Black holes

[Farsight]

And you still don't understand the fire structure constant.

I understand the fine structure constant. I said something about it here. But OK, hands up, you got me. I don't understand the fire structure constant. LOL!

 

[Farsight]

That's one expression for the metric of flat spacetime. Sol gave you another one, which you couldn't handle.

I talked about it, Sol wouldn't say what it described. He kept hiding behind a "flat spacetime" non-answer and refused to explain his terms.

Who is this "everybody" you keep referring to? Because pretty much all the actual people posting here are on DRD's side, not yours. Unless you did some sort of psychic survey of all the lurkers here, in which case you could qualify for a million dollars.

Slip of the tongue. Don't sweat it Ziggy.

 

[ben m]

I talked about it, Sol wouldn't say what it described. He kept hiding behind a "flat spacetime" non-answer and refused to explain his terms.

It never crossed your mind that Sol might have given a perfectly complete explanation, and that you don't have enough differential-geometry training to understand it.

Why not?

 

[Ziggurat]

I talked about it, Sol wouldn't say what it described. He kept hiding behind a "flat spacetime" non-answer and refused to explain his terms.

He told you exactly what it describes. It describes the exact same space that your metric describes, just with different coordinates.

Slip of the tongue. Don't sweat it Ziggy.

It wasn't a slip of the tongue. Your meaning was quite clear: you think that an objective reader will side with you over DRD. Only... nobody seems to be doing that. Doesn't that make you at all curious? Even if we assume you're right about everything, isn't it strange that you can't convince anyone? Why are you unable to effectively communicate your ideas?

 

[ben m]

He told you exactly what it describes. It describes the exact same space that your metric describes, just with different coordinates.

I think what Farsight is waiting for is for Sol to draw him a little picture of the coordinates. "OK, t is the time axis, and x represents distance from the black hole on an inverse-log ruler, y is the Cartesian y axis ..." In other words, he's thinking of it like high-school geometry, where, when they introduce polar coordinates, they draw you a little picture. "theta measures angle around the origin, r measures distance away from it."

Because that's the only way he has ever thought about coordinates. He has no idea what you learn from the metric alone. So he assumes it's Sol's fault that he (Farsight) doesn't know what to do next.

 

[sol invictus]

I talked about it, Sol wouldn't say what it described. He kept hiding behind a "flat spacetime" non-answer and refused to explain his terms.

What "terms" did you want me to explain?

I gave you the metric using an absolutely standard notation that anyone with basic knowledge of general relativity or differential geometry would understand. Clearly, you lack such basic knowledge - in which case the onus is entirely on you to try to learn it.

 

[Farsight]

It never crossed your mind that Sol might have given a perfectly complete explanation, and that you don't have enough differential-geometry training to understand it. Why not?

It did, I checked, and he didn't. I gave my straight answer on page 8 in post #317. I said "I have to say no, I don't know what it describes. I set rₒ to zero and said r²/r is the x term, a spatial distance, but that leaves me with a delta x rather than delta x², and an r multiplier on the delta -t². If go to the other limit and say r=rₒ I'm left with a zero delta -t² indicating travel at c and a division by zero giving me an undefined delta x akin to total length contraction, but I still can't give a positive answer". Sol did not respond in kind, and he's been ducking and diving ever since. He won't say what the interval is, what the expression relates to, and he won't say what r is. All he's said is it describes flat spacetime which is academic since spacetime around a black hole just isn't flat. He's hiding behind mathematics because I whupped his ass in a physics discussion. Kinda sad really, but such is life.

 

[sol invictus]

I set rₒ to zero and said r²/r is the x term, a spatial distance, but that leaves me with a delta x rather than delta x², and an r multiplier on the delta -t². If go to the other limit and say r=rₒ I'm left with a zero delta -t² indicating travel at c and a division by zero giving me an undefined delta x akin to total length contraction, but I still can't give a positive answer".[/i] Sol did not respond in kind

That's because what you said is complete nonsense. It simply shows that you haven't a clue what the notation means or how to manipulate it - in other words, that you don't understand GR or differential geometry.

He won't say what the interval is, what the expression relates to, and he won't say what r is.

It's called a metric, Farsight. It's the most fundamental object in GR. IF you have questions about basic differential geometry, you can go ahead and ask. But you won't, because you're not actually interested in learning anything - you're interested in pretending you know what you're talking about.

All he's said is it describes flat spacetime which is academic since spacetime around a black hole just isn't flat. He's hiding behind mathematics because I whupped his ass in a physics discussion. Kinda sad really, but such is life.

In fact, it proves that your logic is flat-out wrong. That metric exhibits all the features you used to argue that weird things happen on a black hole horizon - but it's not a black hole, and nothing weird can happen on its horizon.

 

[Farsight]

What "terms" did you want me to explain?

The r terms. Here's the standard expression for an invariant interval in flat Minkowski spacetime:

[latex]$ds^2 = -dt^2 + dx^2 + dy^2 + dz^2$[/latex]

which as I explained in post #957 and previously, we can relate to our parallel mirrors via Pythagoras' theorem. I described the real-world scenario that this expression relates to, I put it in context and I explained why this expression holds good. Now here's your expression:

[latex]$ds^2 = -(r-r_0) dt^2 + dr^2/(r-r_0) + dy^2 + dz^2$[/latex]

We now have an r-rₒ as a multiplier on the t term and a divisor on the x term, x being synonymous with r. Why? And what scenario does this expression represent? You won't say, all you will say is flat spacetime and it just isn't good enough. Especially when spacetime around a black hole isn't flat.

I gave you the metric using an absolutely standard notation that anyone with basic knowledge of general relativity or differential geometry would understand. Clearly, you lack such basic knowledge - in which case the onus is entirely on you to try to learn it.

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.

 

[sol invictus]

The r terms. Here's the standard expression for an invariant interval in flat Minkowski spacetime:

[latex]$ds^2 = -dt^2 + dx^2 + dy^2 + dz^2$[/latex]

which as I explained in post #957 and previously, we can relate to our parallel mirrors via Pythagoras' theorem. I described the real-world scenario that this expression relates to, I put it in context and I explained why this expression holds good. Now here's your expression:

[latex]$ds^2 = -(r-r_0) dt^2 + dr^2/(r-r_0) + dy^2 + dz^2$[/latex]

We now have an r-rₒ as a multiplier on the t term and a divisor on the x term, x being synonymous with r. Why?

x is not "synonymous" with r, they are different coordinates. And the "t" in my expression isn't the same as the "t" in the Minkowski metric.

I could give you the explicit coordinate transformations from one to the other - or, with basic knowledge of differential geometry, you could work them out for yourself.

And what scenario does this expression represent? You won't say, all you will say is flat spacetime and it just isn't good enough.

Of course it's good enough.

You might ask a different question - what does constant r correspond to in Minkowski coordinates, for example. The answer is that a trajectory at constant r and varying t is a trajectory that undergoes constant proper acceleration (an accelerometer held at constant r would read a constant, non-zero value in the r direction - just like one held at constant r in the Schwarzschild spacetime).

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 isn't a class, Farsight, and you're not paying me. Why should I teach you basic GR, especially with your attitude?

 

[DeiRenDopa]

I thought you were ignoring me, Farsight?

...Slowly it dawned on me that Farsight hasn't got a quantitative clue about his belovéd pair of parallel-mirror light clocks.

And if he hasn't got a quantitative clue about that, then there's no basis for having a meaningful, physics-based, discussion with him.

But I'm open minded; if Farsight can show that he does have a quantitative clue, I will gladly eat my hat.

Are you for real? Do you really think you can get away with ad-hominems like that when I've already been through this? It's kid's stuff. The expression for a spacetime interval in flat Minkowski spacetime is this:

[latex]$ds^2 = -dt^2 + dx^2 + dy^2 + dz^2$[/latex]

It's related to Pythagoras' theorem, used in the Simple inference of time dilation due to relative velocity. We've got two parallel-mirror light clocks, one in front of us, the other which we've sent on an out-and -back trip. We observe the light moving like this ǁ in the local clock and like this /\ in the moving clock. Treat one side of the angled path as a right-angled triangle and the hypotenuse is the lightpath where c=1 in natural units, the base is the speed v as a fraction of c, and the height gives the Lorentz factor γ = 1/√(1-v²/c²), where we apply a reciprocal to distinguish length contraction from time dilation. So if the moving mirror os going at .99c the Lorentz factor is 1/√(1-0.99²/1²) = 1/√(1-0.98) = 1/√0.2 = 1/0.142 = 7. So there's a sevenfold time dilation. And as I've said previously there's no literal time flowing in these clocks, merely light moving at a uniform rate through the space of the universe, from which we plot straight worldlines through the abstract mathematical space we call Minkowski spacetime. And the underlying reality behind the invariant spacetime interval between the start and end events of our little experiment is that the two light-path lengths are the same. Macroscopic motion comes at the cost of a reduced local rate of motion. Hence the minus in front of the t.

Zig, ben, and sol have already commented on this, pointing out that GR is built on differential geometry.

In that context, 'having a quantitative clue' means understanding enough about differential geometry and how it's used in GR to be able to do coordinate transforms (for example). As the compendium of your posts which W.D.Clinger put together clearly shows, you understand neither*.

'Having a quantitative clue' also means being able to put cold, hard numbers on your belovéd parallel-mirror light clocks diagrams, and so show - in a world with observers who see using ordinary light - how the lower train always explodes before the upper train, and where to put the superhighspeed gedanken camera (not to mention describing - quantitatively - the misted chamber). Care to point to any post, by you, in which you cloth your belovéd in raiments of finest silk numbers?

If you'd slipped up once, maybe twice, on this, your readers here might be prepared to give you the benefit of the doubt; however, when you continue, page after dreary page, to fail to demonstrate 'having a quantitative clue', it would surely be irrational to conclude that the objective evidence is wrong, wouldn't it?

But I'm open minded; if Farsight can show that he does have a quantitative clue, I will gladly eat my hat.

No you won't, you'll just change tack and throw out some other vacuous thread-spoiler ad-hominems, and everybody will see through you. They'll be reminded again that there's no basis for having a meaningful, physics-based, discussion with you.

As Zig said, don't you find it the least bit odd that no one else who's commented on my posts, in this thread, seems to agree with you?

Further, if you do your own research - and read up on some of my JREF posts in other threads, for example - I think you'll find that the only other person who has ever agreed with you (in the broadest sense) is Michael Mozina (see this thread, for example).

Lastly, what's the phrase the mods here use, all too often? Something like 'address the argument, not the arguer'?

* here's a later post which shows yet another aspect of Farsight's misunderstanding (I'm quoting only part of it):

We don't often see an entire sequence of own goals being celebrated with such exuberance.

Oooh, Clinger is slinging mud. I like it when people who have no counterargument do that. It just makes them look stupid and vindictive and bitter. And yawn, Dopa is boring his imaginary audience to death again.

It isn't a question of believing Einstein.

It isn't about believing Einstein. It's about understanding Einstein, working through the mathematical consequences of his theory of general relativity, and comparing those mathematical consequences to experiment.

Farsight has done none of those things.

Throughout this thread, Farsight has been denying what Einstein called "the general postulate of relativity". In what follows, I'll quote from Einstein's 1916 paper on "The Foundation of the General Theory of Relativity", highlighting some of Einstein's words that Farsight's been ignoring or denying.

 

[ben m]

The r terms. Here's the standard expression for an invariant interval in flat Minkowski spacetime:

[latex]$ds^2 = -dt^2 + dx^2 + dy^2 + dz^2$[/latex]

It's possible to lay down a network of arbitrary labels "t,x,y,z", identifying points in spacetime, such that the above equation correctly computes the proper distance ds between two points, using only the coordinate labels.

[latex]$ds^2 = -(r-r_0) dt^2 + dr^2/(r-r_0) + dy^2 + dz^2$[/latex]

It's also possible to lay down a network of arbitrary labels "r,t,y,z", identifying points in spacetime, such that the above equation correctly computes the proper distance between points, using only the coordinate labels.

That's quite literally everything you need to know. For example, if you want to know the curvature of the spacetime labeled by these coordinates, you apply your knowledge of differential geometry. This is done in (since I have it on hand) MTW, page 340, under the subheading "Straightforward curvature calculation."

The elementary and universally applicable method for computing the components R^mu_{nu alpha beta} of the Riemann curvature tensor starts from the metric components g_{mu nu} in a coordinate basis ... to compute the curvature by the standard method, use the formula for ds^2 as a table of g_{k l} values.

You find, by such plug-and-chug manipulations, that it's impossible for Sol's expression to be true in non-flat spacetime. In non-flat space, it's impossible to invent an r,y,z,t coordinate-labeling system for which Sol's equations yields actual intervals. In flat space it *is* possible, and by writing down the metric Sol has effectively done so.

(ETA: actually entering this plug-and-chug into Mathematica took about five minutes. Fun! It's currently spitting out nonzero curvature, but I have no intention of proofreading all of those index-contractions to figure it out ...)

 

[Farsight]

I thought you were ignoring me, Farsight?

I am. I was just proving that Farsight has got a quantitative clue about his belovéd pair of parallel-mirror light clocks. And that you wouldn't eat your hat. Thanks for the confirmation.

...You find, by such plug-and-chug manipulations, that it's impossible for Sol's expression to be true in non-flat spacetime. In non-flat space, it's impossible to invent an r,y,z,t coordinate-labeling system for which Sol's equations yields actual intervals. In flat space it *is* possible, and by writing down the metric Sol has effectively done so.

You've said nothing as usual, apart from showing that you don't know the difference between spacetime and space.

x is not "synonymous" with r, they are different coordinates. And the "t" in my expression isn't the same as the "t" in the Minkowski metric...

Huff puff, you're faking it.

The answer is that a trajectory at constant r and varying t is a trajectory that undergoes constant proper acceleration (an accelerometer held at constant r would read a constant, non-zero value in the r direction - just like one held at constant r in the Schwarzschild spacetime).

Only there's no event horizon trailing behind the object being accelerated. See it zooming through the sky? Yep. See that black curtain behind it blotting out the stars? Er, no.

This isn't a class, Farsight, and you're not paying me. Why should I teach you basic GR, especially with your attitude?

This is a class, sol, but I'm teaching you. One lesson you've learned is not to warble on about the waterfall of infalling space, because it totally contradicts GR. What you've yet to learn is why the light can't get out. But hey, we'll get there.

 

[Farsight]

I have to go now, and I have something on this weekend, so I might not be able to talk much.

Happy Easter everybody.

 

[sol invictus]

Only there's no event horizon trailing behind the object being accelerated.

If you knew how, you could calculate the null geodesics of the metric I gave you and discover that light that originates from r<r0 will never reach an object at r>r0 - just as in a Schwarzschild black hole. But you haven't a clue how to do that, do you? Let alone what it means.

This is a class, sol, but I'm teaching you. One lesson you've learned is not to warble on about the waterfall of infalling space, because it totally contradicts GR. What you've yet to learn is why the light can't get out. But hey, we'll get there.

I'm curious - who do you think you're fooling with these comments? They just make you look ridiculous. I could ask when you're going to get around to identifying the mistake in Visser's math, but I won't bother - you couldn't possibly find one even if it was there. You don't know enough math to balance a checkbook.

 

[DeiRenDopa]

I thought you were ignoring me, Farsight?

I am. I was just proving that Farsight has got a quantitative clue about his belovéd pair of parallel-mirror light clocks. And that you wouldn't eat your hat. Thanks for the confirmation.

Is it just me?

Or is this sort of language eerily reminiscent of MM?

 

[ben m]

I'm curious - who do you think you're fooling with these comments?

"The first principle is that you must not fool yourself, and you are the easiest person to fool." --Feynman

 

[ben m]

Or is this sort of language eerily reminiscent of MM?

I wouldn't isolate Mozina in particular; I think it's a pretty common crackpot delusion. Anyone remember Singularitarian?

http://www.internationalskeptics.com/forums/showthread.php?t=148751

 

[edd]

Only there's no event horizon trailing behind the object being accelerated. See it zooming through the sky? Yep. See that black curtain behind it blotting out the stars? Er, no.

I can't grasp why you are allowed to talk about event horizons this way (as something physical, not just talking about them incorrectly I mean) when you don't want us to talk about light cones (as an example) in the same way.

There's other things I should probably say about your recent posts but my brain seems to have some kind of kernel panic when I attempt to formulate them.

 

[W.D.Clinger]

We don't often see a player celebrate his sequence of own goals with such enthusiasm.

LOL! Talk about evasion. Do you really think you can get away with slippery mathematics greased with abuse? Here, have another go. Redeem yourself.

Einstein said the mathematics we're using is required (nötigen) for general relativity.

It wouldn't be wrong, it would just be that Lorentz invariance wouldn't be absolute. It's no big deal. The principle of equivalence isn't absolute, that doesn't make relativity wrong.

He's lost in maths edd. And he's trying to bamboozle you with it while evading the scientific evidence.

Einstein said the mathematics we're using is required (nötigen) for general relativity.

It's Emperor's New Clothes Ed. You've been bamboozled, and jokes apart, there is psychology at work here. Try giving a blow-by-blow explanation of Clinger's latest expression. In fact, try listing what the terms are. Guys like Clinger never give them. It's no accident. Nor is the evasion.

As edd said, he'd be hard to bamboozle. He knows the math. He knows what the terms mean.

Farsight has no clue. He doesn't ask what any particular term means, because that might reveal his ignorance of Einstein's math.

These threads are full of "relativity tells us" when it doesn't.

Sol does this. And when I oppose him, I present Einstein's ideas.

Several of the contributors to this thread know a great deal about relativity. sol invictus is one of them. Farsight is not.

It's a greyscale Brian. Sure, I can't be certain about everything, but one thing I am certain of, is that when you read "Einstein told us that..." you should go and read what he actually did say.

True.

When we read what Einstein actually said, we often find that it's very much at odds with Farsight's interpretation of what Einstein wrote.

The problem, I think, is that Einstein wrote for mathematically and scientifically literate audiences. Even his popular writings assumed his audience would have some respect for expertise.

Then you get into the fine structure constant. It's the ratio of the strength of electromagnetic force as compared to the strong force.

The fine structure constant was defined in 1916. The strong force wasn't even proposed until 1935.

My reply was pointing out something that demonstrated that somebody didn't know the first thing about electromagnetism and couldn't even spell permittivity. I didn't spell it out though, snigger. I had a laugh when nobody spotted it. Hur, I've got tears in my eyes now!

Whenever we want a good laugh at the expense of someone who doesn't know the first thing about electromagnetism, we can read Farsight's second post in the Relativity+ thread.

I don't lie to you Ed. I might use the wrong phrase from time to time, but it's not in my interest to be dishonest or come out with things that are plumb wrong. It would be nice if at this juncture somebody like sol or Clinger or ct would pop up and say actually, Farsight is right about this.

Although much of what Farsight says is plumb wrong, he's right about this: Saying things that are plumb wrong is not in his interest, and it would be nice if he'd make it easier for an honest scientist to say he's right about something.

Honestly ben, your physics knowledge is so scant it's scary.

Bare assertion, contradicted by evidence.

The principle of equivalence isn't exact. You can tell the difference between being in an accelerating spaceship and being on a planet. There's a 1/r versus a 1/r² factor that distinguishes the two.

There's a huge issue with this. If you have absolutely homogeneous isotropic space, you've thrown away the baby with the bathwater, and you no longer have anything that causes a ray of light to curve. Yes, I've read The Meaning of Relativity. And no, I don't know what happened to Einstein after 1920.

And therefore there is no gravitational force. Shine a light beam, it goes straight as a die, and you don't fall down.

In general relativity, there's a fourth dimension. It's called time. Spacetime can be curved even when there's a coordinate system in which the spatial dimensions are homogeneous and isotropic.

It's not eerie at all if you know how to look at it. Draw a grid with a bulge at the bottom to represent a photon, the horizontals getting flatter higher up. A_μ is the pressure in the bulge, E is the curvature, B is the is the rate of change of curvature. Take a derivative for D and the sinusoidal electromagnetic waveform, and think of electromagnetism as "curved space".

That's technobabble, as spoken by a poseur who doesn't know anything about electromagnetism. A direct current running through an electrically neutral wire provides a simple counterexample in which E is zero everywhere but B is nonzero.

I understand the fine structure constant.

I talked about it, Sol wouldn't say what it described. He kept hiding behind a "flat spacetime" non-answer and refused to explain his terms.

Bare assertion, contradicted by fact. On at least seven different occasions, sol invictus said what his metric form described: flat spacetime.

Farsight never asked for sol invictus to explain any specific term. By asking, Farsight would have revealed his ignorance of the relevant math.

It did, I checked, and he didn't. I gave my straight answer on page 8 in post #317. I said "I have to say no, I don't know what it describes. I set rₒ to zero and said r²/r is the x term, a spatial distance, but that leaves me with a delta x rather than delta x², and an r multiplier on the delta -t². If go to the other limit and say r=rₒ I'm left with a zero delta -t² indicating travel at c and a division by zero giving me an undefined delta x akin to total length contraction, but I still can't give a positive answer". Sol did not respond in kind,

To respond in kind, sol invictus would have to respond with gibberish. So far as I can tell, sol invictus doesn't speak Farspeak.

and he's been ducking and diving ever since. He won't say what the interval is, what the expression relates to, and he won't say what r is. All he's said is it describes flat spacetime which is academic since spacetime around a black hole just isn't flat.

sol invictus never said his metric form describes spacetime around a black hole. As sol invictus has said on at least seven different occasions, his metric form describes flat Minkowski spacetime.

He's hiding behind mathematics because I whupped his ass in a physics discussion. Kinda sad really, but such is life.

Bare assertion, contradicted by reality.

Now here's your expression:

[latex]$ds^2 = -(r-r_0) dt^2 + dr^2/(r-r_0) + dy^2 + dz^2$[/latex]

We now have an r-rₒ as a multiplier on the t term and a divisor on the x term, x being synonymous with r. Why?

Because sol invictus is giving an example of a coordinate singularity that's remarkably similar to the Schwarzschild coordinate singularity Farsight has been misinterpreting for years and years.

And what scenario does this expression represent?

Flat spacetime. sol invictus has said that on at least seven occasions.

You won't say, all you will say is flat spacetime and it just isn't good enough. Especially when spacetime around a black hole isn't flat.

It's good enough for those of us who have some basic knowledge of the mathematics that Einstein was essential for understanding general relativity. Come to think of it, many of us figured out that it was a metric for flat spacetime before sol invictus told us.

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.

Yep, that's "ton of bricks" Farsight. He's actively clue-resistant, but thinks tough talk can make up for his ignorance of the relevant mathematics.

Huff puff, you're faking it.

Bare assertion, contradicted by evidence.

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