Black holes

[ben m]

Buzz. The two plots have exactly the same metric, and both show the same positive curvature and the same test-particle equations of motion along the manifold.

Ctamblyn, I presume you mean "pi/2" rather than "pi".

(ETA: Darn, I type too slow.)

 

[ctamblyn]

Just to add - there are reasons I disapprove of the rubber sheet analogy, but this is a particularly striking example of the misunderstanding it induces, I think.

I agree, it is very misleading. Sadly, it also seems to be the most popular analogy going as far as TV documentaries and pop science books go (from what I've seen, anyway).

MTW's "parable of the apple", though a bit simplistic, is much better IMHO. If anyone wants to read it, someone has kindly copy-typed it here.

 

[ctamblyn]

Ctamblyn, I presume you mean "pi/2" rather than "pi".

You're right, oops.

ETA: I'm going to go back and correct it...

 

[D'rok]

For a layman - the intrinsic curvature should be measurable by instruments constrained to live within the surface. By definition they can't feel if it's going 'up' or 'down' - and indeed that's a meaningless thing to ask. For anyone living solely on those surfaces they cannot distinguish them by laying down lines and angles and measuring them.

Thank you.

 

[Farsight]

Ctamblyn doesn't surprise me by buzzing in correctly - he's more competent than I. Both are identical - the choice of extrinsic curvature direction is irrelevant.

Only you said "Below is another embedding diagram - again I've taken something with intrinsic curvature and embedded it in a 3D Euclidean volume in a way that preserves that curvature. Farsight - can you explain how you think the gravitational field for this solution differs?" I can measure that intrinsic curvature. I can detect that when I'm closer to the planet, things fall faster, and they fall down. When I'm further away from the planet, I don't measure that they fall faster, and fall up.

My intention was to either bring yet more of Farsight's misunderstanding to light or, in the event he correctly identified the two as identical that the two embedding diagrams could be stitched along a fold of identical z in order to demonstrate that an extrinsic fold has no bearing on an intrinsic curvature.

I've already said you can invert the "upturned hat" if you wish. Gravitational potential is said to be lower nearer the surface, but that's where the stress-energy density aka pressure is higher.

For a layman - the intrinsic curvature should be measurable by instruments constrained to live within the surface. By definition they can't feel if it's going 'up' or 'down' - and indeed that's a meaningless thing to ask. For anyone living solely on those surfaces they cannot distinguish them by laying down lines and angles and measuring them.

On those surfaces? They can distinguish between living on the inside or the outside of a sphere. And in a gravitational field, when we do not concern ourselves with mundane things like planets, there are no surfaces. It's just a volume of space. Remember what I said:

When it comes to embedding diagrams, don't get too excited about "higher dimensional spaces". The curvature we're talking about isn't the curvature of light, it's a curvature in the speed of light plotted with distance from the centre of a circular gravitating body. Since we use light to define out second and our metre, it's also a plot in the metrical properties of space. People call it curved spacetime, but space isn't curved, it's just inhomogeneous in a non-linear way.

There are no surfaces present. Or should I say the only surface present where a black hole is concerned is the event horizon, which is shown as an edge in your depiction.

You better try again edd.

 

[edd]

No, I don't think I need to try again.

 

[Farsight]

Yes you do. And you need to explain the distinction between living on the inside of a sphere and the outside, and the distinction between things falling up or down and slower or faster with distance from the centre. And you need to explain the extrinsic curvature in your depictions. What extrinsic curvature? Something we can't measure? Something mystic like your surfaces that aren't surfaces? I gave you a straight answer, if you won't reciprocate I win again.

Like I've said several times now: if I were wrong, you could just link to the post where you provided some empirical evidence which shows GR is wrong while FGR is right. That post doesn't exist, though.

I've responded time and time again to your requests for empirical evidence. I've supplied it. And still you continue to dismiss it and deny that I've supplied any evidence at all. You're exactly like the creationists I've had the misfortune to talk to. It doesn't matter what you show them, nope, that's not evidence.

All the evidence you have presented so far is consistent with ordinary GR, while FGR is so vague that even you seem unsure what counts as potential evidence for it. Two of the things suggested - loss of synch between nuclear and e/m clocks, and "electron stripping" (your term) - turned out not to be potential evidence at all (you stated that failure to observe those phenomena would not affect your confidence in what I called the "core" of FGR/relativity+).

And still you dismiss Einstein and the variable speed of light whilst attempting to paint me as some "my theory" guy. You want the quotes again? The evidence again?

Edd asked, very clearly, whether the folded paper had intrinsic curvature and you said "yes". You were wrong. The folded paper is intrinsically flat for the same reasons that the cylindrical surface is.

Edd's question was on page 30, the context was RC referred to the standard example of cones where all of the curvature is at the vertex. You can take a vertical slice through a cone so it looks like this: V. Then flatten it out and the vertex is like where two flat regions meet. Then edd asked So if I take a sheet of paper and introduce a fold I've introduced some intrinsic curvature into the paper, is that right Farsight?. It's right when that sheet of paper is standing in for the V of the cone. RC blundered absolutely with his geodesic dome insisting that all regions were flat, ignoring the regions that included the vertices. Edd tried to cover it up by switching from analogy to topology, only we're talking about a gravitational field, not a piece of paper. A gravitational field isn't a cone. It has Riemann curvature, you can't transform it away, just like Einstein said. And finite regions are not flat, as we can see from Ed's picture:

If all finite regions were flat, there wouldn't be any curvature. It would be a pink square. Or what, would it be tiled? Nope.

Obviously you're free to keep digging if that's what you choose, but I suggest that it would look better for you if you'd just admit your mistake.

I'm not the one in a hole here. You're the one in the hole, trying to say a gravitational field is flat. Now pay attention and let's see if you get it this time: when all finite regions of a hill are flat, then there isn't any curvature to get off the flat and level, so there isn't any gradient, constant or not, so there isn't any hill. Take away the Riemann curvature and your gravitational field has gone. Only you can't take it away. You cannot transform away a gravitational field. That's what distinguishes it from accelerating through space. That's the limitation of the principal of equivalence. It's a principle that likens a gravitational field to acceleration, but it doesn't say the two are exactly the same. Have you got this yet? And when you are accelerating through space watched by me, I see no black veil sweeping behind you. The Rindler horizon just isn't in the same league as the black hole event horizon.

Are we all clear on this?

 

[sol invictus]

There's mathematical flat and there's common-usage flat. We use analogies featuring the latter to explain the former. Like geodesic domes and rubber sheets. And hills. Hills are like mountains, but they're smaller, and they aren't jagged. They're smoother things, they're curved. They have curvature. And when they don't, they're flat hills. Which means they aren't hills. It's the same for a gravitational field.

Oh, I see. So your logically inconsistent (not to mention flat-out wrong) assertions about curvature aren't actually wrong, it's just that sometimes you were talking about "mathematical curvature" and other times "common-usage curvature". Even though you kept linking to wiki articles you don't understand about Riemann curvature etc.

Sure.

 

[Reality Check]

RC is talking about curved regions as if they're flat. Have a read of this to learn about intrinsic and extrinisc curvature. It's all easy stuff.

You are lying: I am talking about curved spacetime as Einstein talked about it and as anyone who knows about GR has talked about it in the last 90 or or years: as curved spacetime that is locally "flat" as required by GR.

You may try to read your links sometime:

A surface exhibits extrinsic curvature when that surfaces curves into a higher dimension in an embedding space.A surface exhibits intrinsic curvature when the geometry within the surface differs from flat, Euclidean geometry. It is revealed by geodesic deviation.
...
These last two sections show just how complicated curvature can be in geometry. Curvature can vary from place to place in a space; and at one place it can vary according to the direction considered. That capacity for complexity is going to prove very useful. It turns out to be just what Einstein needed to represent gravity geometrically. But now we are getting ahead of ourselves; that will be our topic in the next chapter.

In GR, there is no embedding space. Thus any curvature is intrinsic.
In GR, the manifold is explicitly defined as locally Minkowskian ("flat").

The concept is easy stuff: The principle of equivalence requires that the geometry that GR uses is locally Minkowskian.

If the geometry that a theory of gravity uses is not locally Minkowskian this violates the the principle of equivalence and that theory is invalid. Thus by stating that spacetime is not locally Minkowskian you are stating that GR was invalid from the moment that it was written !

 

[Reality Check]

Edd's question was on page 30, the context was RC referred to the standard example of cones where all of the curvature is at the vertex. You can take a vertical slice through a cone so it looks like this: V. Then flatten it out and the vertex is like where two flat regions meet.

You still have it wrong.
The standard cone example is a 2-cone (like a 2-sphere). It just has a surface so there is no such thing as "vertical". The cut is along the surface from the vertex in a straight line. The cone does not look like a V. It looks like a cone with a cut along a surface !
Think of a child's party hat. Now cut it from the point to the edge.

Now flatten it out and you have one plane (not two regions!) that has a slice cut out of it.

Any triangle on the cone that does not include the vertex adds up to 180 degrees because it does not cross the cut. This is the same mathematics that shows that a cylinder is intrinsically flat in the web page that you linked to: Intrinsic versus Extrinsic Curvature.

RC blundered absolutely with his geodesic dome insisting that all regions were flat, ignoring the regions that included the vertices.

You have blundered absolutely with this strawman (or are just lying). I stated that all of the flat regions were flat and that any region that includes the vertices is curved.

Now pay attention and let's see if you get it this time: when all finite regions of a hill are flat, then there isn't any curvature to get off the flat and level, so there isn't any gradient, constant or not, so there isn't any hill. Take away the Riemann curvature and your gravitational field has gone.

Now ignore this yet again as you have been ignoring physics for most of your posts: No one except you thinks that GR has anything like this "when all finite regions of a hill are flat" fantasy.
What GR states is that is the "hill" is locally flat. This means that any small enough region it acts as if you cannot tell a uniform gravitational field apart from a constant acceleration (the principle of equivalence). This corresponds to what we observe in real life - we measure triangles to sum up to 180 degrees, i.e. locally Euclidean. GR is an extension of SR so we make spacetime locally Minkowskian. Make the region big enough and you can detect the intrinsic curvature.

 

[ctamblyn]

I've responded time and time again to your requests for empirical evidence. I've supplied it.
(...snip...)

That is false, Farsight. I requested empirical evidence showing that the MTW picture of GR is wrong while supporting FGR. I have made very clear, on several occasions, exactly what I am looking for. You have never supplied such evidence, in this thread or elsewhere. The only empirical evidence you have supplied is consistent with "MTW" GR, and thus inadmissible. If you had, as you incorrectly claim, supplied what I asked for you'd have been able to link to it, but your reply here is conspicuously free of such a link. Why? Because the specific type of evidence I requested does not exist.

• Your Einstein quotes are inadmissible - they are not empirical evidence.
• The Shapiro delay is inadmissible - it is predicted by "MTW" GR.
• Gravitational redshift is inadmissible - it is predicted by "MTW" GR.
• The bending of light by the sun is inadmissible - it is predicted by "MTW" GR.
• The advance of Mercury's perihelion is inadmissible - it is predicted by "MTW" GR.
• The change of clock rate (optical or otherwise) with altitude, i.e. redshift again, is inadmissible - it is predicted by "MTW" GR.

You have supplied nothing else except bare assertions.

From what I have seen in this forum and in the "Relativity+" book, FGR/relativity+ is a vague collection of loosely related thoughts lacking any provable coherence and utterly devoid of utility. It fails to make useful, quantitative predictions to match those of standard GR or the SM. When it seemed to make qualitative predictions, on both occasions you stated that if those predictions turned out to be incorrect it would have zero impact on your confidence in your model - in other words, your model was actually unfalsifiable as far as those tests went. It is, in Pauli's words, not even wrong.

Edd's question was on page 30, the context was RC referred to the standard example of cones where all of the curvature is at the vertex. You can take a vertical slice through a cone so it looks like this: V. Then flatten it out and the vertex is like where two flat regions meet. Then edd asked So if I take a sheet of paper and introduce a fold I've introduced some intrinsic curvature into the paper, is that right Farsight?. It's right when that sheet of paper is standing in for the V of the cone.
(...snip...)

As anyone can check for themselves, your reply shows that you appreciated (at the time, at least) that edd was referring to creases, not the apex of a cone.

I'm not the one in a hole here. You're the one in the hole, trying to say a gravitational field is flat.
(...snip...)

That is false, Farsight. As anyone can check for themselves, in my several posts to you on the topic I said that in GR spacetime is locally flat at every event, which it is.

As has been pointed out by several people already, it would be gravely wrong to think that local flatness at every event implies global flatness.

 

[edd]

Yes you do. And you need to explain the distinction between living on the inside of a sphere and the outside, and the distinction between things falling up or down and slower or faster with distance from the centre. And you need to explain the extrinsic curvature in your depictions. What extrinsic curvature? Something we can't measure? Something mystic like your surfaces that aren't surfaces? I gave you a straight answer, if you won't reciprocate I win again.

I don't - when did I last refer to things falling up or down and where did this sphere come from? Also I thought the embedding diagrams were clear enough - the extrinsic curvature is that which exists within the volume and which I arbitrarily chose to have curve one way or the other

Edd's question was on page 30, the context was RC referred to the standard example of cones where all of the curvature is at the vertex. You can take a vertical slice through a cone so it looks like this: V. Then flatten it out and the vertex is like where two flat regions meet. Then edd asked So if I take a sheet of paper and introduce a fold I've introduced some intrinsic curvature into the paper, is that right Farsight?. It's right when that sheet of paper is standing in for the V of the cone. RC blundered absolutely with his geodesic dome insisting that all regions were flat, ignoring the regions that included the vertices. Edd tried to cover it up by switching from analogy to topology, only we're talking about a gravitational field, not a piece of paper. A gravitational field isn't a cone. It has Riemann curvature, you can't transform it away, just like Einstein said. And finite regions are not flat, as we can see from Ed's picture:

I thought I was clear enough, as do apparently others. I also don't think I brought topology into it. Also the fact I showed a region which is curved everywhere doesn't have bearing on spaces that aren't curved everywhere - if you like we can show you the equivalent diagram for a hollow sphere which is Schwarzschild outside a radius and flat inside?

With regards to the geodesic dome geometry RC raised - you were the one insisting curvature was between two flat surfaces and along an edge. Not at a vertex.

You are persistently wrong about the basics here, Farsight. You might have read a lot of Einstein and certainly quote him a lot, but all your understanding seems to have come from the Bluffer's Guide to GR.

 

[DeiRenDopa]

I've responded time and time again to your requests for empirical evidence. I've supplied it.
(...snip...)

That is false, Farsight. I requested empirical evidence showing that the MTW picture of GR is wrong while supporting FGR. I have made very clear, on several occasions, exactly what I am looking for. You have never supplied such evidence, in this thread or elsewhere. The only empirical evidence you have supplied is consistent with "MTW" GR, and thus inadmissible. If you had, as you incorrectly claim, supplied what I asked for you'd have been able to link to it, but your reply here is conspicuously free of such a link. Why? Because the specific type of evidence I requested does not exist.

• Your Einstein quotes are inadmissible - they are not empirical evidence.
• The Shapiro delay is inadmissible - it is predicted by "MTW" GR.
• Gravitational redshift is inadmissible - it is predicted by "MTW" GR.
• The bending of light by the sun is inadmissible - it is predicted by "MTW" GR.
• The advance of Mercury's perihelion is inadmissible - it is predicted by "MTW" GR.
• The change of clock rate (optical or otherwise) with altitude, i.e. redshift again, is inadmissible - it is predicted by "MTW" GR.

You have supplied nothing else except bare assertions.

From what I have seen in this forum and in the "Relativity+" book, FGR/relativity+ is a vague collection of loosely related thoughts lacking any provable coherence and utterly devoid of utility. It fails to make useful, quantitative predictions to match those of standard GR or the SM. When it seemed to make qualitative predictions, on both occasions you stated that if those predictions turned out to be incorrect it would have zero impact on your confidence in your model - in other words, your model was actually unfalsifiable as far as those tests went. It is, in Pauli's words, not even wrong.

Well, I showed that FGR is internally inconsistent, and rather badly so*; does that count?

Recall one of the Einstein quotes Farsight is so fond of repeating: "1911: If we call the velocity of light at the origin of co-ordinates cₒ, then the velocity of light c at a place with the gravitation potential Φ will be given by the relation c = cₒ(1 + Φ/c²)"

Recall that, in FGR, the impedance of space is something concrete, and fixed, like the impedance of a coaxial cable. And that it is tied inextricably to the speed of light.

Now, per Einstein (and in FGR), the speed of light in one room in a tall building (in your local town, perhaps, or maybe in Poole, England) is different than the speed of light in a different room, in the same building, on a different floor (recall his - or Brian-M's - 'bouncing ball' parallel mirror light clocks). Hence the impedance of space will be different in those two rooms also.

But the speed of light in a room on one floor depends on which (other) floor you choose to measure it from! As does the impedance of space!!

So you must conclude that the impedance of space is not a fixed, constant thing; rather it depends on which observer is timing the ticks of the parallel-mirror light clock!

Now Einstein was quite clear about this; he was, after all, explaining relativity. However, FGR is founded on some kind of pre-Newtonian absolute space and time (the local impedance of space cannot be observer-dependent, for example).

In this way, many of the items on your list are actually hard scientific evidence showing that FGR is not an accurate description of the universe in which we live.

* if you're interested, I'll dig up the relevant posts; IIRC, Farsight completely ignored them

 

[ctamblyn]

Well, I showed that FGR is internally inconsistent, and rather badly so*; does that count?

Recall one of the Einstein quotes Farsight is so fond of repeating: "1911: If we call the velocity of light at the origin of co-ordinates cₒ, then the velocity of light c at a place with the gravitation potential Φ will be given by the relation c = cₒ(1 + Φ/c²)"

Recall that, in FGR, the impedance of space is something concrete, and fixed, like the impedance of a coaxial cable. And that it is tied inextricably to the speed of light.

Now, per Einstein (and in FGR), the speed of light in one room in a tall building (in your local town, perhaps, or maybe in Poole, England) is different than the speed of light in a different room, in the same building, on a different floor (recall his - or Brian-M's - 'bouncing ball' parallel mirror light clocks). Hence the impedance of space will be different in those two rooms also.

But the speed of light in a room on one floor depends on which (other) floor you choose to measure it from! As does the impedance of space!!

So you must conclude that the impedance of space is not a fixed, constant thing; rather it depends on which observer is timing the ticks of the parallel-mirror light clock!

Now Einstein was quite clear about this; he was, after all, explaining relativity. However, FGR is founded on some kind of pre-Newtonian absolute space and time (the local impedance of space cannot be observer-dependent, for example).

In this way, many of the items on your list are actually hard scientific evidence showing that FGR is not an accurate description of the universe in which we live.

* if you're interested, I'll dig up the relevant posts; IIRC, Farsight completely ignored them

Yes, you're right. The "gravitation" part of FGR/relativity+ isn't "not even wrong", it's just wrong, along with the "neutrinos don't have non-zero rest mass" and "electrons are loopy photons" claims.

The "not even wrong" label should probably be reserved for those situations where Farsight has said "if X happens, it supports my position" and then a moment later "if X doesn't happen, it has no bearing on my position".

 

[W.D.Clinger]

Farsight versus Einstein, part 5

Farsight continues to contradict Einstein:

I'm not the one in a hole here. You're the one in the hole, trying to say a gravitational field is flat.

Farsight's saying Albert Einstein is in a hole.

As Einstein explained in §13 of Die Grundlage der allgemeinen Relativitätstheorie, nonzero gravitational fields can occur in flat spacetime.

Now pay attention and let's see if you get it this time: when all finite regions of a hill are flat, then there isn't any curvature to get off the flat and level, so there isn't any gradient, constant or not, so there isn't any hill. Take away the Riemann curvature and your gravitational field has gone.

Farsight's accusing Albert Einstein of not paying attention.

As Einstein explained in §13 of Die Grundlage der allgemeinen Relativitätstheorie, nonzero gravitational fields can occur in flat spacetime, where the Riemann curvature is zero.

Only you can't take it away. You cannot transform away a gravitational field. That's what distinguishes it from accelerating through space. That's the limitation of the principal of equivalence. It's a principle that likens a gravitational field to acceleration, but it doesn't say the two are exactly the same.

Albert Einstein said gravity and acceleration are (locally) indistinguishable. That's the fundamental principle of Einstein's general theory of relativity.

In Farsight general relativity (FGR), that fundamental principle becomes some kind of vague and limited analogy. Farsight has been unable to provide any quantitative explanation of how that principle holds or doesn't hold in FGR.

The Rindler horizon just isn't in the same league as the black hole event horizon.

Are we all clear on this?

Except for Farsight, all of us appear to be clear on this.

We have given Farsight a concrete example of what Einstein was talking about in §13 of the most important paper he ever wrote about general relativity. In that section, Einstein identifies "the components of the gravitational field" with the connection. In our example, some of those components are nonzero, even though spacetime is (globally!) flat. Hence flat spacetime does not rule out the existence of a nonzero gravitational field.

That counterexample to FGR has already been presented in considerable detail:

• Farsight versus Einstein, part 1
• Farsight versus Einstein, part 2
• Vorpal's generalization of that counterexample (which, by including Schwarzschild spacetime as another special case, refutes Farsight's unsupportable claim (quoted above) that the Rindler horizon is unrelated to a black hole's event horizon)
• Farsight versus Einstein, part 3
• Farsight versus Einstein, part 4

As Farsight himself admitted, Farsight got lost at Einstein's equation (3). Einstein's paper includes 72 numbered and 115 unnumbered equations and formulas after equation (3), so Farsight understood at most 1% of the math in Einstein's paper.

It's hard for Farsight to convince people that he's an expert on Einstein's theory of relativity when he understands so little of what Einstein wrote, but Farsight's doing the best he can.

Those of us who understand Einstein's theory somewhat better will continue to point out that, throughout this thread, Farsight has been denying the two fundamental principles of Einstein's general theory of relativity:

• the equivalence principle
• the admissibility of all coordinate transformations allowed by differential geometry

Those principles are related, of course. In §13 of Die Grundlage der allgemeinen Relativitätstheorie, Einstein derived the first of those principles from the second.

 

[Farsight]

Well, I showed that FGR is internally inconsistent, and rather badly so*; does that count?

LOL! No you didn't. And it's Einstein's GR!

Recall one of the Einstein quotes Farsight is so fond of repeating: "1911: If we call the velocity of light at the origin of co-ordinates cₒ, then the velocity of light c at a place with the gravitation potential Φ will be given by the relation c = cₒ(1 + Φ/c²)"

Yes, it's an Einstein quote.

Recall that, in FGR, the impedance of space is something concrete, and fixed, like the impedance of a coaxial cable. And that it is tied inextricably to the speed of light.

Huh? It isn't fixed. It's Z₀ = √(μ₀/ε₀). Note that c = √(1/ε₀μ₀). And that c varies. Like Einstein said.

Now, per Einstein (and in FGR), the speed of light in one room in a tall building (in your local town, perhaps, or maybe in Poole, England) is different than the speed of light in a different room, in the same building, on a different floor (recall his - or Brian-M's - 'bouncing ball' parallel mirror light clocks). Hence the impedance of space will be different in those two rooms also.

It's different even in one room. The super-accurate optical clocks lose synchronisation when separated by only a foot of elevation. They can be in the same room. It doesn't matter whether they're down near the floor or up near the ceiling, provided one's a foot higher than the other, they lose synchronisation. And when we simplify them to parallel-mirror light clocks, this is what's going on:

But the speed of light in a room on one floor depends on which (other) floor you choose to measure it from! As does the impedance of space!!

No it doesn't. They're in front of your nose. You can see that the speeds are different. There's a gradient in the impedance of space. And a gradient in gravitational potential. And a gradient in the speed of light. Like Einstein said:

"If we call the velocity of light at the origin of co-ordinates cₒ, then the velocity of light c at a place with the gravitation potential Φ will be given by the relation c = cₒ(1 + Φ/c²)".

Would you like the other quotes again from all the other years during the developments of GR?

So you must conclude that the impedance of space is not a fixed, constant thing; rather it depends on which observer is timing the ticks of the parallel-mirror light clock!

Now Einstein was quite clear about this; he was, after all, explaining relativity. However, FGR is founded on some kind of pre-Newtonian absolute space and time (the local impedance of space cannot be observer-dependent, for example).

Bizarre.

Dopa, your attempt at sophistry fails miserably, and your dishonesty is palpable. You shredded your own reputation long ago, and nobody is listening to you.

 

[Farsight]

Farsight continues to contradict Einstein...

Farsight's saying Albert Einstein is in a hole....

Surreal!

As Einstein explained in §13 of Die Grundlage der allgemeinen Relativitätstheorie, nonzero gravitational fields can occur in flat spacetime...

Which he distinguished from "special" gravitational fields which we call real gravitational fields, which can be distinguished because you cannot transform them away.

OK guys, that's enough. Your dishonesty is not conducive to sincere discussion.

 

[Kwalish Kid]

Here I thought that Farsight had nothing left to lie about, and you guys get him to lie about intrinsic curvature! I'm glad to see that his go-to defense about his own mistakes and lies is to accuse other people of lying.

Can someone point to me where Farsight calculated the behaviour of a black hole using c = cₒ(1 + Φ/c²)?

 

[DeiRenDopa]

Here I thought that Farsight had nothing left to lie about, and you guys get him to lie about intrinsic curvature! I'm glad to see that his go-to defense about his own mistakes and lies is to accuse other people of lying.

It's a tactic he uses often.

Strangely, he has - apparently - been trying to explain his ideas to the world for several years now, and not a single other person seems to even understand them, let alone agree with them.

Farsight's response to this totally failure to communicate? Well, there's no prize for the correct answer to that ...

Can someone point to me where Farsight calculated the behaviour of a black hole using c = cₒ(1 + Φ/c²)?

As far as I know, there's nothing in what Farsight has written, here or elsewhere, which suggests that he actually understands the equation.

Further, there are essentially zero examples of Farsight presenting calculations of anything (he prefers verbal analogies and diagrams).

Interestingly, there are many examples of people asking Farsight to provide calculations, or point to where he's published them; as far as I know, Farsight has never answered any such queries, and no one has managed to find any such either ...

 

[DeiRenDopa]

I thought you were ignoring me; oh well ...

Well, I showed that FGR is internally inconsistent, and rather badly so*; does that count?

LOL! No you didn't. And it's Einstein's GR!

No matter how many times I point to 50.7167° N, 1.9833° W on a map of the world, and declare that that's Palermo, Sicily, it remains Poole, England.

Recall one of the Einstein quotes Farsight is so fond of repeating: "1911: If we call the velocity of light at the origin of co-ordinates cₒ, then the velocity of light c at a place with the gravitation potential Φ will be given by the relation c = cₒ(1 + Φ/c²)"

Yes, it's an Einstein quote.

Recall that, in FGR, the impedance of space is something concrete, and fixed, like the impedance of a coaxial cable. And that it is tied inextricably to the speed of light.

Huh? It isn't fixed. It's Z₀ = √(μ₀/ε₀). Note that c = √(1/ε₀μ₀). And that c varies. Like Einstein said.

Quite right, I was insufficiently careful with my words.

Here's a more accurate statement of what the impedance of space is, in FGR:

The impedance of space, at a particular point in space, is something concrete, and fixed, like the impedance of a coaxial cable. And that it is tied inextricably to the speed of light, at that particular point in space. Like the number of atoms of platinum in the international prototype kilogram, it has just one value, for all observers; like the air temperature in a building, that value varies with location.

Now, per Einstein (and in FGR), the speed of light in one room in a tall building (in your local town, perhaps, or maybe in Poole, England) is different than the speed of light in a different room, in the same building, on a different floor (recall his - or Brian-M's - 'bouncing ball' parallel mirror light clocks). Hence the impedance of space will be different in those two rooms also.

It's different even in one room. The super-accurate optical clocks lose synchronisation when separated by only a foot of elevation. They can be in the same room. It doesn't matter whether they're down near the floor or up near the ceiling, provided one's a foot higher than the other, they lose synchronisation. And when we simplify them to parallel-mirror light clocks, this is what's going on:

But the speed of light in a room on one floor depends on which (other) floor you choose to measure it from! As does the impedance of space!!

No it doesn't. They're in front of your nose. You can see that the speeds are different. There's a gradient in the impedance of space. And a gradient in gravitational potential. And a gradient in the speed of light. Like Einstein said:

"If we call the velocity of light at the origin of co-ordinates cₒ, then the velocity of light c at a place with the gravitation potential Φ will be given by the relation c = cₒ(1 + Φ/c²)".

OK, so pick a point inside a small vacuum tube, resting on the coffee table in an apartment on the ground floor of a ten story building. Show us all, please, how to calculate the impedance of space at that point. Using Einstein's equation.

Repeat the exercise for observers in each of the apartments directly above this one. To be clear: each observer is calculating the value of the impedance of space in the small vacuum tube resting on the coffee table in the ground floor apartment. Using parallel-mirror light clocks.

Show that the ten values of same physical thing - the value of the impedance of space in the small vacuum tube resting on the coffee table in the ground floor apartment - are the same.

So you must conclude that the impedance of space is not a fixed, constant thing; rather it depends on which observer is timing the ticks of the parallel-mirror light clock!

Now Einstein was quite clear about this; he was, after all, explaining relativity. However, FGR is founded on some kind of pre-Newtonian absolute space and time (the local impedance of space cannot be observer-dependent, for example).

Bizarre.

Dopa, your attempt at sophistry fails miserably, and your dishonesty is palpable. You shredded your own reputation long ago, and nobody is listening to you.

Nice try.

Earlier when you attempted this sort of thing you ended up with egg on your face (i.e. I asked JREF members to state if they agreed with me, or you, concerning a similar claim you made; no one agreed with you).

Perhaps, this time, you might like to put some effort into explaining what you see as "sophistry"? I'm sure all those who "are listening to me" would be quite interested to read such an explanation.