Black holes

[ben m]

Huh? The issue with the hill is that if you take a small portion of it and say it's locally flat, then take another small portion and say that's locally flat too, and then repeat for all small portions, you've now got a flat hill. You haven't got a hill any more.

Nope. Flat wrong. Differential geometry includes *both* the "local areas look flat" behavior and the "global curvature" behavior. This has been known for centuries---it is simultaneously true that (a) any local mapmaker can draw a flat map, and (b) when you try to build a large-area map, you can't just tile flat maps together because the Earth's surface is a sphere.

That's the anecdotal version. The mathematical version is Carl Gauss's "Theorema Egregium" of 1827, which Einstein knew and which you do not.

 

[ctamblyn]

Nope. Flat wrong.

I see what you did there.

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

 

[W.D.Clinger]

Farsight versus Einstein, part 3

Huh? The issue with the hill is that if you take a small portion of it and say it's locally flat, then take another small portion and say that's locally flat too, and then repeat for all small portions, you've now got a flat hill. You haven't got a hill any more.

Nope. Flat wrong. Differential geometry includes *both* the "local areas look flat" behavior and the "global curvature" behavior. This has been known for centuries---it is simultaneously true that (a) any local mapmaker can draw a flat map, and (b) when you try to build a large-area map, you can't just tile flat maps together because the Earth's surface is a sphere.

That's exercise 8 of the first set of homework problems I suggested to Farsight a little over two months ago.

I offered to sketch a proof of exercise 8 if it was too hard for him, but Farsight never took me up on that offer. Apparently it was too hard for him and he didn't want to learn anything.

That's the anecdotal version. The mathematical version is Carl Gauss's "Theorema Egregium" of 1827, which Einstein knew and which you do not.

Gauss's Theorema Egregium implies that even small charts will have some distortion, but differential geometry lets us work with distorted charts. The connection (which Einstein referred to as "the gravitational field") tells us how to adjust for that distortion.

Farsight's argument above can be simplified to this: You can't take an infinitesimal step away from zero along the positive direction of the real line, then take another infinitesimal step, and repeat, and say you've gotten anywhere. Therefore (in Farsight's mind) Zeno's paradox was a real paradox. Farsight appears to be unacquainted with first-year calculus.

More to the point, Farsight is still lying when he says he agrees with Einstein. According to Einstein, nonzero connection coefficients imply a nonzero gravitational field. Einstein explained how that nonzero gravitational field could arise in flat spacetime, sol invictus gave a concrete example, and I posted the calculation, citing which of Einstein's equations I was using. Farsight got lost at Einstein's equation (3).

I see that Farsight is still saying we're "hiding behind mathematical expressions where they will not list the terms and they will not say what the expression represents". I offered to explain any terms he doesn't understand, but I asked him to specify which terms he doesn't understand and to tell us about his mathematical background so we won't waste time telling him stuff he already knows or stuff he can't hope to understand given his background.

Farsight ignored that offer. Taking me up on that offer would have made it even more obvious that he's lying about our willingness to explain the math.

 

[xtifr]

He didn't resolve them using math.

Yes he did. I'd point you to the Princeton lectures, but you haven't got the math to follow them. So I'll just point out that Einstein didn't die in 1915. He lived forty more years. In all that time, every physicist in the world, including close friends of his, continued to state that the speed of light in a vacuum is constant. Why didn't Einstein correct them if they were wrong? Why did Einstein continue to state himself that that was correct? Why did Einstein endorse and contribute to writings that stated that? Some of these people who were, according to you, so incredibly incorrect about what Einstein "really" meant were close friends of his. Do you really think he wouldn't have mentioned, at least in passing, "oh, by the way, you seem to be assuming that the speed of light is constant; didn't I explain that that's incorrect?" Somehow, magically, those forty years went by when Einstein could have corrected one of his friends, yet he never did. Instead, he left it to some loon who doesn't even understand the math to discover his "true" meaning and proclaim it to the world and become world-famous and satisfy all his dreams of glory.

If you are capable of stopping to think for a minute, please try to imagine how insane that notion is! Basically, you're accusing Einstein of lying by omission for forty years!

In any case, it hardly matters what the "true" interpretation of GR is, because GR is almost certainly wrong! We have experiment after experiment that shows that GR fails at a small scale, and it seems to be completely irreconcilable with QM, which has withstood every experiment thrown at it. We still have details to work out, but it's clear to everyone (except, perhaps, you) that GR is no more than a useful approximation! Better than Newton (which is also a useful approximation at a small, slow scale), but ultimately flawed. So your "amazing" discovery of the True Meaning of GR(tm, pat. pending), which Einstein apparently jealously kept hidden for forty years, doesn't give us any new insight into the universe, because it's the True Meaning of a bankrupt theory.

 

[Reality Check]

Huh? The issue with the hill is that if you take a small portion of it and say it's locally flat, then take another small portion and say that's locally flat too, and then repeat for all small portions, you've now got a flat hill. You haven't got a hill any more.

Sorry, Farsight, that only demonstrates that you need to learn what locally Euclidean means.
It does not mean that there is some magic plane out there which defines the concept of "flat" for the hill and that every locally Euclidean space is aligned to be flat according to the plane.
What it means is that every point is contained in a locally Euclidean space and that each locally Euclidean space has a different "orientation" related to the global curvature of the hill at that point.

An analogy would be to look a a geodesic dome. It is globally curved. But there are points where it is locally flat.

So: The non-issue with the hill is that if you take a small portion of it and say it's locally flat, then take another small portion and say that's locally flat too, and then repeat for all small portions, you've now got a curved hill with locally flat portions. You still got a hill.

 

[W.D.Clinger]

What it means is that every point is contained in a locally Euclidean space and that each locally Euclidean space has a different "orientation" related to the global curvature of the hill at that point.

No, locally flat means that, for every point p of the space, there's at least one coordinate system in which the metric's ten components (the g_μν) have the same values at p as in flat Minkowski space.

Farsight's been going on about the g_μν for at least two years, without ever understanding what these components have to do with local flatness. Farsight didn't even understand Einstein's equation (3).

 

[Farsight]

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

Why has nobody presponded to what I said about Riemann curvature? The usual pictures of curved spacetime are showing you Riemann curvature. The curvature of "the rubber sheet" is the Riemann curvature.

And what RealityCheck said is right. When you zoom in on that rubber sheet, you see a region where there's no apparent curvature, much like one panel of his geodesic dome. You cannot measure any tidal force, and yet things still fall down and light still curves. Because this region is tilted, because the Riemann curvature is there altering the gradient. If you're walking across a plane and the gradient doesn't alter, you've got a flat hill. You've got no hill!

xtifr: go and read The golden age of general relativity. Do your own research.

 

[xtifr]

xtifr: go and read The golden age of general relativity. Do your own research.

I'm not the one who believes that Einstein spent forty years deliberately misleading all his friends and colleagues. You're the presenting that hypothesis; it's up to you to defend it, if you want anyone to even think about believing your claims.

Again, you are the one that wants us to believe that Einstein changed his mind in 1915! He lived for forty more years, during which time, his friends and colleagues all still plainly believed that the speed of light was invariant, and repeatedly said so, in public, where Albert could hear them. And during that forty years he never once corrected anyone! Leaving it up to you, and you alone, to discover this amazing discrepancy in the common theory held by every other physicist. If you want me to believe that, how do you explain his silence?

 

[Farsight]

This thread is getting increasingly bizarre. It's just like talking to creationists. You show them the evidence, but they won't even look at it, they just aren't thinking, they're in total denial.

xtifr, are you going to call me a liar too? Go and read what Einstein actually said. Go and read the link I gave you:

"The golden age of general relativity is the period roughly from 1960 to 1975 during which the study of general relativity,[1] which had previously been regarded as something of a curiosity, entered the mainstream of theoretical physics".

There was no silence. You're believing another myth. General relativity wasn't mainstream, that's all. And when it did become mainstream and suffered its "paradigm shifts", Einstein was dead.

 

[xtifr]

There was no silence. You're believing another myth. General relativity wasn't mainstream, that's all. And when it did become mainstream and suffered its "paradigm shifts", Einstein was dead.

General relativity was well-known throughout Einstein's life. Physicists who were his close friends published numerous works about relativity during that time, and every one of them asserted that the speed of light was invariant. The idea that the speed of light is invariant didn't spring out of nowhere in 1960. It was well known, if not universally accepted, within the physicist community long before Einstein died.

I've given up trying to get you to figure out your elementary errors in mathematics, because you clearly aren't capable of understanding the questions. That's ok, maths aren't really my strong suit either. I'm trying to get you to explain how this amazing discovery of yours could have been hidden all those years, while Einstein was still alive. Trying to pretend that nobody knew about GR till after Einstein died is simply preposterous! Give me a sensible explanation if you can.

 

[sol invictus]

In any case, it hardly matters what the "true" interpretation of GR is, because GR is almost certainly wrong! We have experiment after experiment that shows that GR fails at a small scale

That's not true - all experimental data is consistent with GR (plus the other forces, obviously).

and it seems to be completely irreconcilable with QM, which has withstood every experiment thrown at it.

That depends on what you mean. String theory is an example of a quantum theory that reduces to GR plus other forces at "low" energies, so quantum versions of GR are possible in that sense. On the other hand string theory is a lot more than just GR, and at sufficiently high energies looks very little like it at all.

In general, one certainly expects quantum corrections to change GR substantially at high energies.

 

[sol invictus]

This thread is getting increasingly bizarre. It's just like talking to creationists. You show them the evidence, but they won't even look at it, they just aren't thinking, they're in total denial.

Many people have posted in this and other threads, and you're the only one that sees it like that.

Before, I would have added a comment like "if everyone seems crazy, it's probably you" or "why have you failed to convince anyone after all this time?".

But I realize now that such comments are pointless, because you don't care about that. You want to feel like a victim, it feeds your fantasy. I don't think you're actually interested in the physics at all, or in what Einstein said.

 

[Farsight]

General relativity was well-known throughout Einstein's life. Physicists who were his close friends published numerous works about relativity during that time, and every one of them asserted that the speed of light was invariant. The idea that the speed of light is invariant didn't spring out of nowhere in 1960. It was well known, if not universally accepted, within the physicist community long before Einstein died.

It's the measured speed of light that's invariant.

I've given up trying to get you to figure out your elementary errors in mathematics, because you clearly aren't capable of understanding the questions. That's ok, maths aren't really my strong suit either. I'm trying to get you to explain how this amazing discovery of yours could have been hidden all those years, while Einstein was still alive. Trying to pretend that nobody knew about GR till after Einstein died is simply preposterous! Give me a sensible explanation if you can.

Oh here we go, dismissal of evidence, total denial, and absolute fiction. The typical traits of conviction. Forget it xtifr, I'll give you the hard scientific evidence, I'll give you the Einstein quotes, and I'll give you the reason why people like you believe what you do. But you won't believe any of it. It is exactly like trying to talk to a creationist.

 

[catsmate]

Rudeness might be part of the pattern as well.

What gets me is the Einstein obsession; there have been numerous other physicists who've studied relativity, gravity, quantum mechanics et cetera.

 

[Hellbound]

It's the measured speed of light that's invariant.

Ah, that makes sense.

So basically, if you don't measure it at all, you can then claim it moves at whatever speed you want. It's only when that's actually tested that the speed of light is invariant.

So are you proposing some sort of quantum etnanglement concerning the speed of light?

I'm curious, because this statement you made makes no sense whatsoever. The speed can't be determined without measurement...the measurement is the speed. Einstein spent a LOT of time pointing this out: time is what clocks measure, space is what yardsticks measure. In other words, space and time only exist as measured. IIRC, this is in the first chapter of Einstein's "Relativity", the book he wrote about his theory, and forms the basis of the entire thing.

So basically, you're attempting to toss out the entire basis of special and general relativity, and go back to an idea of an absolute space and absolute time.

 

[DeiRenDopa]

... I'll give you the hard scientific evidence, ...

What is this? The "hard scientific evidence"?

If I am not mistaken - and I may well be - it is "Shapiro time delay", "gravitational lensing", and "clocks at different elevations lose synchronization".

Are the hard scientific (experimental and observational) quantitative results (a.k.a. evidence) consistent with MTW GR? Why yes, they are.

Is this hard scientific evidence - which is (and must be) quantitative - consistent with FFGR (Farsight's Fantasy GR)? Why no, it isn't.

How can that be? Farsight has written a great many words (over a million?), in many different venues (book, internet discussion boards, etc), over many years explaining and explaining and explaining once again just what the central FFGR claims are, and how they are derived from words Einstein certainly wrote, nearly a century ago.

Well, the answer to that is both very simple and very depressing: FFGR is not physics, in the manner of Newton's optics, mechanics, etc (or Maxwell's electromagnetism, or Gibbs' thermodynamics, or ...); FFGR is purely qualitative, and is built on simple diagrams and mental images rooted firmly in the absolute time and space notions of the Greeks.

In that sense, "the hard scientific evidence" is irrelevant to FFGR; being quantitative, it cannot be explained, or even understood, within FFGR.

Now you may feel I'm being too harsh; after all, hasn't Farsight written at least something quantitative? Hasn't he tried - at least once - to put hard numbers (with the appropriate units) onto this signature diagrams, to at least allow the possibility that FFGR could be tested, using hard scientific evidence? Well, no, I don't think he's ever done that.

Don't believe me? A single counter-example would demolish my hypothesis.

I'd greatly welcome hard evidence that such a counter-example exists.

 

[ben m]

"The golden age of general relativity is the period roughly from 1960 to 1975 during which the study of general relativity,[1] which had previously been regarded as something of a curiosity, entered the mainstream of theoretical physics".

There was no silence. You're believing another myth. General relativity wasn't mainstream, that's all. And when it did become mainstream and suffered its "paradigm shifts", Einstein was dead.

Let's look at the aspects of GR that you've rejected in this thread.

Gullstrand-Painleve coordinates, published 1921. Lemaitre coordinates, published 1938. Eddington-Finkelstein coordinates, constructed in 1924 by Eddington, one of GR's main promotors and a close associate of Einstein's. (Finkelstein popularized it later.). The flowing-spacetime analogy, Laschkarew 1926.

You see, Farsight, you're not rejecting advanced GR concepts, of the sort discovered in the later Golden Age. You're not rejecting the no-hair conjecture, or the censorship hypothesis, or gravity waves, or the Hawking-Hartle state. You're rejecting all of the 19th-century math Einstein used in his 1916 paper; you're rejecting four out of five sentences in that paper and misinterpreting the remainder.

 

[Reality Check]

It's the measured speed of light that's invariant.
...snipped usual ranting...

Still wrong: It is the measured local speed of light that's invariant.
The measured coordinate speed of light varies according to the coordinate system used.

Once once angain with the inanity of the Einstein quotes which shows that the answer to Farsight: Do you understand the fallacy of argument by authority?asked on 27th March 2012 is still no !

Sorry Farsight, you are the one acting like a creationist here:

• You have your "holy Bible" - the Einstein quotes.
• You dismiss the science, e.g. that GR is coordinate free.
• You dismiss the math, e.g. W.D.Clinger's posts.
• You dispay ignorance of GR but still tout yourself as an expert, e.g. not understanding sol invictus's metric for flat spacetime is for .... flat spacetime .
• You seem to ignore over 90 years of progress in teaching, using and understanding GR.
• You cite textbooks that explicitly contradict what you state:
  

  What I find curious is that he's shown parts (a) and (b) of MTW Figure 32.1 on many occasions, but has never said a word about part (c) of that figure or about the text in section 32.4 that refers to Figure 32.1. It's as though he doesn't own a copy of MTW himself, and knows nothing about it apart from what he's read on the World-Wide Web.

 

[ctamblyn]

It's the measured speed of light that's invariant.

Nice to get that one out the way, too.

 

[Reality Check]

And what RealityCheck said is right. When you zoom in on that rubber sheet, you see a region where there's no apparent curvature, much like one panel of his geodesic dome.You cannot measure any tidal force, and yet things still fall down and light still curves.

Up to there you have it sort of right but then you go off the rails yet again:

Because this region is tilted, because the Riemann curvature is there altering the gradient.

There is no "tilt" because there is no external reference against which to measure such a "tilt". The curvature of spacetime is intrinsic.

FYI: The Riemann curvature tensor is zero in any Euclidean space.

AFAIK: It is the manifold's global intrinsic curvature which means that "things still fall down and light still curves" but the property of having the manifold locally Euclidean means that there is no way to tell the effects of this curvature (gravity!) from an acceleration.

This statement is especially wrong:

If you're walking across a plane and the gradient doesn't alter, you've got a flat hill. You've got no hill!

Think about the geodesic dome analogy yet again: If you walk along the surface of the dome then the gradient does alter and you are not walking on flat ground !

One more time for you, Farsight: A manifold that is locally Euclidean does not mean that the manifold is globally or intrinsically Euclidean.