Black holes

[Brian-M]

Can you explain to us what the difference is between our concept of time slowing down and your concept of light slowing down? Because if there is no difference, you've just wasting our time with a mangled attempt to describe the same thing with different words.

There's a lot of differences.

Okay, glad to hear it.

You appreciate that gravity is there because space is inhomogeneous so light "veers", not because spacetime is curved. That's the effect, not the cause. Time travel is totally out of the window, CTCs get junked. Black holes go back to being frozen stars, you then liken them to the early universe expanding at a constant rate, but because everything in it is moving in slow slow motion that gets less and less slow, from inside the universe the expansion looks as if it's initially very rapid. That's inflation. And the black hole is also like an inside-out universe, there is no outside to it, and it doesn't curve round on itself, it's expanding because stress-energy is like pressure, so the universe has to have an edge. You realise that the so-called constants aren't really constant, so all that anthropic "goldilocks" multiverse stuff gets the boot. And it dawns on you what Minkowski was on about with "Then in the description of the field produced by the electron we see that the separation of the field into electric and magnetic force is a relative one with regard to the underlying time axis; the most perspicious way of describing the two forces together is on a certain analogy with the wrench in mechanics, though the analogy is not complete". And Maxwell when he said "A motion of translation along an axis cannot produce a rotation about that axis unless it meets with some special mechanism, like that of a screw". You can relate it to the frame-dragging of gravitomagnetism and then Thomson and Tait's vortex atoms, only you're then into soliton elementary particles appreciating what TQFT is all about, wherein massive stable particles are like chiral stress-energy "knots" and antimatter particles are like you tying your shoes right-over-left instead of left-over-right. (See this essay for an intro. I must look at this video by the way). Then you understand the photon-in-the-box and the radiating body losing mass, and see the symmetry between momentum and inertia aka mass. The list goes on. It's like you pull a thread with Einstein's name on it and out comes this string of pearls, pop pop pop, one after the other. That one little shift changes so much.

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

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.

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

 

[Reality Check]

There's a lot of differences. You appreciate that gravity is there because space is inhomogeneous so light "veers", not because spacetime is curved.

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.
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.

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.

 

[Ziggurat]

I'm afraid it isn't, Zig. Entropy isn't something fundamental.

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

It's a measure of "sameness". Think about a system containing gas molecules. You start off with some fast-moving molecules and some slow. You end up with all your molecules moving at a similar speed.

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

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

She's measuring the patient's temperature.

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

When you measure the temperature of a container of gas, no one gas molecule has any property of temperature or heat, it's either moving fast or it isn't. Collectively the gas molecules in the system have an average speed and an average kinetic energy, and when we measure the thing we call the temperature, that's what we're measuring.

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.

No I'm not.

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

No you don't, you just look at it. When it's glowing and red, it's hot, and you make sure you don't grab it by the wrong end.

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

It's the other way round. Physical things have physical consequences. They can be described using abstract theory, but it's important to remember that the abstract theory is abstract.

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. 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.

 

[Farsight]

OK, I won't hesitate. Let's start with the very post you replied to here. My first question was:

First, it is a fact (that anyone can verify) that "MTW"-style black holes are valid solutions of the mathematical model we've been calling "MTW" GR. On the other hand, you assert (without details) that this is incompatible with FGR, which advocates a frozen star picture. I'm going to anticipate the answer to ben m's question above, and say that there is no available evidence which favours FGR over "MTW" GR on this issue. In fact I will go further and bet that there is no empirical evidence whatsoever that favours FGR over "MTW" GR (feel free to prove me wrong). Given that, on what rational basis are you actually rejecting the one and embracing the other?

Your response was:

I keep showing you how the speed of light really does vary with position, like Einstein said. And I've given lots of details. Pay careful attention to my conversation with Brian about the NIST clock and how we define the second.

That I can see that the speed of light varies with gravitational potential:

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These two light beams are not going at the same speed.

As you requested, I won't hesitate to point out that you have completely evaded my first question. You did not provide any evidence which favours FGR over "MTW" GR, and you did not explain what the rational reasons for your preference are.

I haven't "completely evaded" your question at all. I answered it. The evidence is crystal clear, we can measure the Shapiro delay, we can see optical clocks lose synchronisation when separated by only a foot of vertical elevation. The speed of light varies with position, just like Einstein said. This isn't my model, it's Einstein's. Doubtless you will repeat your assertion that I have evaded your question and that no evidence exists!

My second question was:

Second, the "details" issue. You claim that FGR can be understood in terms of vacuum permittivity and permeability varying through space. You further claim that the predictions of FGR are in accord with the predictions of "MTW" GR when it comes to the classical tests of general relativity, but disagree in some other areas (e.g. black hole interiors and Hawking radiation). However, you have not given us any details; you have not shown us any quantitative laws. You are just asking us to take your word for it.

Indeed, in light of the demonstrated inequivalence of certain other similar-sounding models to GR there is every reason for a good skeptic to assign a very low prior probability to the truth of your claims. Given the lack of detail you have provided there is no way to know if they are even self-consistent.

To which you replied:

I'm asking you to look at the evidence and think for yourself.

Whoa. I'm the skeptic here. Not you.

So, I explain my reasons for disbelieving you - namely, that you have still not provided sufficient evidence to favour your model over standard, modern GR, and you have not even provided sufficient detail to determine whether your model is self-consistent - and you say that somehow that makes me non-skeptical. I ask you for details that would help me evaluate your model correctly, and you decline.

Again, it isn't my model. What we have here is patent scientific evidence along with the Einstein quotes. You dismiss it all. I've previously explained the signficance of the Schwarzschild "coordinate singularity" and why it cannot be transformed away, but this has been similarly dismissed. Asking for mathematical details of "my model" is not relevant, it's a deliberate distraction.

You did not provide the quantitative laws that determine how the permittivity and permeability are affected by the distribution of matter and energy, and likewise how matter and energy move in response to variations in permittivity and permeability. You did not give us the field equations of FGR, or the equations of motion. You did not provide a proof that FGR reproduces the results of "MTW" GR as far as the classical tests are concerned. Nor did you did provide any details whatsoever. Please, put your mathematical model where your mouth is, and stop expecting us to be so gullible as to simply take your word for it.

We both know that you do not need a mathematical model from me to observe the scientific evidence that the speed of light varies with position. The mathematical model of the black hole interior provided by Kruskal-Szekeres coordinates contradicts this reality. No mathematical model from me will prove this. I reject your demand on that grounds that it is specious erudition and sophistry. Here's the Einstein quotes again:

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).

1912: On the other hand I am of the view that the principle of the constancy of the velocity of light can be maintained only insofar as one restricts oneself to spatio-temporal regions of constant gravitational potential.

1913: I arrived at the result that the velocity of light is not to be regarded as independent of the gravitational potential. Thus the principle of the constancy of the velocity of light is incompatible with the equivalence hypothesis.

1915: the writer of these lines is of the opinion that the theory of relativity is still in need of generalization, in the sense that the principle of the constancy of the velocity of light is to be abandoned.

1916: In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust.

What he actually said in 1916 was die Ausbreitungs-geschwindigkeit des Lichtes mit dem Orte variiert which translates to the speed of light varies with the locality.

 

[Farsight]

OK. Then I agree that a reasonable and consisten interpretation is that the speed of light is different.

Good. I'm pleased to hear it.

Another reasonable and consistent interpretation is that the speed of light is the same, but the lower mirror is accelerating up at a faster rate than the one above.

It isn't reasonable and consistent at all. Those mirrors aren't going anywhere. Whilst the principle of equivalence relates an accelerating observer to an observer standing on the surface of the earth, he isn't actually accelerating. He isn't gaining energy, and the sky isn't falling in. Those mirrors aren't accelerating either, and we don't actually need them. We could repeat our experiment without any mirrors:

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Therefore, light has farther to travel between bounces. There are infinitely many more reasonable and consistent explanations.

Ah, such as heavenly angels whipping the light harder? Pull the other one sol. We know about length contraction, and we can see that the light moves faster at the higher elevation.

I've already told you, three times now: flat, empty space. Nevertheless, you've asserted (correctly) that light clocks held close to r=r0 run slower than those at larger r. And yet, this is flat spacetime, and you've asserted that means the speed of light is uniform. So you have a problem. A big one.

Not me. The expression you gave was [latex]$ds^2 = -(r-r_0) dt^2 + dr^2/(r-r_0) + dy^2 + dz^2$[/latex]. The expression for flat empty spacetime is [latex]$ds^2 = -dt^2 + dx^2 + dy^2 + dz^2$[/latex]. We can relate that to Pythagoras' theorem and the parallel-mirror light clock, wherein the macroscopic motion of light through the universe reduces the local motion within a light clock. But you still won't say what your expression is meant to represent.

 

[Farsight]

Noooo. No. No? Farsight, I meant what I said. "Optical clocks run at different speeds at different heights" is a standard GR prediction. (Similarly, optical clocks run at different speeds if they are moving at different speeds.)

I know this. See post #489 for example.

Different observers will disagree on the separation of the mirrors, not on the local speed of light

I know that too. We always measure the local speed of light to be 299,792,458 m/s. Not as something else.

When I said "This is derived in section 38.5 of MTW", that's what I meant. Let me say it again. Gravitational redshift of, including optical clocks, is a standard prediction of standard general relativity. You thought otherwise? Too bad for you, you were wrong. It's right here in front of me.

No I didn't think otherwise. Sheesh ben, have you been asleep?

ETA: If you had some actual complaint about it --- "Yes, I know that derivation, and it doesn't apply because X" --- but you don't even own a GR textbook. You've been guessing that the derivation doesn't exist, apparently because you don't want it to exist, because you're so certain you've found an error in GR.

I haven't found an error in GR, I'm pointing to scientific evidence and Einstein quotes and highlighting misinterpretation of GR.

The point of the derivation, by the way, is a recurring problem with your mythical "optical clock". If I see a distant pair-of-mirrors, and I see that it takes light 1.00 nanoseconds to complete one round-trip, I don't conclude "Hey, light is slow over there". I conclude "Those mirrors are 15cm apart". If I look somewhere else, and I see two other mirrors where light takes 10 nanoseconds roundtrip, I say "Those mirrors are 1.5 meters apart". Other observers, in other regions of space (or with motion relative to me and/or the mirrors) will disagree with me about these lengths, because they disagree with me about the time, which is (as perhaps you've heard) a common and uncontroversial aspect of relativity.

It isn't a mythical clock. It's this clock. Two identical clocks like this lose synchronisation when separated by a foot of vertical elevation. And you know that parallel-mirror light clocks will do the same. And you know about the definition of the second and the metre. The definition of the second changes with elevation, but not the definition of the metre. So your conclusion is wrong.

 

[Farsight]

That's because, for one thing, exactly the same "logic" you are applying to black hole horizons applies equally well to Rindler horizons - but we know for certain that nothing out of the ordinary can happen at a Rindler horizon...

And yet, all of that holds true at Rindler horizons...

And yet, the precise analogue of Kruskal coordinates for the Rindler horizon are simply the standard Minkowski coordinates...

And we also know that the Rindler horizon is an observer effect. I could take you outside to gaze at the dark starry sky, and I could point out an accelerating spaceship. The crew on that spaceship will observe a dark area at their rear, which we label the Rindler horizon. But we see no black swathe of darkness sweeping along behind them. Just as rain doesn't suddenly start falling diagonally because you started to run through it. The black hole event horizon is something very different.

In other words, you're "doing a runner".

Not me, sol. I despair at ignorance and quackery and dishonesty, but I don't run.

 

[Farsight]

Like this:

Yes it does. You are simply wrong to claim that it doesn't. In fact, it's rather trivial to see on a plot that a distant observer staying at a fixed radius in Scharzchild coordinates, when transformed into Kruskal coordinates, will still see exactly the same redshifted signal from an infalling object. It's trivial to prove this mathematically as well: not only do the coordinates transform reversibly from one reference frame to the other, but the metrics will give the same distances for all curves. So we're guaranteed to calculate the exact same properties for EVERYTHING except where quantities are not defined in one coordinate or the other. But since that only happens at the event horizon in Schwarzchild coordinates, and since even by your own admission we can't see what happens there, it is literally impossible for there to be any disagreement for what a distant observer will observe, whether we calculate that with Kruskal coordinates or Schwarzchild coordinates.

No, they don't. You have made an assertion about Kruskal coordinates which is simply wrong. Your understanding of Kruskal coordinates is therefore wrong as well (assuming that you're not just a liar).

No, Farsight. It's a displacement. That's how you know it's a square: there are two orthogonal displacements. If all you had was two lengths, well, two lengths don't make a square.

Are you all going to keep quiet and refuse to point out that Zig is wrong on these points? Who's got the honesty to say that the edge of a carpet has a length rather than a displacement? And who's got the honesty to say that Zig has evaded the issue at hand, namely that Kruskal-Szekeres coordinates describe a black hole interior that Schwarzschild coordinates do not, and that Kruskal-Szekeres coordinates demands a constant speed of light that contradicts the patent scientific evidence that we can see with our own eyes?

 

[sol invictus]

It isn't reasonable and consistent at all. Those mirrors aren't going anywhere.

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

Not me. The expression you gave was [latex]$ds^2 = -(r-r_0) dt^2 + dr^2/(r-r_0) + dy^2 + dz^2$[/latex]. The expression for flat empty spacetime is [latex]$ds^2 = -dt^2 + dx^2 + dy^2 + dz^2$[/latex].

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

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.

And we also know that the Rindler horizon is an observer effect. I could take you outside to gaze at the dark starry sky, and I could point out an accelerating spaceship. The crew on that spaceship will observe a dark area at their rear, which we label the Rindler horizon. But we see no black swathe of darkness sweeping along behind them. Just as rain doesn't suddenly start falling diagonally because you started to run through it. The black hole event horizon is something very different.

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.

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.

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

 

[W.D.Clinger]

I'm asking you to look at the evidence and think for yourself.

Okay. Let's look at the evidence Farsight has provided, and think for ourselves.

I've already told you, three times now: flat, empty space. Nevertheless, you've asserted (correctly) that light clocks held close to r=r0 run slower than those at larger r. And yet, this is flat spacetime, and you've asserted that means the speed of light is uniform. So you have a problem. A big one.

Not me. The expression you gave was [latex]$ds^2 = -(r-r_0) dt^2 + dr^2/(r-r_0) + dy^2 + dz^2$[/latex]. The expression for flat empty spacetime is [latex]$ds^2 = -dt^2 + dx^2 + dy^2 + dz^2$[/latex]. We can relate that to Pythagoras' theorem and the parallel-mirror light clock, wherein the macroscopic motion of light through the universe reduces the local motion within a light clock. But you still won't say what your expression is meant to represent.

As sol invictus has told Farsight three times already, his metric form represents flat, empty Minkowski space. His metric is equal to the more familiar metric form Farsight quoted.

Many of us figured this out when sol invictus first posted his metric form. We've done our homework. Farsight still hasn't figured it out, despite being told the answer on three separate occasions.

GR is a well tested theory, and I've previously referred to The Confrontation between General Relativity and Experiment.

That's the third or fourth time Farsight has linked to that paper, but he still hasn't explained why he thinks that paper supports his position.

Thinking for myself, and looking at the evidence in that paper, I can't help but notice that the paper Farsight's been citing refutes his position. Consider, for example, this extract from section 3.1.1:

The empirical evidence supporting the Einstein equivalence principle, discussed in the previous section, supports the conclusion that the only theories of gravity that have a hope of being viable are metric theories, or possibly theories that are metric apart from very weak or short-range non-metric couplings (as in string theory).

...snip...

Consequently, if EEP is valid, the non-gravitational laws of physics may be formulated by taking their special relativistic forms in terms of the Minkowski metric η and simply "going over" to new forms in terms of the curved spacetime metric g, using the mathematics of differential geometry. The details of this "going over" can be found in standard textbooks ([190, 270], TEGP 3.2. [281]).

That's an endorsement of coordinate transformations (EEP), which Farsight rejects.

That's an endorsement of differential geometry, which Farsight derides.

That's an endorsement of Misner/Thorne/Wheeler (reference [190]), which Farsight says is wrong.

When the best evidence that Farsight can come up with says Farsight is wrong, I'm inclined to doubt Farsight's position.

The mathematical model of the black hole interior provided by Kruskal-Szekeres coordinates contradicts this reality. No mathematical model from me will prove this. I reject your demand on that grounds that it is specious erudition and sophistry.

To put it more plainly, Farsight rejects a properly skeptical request for evidence.

Here's the Einstein quotes again:

...snip...

1916: In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. [/i]

What he actually said in 1916 was die Ausbreitungs-geschwindigkeit des Lichtes mit dem Orte variiert which translates to the speed of light varies with the locality.

A genuine skeptic would check to see whether Farsight is misinterpreting Einstein. He is.

Einstein goes into more detail (while using some of the same words) at the end of section 2 of his 1916 paper on "The Foundation of the General Theory of Relativity". He's discussing two distinct reference frames (coordinate systems), K and K'. In K, a mass is "moving with uniform motion in a straight line". K' is "a second system of reference which is moving relatively to K in uniformly accelerated translation." (The italics are in the original.)

Then Einstein says:

...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.

It will be seen from these reflections that in pursuing the general theory of relativity we shall be led to a theory of gravitation, since we are able to "produce" a gravitational field merely by changing the system of co-ordinates. It will also be obvious that the principle of the constancy of the velocity of light in vacuo must be modified, since we easily recognize that the path of a ray of light with respect to K' must in general be curvilinear, if with respect to K light is propagated in a straight line with a definite constant velocity.

Einstein is talking about a single ray of light here. Whether you regard that ray of light as travelling in a straight line with definite constant velocity, or regard that exact same ray of light as travelling in a curvilinear path with changing velocity (not speed) depends on the coordinate system you choose to use. According to Einstein, both coordinate systems (and both points of view) are equally valid.

Note also that Einstein explicitly says we can produce a gravitational field "merely by changing the system of co-ordinates".

Farsight has been denying both of those facts, even as he pretends to be the one who's standing up for Einstein's original point of view.

Whoa. I'm the skeptic here. Not you.

Bare assertion, contradicted by evidence.

Cornered? Me?

 

[Farsight]

I missed that until Zig quoted it. That's flat-out totally wrong. There is absolutely no scientific evidence that "contradicts" Kruskal coordinates.

Oh yes there is. Kruskal-Szekeres coordinates are defined using a "new time coordinate" which ignores the scientific evidence that light clocks tick slower with gravitational potential. They ignore the infinite gravitational time dilation that means those clocks stop. Instead they carry on regardless, brushing aside the original frozen star concept with the never-neverland fantasy that a stopped observer sees his stopped clock ticking.

Kruskal coordinates make precisely the same predictions for every physical experiment that Schwarzschild coordinates do, including the fact that light clocks near the horizon run slow compared to those far from it.

But they fail to account for light clocks that stop, and then say the infalling observer notices nothing unusual. Schwarzschild coordinates do not. The two coordinate systems lead to very different conclusions concerning the nature of black holes, and to "space-sucking sky falling in" analogies that have no basis in fact.

 

[sol invictus]

Oh yes there is. Kruskal-Szekeres coordinates are defined using a "new time coordinate" which ignores the scientific evidence that light clocks tick slower with gravitational potential. They ignore the infinite gravitational time dilation that means those clocks stop. Instead they carry on regardless, brushing aside the original frozen star concept with the never-neverland fantasy that a stopped observer sees his stopped clock ticking.

But they fail to account for light clocks that stop, and then say the infalling observer notices nothing unusual. Schwarzschild coordinates do not. The two coordinate systems lead to very different conclusions concerning the nature of black holes, and to "space-sucking sky falling in" analogies that have no basis in fact.

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?

If so, and if you are proven wrong, would that cause you to re-evaluate your overall views of this?

 

[Farsight]

...But you're right, we don't use cycles per second to define the second. We just use cycles (or periods).

Yes. A period is a duration, so's a second.

However, if one second is defined as X cycles of radiation Y, then radiation Y must, by definition, have a frequency of X cycles per second.

Yes it does. But we can't say what the frequency of that radiation is before we've defined the second.

By your logic we can say:

S = XY​

But we can't say:

1/Y = X/S​

Until we know S?

Exactly. When we have said that S=XY, then we can say 1/Y=X/S. But not before.

Are you seriously arguing that we can't take S=XY and conclude that 1/Y=X/S until after we determine the value of S?

Yes. That's how it works. You count X durations to make up the duration you call a second, and then you say the frequency is X by definition.

No. That's a result of a different scenario, one where distance is accumulating between the ships. A commonly presented scenario, but not the scenario I described.

The people on each spaceship get a single glimpse of each-other's clocks each time they pass each-other, always from the same distance apart (just as people looking at each-other's clocks at different elevations on earth would always be the same distance apart).

The people on the slow ship will see that less time has elapsed on the fast ship than their own since they last passed, while the people on the fast ship will see that more time has elapsed on the slow ship than their own since the last time they passed each-other.

No problem.

Firstly, gravitational potential is a negative value, so gravitational potential will be higher in the center of the earth than on the surface.

No, it's lower. The negative is just a convention, there's no actual negative energy involved. Just positive energy, and less positive energy.

Secondly, there may be no gravitational potential, but there's lots of gravity in the center of the earth (pulling in opposing directions, so there's no net force). Wouldn't it make more sense to say that where gravity is strongest, clocks go slowest?

No. Generally speaking, potential is "more fundamental" than force, which is the result of a non-uniform potential.

Thirdly, an object infinitely distant from the earth would have a gravitational potential of zero, the same potential you say the clock in the center of the earth would have. Assuming that the earth and the clocks were the only masses in the universe, would you argue that a clock in the center of the earth would tick at the same speed as a clock infinitely distant from the earth?

No. It ticks slower.

Let's assume that the gravitational field is constant with height.

OK. That means the local slope in gravitational potential is uniform. Real gravitational fields aren't quite like this because they diminish with distance, but it isn't much of an issue.

Maybe because the difference is infinitesimal (because we're doing our experiments on a planet with the density of a sack of ping-pong balls, but big enough that it's surface gravity much higher than that of Earth).

OK.

But if you want it perfectly constant, then we're doing our experiments in a spaceship undergoing constant acceleration. Or are you claiming the equivalence principle (which states that the gravitational force experienced while standing on a planet is exactly the same force experienced while accelerating) is also false?

it isn't false, but the spaceship scenario isn't exactly the same as a real gravitational field. There's a slight difference in the way the force of gravity diminishes with altitude, it's 1/r rather than 1/r², but it isn't much of an issue.

 

[Farsight]

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? If so, and if you are proven wrong, would that cause you to re-evaluate your overall views of this?

No.

 

[sol invictus]

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?

If so, and if you are proven wrong, would that cause you to re-evaluate your overall views of this?

No.

"No" to which question, Farsight?

If it's the latter, you're doing a runner. If it's the former, you're incoherent.

 

[DeiRenDopa]

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

how do you use a distant pulsar to measure the local speed of light?

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. If you time it with your parallel-mirror light clock, you are using the motion of light to time the motion of light, hence you will never measure any change in the speed of light.

You define the second, and you use it to calibrate your clock. You note that your clock ticks at the same rate as some pulsar. Then I press my button to send you to a lower gravitational potential, and you repeat the whole exercise. This time you find that your clock doesn't tick at the same rate as the distant pulsar. You're smart enough to work out that I haven't changed the pulsar, and that what's changed is your local environment.

My clock hasn't slowed down, you've just changed my frame of reference to one where the pulsar oscillates at a faster rate.

Your clock has slowed down because I moved you to a lower location. The pulsar hasn't changed a jot. And your frame of reference is an artefact of measurement. You now measure things differently because the environment you're now in different to the environment you were in.

First, let's clarify a few things in these parts of Farsight's posts.

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.

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.

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?

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.

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?

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.

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

* some have also been observed to emit in other parts of the spectrum; e.g. the Crab pulsar (light, x-rays, gammas, ...)

 

[Ziggurat]

Are you all going to keep quiet and refuse to point out that Zig is wrong on these points? Who's got the honesty to say that the edge of a carpet has a length rather than a displacement?

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.

And who's got the honesty to say that Zig has evaded the issue at hand, namely that Kruskal-Szekeres coordinates describe a black hole interior that Schwarzschild coordinates do not, and that Kruskal-Szekeres coordinates demands a constant speed of light that contradicts the patent scientific evidence that we can see with our own eyes?

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

 

[DeiRenDopa]

Here is that later post ...

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.

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

This modified pulsar clock is like Farsight's idealized one, in that the signal it emits is stable, and consists of periodic pulses (of identical shape).

Unlike Farsight's pulsar clock, the DRD pulsar clock (DPC, for short) emits at several, fixed, frequencies. These are 1 GHz, 1 THz, and 500 THz. The frequencies are calibrated using local instruments (and sources). Each DPC - they are identical, remember - emits continuously at each of these frequencies; the pulses (which form the 'ticks') are short-duration, many-hundred-fold increases in the otherwise constant intensity output.

Here are some experimental results which I think are completely uncontroversial (i.e. Farsight and every other active reader of this thread will agree):

* on each platform, all the clocks 'keep the same time'; specifically, the muon clock, radioisotope clocks (several, based on different combinations of underlying physical processes), P-MLC, quartz crystal clock, optical clock, SAW clock, tuning-fork clock, and grandfather clock all remain in synch (to within the relevant experimental uncertainties)

* when an observer on one platform checks the results of an observer on another platform - by looking at the dials and readouts through a telescope, say - they find no discrepancies

* the 'carrier frequencies' of the DPCs, as perceived by observers on each platform, vary. The variation - from 1 GHz, 1 THz, and 500 THz - is fully reproducible, and can be modeled with a relatively simple formula, based on objective, independently verifiable and measurable parameters (we'll discuss this further in a later post).

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?

 

[ctamblyn]

I haven't "completely evaded" your question at all. I answered it. The evidence is crystal clear, we can measure the Shapiro delay, we can see optical clocks lose synchronisation when separated by only a foot of vertical elevation. The speed of light varies with position, just like Einstein said. This isn't my model, it's Einstein's. Doubtless you will repeat your assertion that I have evaded your question and that no evidence exists!

Again, it isn't my model. What we have here is patent scientific evidence along with the Einstein quotes. You dismiss it all. I've previously explained the signficance of the Schwarzschild "coordinate singularity" and why it cannot be transformed away, but this has been similarly dismissed. Asking for mathematical details of "my model" is not relevant, it's a deliberate distraction.

We both know that you do not need a mathematical model from me to observe the scientific evidence that the speed of light varies with position. The mathematical model of the black hole interior provided by Kruskal-Szekeres coordinates contradicts this reality. No mathematical model from me will prove this. I reject your demand on that grounds that it is specious erudition and sophistry.

(...snip...)

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.

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.

 

[Reality Check]

So much crackpottery in one sentence !

I haven't found an error in GR, I'm pointing to scientific evidence

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. The local speed of light is always c. It is the coordinate speed of light that varies.

and Einstein quotes

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.

and highlighting misinterpretation of GR.

You have been highlighting your ignorance of GR, e.g. that different coordinate systems give different measurements (especially for the coordinate speed of light)

Originally Posted by Reality Check
In Schwarzschild coordinates the coordinate speed of light is zero at the event horizon (there is a coordinate singularity there).

In Kruskal–Szekeres coordinates the coordinate speed of light is the same everywhere (there is no coordinate singularity at the event horizon).

One of your replies to this was

It's wrong to use a coordinate system that ignores what happens in the real world.

It is wrong of you Farsight to ignore what happens in the real world, i.e. that GR exists and its predictions do not depend on any coordinate system.

It is wrong of you Farsight to think that a coordinate system (which you acknowledge are not real) somehows make the real world act in a specific way. In the real world no one has reported back from falling into a black hole. In the real world no one has observed matter falling into a black hole. In the real world no one has even directly observed that black hole's have event horizons!

It is wrong of you Farsight to obsess on Schwarzschild coordinates when Kruskal–Szekeres coordinates are just as valid coordinates to use.