or

(2) Identify a problem with the physics, namely an experiment (real or a thought experiment) which when conducted for sonic black holes gives different results than the analogous experiment conducted for real black holes.

You've done neither (1) nor (2).

But instead I've referred to real-world experiments and pointed out that the sky is not falling in. You're advancing specious pseudoscience that says it is, and taking cover behind mathematics.

This is a skeptic's forum, where you need to back up assertions with evidence. Thus far, you've failed completely.

I'm the one who's skeptical here. I've offered evidence, you haven't. I've given the evidence of the Shapiro delay and optical clocks which demonstrate that the coordinate speed of light varies:

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And we know that a light beam emitted vertically from a massive star does not slow down, does not fall back, and does not curve. We also know that the space around this star is not moving inwards towards the star, and that we can extend this scenario to the black hole situation. There is no waterfall!