Mainstream GR versus Farsight, mote in their eye or beam in his?

Note that Einstein rejected Gullstrand-Painlevé coordinates:

"Painlevé wrote to Einstein to introduce his solution and invited Einstein to Paris for a debate. In Einstein's reply letter (December 7),[6] he apologized for not being in a position to visit soon and explained why he was not pleased with Painlevé's arguments, emphasising that the coordinates themselves have no meaning. Finally, Einstein came to Paris in early April. On the 5th of April 1922, in a debate at the "Collège de France" [7][8] with Painlevé, Becquerel, Brillouin, Cartan, De Donder, Hadamard, Langevin and Nordmann on "the infinite potentials", Einstein, baffled by the non quadratic cross term in the line element, rejected the Painlevé solution."

Also note that falling bodies such as raindrops don't slow down but the descending light beam does. Matter falls down because the speed of light is spatially variable, here's the reference: "As a simple geometric consideration shows, the curvature of light rays occurs only in spaces where the speed of light is spatially variable". There are others. The moot point about black holes is that light can't get out because the "coordinate" speed of light at the event horizon is zero, see Wikipedia. Gravitational time dilation is infinite at that location, so an optical clock doesn't tick. And nothing you can do will make it tick. Sticking a stopped observer in front of it and claiming that he sees it ticking normally "in his frame" just doesn't work because it takes forever for that optical clock to tick. It hasn't ticked yet, and it never ever will. So the next sentence in the Wikipedia article is wrong: the local instantaneous proper speed of light is not always c. If it was, the black hole wouldn't be black.

Finally, note that a gravitational field is a place where the speed of light is spatially variable. At the event horizon the speed of light is zero, and it can't go lower than that. So gravity vanishes.

 

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The speed of light/photons, is always "c" despite what you like to present and what you have been criticised for many times in the past.
The coordinate speed of light maybe variable, and is explained by the fact that it simply has a longer path to travel in curved spacetime.

 

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Can you explain to us exactly what you understand by the "quadratic cross term in the line element" and why Einstein objected to its omission? For your information, I am very familiar with the invariant Riemann line element

Are you seriously suggesting that gravitation is caused by the local variability of light speed? I rather think it is the other way round. Please explain, in your own words, why I am wrong

 

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Learning is hard. Here Einstein couldn't manage his own theory. That's a shame, but Farsight's own source says Einstein didn't get it, not that it was wrong.

I assume that Farsight means off-diagonal terms in the symmetric metric -- the same metric that Einstein says has ten independent components.

 

Yes well, I was rather more interested to see whether Farsight himself could see this.

 

ngul

I would urge you to read my references. The important point to appreciate is that a gravitational field is a place where the speed of light is "spatially variable". By extension the event horizon is where the speed of light is zero. Not the "coordinate" speed of light, the speed of light. And it can't go lower than that.

You're missing the frozen star "hailstone" growth. You're a water molecule, and you alight upon the surface of the hailstone. You can't pass through the surface, but other water molecules surround you and bury you. So the surface passes through you. Think of the event horizon in similar terms. It forms from the inside out.

There is no point-singularity. The event horizon is a singularity of sorts. It isn't a bad choice of coordinates,. It's where light stops, so all measures of time and space stop, so all coordinates stop.

 

No, because it takes me into abstract things that don't exist, and which don't square with Einstein's explanation of the gravitational field.

Yes. That's what Einstein said. A concentration of energy ins the guise of a massive star conditions the surrounding space, altering its properties, this affect diminishing with distance. As a result space is neither homogeneous nor isotropic, and the speed of light varies with position. Because of this, light curves. Light doesn't curve because spacetime is curved. That's like saying optical clocks go slower when they're lower because your plot of optical clock rates at different elevations is curved.

Because there is no time flowing in an optical clock. Just light (or more generally electromagnetic phenomena) moving. When the clock goes slower it's because the light goes slower. And light goes slower when you're lower because the space down there is different to the space up here. See my references above, and note that sonar waves curve because the speed of sound is "spatially variable" in the ocean:

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The water isn't curved, it's neither homogeneous nor isotropic. Because of pressure, salinity, temperature, etc.

 

I'm sure you would love to urge others to purchase your pop science book also.

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Let me again inform you that the speed of light is always constant at "c" in a vacuum: The coordinate speed of light may appear variable but it is actually travelling a longer path.

No, wrong again: Nothing is actually ever seen to be stopped from any frame of reference....From a remote frame any object including light is just infinitely red shifted to infinity, gradually fading from view.
From a local frame though, everything passes as per normal as one crosses the EH [ignoring tidal gravity effects] The only exception to this from the point of view of a local frame, is in the case of a photon/light emitted just this side of the EH, directly radially away: In this case it will seemingly hover forever, never falling in and never getting away.
Think of a fish swimming upstream at 10kms/hr against a current of 10kms/hr.
http://arxiv.org/pdf/gr-qc/0411060.pdf

 

Farsight: I asked you if you were asserting that gravitation is caused by the local variability of light speed. You answer thusly.....

But then you said

This makes no sense to me. Why agree that gravitation is caused by local variability of light speed (your "yes" above), and then introduce a "massive star" in support of this assertion? Does the massive star have any effect on the local gravitational field or not?

 

The above paragraph admirably highlights the confusion that Farsight often posts. He is continually quoting/interpreting the great man who must be actually turning in his grave at such contradictory nonsense.
Farsight simply appears to be ignoring the validity and equality of all frames of references: A firm postulate of SR as created and revealed by the great man.

What Farsight says in the quote is applicable only from the position and view of a remote distant frame of reference. Time will stop at the EH, but we will never see that: Light and anything else will be gradually redshifted beyond view and will never be seen to cross that EH.
That is what we see [or don't see] from a remote frame of reference.

But from a local frame, say me with a torch falling towards the EH.
Firstly nothing will distinguish that EH from any other region of spacetime: I will not see it or feel it [again ignoring tidal gravity effects] and I will cross it without anything extraordinary happening, along with the light from my torch, which will be also pulled in with me: With one exception as I mentioned previously. The light beam/photons emitted directly radially away, will hover just above the EH forever.
The speed of light will always be "c" despite what Farsight claims.

 

Because the concentration of energy causes the speed of light to vary in the surrounding space, which causes light to curve. Your pencil then falls down because of the wave nature of matter. Boil your pencil down to one electron, then simplify that to light going round a square path, and only the horizontals curve downwards, which is why light is deflected twice as much as matter:

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Yes of course. If that star wasn't there, there wouldn't be any local gravitational field. Re Paddoboy's rather abusive post above, there's other Einstein references to the varying speed of light, such as this.

 

There's no evidence for inflation, paddoboy. Balloon observations won't provide any. Of course, there are people who will blow their own trumpet about possibly detecting the "signature" of primordial gravitational waves. But what they won't tell you is that the early universe was a seething maelstrom for 400,000 years.

Imagine a jelly on a plate. Tap it with a spoon to emulate primordial gravity waves: wibble wobble wibble wobble jelly on a plate. So far so good huh? Then stick your jelly in a blender for 400,000 years. Now try detecting those primordial gravitational waves. Meh, it's popscience bollocks for kids. When you understand GR you will understand why inflation is superfluous. And when you understand electromagnetism you will understand that it was misconceived to begin with. And why 36 years later there's still no evidence for it. That's not to say the universe is not expanding - there's evidence for that. But we simply don't need inflation to smooth it out. Read this, and note that the people who have staked their reputations on inflation will say anything to avoid losing face.

 

^^again--it is like reading from the book " the little engine that could, " also " story of the engine that thought it could(1906), " and " Thinking One Can(1906). "

 

Farsight, this is nonsense. The evidence for inflation is quite strong. And, in fact, even quite easy to understand even for laymen.

I will write a file for my homepage where I explain this in some more detail.

 

Abusive???

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Simply refuting your nonsense as most here already have over the years and the misquotes and misinterpretations you apply to the great man...
what I said.....................
The above paragraph admirably highlights the confusion that Farsight often posts. He is continually quoting/interpreting the great man who must be actually turning in his grave at such contradictory nonsense.
Farsight simply appears to be ignoring the validity and equality of all frames of references: A firm postulate of SR as created and revealed by the great man.

What Farsight says in the quote is applicable only from the position and view of a remote distant frame of reference. Time will stop at the EH, but we will never see that: Light and anything else will be gradually redshifted beyond view and will never be seen to cross that EH.
That is what we see [or don't see] from a remote frame of reference.

But from a local frame, say me with a torch falling towards the EH.
Firstly nothing will distinguish that EH from any other region of spacetime: I will not see it or feel it [again ignoring tidal gravity effects] and I will cross it without anything extraordinary happening, along with the light from my torch, which will be also pulled in with me: With one exception as I mentioned previously. The light beam/photons emitted directly radially away, will hover just above the EH forever.
The speed of light will always be "c" despite what Farsight claims.

 

I (politely) ask you again to explain the following

as compared to

Do you not see the inconsistencies between these 2 assertions about causation?

 

There is no inconsistency. A concentration of energy causes the speed of light to be spatially variable in the surrounding space, and this causes light to curve.

 

There's good evidence that the universe is expanding, and that this expansion is speeding up. But there's no evidence for inflation. And there's none mentioned on your web page. By the way, this looks suspect:

"Now, if we have some evolution with a big bang, that means, we have some big bang singularity, say, at τ=0 , a(0)=0 , at a first look it seems that aˉ¹ (0)=∞, the speed of light becomes infinite at the singularity..."

A gravitational field is a place where the speed of light varies with energy density. People usually say the "coordinate" speed of light varies, but Einstein didn't use that word He just said the speed of light varies. As you descend, the energy density increases, and the speed of light decreases. At the event horizon it's zero. It can't go lower than this, so there's no more force of gravity and no central point-singularity. When you rewind the universe the energy density increases, so IMHO you should expect the speed of light to decrease to zero. Again there's no point-singularity.

 

I see no reason why people should question Einstein murmuring on variable speed of light due to Gravity. It is just that it is being ignored.....and what is embraced, all sort of funny nonsenses...in another thread you stated that speed of light is zero at EH, what you are trying to say that a light emitted at EH in radial away direction, will invert and fall towards singularity ?

 

Wrong. I explain in some detail the cosmological horizon problem. Which is very good evidence for inflation. Without inflation, there would have to be a finite, and small maximal radius of causal influence. $1.7^o$ are a few pixels on the picture, which covers all the $360^o$. Can you see on the picture inhomogeneities larger than a few pixels? I can. So, the real radius of possible causal influences before the creation of CMB radiation has to be much larger. And this requires inflation.

Wrong. Look at the formulas, which is much better than to think what one "should not expect". The definition of the proper time $\tau=\int ds$, in coordinates, thus, with coordinate speed of light: $$ ds^2 = d\tau^2 - \frac{1}{c(\tau)^2}(dx^2+dy^2+dz^2).$$ This means, the coordinate speed of light in the FLRW universe is $c(\tau) = 1/a(\tau)$.