Black holes

[DeiRenDopa]

Probably not that important, but does anyone - including Farsight - know what this is about?

Of course. If you followed the path of the Shapiro radar signal in your gedanken spaceship carrying a parallel-mirror light clock and your metre rod, at no point in your journey will you measure a reduced speed of light. Where the speed of light is reduced, it is also reduced in your parallel-mirror-light clock. It's similarly reduced in your optical clock, your microwave atomic clock, your UV optical clock, and so on.

But I shun such clocks, and elect to use a combination of weak and strong decay processes to measure time. Still, I get a result that agrees with the rest of humanity's primitive electromagnetic-interaction clocks. Coincidence?

No. They decay to simpler nuclei, like unbalanced machines. Then you can chop them up further and annihilate them to photons. E=mc² and all that.

ctamblyn seems to be addressing a point (fixation?) that Farsight has with the relationship between clocks and electromagnetism, by pointing out that clocks which run ('tick') by physical processes other than those directly involving electromagnetism 'tell the same time' as electromagnetism-based clocks.

Farsight seems to be saying that yes, all (good) local clocks tell the same time ... because every physical process can be reduced to electromagnetism. Or maybe he's saying something quite different. I really can't tell.

What do you think?

 

[ctamblyn]

Probably not that important, but does anyone - including Farsight - know what this is about?

ctamblyn seems to be addressing a point (fixation?) that Farsight has with the relationship between clocks and electromagnetism, by pointing out that clocks which run ('tick') by physical processes other than those directly involving electromagnetism 'tell the same time' as electromagnetism-based clocks.

Farsight seems to be saying that yes, all (good) local clocks tell the same time ... because every physical process can be reduced to electromagnetism. Or maybe he's saying something quite different. I really can't tell.

What do you think?

Based on his request for me to use the term "relativity+" in place of "FGR" (near the end of this post), my money would be on him thinking of the ideas he expressed in the Relativity+ thread. It's his "theory of everything" in which particles we normally think of as fundamental are in fact photons somehow trapped in "self-bound states", or something like that. Every particle would then carry a kind of internal clock that runs at a rate proportional to the speed of light. If that's what FGR (as presented in this thread) depends on then it obviously cannot be some "correct", "true-to-Einstein" interpretation of GR.

(Sorry for all the scare quotes.)

 

[DeiRenDopa]

Is it true that, according to Farsight, the local speed of light can have any value, between zero and c (or more)?!?

Here's why I think this might be true ...

Which brings me to the main part of this post: using the Farsight method (see my last post), what is the speed of light, as determined by the (various) DPCs?

Recall that a "DPC" is a "DRD pulsar clock", which is very much the same as Farsight's pulsar clock, with some extras.

Recall that Farsight's method of measuring the local speed of light is to time a light pulse as it travels between emitter and detector (whose separation has been determined by a local ruler, calibrated using the SI definition of meter), using a pulsar clock. Or, in his own words: "You measure the speed of light with a Foucault-Fizeau device over a distance which you measured with your tape measure, timing it with your pulsar clock."

Now consider a typical Farsight post, concerning the speed of light, parallel-mirror clocks (P-MLCs), and elevation:

You merely consider two parallel-mirror light clocks at different elevations, you're aware that GR predicts that these clocks do not stay synchronised, and then you draw yourself a picture showing one beam of light moving faster than the other. Like this:

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If we now have a vertical stack of pairs of P-MLCs and DPCs, together with Foucault-Fizeau devices, each separated from its neighboring sets of instruments by a fixed distance, with the base of the stack on the surface of neutron star whose mass is almost-but-not-quite enough to make it a black hole, then we can observe - using the Farsight method - that the local speed of light has many different values!

For an observer somewhere in the middle of the stack, the local speed of light is c. Using the two DPCs immediately adjacent (one above, one below), the local speed of light is somewhat greater than c, as well as somewhat less than c. Using the next-closest DPCs, the local speed of light is also both greater than and less than c, and the deltas (absolute differences between thusly measured local speed of light and c) are greater than for the first pair (the immediately adjacent ones).

And so on.

What a wondrous thing light is! The very same light can have so many different, local, speeds, all at the same time!!

Hey Farsight, why don't you write this up, and get it published? I'm sure you'll get a phone call from Stockholm not long afterwards ...

 

[W.D.Clinger]

A couple of very minor points...

Who cares abnout these pre-1917 Einstein quotes?
These quotes are irrelevent because thus is the crackpot fallacy of argument by authority. You cannot even understand that these quotes are from before 1917 when Einstein was constructing GR. His understanding and interpretation of GR changed during this period.

By 1916, when Einstein published "The Foundation of the General Theory of Relativity", his understanding and interpretation of GR had evolved to the point where (so far as I can tell) it was consistent with modern, MTW-style GR.

By 1916, Einstein's theory of general relativity was certainly more compatible with a modern, MTW-style interpretation of GR than with Farsight's interpretation.

The Schwarzchild coordinates do describe the black hole interior. They don't stop at the event horizon.

That's a matter of how you define the domain of a Schwarzschild chart, and that's just a matter of terminology.

First of all, a Schwarzschild chart can't include the event horizon, because there's a coordinate singularity at that horizon.

Secondly, the Schwarzschild t and r coordinates exchange roles inside the event horizon: t becomes a spatial coordinate, and r becomes a time-like coordinate. Although that exchange of role is directly related to the coordinate singularity, allowing r < 2m makes Schwarzschild coordinates harder to explain (IMO).

Thirdly, the Schwarzschild metric is not static inside the event horizon, because two coefficients of the Schwarzschild metric form vary with r, which becomes time-like inside the event horizon.

Whether the domain of a Schwarzschild chart includes a region inside the event horizon is a matter of convention. I've been using the convention that r > 2m for Schwarzschild coordinates, which allows the Schwarzschild metric to be static throughout its domain.

 

[Ziggurat]

I've been using the convention that r > 2m for Schwarzschild coordinates, which allows the Schwarzschild metric to be static throughout its domain.

I somehow doubt Farsight appreciates the subtleties of that statement. But he kept referring to that figure from MTW that plots of Kruskal and Schwarzchild coordinates, and in that figure, the Schwarzchild coordinates included the interior. So if he wants to use the MTW figure, I say let him.

 

[W.D.Clinger]

I've been using the convention that r > 2m for Schwarzschild coordinates, which allows the Schwarzschild metric to be static throughout its domain.

I somehow doubt Farsight appreciates the subtleties of that statement. But he kept referring to that figure from MTW that plots of Kruskal and Schwarzchild coordinates, and in that figure, the Schwarzchild coordinates included the interior. So if he wants to use the MTW figure, I say let him.

 

[Farsight]

So in other words, there's no difference that can feasibly tested by experiment?

Not at all. Your presumption speaks volumes.

Which makes this a purely theoretical conjecture based on conceptual elegance. But to be valid, it'd have to have supporting math to demonstrate that it's consistent with existing experimental results.

Er, no. It's based on scientific evidence.

Do you have the math? I'm sure others here will be willing to look it over.

No, just the scientific evidence, and they aren't.

 

[Roboramma]

Er, no. It's based on scientific evidence.

I don't think those words mean what you think they mean.

 

[Farsight]

I am sure that you appreciate that you have just thrown away GR which states that spacetime is curved and it is this that causes gravity.

No I haven't. I've thrown away the cargo-cult myth that contradicts what Einstein actually said:

"According to this theory the metrical qualities of the continuum of space-time differ in the environment of different points of space-time, and are partly conditioned by the matter existing outside of the territory under consideration. This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that “empty space” in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials gμν), has, I think, finally disposed of the view that space is physically empty".

A concentration of matter "conditions" the surrounding space, making it inhomogeneous such that light moving through it over time curves. Curved spacetime is the effect, not the cause.

So now all you have to do is produce the mathematics behind your idea, generate predictions, e.g. for the anomalous perihelion advance of Mercury, and show that the observations do not invalidate your theory.

No I don't. Besides, you surely must recall this post where I pointed out that Einstein's equation was the same as Paul Gerber's 1902 equation?

I do hope we do not see the usual thing we see from cracks - building in the theory that they have thrown away into their idea to get the same results.

I'm not throwing away the theory. I'm throwing away the myth that has hamstrung it. Now look to that evidence. The speed of light varies. You can see it varies, just like Einstein said.

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[DeiRenDopa]

If we now have a vertical stack of pairs of P-MLCs and DPCs, together with Foucault-Fizeau devices, each separated from its neighboring sets of instruments by a fixed distance, with the base of the stack on the surface of neutron star whose mass is almost-but-not-quite enough to make it a black hole, then we can observe - using the Farsight method - that the local speed of light has many different values!

For an observer somewhere in the middle of the stack, the local speed of light is c. Using the two DPCs immediately adjacent (one above, one below), the local speed of light is somewhat greater than c, as well as somewhat less than c. Using the next-closest DPCs, the local speed of light is also both greater than and less than c, and the deltas (absolute differences between thusly measured local speed of light and c) are greater than for the first pair (the immediately adjacent ones).

And so on.

What a wondrous thing light is! The very same light can have so many different, local, speeds, all at the same time!!

I'm not throwing away the theory. I'm throwing away the myth that has hamstrung it. Now look to that evidence. The speed of light varies. You can see it varies, just like Einstein said.

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So here's an illustration, in the Farsight mode, of part of that vertical stack, using one particular DPC (the platforms are numbered, with higher numbers illustrating greater elevation:

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126 |-------------------|
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122 |-------------------|
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And here's a Farsight illustration, using a different DPC:

128 |-------------------|
127 |-------------------|
126 |-------------------|
125 |-------------------|
124 |-------------------|
123 |-------------------|
122 |-------------------|
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And yet a third, different DPC:

128 |---------------------|
127 |---------------------|
126 |---------------------|
125 |---------------------|
124 |---------------------|
123 |---------------------|
122 |---------------------|
121 |---------------------|

Using the Farsight method, the local speed of light not only varies with location, but depends upon which non-local clock you use to determine it.

 

[Farsight]

Yes, actually, it is very fundamental. Far more fundamental than temperature.

No it isn't. Matter is made of energy. Not entropy. And both temperature and entropy are emergent properties of a system.

Your definition of entropy is completely wrong. Not a little bit wrong, not kind of wrong, very wrong.

No it isn't. Go look it up. See the ice in the glass? That ice is cold. Let's say the water in the glass is hot. The ice melts, and you're left with warm water. All the water is now at the same temperature. Entropy has increased.

And your description of what happens in a gas is also wrong. You most definitely do not end up with all the molecules moving at a similar speed. That would be a low-entropy situation. What you get is a broad spread of velocity distributions

It isn't wrong at all. I said similar, not identical. If you start off with one fast molecule and one slow molecule, you end up with two molecules moving at some middling speed.

Not directly. The only thing she's measuring directly is the volume of alcohol inside the thermometer.

She's measuring the patient's temperature using a thermometer! Strewth!

That's almost never what we measure with a thermometer. In fact, I don't know of any common thermometer which actually does that. Standard alcohol or mercury thermometers measure the volume of a liquid, bimetalic coils measure a length differential between two materials, thermocouple thermometers measure a voltage across a junction, etc, etc. Measuring the kinetic energy of gas molecules is actually a pretty crappy way to try to measure temperature.

Yeah yeah, we don't measure temperature with a thermometer.

Yes, you really are in over your head. As evidenced by your nonsensical description of entropy.

Not me, Zig.

The fact that it will burn me if I touch it doesn't tell me what the temperature is.

No, the colour of the red-hot or yellow hot poker tells you what temperature it is. A device used in kilns is called a pyrometer.

And that proves that temperature is not abstract... how? It doesn't. You think temperature is physical but entropy is abstract, even though temperature can only be accurately defined in terms of entropy. You think temperature isn't abstract, but you don't actually know what it even means. That's OK, I don't hold that against you: very few people actually do, and the real definition turns out to be subtle.

They're both emergent system properties. Temperature is a measure of the average motion, entropy is a measurement of the similarity.

If you really like, we can go down this road and I'll tell you all about temperature and entropy, but I'll warn you again: you have no idea what you're talking about in regards to thermodynamics. And you're going to make a fool of yourself if you keep pretending that you do.

Stow your pompous bluster. I know plenty about thermodynamics. And as for making a fool of yourself, tell us about that negative carpet again. You know, the one where each edge is -4m long.

 

[Farsight]

Says who? Not the observer falling into the hole - for her, they are accelerating outwards, and that is a perfectly reasonable explanation.

This thread is getting increasingly bizarre. We've got Zig talking about negative carpets and nurses who don't take temperatures, and now you're trying to suggest that a mirror on the wall is accelerating outwards? Aaaaggh! Sol, the principle of equivalence does not mean that you are literally accelerating when you're standing on the ground. It's academic anyway. You can conduct the experiment when you and your two-parallel-mirror light clocks are in free fall. At all times the lower clock is below the upper clock, so you continue to see that the light beam in the lower clock goes slower than the light beam in the upper clock:

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Wrong. The latter is an expression for flat empty spacetime. The former is another.

And you still won't say what it represents! What's the problem?

Your argument is manifestly insufficient, Farsight. You claim that the fact that light clocks run slow near the horizon of a black hole shows that the speed of light varies and that everything freezes on the horizon. But lightclocks run slow near r=r0 in my metric, in exactly the same way as near a black hole horizon - and yet your conclusions don't apply to it. Therefore your conclusions are not justified by any of the "evidence" you've presented.

See above. You're fighting shy of revealing your metric. And my argument is that the lower light beam moves slower than the upper, and that's why th e lower light clock runs slow, and that's why we see the thing we call gravitational time dilation. And that the upward vertical beam of light at the event horizon, the one that doesn't slow down, doesn't curve round, and doesn't fall back, doesn't get out. At the event horizon sol. Where we say that gravitational time dilation is infinite. I'm afraid the only thing that's manifest, sol, is that you've lost this argument.

No, it's not very different. The near-horizon Schwarzschild metric is identical to the metric I posted. All geometric effects, like lightclocks running slow, measured accelerations of static observers, etc. are identical.

A metric is an artefact of measurement. It isn't reality, and your motion alters what you measure. There is no black swathe following behind that accelerating spaceship, eating up the stars behind it. But there is a massive monster of a black hole at the centre of our galaxy.

So since you seem to agree that the behavior of lightclocks etc. at the Rindler horizon does not provide evidence for it being a special place where things freeze, by simple logic you must also agree that the identical behavior of lightclocks etc. at the Schwarzchild horizon does not provide evidence for it being a special place where things freeze.

By broken logic. The people in that accelerating spaceship see what they think of as a special place behind them. But we're observing them, and guess what? It isn't special at all. But a black hole is.

I look forward to your retraction of everything you've posted in this thread.

Now you're really getting desperate.

 

[Farsight]

"No" to which question, Farsight? If it's the latter, you're doing a runner. If it's the former, you're incoherent.

To this question: So let's be very clear - is it your position that the Kruskal-Szekeres coordinates predict that clocks held in place close to a black hole horizon - at fixed areal radius, or fixed "r" in Schwarzchild coordinates - do not run slow compared to clocks far away? And you're clutching at straws.

 

[Farsight]

In this post I'll take a closer look at Farsight's "pulsar clock".

And I'll take a closer look at Dopa's post.

The pulsars Farsight seems to be referring to are point sources of light in the radio part of the electromagnetic spectrum*, most with a parallax too small to measure (so they are at least many hundred parsecs distant). They 'tick' in the sense that a plot of the strength of the signal vs time shows strong, periodic peaks. The stability of the ticks is quite good, for some pulsars; they can 'keep time' over days or even months as well as a quartz crystal clock can for example. The pulsar clock frequencies range from sub-Hertz to kilo-Hertz; i.e. the ticks, from different pulsars, can be as slow as ~one every few seconds to ~a thousand per second.

Tell us something we don't know.

Farsight has left off quite a few pesky - but important - details in his oh-so-brief description. For example, the local P-MLCs (parallel-mirror light clocks) are in some room in some lab here on the surface of the Earth, separated in elevation by ~a meter. If this lab is located in Poole, England, this experiment can only be carried out within a fraction of each day, when the pulsar is above the horizon, in Poole, England (or maybe not at all, if the pulsar's declination is too far south). Further, the lab is moving, with respect to the pulsar, and the relative velocity is constantly changing (the Earth the lab is on rotates, and revolves around the solar system barycenter). Then the radio waves - which carry the clock's signal - pass through the interstellar medium and interplanetary medium and the Earth's ionosphere before they are received in the room in the lab in Poole, England. All three are dynamic, and all three affect the signal. And so on.

Ditto.

But let's do what Farsight did not; let's spell out more clearly what the experimental set-up actually is. Our lab is located on the surface of a perfectly spherical, non-rotating, solid, isodense planet which is a very long way from any other dense object (star, planet, etc). This planet has no atmosphere. The pulsar clock is located directly overhead, has no observable proper motion, and emits a light signal of stable 'ticks' (we verify this by observing it for many years, from a fixed location on the surface, and comparing the signal with a variety of local clocks, calibrated with equipment that is keyed to the SI definition of the second). Anything more we need to specify?

Yawn. No.

Next, "gravitational potential", as in "send you to a lower gravitational potential". This time, unlike in many other posts, Farsight did not write "different elevation". Nevertheless, perhaps we can combine them, and describe the experimental set-up in more detail.

Uh huh.

There are identical copies of all the equipment on a dozen or so ultra-light platforms, each platform attached to an ultra-light, vertical tower. The distance between each adjacent pair of platforms is the same, as measured by a ruler. The equipment on each platform includes a gravimeter, which measures the local g. Anything more we need to specify?

No. But don't forget that the local g is gives you the local gradient in gravitational potential, not the gravitational potential.

Now we're almost ready to do the Farsight experiment! Or are we? Is there anything I've left out? Oh, and I'm going to propose an interesting variation: each platform also has a (modified) pulsar clock! And there's one at the base of the tower too, along with yet another identical copy of all the equipment.

Why not make it a parallel-mirror light clock? Why, then you can use it to measure the speed of light!

In a later post I'll describe this modified pulsar clock in more detail ...

LOL. Don't bother. Your "interesting variation" demonstrates that you still don't get it.

 

[Farsight]

Oh, it's also got a length. But you need the displacement to get the area, otherwise you don't know what length you're measuring. There are many different lengths on a piece of carpet, and it all you tell me are a few of them, I don't even know what shape it is. But if you tell me the displacement, then I do.

Not so. Now go and show somebody your negative carpet with three edges measuring -3m -4m and -5m. Or any other negative lengths and number of edges. Then get real. A length can't be less than zero. Nor can a speed.

The Schwarzchild coordinates do describe the black hole interior. They don't stop at the event horizon..

Are you sure about that Zig? Anybody else care to back him up?

Furthermore, even if we simply truncate the Kruskal coordinates at the event horizon so as to avoid the Schwarzchild coordinate singularity, the constancy of the speed of light in Kruskal coordinates is explicitly NOT contradicted by the evidence. It matches the evidence exactly. We get identical observed red shifts when we do our calculations in Kruskal coordinates. It is a mathematically guaranteed that predicted observations in Kruskal and Schwarzchild coordinates will match. Math itself (not the math of GR, but ALL math) would have to be inconsistent for that to happen, and it's not. You still can't grasp this rather fundamental fact.

But we aren't talking about outside the event horizon. We're talking about the nature of a black hole. What lies beneath. And when we do, we remember that mathematics isn't fact. We remember that scientific evidence is fact. It trumps mathematics. And you still can't grasp the scientific evidence that shows you a really fundamental fact: that the speed of light varies. Because your maths tells you it doesn't? Groan. It's cargo-cult science all right. Whatever next? Is somebody going to tell me that a coordinate system where the sun goes round the earth is all fine and dandy?

 

[Farsight]

Thank you, you have finally addressed my second point, which was (paraphrased for brevity): Without details or quantitative laws, you are just asking us to take your word for it that a model in which the permittivity and permeability of the vacuum vary through space is a viable theory of gravitation. You have addressed this by making it crystal clear that you have no intention of ever providing us with those details. Presumably, then, you expect us to take your word for it that it all works out as you have claimed. In reality, no skeptic worth his or her salt could possibly agree with you on the basis of this evidence.

The evidence that supports Einstein is right there in optical clocks losing synchronisation at different elevations. You know they'll each stay synchronised with parallel-mirror light clocks at those elevations, so you know that parallel-mirror light clocks at different elevations lose synchronistion. We can represent that like this:

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Coupled with say the Shapiro delay, it's clear that the speed of light varies. We are aware of the impedance of free space, usually written as Z₀ = √(μ₀/ε₀). The μ₀ is permeability whilst ε₀ is permittivity. The speed of light c = √(1/ε₀μ₀). Given this, and given that we can see that the speed of light varies, it would be unreasonable to insist that it does not. Especially since there’s a similar expression in mechanics, wherein a transverse wave travels at a speed determined by the stiffness and density of the medium. The expression for this is v = √(G/ρ) where G is the shear modulus of elasticity, and the ρ is the density. And we know that impedance is measured in Ohms, and is “resistance to alternating current”. We also know that it applies to space because electromagnetic waves are a form of alternating current. Not alternating conduction current, which is the motion of charged particles, but displacement current. Displacement current is a "time-varying electric field", this being a feature of a passing electromagnetic wave. Have a read of the physicsworld article Taming Light at the Nanoscale for more on displacement current. Given the robust and well-understood nature of all of this, it's actually rather cut and dried. In reality, no skeptic worth his or her salt could possibly agree with you that there is no evidence.

My first point, which you have still not answered, was this (paraphrased again): Given that there is no empirical evidence whatsoever that favours FGR over "MTW" GR, why do you prefer FGR? Implicit in that was a challenge to present any empirical evidence that contradicted my assertion, but all the experimental evidence you have mentioned is perfectly consistent with standard "MTW" GR. As for whether it is also consistent with FGR - who knows? You haven't given us the details that would enable us to decide; you have rejected requests for the same as "not relevant", "a deliberate distraction", "specious erudition" and "sophistry".

So here's the Executive Summary:

• There is no actual empirical evidence favouring FGR over "MTW" GR. Even if all the other objections to FGR were met, this point by itself means there is no rational basis for claiming that FGR is preferable to "MTW" GR. (Unless FGR were somehow easier to learn or use, naturally, but on the basis of this thread that seems highly unlikely).
• There is no mathematical model for FGR, just a handful of assertions and analogies. As a result, nobody (not even Farsight) can know if it is equivalent to "MTW" GR as far as current observations go, whether it makes correct predictions at all, or even if it is self-consistent.

I would be perfectly willing to change my mind if you address those points, but for now I am completely unconvinced by the case you have put forward. Your failure to present relevant evidence is a show-stopper, and I don't think you appreciate the gravity of the situation.

You are completely unconvincing. I've presented the evidence. It's very simple. Einstein was right. Die Ausbreitungs-geschwindigkeit des Lichtes mit dem Orte variiert. The speed of light varies with location. The evidence is robust, but you dismiss it. And you continue to try to assert that this is my theory. It isn't. It's Einstein's. MTW is not in accord with it.

 

[W.D.Clinger]

Says who? Not the observer falling into the hole - for her, they are accelerating outwards, and that is a perfectly reasonable explanation.

This thread is getting increasingly bizarre. We've got Zig talking about negative carpets and nurses who don't take temperatures, and now you're trying to suggest that a mirror on the wall is accelerating outwards? Aaaaggh! Sol, the principle of equivalence does not mean that you are literally accelerating when you're standing on the ground.

We've also got Farsight arguing with Einstein:

Therefore, from the physical standpoint, the assumption readily suggests itself that the systems K and K' may both with equal right be looked upon as "stationary," that is to say, they have an equal title as systems of reference for the physical description of phenomena.

But we're making progress here. Farsight is finally starting to give us some predictions of FGR (Farsight general relativity) that disagree with the predictions of standard GR (as developed by Einstein and explained in standard textbooks such as MTW).

Wrong. The latter is an expression for flat empty spacetime. The former is another.

And you still won't say what it represents! What's the problem?

sol invictus has explained what it represents on at least four occasions, including the sentences Farsight quoted above, so the problem appears to lie with Farsight's reading comprehension:

You're fighting shy of revealing your metric.

...snip...

No, it's not very different. The near-horizon Schwarzschild metric is identical to the metric I posted. All geometric effects, like lightclocks running slow, measured accelerations of static observers, etc. are identical.

A metric is an artefact of measurement. It isn't reality, and your motion alters what you measure.

Once again, Farsight is arguing with Einstein. According to Einstein, the metric is reality, but particular metric forms are artifacts of the coordinate system you choose to use when describing that metric.

Farsight has that backwards. Farsight thinks the metric itself is an artifact, but interprets one particular metric form (in Schwarzschild coordinates) as reality, and bases his argument upon the coordinate singularity of that metric form. As Lemaître wrote, that singularity is fictitious: it's nothing more than an artifact of Einstein's and Schwarzschild's hope that spacetime surrounding an isolated mass would always be static.

So since you seem to agree that the behavior of lightclocks etc. at the Rindler horizon does not provide evidence for it being a special place where things freeze, by simple logic you must also agree that the identical behavior of lightclocks etc. at the Schwarzchild horizon does not provide evidence for it being a special place where things freeze.

By broken logic. The people in that accelerating spaceship see what they think of as a special place behind them. But we're observing them, and guess what? It isn't special at all. But a black hole is.

Black holes are special all right, and the event horizon is physically meaningful, but the event horizon is not a special place where things actually freeze.

That's what it looks like to outside observers, because outgoing light is swimming against the stream of infalling space, but an observer who's going with that flow will see spacetime as locally Minkowskian.

By taking Einstein's theory of general relativity as axiomatic, we can give a mathematical proof of that last fact. Whether Farsight can comprehend that proof is doubtful. Farsight is, after all, having a lot of trouble with sol invictus's metric form for flat spacetime.

 

[Farsight]

So much crackpottery in one sentence ! That is close to a lie. You have been pointing out evidence for GR and saying it is evidence for "Farsight-GR" (FGR) that you have not defined except for vague "space is inhomogeneous" assertions and the even more vague "speed of light varies" statement. The speed of light c is constant by definition.

Enough. I cannot respond adequately to somebody who says it's constant because I say it's constant and moreover is abusive and untruthful whilst dismissing scientific evidence and what Einstein actually said.

 

[Farsight]

Probably not that important, but does anyone - including Farsight - know what this is about?

ctamblyn seems to be addressing a point (fixation?) that Farsight has with the relationship between clocks and electromagnetism, by pointing out that clocks which run ('tick') by physical processes other than those directly involving electromagnetism 'tell the same time' as electromagnetism-based clocks.

Farsight seems to be saying that yes, all (good) local clocks tell the same time ... because every physical process can be reduced to electromagnetism. Or maybe he's saying something quite different. I really can't tell. What do you think?

I'm not quite saying that every physical process can be reduced to electromagnetism. I have already said that nuclear clocks might show some discrepancy as compared to electromagnetic clocks. I don't think they will, but let's see what experimentation tells us.

IMHO it's better to say that all physical processes are affected because there is an underlying "unification" of the forces. Proton-antiproton annihilation to gamma photons offers a clue to this, wherein the "fundamental" strong force appears to vanish.

 

[DeiRenDopa]

Some follow-ups ...

Following up on one of DeiRenDopa's questions:

First question: in the relevant literature on GR, is there anything which suggests that the "modern notation and differential geometry in textbooks such as MTW and Wald" is inconsistent with the foundations of the standard theory of general relativity, as "laid out in Einstein's 1916 paper (cited above by ben m and" W.D. Clinger)?

Yesterday, in a bookstore, I stumbled across this book:

Antoni A Kosinski. Differential Manifolds. Dover, 2007.​

It's basically a reprint of Kosinski's 1993 book, with a new appendix that discusses Perelman's proof of the Poincaré conjecture. Although the book covers only Riemannian (and not pseudo-Riemannian) manifolds, the "Historical Remarks" at the end of chapter 2 shed light on DeiRenDopa's question above.

Up to the time of B. Riemann manifolds thus appear only as curves or surfaces in R3. While Riemann is generally credited with the idea of an abstract n-dimensional manifold, what actually appears in [R] is what we would call one chart with a metric given by a linear element ds2....

The "modern" definition of a differentiable manifold appears for the first time in the 1895 paper of H. Poincaré [P1]. Manifolds are still submanifolds of Rn, but all necessary elements are present: The definition is by overlapping charts and the condition on the rank of the Jacobian is stated explicitly...

By 1916, Einstein's "absolute differential calculus" had advanced 20 years beyond Poincaré's "modern" definition of a differentiable manifold.

Kosinski continues:

....The first intrinsic definition of a manifold---that is, not as a submanifold of anything else---appeared, in a rather awkward form as a set of axioms, in the work of O. Veblen and J.H.C. Whitehead ([VW]) in 1931.

In my opinion, that's giving Einstein too little credit. In Einstein's 1916 paper, it looks to me as though the spacetime manifold is already intrinsic.

Einstein does appear to be working within the domain of a single chart, but I can't tell whether he's doing that because he's writing a tutorial introduction to general relativity, or because he thinks all physically plausible spacetime manifolds can be covered by a single chart, or because he doesn't know any better.

Note well that assuming all of spacetime can be covered by a single chart is not at all the same as assuming a single chart. Sections 5 and 6 of Einstein's paper are all about coordinate transformations (from one chart to another, which are implicitly assumed to share the same domain), and the rest of part B is related to coordinate transformations.

When Farsight denies the validity of coordinate transformations (as he did above, and has been doing for years), he's arguing with The Foundation of the General Theory of Relativity by Albert Einstein.

Thanks for this.

Combined with several others' posts (and an earlier one of your own), this make it clear that whatever set of ideas Farsight has presented in this (and other) threads, on GR, they are not Einstein's GR (we have all known for some time that Farsight's ideas are not "MTW" GR).

Probably not that important, but does anyone - including Farsight - know what this is about?

ctamblyn seems to be addressing a point (fixation?) that Farsight has with the relationship between clocks and electromagnetism, by pointing out that clocks which run ('tick') by physical processes other than those directly involving electromagnetism 'tell the same time' as electromagnetism-based clocks.

Farsight seems to be saying that yes, all (good) local clocks tell the same time ... because every physical process can be reduced to electromagnetism. Or maybe he's saying something quite different. I really can't tell.

What do you think?

Based on his request for me to use the term "relativity+" in place of "FGR" (near the end of this post), my money would be on him thinking of the ideas he expressed in the Relativity+ thread. It's his "theory of everything" in which particles we normally think of as fundamental are in fact photons somehow trapped in "self-bound states", or something like that. Every particle would then carry a kind of internal clock that runs at a rate proportional to the speed of light. If that's what FGR (as presented in this thread) depends on then it obviously cannot be some "correct", "true-to-Einstein" interpretation of GR.

(Sorry for all the scare quotes.)

Thanks for this.

It would be nice if Farsight were to confirm what you've written, or provide an explanation which is consistent with GR.

Two years ago? That's nothing, Farsight's view hasn't changed since at least 2008.

The funny thing about 2008? It's about 4 years ago. An 18-year-old high school graduate could have entered college in 2008, learned vector calculus, learned mechanics, learned differential equations, learned special relativity, learned differential geometry, learned general relativity, and (preparing to graduate in a few months) actually become a physicist. (And, simultaneously: learned a language, learned critical theory, played Ultimate, worked nights and weekends, took summers off, etc..)

I wonder how many times, over those same four years, Farsight said "don't demand that I do the math, I'm not a physicist"? If he had spent those four years becoming a physicist he'd be sitting here *calculating* whether or not GR predicts altitude-based clock disagreements, not guessing wildly that it doesn't.

Perhaps he had different priorities, such as writing and promoting his book.

But you are right, and he could have been writing and publishing papers in credible journals instead.

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(ETA: It seems this goes back to at least 2006. Note the last sentence of the opening post .)

That's pretty amazing.

So, much like MM, Farsight has not - in the last ~five years - been able to either a) put quantitative meat on the word-skeleton of his ideas, or b) explain his ideas in a sufficiently clear way that others* can understand them^.

Also, much like MM, Farsight seems to have a tin ear. Given the enormous amount of time he's put in to writing posts here, and his stunning lack of success at communicating his ideas, I think a reasonable response would have been to deeply examine the form and content of the communication. Try to find some common ground on which to start building a meaningful dialog. Ask questions. Etc. Yet what Farsight actually writes is this sort of thing: "LOL. Don't bother. Your "interesting variation" demonstrates that you still don't get it."

Someone - perhaps PS - characterized MM's posting as having a strong narcissistic tendency; why else persist in behavior that is so obviously unsuccessful (in terms of attaining its explicit goal)? Perhaps Farsight too ...

* by 'others' here I mean, roughly, any JREF (or other forum) member who has participated, actively, in the discussion in any of the threads.
^ actually that's not quite true; MM's ideas (some of them anyway) have, apparently, been well-understood by others ...