Black holes

[edd]

I still feel like someone is threatening to bite my legs off.

 

[W.D.Clinger]

Farsight's declarations of victory

Time after time, Farsight has declared victory:

I'm the one cutting down quacks here sol.

Besides, nobody's listening to you any more anyway. Your credibility is shot to pot.

He's hiding behind mathematics because I whupped his ass in a physics discussion.

No, the onus is on you to explain yourself instead of trying to hide behind mathematical expressions where you won't define the terms and you won't give the scenario. I gave an honest answer, but all we get from you is pompous guff like clearly, you lack such basic knowledge. Pah, you're faking it. You won't give the scenario because you're afraid I'll rip it apart.

This is a class, sol, but I'm teaching you.

Huff puff, sol really doesn't like it when I explain the gravitational field with reference to Einstein. He behaves like a witchdoctor faced with a pharmacist, all outraged, saying "you don't understand it". Tough. I do.

I told you how it works. Get used to it. It isn't in your textbooks yet, but it will be.

I understand this sol, you don't.

It's cargo-cult science, and I will not permit it.

...snip...

I'm arguing for relativity. It's the sleeping beauty of contemporary physics. And I'm doing my bit for physics because this is important. More imporatant than you know. Must dash.

I'm not wrong about this RC. Note the ominous silence and the evasion from your "friends". They don't have the honesty to tell you that Actually, RC, Farsight is right about this.

I'm not confusing anything.

...snip...

I'm not conflating anything. It's all perfectly simple.

I understand it.

...snip...

And I'm not wrong. I would urge you to ask elsewhere to check what I'm saying. Then you'll understand something important about some of the other posters here.

My "claim" is correct.

Anyway, I think this thread has run its course guys. I hope you've found it useful, and that some of your have learned some physics.

Speaking of running a course, Rosie Ruiz^WP still says she won the Boston Marathon (women's division) in 1980.

No one can deny that Ruiz was the first woman to cross the finish line. Her finishing time of 2:31:56 was the third-fastest time ever run by a woman.

Unfortunately, Ruiz remembered very little of her race, including the course itself. No one else remembered seeing Ruiz either, until a couple of Harvard students said they saw Ruiz join the race just half a mile from the finish.

Thirty-two years later (to the day!), hardly anyone believes Rosie Ruiz. That's what comes of relying on your own authority when asserting victory.

Farsight hasn't crossed the finish line. He doesn't appear to have started the race either: He ignores relevant questions about his math and science background, but his mistakes strongly suggest he has never taken a course in first-year calculus or physics.

This thread is getting increasingly bizarre. It's just like talking to creationists.

It is exactly like trying to talk to a creationist.

Farsight reminds me of Michael Mozina:

This conversation is *EXACTLY* like arguing with creationists.

Yep, this is *EXACTLY* like arguing with creationists.

You're EXACTLY like arguing with a creationist that INSISTS "God did it" through some process that has absolutely NOTHING to do with "God".

Haters are like creationists.

In other words, just like any good creationist, you absolutely, positively refuse to provide ANY kind of published work to support your OUTRAGEOUS claims,

You keep handwaving away, attacking the individual, refusing to address my questions and acting like any good creationist.

It's really frustrating arguing with creationists and EU haters that refuse to educate themselves and that are too cheap and too lazy to read a related textbook. After awhile I guess I start shouting.

EU haters argue like creationists.

It's irrational absurd behavior on par with the very WORST type of denial based "creationist" beliefs.

Michael Mozina argued like that because he didn't know enough math and science to formulate a relevant argument. I assume that's why Farsight resorted to the same style of argument.

Are you for real? It isn't false, and it is connected to reality and math. Go and read up on a manifold.

As if Farsight telling us to read up on math weren't funny enough, he added this punch line:

Don't be facile. The reality of gravitational fields forbids all finite regions from being flat.

Yes, folks, Farsight said there is no such thing as flat spacetime.

Instead of citing himself or his own personal exegesis of Einstein as authority, Farsight cited "reality". That might have been more convincing had Farsight's declarations of victory shown greater familiarity with reality.

 

[CapelDodger]

In other words, the probability that the core of Relativity+ is true if the experiment observes photons is just the same as the original probability that the core of Relativity+ is true. In other words, the observation of photons is not evidence for the core of Relativity+.

So you guys aren't going to be hustling up a black-hole and throwing stuff into it after all? I'm off then, I only came in to watch that.

 

[Farsight]

After all this, your argument is defeated by a geodesic dome?

Not at all. The geodesic dome is an idiotic way of trying to say local regions are flat. Even a blind man can see that the curvature has been bundled into the infinitestimal intervening regions. Some of the other guys here know it, but won't let on because they're dishonest. For example Clinger knows it, but he won't address the issue and hurls ad-hominem abuse as a distraction instead. It's never been a particularly sincere discussion, but now it's gone totally downhill so there's no mileage in continuing it.

 

[sol invictus]

Not at all. The geodesic dome is an idiotic way of trying to say local regions are flat. Even a blind man can see that the curvature has been bundled into the infinitestimal intervening regions. Some of the other guys here know it, but won't let on because they're dishonest. For example Clinger knows it, but he won't address the issue and hurls ad-hominem abuse as a distraction instead. It's never been a particularly sincere discussion, but now it's gone totally downhill so there's no mileage in continuing it.

You asserted: "If your manifold is exactly flat locally in a region that is other than infinitesimal, it's exactly flat globally."

A geodesic dome (or a cube) is exactly flat locally in a region that isn't infinitesimal, but it's not exactly flat globally, because it has curvature at the vertices.

Indeed, now you're admitting that "Even a blind man can see that the curvature has been bundled into the infinitestimal intervening regions."

You were wrong, and I think even you know it. Admit it, learn from it, and move on. Can you do that?

 

[ctamblyn]

So you guys aren't going to be hustling up a black-hole and throwing stuff into it after all? I'm off then, I only came in to watch that.

Sorry about that. I was all up for it, but my grant application was turned down

 

[Farsight]

Sadly, ct, there where the whole of physics is heading. I'm trying to head it off at the pass, but hey, it's a tough old job.

You asserted: "If your manifold is exactly flat locally in a region that is other than infinitesimal, it's exactly flat globally." A geodesic dome (or a cube) is exactly flat locally in a region that isn't infinitesimal, but it's not exactly flat globally, because it has curvature at the vertices.

Yep. But there aren't any creases in space, sol. Ever seen a gravitational field with an abrupt discontinuity in it. Er, no.

You were wrong, and I think even you know it. Admit it, learn from it, and move on. Can you do that?

I wasn't wrong. I was right. The geodesic dome analogy for a gravitational field is garbage, so is your waterfall chicken-little sky's falling in. And you're a busted flush with your reputation in tatters. You might huff and puff and pretend otherwise, but it's too late sol, the game is up. Have a nice day.

FFS, where do they get these people?

 

[edd]

I'm bordering on seeing a point about the actual geometry of space time in the messy universe we live in but I've completely lost what significance it has in the broader argument and still think Farsight lost this argument long before he even got as far as perversely thinking he'd won it.

 

[sol invictus]

You asserted: "If your manifold is exactly flat locally in a region that is other than infinitesimal, it's exactly flat globally." A geodesic dome (or a cube) is exactly flat locally in a region that isn't infinitesimal, but it's not exactly flat globally, because it has curvature at the vertices.

Yep.

Good - so you're finally admitting you were wrong.

I wasn't wrong. I was right. The geodesic dome analogy for a gravitational field is garbage

Nope, I guess not....

You said: "If your manifold is exactly flat locally in a region that is other than infinitesimal, it's exactly flat globally" and "Go and read up on a manifold". No qualifiers, no "Or at least I've never seen one". Nothing about analogies to gravity (which don't help anyway, since there are plenty of solutions to GR that prove you wrong).

When we gave you explicit counterexamples - simple manifolds (like geodesic domes and cubes), and simple configurations in GR (spherically symmetric shells of stress-energy), you still insisted you were right.

Now you're explicitly contradicting your earlier assertion by acknowledging that geodesic domes are globally but not locally curved. But instead of admitting your mistake like an honest person, you're squirming and lying and and trying to pretend you were talking about realistic gravity fields all along, or something.

All you're doing is further undermining your credibility, Farsight - if that's possible.

 

[Farsight]

Oh sol, gravitational fields do not have creases. Stop digging.

I'm bordering on seeing a point about the actual geometry of space time in the messy universe we live in but I've completely lost what significance it has in the broader argument and still think Farsight lost this argument long before he even got as far as perversely thinking he'd won it.

I won it edd. The argument was about the nature of black holes, and whether space is falling inwards in a gravitational field. It isn't.

See this thread and look at post 344 where Vorpal talks about pressure. There's "spatial pressure" around a gravitating body, and it reduces with distance broadly in line with the inverse square rule. It isn't infalling space around a black hole, it's a pressure gradient in space. The upturned hat on the wiki gravitational potential page and all those rubber-sheet depictions plot this pressure gradient, the curvature you can see being the Riemann curvature.

 

[Reality Check]

It's still garbage RC.

Wrong - it is still a demonstartion of your inability to understand GR and a simple analogy.

You labor under the delusion that each of the flat patches of a geodesic dome in the analogy is

• Oriented to be paralell to an imaginary plane.
• And (maybe) has moved to be actually on that plane.
• Thus the entire dome is flat.

Anyone who has seen a geodesic dome knows that

• Each patch is locally flat without any reference to an external space, e.g. draw a triangle in the patch and it's internal angles will sum up to 180 degrees.
• The dome is globally curved. Draw a triangle that covers multiple patches and and it's internal angles will not sum up to 180 degrees.

That is what happens in GR. A manifold is made up of "patches". Each patch is intrinsically Minkowskian ("flat"). The mathematical statement of this looks like "A manifold M with affine connection is said to be locally flat if for every point p in M there is a chart (U; x^i) with such that all the components of the connection vanish throughout U. This implies of course both torsion tensor and curvature tensor vanish throughout U, ..." (Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry by Peter Szekere). Here a chart is one of the patches we have been talking about.

Spacetime remains curved despite the local "flatness" because the curvature is global.

 

[Reality Check]

A geodesic dome (or a cube) is exactly flat locally in a region that isn't infinitesimal, but it's not exactly flat globally, because it has curvature at the vertices.

Given Farsight's inability to understand this simple point about geodesic domes or cubes, should we tell him about the standard example of cones where all of the curvature is at the vertex?

FYI, Farsight: Curvature for a cone is given as an example in GR classes because it is easy to visualize. The first thing to realize is that a cone is equivalent to a plane with a slice cut out of it so you can flatten out a cone into a plane by making a cut from the vertex.
Lecturers introduce the concept of parallel transport. Basically this is a manifold equipped with way of moving a tangent vector defined at one point along a path. This path can return to the original point, i.e. a closed path. The question then becomes: Is the transported vector the same as the original vector?

The answer is that it depends!
Consider the cone and a closed path that encloses the vertex. That means that the path has to jump across the slice in the equivalent plane representation. On each side of the slice the tangent vector will point at the vertex but it's direction will change. Thus the transported vector is different from the original vector for a closed path that encloses the vertex.
Consider the cone and a closed path that excludes the vertex. The transported and original vectors are the same.
Any change in the tangent vector is interpreted as curvature, e.g. the steeper the sides of the cone, the wider the slice and the larger the curvature.

Thus a cone has global curvature but is locally flat. Global means that you consider every single bit of the cone including the vertex. Local means a neighbourhood of a point. In the case of a cone it is any neighbourhood that does not include the vertex.

 

[Reality Check]

Oh sol, gravitational fields do not have creases.

Oh, Farsight - the fact that cones have all of their curvature at the vertex will then really blow your mind !

No one here is stating that the analogies of geodesic domes and cubes (or even the cone example) are used in GR. What is used in GR is Riemannian geometry.
There are no "creases" in Riemannian geometry. AFAIK the Riemannian manifolds explicitly exclude "creases" since the overlap between each chart has a mapping function that is smooth (infinitely differentiable). A "crease" would give a delta (or step?) function on the first differentiation and be undefined on further differentiation.

 

[sol invictus]

Oh sol, gravitational fields do not have creases. Stop digging.

It's all right there in black and white for anyone to read, Farsight - you made false assertions, you arrogantly defended them, now you're directly contradicting your own previous assertions while denying you're doing so and declaring victory.

What's next? Are you going to bite our ankles?

 

[W.D.Clinger]

That is what happens in GR. A manifold is made up of "patches". Each patch is intrinsically Minkowskian ("flat"). The mathematical statement of this looks like "A manifold M with affine connection is said to be locally flat if for every point p in M there is a chart (U; x^i) with such that all the components of the connection vanish throughout U. This implies of course both torsion tensor and curvature tensor vanish throughout U, ..." (Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry by Peter Szekere).

Szekeres's definition is incompatible with the definition most of us have been using in this thread. According to Szekeres's definition, a geodesic dome is not locally flat because the curvature tensor, being a tensor, is independent of the chart (coordinate system). If the curvature tensor vanishes throughout a chart U, then the curvature tensor will vanish throughout the intersection of U with every chart that intersects U. Since the full atlas of charts must cover every point of the space, the curvature tensor must vanish at every point of the space, from which it follows that the space is globally flat.

It doesn't make much sense for Szekeres to define local flatness in such a way that local flatness is equivalent to global flatness, so I suspect that Szekeres made a mistake in his definition. Can you provide a more specific citation and/or context?

Within this thread, I believe that most of us have been using "locally flat" to mean "locally Minkowskian" in the sense that, for every point p, there exists a chart (coordinate system) defined on an open neighborhood of p for which the chart-dependent components of the metric at p coincide with the familiar components of the Minkowski metric of special relativity.

As Einstein remarked in §4 of "The Foundation of the General Theory of Relativity", it is not always possible to choose a chart (coordinate system) in which the metric takes that special form for a finite neighborhood around p.

Oh, Farsight - the fact that cones have all of their curvature at the vertex will then really blow your mind !

Which implies that the curvature tensor cannot be made to vanish at the vertex, which means the cone with vertex is not locally flat by the definition you attributed to Szekeres.

This entire discussion of locally flat manifolds is a bit of a sideshow, which we're pursuing only because Farsight dug himself such a deep hole and is still digging. The subject came up when Farsight was contradicting Einstein by denying the possibility of a nonzero gravitational field in flat spacetime:

You're lying, as Clinger already pointed out:

Farsight: "When spacetime is flat, no gravitational field is present."
Einstein: "the Γ^τ_μν...are the components of the gravitational field."

Γ^τ_μν is non-zero even in flat spacetime in some (actually, almost all) coordinate systems - for instance, the coordinates I've been asking you about all this time.

...snip...

You were wrong. Admit it, learn from it, move on. Can you do that?

You're completely wrong, not just about the physics, but about what Einstein said (in 1920 and at other times)....

According to Einstein gravity can exist even in perfectly flat, homogeneous spacetime. You're directly contradicting what Einstein said in 1920, Farsight....

According to Einstein, rays of light curve in perfectly flat spacetime when viewed from accelerated reference frames, because acceleration is gravity and light curves in response to gravity. Wrong again, Farsight.

Saying that it isn't a "real" gravitational field directly and explicitly contradicts Einstein, Farsight. Yes, it's true that in flat spacetime one can choose coordinates in which there is no gravitational field. But it's also true that one can choose coordinates in which there is one, just as he says....

You're wrong. Accept it, learn from it, move on.

The "locally" qualifier seems to have been brought up by ctamblyn:

The principle of equivalence - understood correctly - is indeed exact. Saying "it's a principle" as though it were only meant as an approximation or guideline is laughable. In GR, spacetime is locally Lorentzian flat, and as far as the clocks in my thought-experiment go, the deviations we expect due to tidal forces can be made negligible with an appropriate experimental setup.

That's entirely true, but Farsight took issue with it:

I'd like to say I'm astonished that Farsight has equated local flatness and global flatness... but I'm not.

After Reality Check mentioned a geodesic dome, Farsight wrote:

Aaagh! That only happens in an infinitesimal region. The locally flat region has zero extent!

That's what mathematicians refer to as a howler, but it's a bit too subtle for people who don't understand quantifier alternation to appreciate. For any particular point p, the locally flat coordinates at p are Minkowskian only for an infinitesimal region, but there's a locally flat coordinate system at every point p. Hence the "locally flat region" of the manifold consists of the entire manifold.

Farsight followed up with this howler, which isn't subtle at all:

If your manifold is exactly flat locally in a region that is other than infinitesimal, it's exactly flat globally. It's like saying this part of the surface of the earth is exactly flat. Absolutely utterly flat. And the next part, and the next, and all other parts. Then the surface of the earth isn't a sphere any more, it's a flat plane. It isn't curved at all.

That's just laughable, which is why we've been laughing.

It also contradicts Einstein rather dramatically, because Einstein discussed the possibility that "the special theory of relativity holds good for a finite region of the continuum" (italics in the original), and used that as the motivation for his equation of motion in spacetimes that aren't necessarily flat:

[latex]
\[
\frac{d^2 x_\tau}{d s^2} = \Gamma^{\tau}_{\mu\nu}
\frac{d x_{\mu}}{ds} \frac{d x_{\nu}}{ds}
\hbox{\hspace{24pt}(46)}
\]
[/latex]​

That's in Einstein's §13, which ends with the definition of a gravitational field that Farsight's been denying throughout this thread:

http://www.internationalskeptics.com/forums/showpost.php?p=8188847&postcount=1034
http://www.internationalskeptics.com/forums/showpost.php?p=8194020&postcount=1066
http://www.internationalskeptics.com/forums/showpost.php?p=8194113&postcount=1067
http://www.internationalskeptics.com/forums/showpost.php?p=8201601&postcount=1083
http://www.internationalskeptics.com/forums/showpost.php?p=8213442&postcount=1134
​

As sol invictus posted while I was writing the above:

It's all right there in black and white for anyone to read, Farsight - you made false assertions, you arrogantly defended them, now you're directly contradicting your own previous assertions while denying you're doing so and declaring victory.

What's next? Are you going to bite our ankles?

 

[Reality Check]

It doesn't make much sense for Szekeres to define local flatness in such a way that local flatness is equivalent to global flatness, so I suspect that Szekeres made a mistake in his definition. Can you provide a more specific citation and/or context?

The quote from Szekeres was from another forum. It looked reasonable according to my limited knowledge of the mathematics but I suspect there are more details hidden in the ellipsis.

 

[Farsight]

It's all right there in black and white for anyone to read, Farsight - you made false assertions, you arrogantly defended them, now you're directly contradicting your own previous assertions while denying you're doing so and declaring victory. What's next? Are you going to bite our ankles?

No I did nothing of the sort. I said a gravitational field was only flat in an infinitesimal region. Then RC tried to say I was wrong by likening it to a geodesic dome where finite regions are truly flat and the Riemann curvature is bundled into the place where two flat regions meet. It's garbage and you know it, and your howls of outraged accusation don't conceal that it's garbage.

 

[Farsight]

Wrong - it is still a demonstration of your inability to understand GR and a simple analogy.

No it isn't. It's a demonstration of your inability to understand GR and a simple analogy.

You labor under the delusion that each of the flat patches of a geodesic dome in the analogy is

• Oriented to be paralell to an imaginary plane.
• And (maybe) has moved to be actually on that plane.
• Thus the entire dome is flat.

Anyone who has seen a geodesic dome knows that

• Each patch is locally flat without any reference to an external space, e.g. draw a triangle in the patch and it's internal angles will sum up to 180 degrees.
• The dome is globally curved. Draw a triangle that covers multiple patches and and it's internal angles will not sum up to 180 degrees.

It's garbage RC. Go and look at a gravitational field. It isn't plated with little flat patches. It's curved.

That is what happens in GR. A manifold is made up of "patches". Each patch is intrinsically Minkowskian ("flat"). The mathematical statement of this looks like "A manifold M with affine connection is said to be locally flat if for every point p in M there is a chart (U; x^i) with such that all the components of the connection vanish throughout U. This implies of course both torsion tensor and curvature tensor vanish throughout U, ..." (Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry by Peter Szekere). Here a chart is one of the patches we have been talking about.

And each patch is infinitesimal in extent!

Spacetime remains curved despite the local "flatness" because the curvature is global.

No, it's because the local flatness is only an approximation. It isn't actually flat. It's just so nearly flat that you can't detect the curvature that's there. Come on RC, think it through. You're in a room and you measure g to be 9.8 m/s at both the floor and at the ceiling. What do think happens when you go upstairs? Do you think you measure g to be 9.799999 m/s at both the floor and ceiling? And then when you go upstairs again do you think you measure g to be 9.799998 m/s at both the floor and ceiling? No way. That's the equivalent of your geodesic dome, and it's garbage.

 

[Farsight]

Given Farsight's inability to understand this simple point about geodesic domes or cubes, should we tell him about the standard example of cones where all of the curvature is at the vertex?

Tell me anything you like. Take a vertical slice through the cone and what you've got is this: V. That's locally flat rather than curved. But gravitational fields aren't like that. The force of gravity diminishes with distance. The gradient diminishes. It isn't constant like in the / on one side of the V which is a slice through the cone.

FYI, Farsight: Curvature for a cone is given as an example in GR classes because it is easy to visualize.

It's the wrong example. And the upturned-hat plot of gravitational potential is easy to visualise anyhow, plus it matches the ubiquitous rubber-sheet depictions of curved spacetime.

The first thing to realize is that a cone is equivalent to a plane with a slice cut out of it so you can flatten out a cone into a plane by making a cut from the vertex.

Tell me something I don't know.

Lecturers introduce the concept of parallel transport. Basically this is a manifold equipped with way of moving a tangent vector defined at one point along a path. This path can return to the original point, i.e. a closed path. The question then becomes: Is the transported vector the same as the original vector? The answer is that it depends! Consider the cone and a closed path that encloses the vertex. That means that the path has to jump across the slice in the equivalent plane representation. On each side of the slice the tangent vector will point at the vertex but it's direction will change. Thus the transported vector is different from the original vector for a closed path that encloses the vertex.

Forget the vertex. It's irrelevant to this discussion. And don't try to put up a smokescreen, because it won't do you any good.

Consider the cone and a closed path that excludes the vertex. The transported and original vectors are the same.
Any change in the tangent vector is interpreted as curvature, e.g. the steeper the sides of the cone, the wider the slice and the larger the curvature. Thus a cone has global curvature but is locally flat. Global means that you consider every single bit of the cone including the vertex. Local means a neighbourhood of a point. In the case of a cone it is any neighbourhood that does not include the vertex.

Only gravitational fields aren't cones. They have Riemann curvature. Because of the inverse square rule. If they were cones the vertex is inaccessible and irrelevant in the centre of the gravitating body, and the force of gravity due to that body doesn't diminish with distance. Instead gravitational fields are like flared bells. Or like curvy upturned hats with a wide brim. They aren't like dunces hats. How much simpler do I have to I make this before you stop embarrassing yourself?

 

[edd]

No I did nothing of the sort. I said a gravitational field was only flat in an infinitesimal region. Then RC tried to say I was wrong by likening it to a geodesic dome where finite regions are truly flat and the Riemann curvature is bundled into the place where two flat regions meet. It's garbage and you know it, and your howls of outraged accusation don't conceal that it's garbage.

Where two flat regions meet? I'm not sure about that.