Black holes

[theprestige]

I'm objecting to the lack of explanation of terms and scenario.

Am I the only one who gets the impression that Farsight is hoping for a grade-school word problem? Probably so that he can object to the wording rather than working out the solution?

"Jack is walking up a hill of height H and slope S, at rate R. As the hilltop approaches Jack-"

"Hold it right there! The hilltop is stationary! Jack is the one moving! Obviously you don't really understand hills, Jack, or motion! Your problem is stupid and wrong and there's no point in solving it!"

 

[ben m]

Am I the only one who gets the impression that Farsight is hoping for a grade-school word problem? Probably so that he can object to the wording rather than working out the solution?

Well, that's what he seems to think Einstein did. As far as Farsight can tell, Einstein wrote a three-page paper consisting of epigrammatic, koan-like verses subject to intertextual commentary. He interspersed this (for reasons Farsight doesn't know and doesn't care to ask about) with 20 pages of useless mathematical gibberish.

 

[ctamblyn]

Your "perfectly good model" has led you astray when it comes to black holes, and in other respects. Yes, this is an application of Occam's Razor. You can see that the speed of light isn't constant.

You have zero evidence that "MTW" GR has led us astray with regard to black holes, since no-one here has ever seen a black hole sufficiently close up.

Furthermore, given that "MTW" GR - or GR, henceforth - is mathematically self-consistent and has passed all relevant experimental tests thus far, there is no sound scientific reason for withholding the usual provisional belief we'd allow ourselves to have in such a theory. The only objections you have are (from where I'm standing) purely aesthetic, and you haven't even given us anything equal to GR to use in its place (you won't provide the mathematical model, remember).

Here you go avoiding the scientific evidence and what Einstein said again, and pretending that I'm being evasive!

No, I'm taking you at your own word. You said, quite explicitly, that you did not want to provide a mathematical model. This particular sub-issue is technically not even one of the scientific evidence; it's one of logical self-consistency and your refusal to provide adequate information for us to assess your proposal.

Yes, because relativity+ includes elements that GR doesn't cover. Hence the plus sign.

Right. So when you were saying you were merely presenting GR as Einstein originally intended, you were mistaken.

No, it's a principle. The principle of equivalence isn't exact. You can tell the difference between being in an accelerating spaceship and being on a planet. There's a 1/r versus a 1/r² factor that distinguishes the two.

The principle of equivalence - understood correctly - is indeed exact. Saying "it's a principle" as though it were only meant as an approximation or guideline is laughable. In GR, spacetime is locally Lorentzian flat, and as far as the clocks in my thought-experiment go, the deviations we expect due to tidal forces can be made negligible with an appropriate experimental setup.

OK, but it isn't my model.

"FGR" or "Relativity+" is something only you are arguing for. Furthermore, only you have written a book about it and argued about it with such tenacity for such a length of time on so many internet forums.

GR doesn't say anything about strong interaction. You're reading too much into it.

You are wrong; the equivalence principle is relevant to strong and weak interaction processes. Hence, a loss of synchronisation between strong-interaction clocks (or weak-interaction ones) and e/m ones would, if observed, mean that GR is wrong.

That's right. That's why I'm interested in the experiment.

And yet, below, you say you don't have a position on this. Whichever way the experiment turns out, it would not reduce your confidence in your position - therefore, the experiment is completely irrelevant as far as FGR goes (I might expand on this later).

No. Let's get this nailed down, and why the strong force is called the strong force, and why the coupling constant is given as 1 whilst for electromagnetism it's given as 1/137 and for gravity it's given as 10^-39.

Indeed, you need to refine your understanding of this. This is truly a topic for another thread though.

I feel sorry for the guys who've resigned, and irritated that the media people who hyped it don't come clean about their part in it.

It is a shame, but I'm sure they'll bounce back.

I didn't say it supported my position. I just pointed out a couple of interesting bits to it, that's all.

OK. I found it mildly amusing that not only didn't they support your position but actually highlighted the usefulness of the "flowing space" analogy.

I missed an s off clocks too. You missed that didn't you? I'm sometimes pushed for time here, and don't subject posts to the same degree of quality control as I might.

It was another mildly amusing event, that's all; you made those errors in exactly the same post in which you boasted about your proof-reading abilities. Pride comes before a fall, and all that. We've all done similar things, I suppose.

You can see that the speed of light isn't constant. Like Einstein said. That's it.

And the only actual observational evidence you have to back that up your position is perfectly consistent with "MTW" GR. So despite your objections at the time, you are now admitting that I was right, after all, when I said things like the following:

...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)...

...There is no actual empirical evidence favouring FGR over "MTW" GR...

...you cannot point to a single piece of relevant experimental evidence that contradicts "MTW" GR while simultaneously supporting FGR.

Well, it's good to wrap that one up at last.

 

[ctamblyn]

I don't have a position on this, that's why I'm so interested in the experiment. If we find that nuclear clocks aren't in line with electromagnetic clocks, we might assert that "the properties of space" are already altered down in the nucleus, and that changing altitude has less affect there than it does out amongst the electrons. If we find that nuclear clocks are exactly in line with electromagnetic clocks, then when we look at low-energy proton-antiproton annihilation to gamma photons as well, we might assert that the strong interaction is just an "aspect of electromagnetism". You know how electricity and magnetism are sometimes portrayed as being orthogonal? If you have two things that are orthogonal to each another, you can have a third thing that's orthogonal to them both.

I think the right thing to do is to do the experiment and see what happens. Gravitational changes are however very slight, so I wouldn't get too excited about it.

If the nuclear clocks lose sync with the e/m ones then it's time to either fix or replace GR. Thus, my confidence in GR (as a theory applicable to the relevant domain) would be reduced dramatically if such an effect were detected and verified. So, the outcome of the experiment is either very weak evidence in support of GR, or very strong evidence against it.

For FGR, we can't count it as evidence either way - your confidence is unaffected by the result. The experiment is irrelevant to to FGR, and hence irrelevant to the current discussion.

IMHO it would be more interesting if we had a black hole handy and could throw something straight in and see if we can detect electron stripping and 511KeV gamma photons etc.

OK, and if we could somehow do that and didn't detect any 511keV photons, would your confidence in Relativity+ be weakened (and by how much)? If you did detect those photons, would it be strengthened (and by how much)?

 

[ctamblyn]

A spacetime metric that represents what, exactly? Here it is, it's like Pythagoras's theorem, we've got a spacetime interval and the usual y and z terms, but we've now got r terms. What do they represent exactly, and what real-world scenario does the overall expression describe?

[latex]$ds^2 = -(r-r_0) dt^2 + dr^2/(r-r_0) + dy^2 + dz^2$[/latex]

Just out of interest... if you are unable to figure out what the terms above mean, how did you do it for the Schwarzschild metric? And how did you arrive at the conclusion that certain ranges of the Kruskal coordinates were unphysical, without first figuring out what the various terms meant? Did you just take someone's word for it?

 

[W.D.Clinger]

Farsight versus Einstein, part 2

...Let's use the metric form posted by sol invictus. In that coordinate system, the four nonzero components of the covariant metric tensor are

[latex]
\[
\begin{align*}
g_{00} &= - (x^1 - r_0) \\
g_{11} &= \frac{1}{x^1 - r_0} \\
g_{22} &= 1 \\
g_{33} &= 1
\end{align*}
\]
[/latex]​

You lost me, and everybody else.

I didn't lose anybody who understands general relativity. Not at that point, anyway.

But I lost you.

That means you never understood Einstein's equation (3), in the most important paper he ever wrote on general relativity (Die Grundlage der allgemeinen Relativitätstheorie). There are 75 numbered equations in that paper, and you got lost at equation (3).

How can that be? You said you understood this stuff.

That means you never even came close to understanding what Einstein called "the fundamental tensor g_μν". How can that be? You said you understood this stuff.

That means you never had a clue concerning Einstein's "ten functions" that you've been yammering about for years. How can that be?

What does sol's metric represent again?

Flat spacetime. That question has been answered at least a dozen times now, including several answers within the past 24 hours.

All I've managed to squeeze out of him is "flat spacetime", and more recently "constant proper acceleration".

The first of those answers took me less than five minutes to prove (using a far simpler technique than calculating the Riemann tensor).

You said this is a class, but you're teaching us. Why is this stuff so much harder for you than for your students?

Look, go back to what Einstein said and think it through then contribute sensibly to the discussion instead of hiding behind mathematics.

I'm using Einstein's math. To be more specific, my previous post used Einstein's equations (21), (23), (43), and (45), although I combined (21), (23), and (45) into a single equation and used more modern notation for both.

Why do you think Einstein's equations aren't sensible? Why do you think Einstein was hiding behind all that math?

"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".

Do you get it yet? Space isn't nothing. And you don't change space by moving through it.

I get it, all right. You must have had no idea of what Einstein meant by "ten functions (the gravitation potentials g_μν)". Here's a hint: You got lost when I wrote four of those functions down and said the other six were zero.

You've been quoting that passage for at least two years. Why do you continue to quote passages you don't understand?

Clinger's dollop of Emperor's New Clothes doesn't change that one bit. Care to list the terms, explain what they mean, and talk us through that maths? Never seems to happen does it?

You never seem to tell us which terms you don't understand. You don't appear to understand the terms used in differential calculus, but it would be silly to explain freshman-level concepts to "a cage-fighter working out toddlers". At the same time, we don't want to waste time explaining PhD-level material only to find you're still struggling with calculus.

To make it easier for us to know what kind of help you need, I'm going to ask you to answer each of the following questions. (I'm asking for the textbooks you used because some of us may own copies of those same textbooks and can refer you to the relevant sections.)

Questions for Farsight to answer if he honestly wants us to explain the terms he doesn't understand:

• Have you taken a course in differential calculus? If so, please name the textbook you used.
• Have you taken a course in integral calculus? If so, please name the textbook you used.
• Have you taken a course in vector calculus? If so, please name the textbook you used.
• Have you taken a course in differential equations? If so, please name the textbook you used.
• Have you taken a course in linear algebra? If so, please name the textbook you used.
• Have you taken a course in general topology? If so, please name the textbook you used.
• Have you taken a course in differential geometry? If so, please name the textbook you used.
• Have you taken a course in Newtonian mechanics? If so, please name the textbook you used.
• Have you taken a course in electromagnetism that covers Maxwell's equations? If so, please name the textbook you used.

And yet he presented it as a fait accompli without explanation, and there's still no explanation of what [latex]$ds^2 = -(r-r_0) dt^2 + dr^2/(r-r_0) + dy^2 + dz^2$[/latex] represents. This is getting laughable. It's like priests in a corner desperately spouting Latin.

No, it's like physicists speaking the language Einstein spoke fluently: math.

I related the standard coordinates of flat space time to sol's. And sol is still fighting shy of explaining why his expression relates to [latex]$ds^2 = -dt^2 + dx^2 + dy^2 + dz^2$[/latex]. Talk about smoke and mirrors. Do you really think you can ignore the hard scientific evidence and what Einstein said, and get away with it by use of a mathematical smokescreen?

It is not possible to participate in a scientific discussion of what Einstein said about general relativity without discussing his math. Charlatans may pretend otherwise, but they're charlatans.

A spacetime metric that represents what, exactly? Here it is, it's like Pythagoras's theorem, we've got a spacetime interval and the usual y and z terms, but we've now got r terms. What do they represent exactly, and what real-world scenario does the overall expression describe?

It's a concrete example of Einstein's equation (3). It's a very nice example of what Einstein was talking about in his § 13, where he presents equations (45) and (46) as examples of a nonzero gravitational field in flat spacetime, and goes on to say he's going to assume those equations hold also for curved spacetime. Einstein's § 13 is one of the high points of one of the high points of 20th century physics, but you aren't going to understand what Einstein was saying until you understand equation (3).

[latex]$ds^2 = -(r-r_0) dt^2 + dr^2/(r-r_0) + dy^2 + dz^2$[/latex]

I know what a metric is.

But we still don't know what Clinger is computing the curvature of now do we? It's been weeks now, you've got nothing, and you're still trying to dismiss Einstein and scientific evidence

Yes, we've been telling you for weeks now that the metric form you wrote above describes flat spacetime. You may not know that I computed the curvature of that flat spacetime, but those of us who have some basic understanding of general relativity know that.

and defend your waterfall neverland fantasies with mathematics that you will not relate to a real-world scenario.

How can you dismiss the waterfall analogy and its real-world implications when you so obviously don't understand the mathematics? You're beginning to look a wee bit arrogant.

Who said you did? The metric is just a representation. Space is the same regardless of what metric you use. Nobody is contesting that. But that is rather the point: you have mistaken features of the metric for features of the space. And so when Sol presents you with a metric for flat spacetime which has these strange features, you can't grasp that they are only features of the metric, and of the space itself.

I think Ziggurat meant to say "and not of the space itself", but he's being a mite sloppy here. The metric tensor really is a feature of spacetime itself, and is independent of the coordinate system. What Ziggurat meant to say is that the metric form is not a feature of spacetime itself, but depends upon the coordinate system.

With that minor terminological correction, what Ziggurat said is entirely consistent with what Einstein wrote. Farsight disagrees, but he's arguing with Einstein.

I don't think so Edd. One of the big problems here is that people confuse spacetime with space and think of "the metric" as space.

Nonsense. The metric tensor itself is a feature of spacetime, and is independent of coordinate systems, but what counts as space depends on the coordinate system, as does the metric form.

As can be seen from the preceding paragraph, terminology is important. Before we try to explain that terminology, we need to know more of Farsight's mathematical background.

To conclude this part 2, I urge Farsight to follow the advice given by sol invictus:

Stop pretending to understand when you don't, drop the attitude, start over, and ask some basic questions, nicely. We'll help you.

 

[Vorpal]

For the 1+1-dimensional static metric (λ independent of the time coordinate)
[latex]\[ ds^2 = -e^{2\lambda}dt^2 + e^{-2\lambda}dr^2 \][/latex]
the connection coefficients are simple, since the metric is diagonal:
[latex]\[ \Gamma^{\alpha}_{\mu\nu} = \frac{1}{2}g^{\alpha\alpha}\left[ g_{\alpha\mu,\nu} + g_{\alpha\nu,\mu} - g_{\mu\nu,\alpha}\right] \][/latex]
[latex]\begin{eqnarray*} \Gamma^t_{tr} = \Gamma^t_{rt} = \lambda_{,r} & \Gamma^r_{tt} = e^{4\lambda}\lambda_{,r} & \Gamma^r_{rr} = -\lambda_{,r} \end{eqnarray*}[/latex]
the rest being zero. An observer would have the four-velocity u has the four-acceleration components
[latex]\[ (\nabla_uu)^\alpha = u^\alpha{}_{;\mu}u^\mu = \left[\left(\frac{dx^\alpha}{d\tau}\right)_{,\mu} + \Gamma^\alpha_{\mu\nu}\frac{dx^\nu}{d\tau}\right]\frac{dx^\mu}{d\tau} \] [/latex]

Exercise: (Basic calculus) Show that this implies that the geodesic equation is exactly ∇_uu = 0.​

On the other hand, a stationary observer would have a four-velocity u with u^t = dt/dτ = e^-λ and u^r = dt/dτ = 0. The factor in the front is required by normalization of timelike wordlines, g_μνu^μu^ν = -1. Plugging this in, only the r-component of the four-acceleration is nonzero:
[latex]\[ a^r = e^{2\lambda}\lambda_{,r} \][/latex]

Example: For the radial Schwarzschild spacetime,
[latex]\[ e^{2\lambda} = \left(1-\frac{2M}{r}\right) \implies \lambda_{,r} = \frac{M/r^2}{1-2M/r^2}\implies a^r = \frac{M}{r^2} \][/latex]

Exercise: For an observer of mass m, how much thrust is required to keep stationary?​

*This also corresponds to local acceleration from rest of a freefalling particle in sense of d²r/dτ²*. If for some reason we wanted this to be independent of spatial position, we would solve the differential equation
[latex]\[ e^{2\lambda}\lambda_{,r} = g \implies e^{2\lambda} = 2g(r-r_0) \][/latex]
Playing around in this way of course does not ensure that the spacetime is flat. But this particular case is.

 

[xtifr]

Hmm, I'm beginning to suspect the reason that Farsight is so fond of Einstein (or what he imagines Einstein to be/have said) is that AE was so fond of his little gedankenexperiments. Farsight would like to solve the puzzles of the universe using gedankenexperiments rather than math. What he seems to fail to understand is that AE used his thoughts as a starting point, and then followed up by doing the math! Farsight doesn't want to do that, quite probably because he can't. I suspect he's learned to parrot a few keywords without the faintest idea of what they mean.

I'm no physics expert (to put it mildly), but back around page seven of this discussion, when I realized he didn't even understand frames of reference, my head hit the desk! I'd managed to work out that much by the time I was in high school!

it's a fallacy because it takes you forever in terms of "universe time" to see anything.

"Universe time"?

 

[Farsight]

This isn't an issue of doing the maths xtifr, it concerns reading what Einstein said about the speed of light varying with gravitational potential, and looking at the experimental evidence that shows you that it does. Then with some alarm you come to appreciate that people who tell you fairytales about space falling inwards towards a black hole are totally out of line with Einstein, and are peddling cargo-cult science and are defending it with mathematics rather than evidence.

I do understand frames of reference by the way. They're very simple. The thing to understand about them is that they aren't something real, but instead are abstract things associated with motion and measurement. Simply put, if you change your motion, you change your frame of reference, and your measurements change. But the world doesn't change, what changed is your motion.

 

[Farsight]

I don't think you know what a metric is.

I do. I think you confuse it with space.

You are in some spacetime.

No. I'm in space. I can move through that space, and I can observe light moving through it. Whilst I can construct a mathematical artefact called spacetime for use in calculations and predictions, this combines space with time, and is an all-times depiction of events. I'm merely a static pink timeless motionless streak in this spacetime.

There's a 4D measurement grid laid out in that spacetime, and at each grid-line-intersection you'll find a little label like "r = 4.5, z = 0.00, y = 1.39, t = 86400.2". You have no other measuring devices, so any time you do an experiment you'll label the experimentally relevant events by consulting the nearest grid-label.

I can imagine myself to be in space free of any gravitational fields, and I can label points in space with x y z coordinates. Then I can simplify matters for visualisation by dropping the z coordinate to go from a cube to a square, and then add a t dimension to give myself a block universe. If I sit motionless in space, I can then draw my worldline as a vertical line. I can also observe other things moving through space, and draw their worldlines as sloping. I can also draw a grid and assign points in this mathematical space to real-world events such as collisions, and calculate space-time intervals between these points. There's no problem with any of that. As I've said previously, we're using a variant of Pythagoras' theorem and it's the light-path length that underlies the invariant Lorentz interval.

("I'm bouncing light between two mirrors. Light hit the first mirror at the grid point labeled {4.5,0.00,1.39,86400.2}, later it hit another mirror near the grid point labeled {6.8,1.9,1.39,86401.2}") The expression that Sol gave you is the equivalent of the Pythagorean Theorem, in that it tells you how to calculate a hypotenuse from these {r,x,y,t} grid-point-labels.

Sol isn't telling me anything. I can move through space, and when I do I can draw my worldline in spacetime as sloping. If I move faster, my worldline slopes more. If I keep on moving faster my worldline slopes more and more and traces a curve. Then I can mentally get hold of my block of spacetime and deform it to straighten my worldline so that it's vertical again. Now it's as if I'm not moving, and I'm focussing on how other things move relative to me. If I had no CMBR and nothing to gauge my motion through the universe, I couldn't even tell if it was the other things moving rather than me. And again I can calculate a hypotenuse, and I can work out how I see the world and the other things in it.

The point (or one of the points) that you're missing is that Sol's hypotenuse-calculation-prescription, IF YOU KNEW ENOUGH MATH TO INTERPRET IT would tell you how the gridlines work, and would tells you whether (and where, and how, and how much) the spacetime is curved. Clinger did the algebra for you using a straightforward plug-and-chug technique.

This is nothing to do with maths, which is simple. It's to do with understanding spacetime and the difference between it and space.

If you don't like Sol's grid, you can use his hypotenuse-prescription to lay down an alternative grid, and to convert Sol's {r,z,y,t} to your own arbitrary {u,v,w,t'}.

No. What I'll do is change my speed and feel the acceleration and note that my measurements change, and that I need to use a different grid. Then I'll work out that I don't change the world by changing the way I move. I just change the way I see it. In my gravity-free world where light doesn't curve, it appears to curve because I change speed.

And then back in the real world where I'm not changing my speed, I can work out that light curves because it changes speed. Just like Einstein said. Just like the evidence says.

Do not allow a misplaced faith in mathematics and abstraction blind you to this.

 

[Farsight]

Your questions are nonsensical, and simply make it obvious that you don't know what a metric is. There's no shame in that - the vast majority of the world's population has even less of a clue than you do. But if you want to discuss it, the appropriate course of action is to try to learn what you don't know. Stop pretending to understand when you don't, drop the attitude, start over, and ask some basic questions, nicely. We'll help you.

I understand this sol, you don't. You drop the attitude wherein you come out with poppycock like space is falling inwards in a gravitational field and then defend your cargo-cult assertions with huff and puff and you don't understand the mathematics. Ask some basic questions, and I'll help you.

 

[xtifr]

This isn't an issue of doing the maths xtifr, it concerns reading what Einstein said about the speed of light varying with gravitational potential, and looking at the experimental evidence that shows you that it does.

Yes, he said that, and he also said that the speed of light is invariant. You can't resolve those two statements because you're stuck in a bizarre pseudo-Newtonian view of the world, peppered with a few oddball results from relativity that you think you understand, while ignoring the whole of relativity. Einstein resolved those two apparently contradictory statements and proved them both true by using math! Which you don't seem to be capable of doing. Grasping how those two statements of Einstein's can both be true is extremely difficult if you can't do the math!

I do understand frames of reference by the way.

No, you don't. You may understand a pseudo-Newtonian approximation of the concept of frames of reference, but you don't understand relativistic frames of reference.

To put it simply, you don't have the frame of reference to understand frames of reference.

 

[Farsight]

We can indeed, given a specific set of coordinates and performing our experiments in specific ways. Nobody ever said otherwise.

Good. Now we're getting somewhere. But learn this, and learn it well: we don't need any coordinates to see that the speed of light varies with gravitational potential:

But we do need the motion of light to define the second and the metre. Then we use them to measure the local speed of light, and thus regardless of how fast it's moving, we always say that the local speed of light is 299,792,452 metres per second. Then we use our seconds and metres, via our rods and clocks, to define the abstract thing we call a coordinate system. So do not allow the assertion that "in some coordinate systems the speed of light is constant" blind you to the very real fact that the speed of light really does vary with gravitational potential.

Not at all. He gave a thorough explanation. You just couldn't follow it, because you can't do the math. You seem to think that with the right conceptual framework, the math becomes irrelevant. But that's simply not true. You can't construct the right conceptual framework without the math.

You've constructed the wrong conceptual framework by elevating mathematics above hard scientific evidence.

Also not true. It's been explained to you multiple times. It's flat space-time, the same flat space-time that the canonical Minkowski metric describes. We can pick different coordinates to describe flat space-time, and this is just one set of coordinates. What else do you want to know? Do you need an equation to describe how to get from the more conventional coordinates to these ones? I don't recall you asking, but if you had a clue about GR you could find the transforms yourself, and even if we gave them to you, you probably wouldn't know what to do with them.

See my answer to Ben above. You are confusing spacetime with space, and you're blinding yourself to reality by retreating behind mathematics and accusations.

That's how you think of math, isn't it? It's just Latin: incomprehensible and irrelevant gibberish, as far as you're concerned.

No, I think maths is a vital tool for physics. But I also think some people come out with gibberish like infalling space and neverneverland, then defend it by hiding behind mathematical expressions where they will not list the terms and they will not say what the expression represents. They abuse mathematics to dismiss scientific evidence that challenges their cargo-cult assertions.

That wasn't what you said. You said, "Things don't fall down as you pass by." And you said this in regards to the use of an accelerating reference frame. But you're rather obviously wrong. If you're accelerating, then everything in the universe is falling down in your reference frame, where down is the direction opposite to your acceleration. You don't want to call it gravity. Fine, that's a semantic issue. The math, however, is not. But of course, math is what you're allergic to.

Wake up Zig. If you zoom past an asteroid, it doesn't move at all. It doesn't fall towards some other asteroid just because you're going by. Everything in the universe isn't falling down. You're just moving through the universe, that's all.

I haven't dismissed anything Einstein has said. But what he says with words is often ambiguous, because that's a fundamental problem with human language. It is imprecise. But his math does not suffer this weakness. Furthermore, math is what makes his theory quantifiable and testable. The words can help explain the math, but at the end of the day, it is the math which actually matters. And you have done nothing but dismiss Einstein's math. Because it's so far beyond your capacity that it's like Latin to you. And so you lash out at people who understand the math, and can use the math, because they don't agree with you. But the people who can do the math, and who use it correctly, are in far better agreement with Einstein than the person who doesn't have a clue how any of that math works...

And I'm the one lashing out am I? Zig, I'm in agreement with Einstein. Get used to it.

How do you define "curve"? If you mean that light always follows a geodesic (in a vacuum), then that's true no matter what spacetime you're in. If you define "curve" in terms of how it relates to your coordinate system, then whether or not light curves depends on what you choose for that coordinate system. But of course, this is a mathematical question, and you're allergic to those.

Stop elevating mathematical abstraction above reality. You're in space, not spacetime. If you see light curving it's because you're changing your speed, or the light is. It's that simple.

 

[Farsight]

Yes, he said that, and he also said that the speed of light is invariant. You can't resolve those two statements because you're stuck in a bizarre pseudo-Newtonian view of the world, peppered with a few oddball results from relativity that you think you understand, while ignoring the whole of relativity. Einstein resolved those two apparently contradictory statements and proved them both true by using math! Which you don't seem to be capable of doing. Grasping how those two statements of Einstein's can both be true is extremely difficult if you can't do the math!

He didn't resolve them using math. He started with the postulate that the speed of light is contant in 1905. Six years later he was getting ready to abandoned it. Here, read what he said:

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.

No, you don't. You may understand a pseudo-Newtonian approximation of the concept of frames of reference, but you don't understand relativistic frames of reference. To put it simply, you don't have the frame of reference to understand frames of reference.

I understand this xtifr. Stop fooling yourself that I don't, and stop clinging to conviction.

ETA: don't be fooled by the word velocity in the English translation. It's the common usage as per "high velocity bullet", not the vector quantity.

 

[Farsight]

Saying that it isn't a "real" gravitational field directly and explicitly contradicts Einstein, Farsight. Yes, it's true that in flat spacetime one can choose coordinates in which there is no gravitational field. But it's also true that one can choose coordinates in which there is one, just as he says...

We all know that accelerating through space doesn't actually create a gravitational field. Things fall down in your cabin as per the principle of equivalence, but there is no gravitational field generated around a rocket. Stop clutching at straws.

 

[Farsight]

I'm objecting to the lack of explanation of terms and scenario.

Am I the only one who gets the impression that Farsight is hoping for a grade-school word problem? Probably so that he can object to the wording rather than working out the solution?

"Jack is walking up a hill of height H and slope S, at rate R. As the hilltop approaches Jack-"

"Hold it right there! The hilltop is stationary! Jack is the one moving! Obviously you don't really understand hills, Jack, or motion! Your problem is stupid and wrong and there's no point in solving it!"

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

 

[Farsight]

You have zero evidence that "MTW" GR has led us astray with regard to black holes, since no-one here has ever seen a black hole sufficiently close up.

Check back through the thread, I came in at post #59 on page 2, objecting to the waterfall analogy. There is no sense in which space within the region we call a gravitational field is infalling. That's an example of sol being led astray, and leading readers astray too. It's cargo-cult science, and I will not permit it.

Furthermore, given that "MTW" GR - or GR, henceforth - is mathematically self-consistent and has passed all relevant experimental tests thus far, there is no sound scientific reason for withholding the usual provisional belief we'd allow ourselves to have in such a theory. The only objections you have are (from where I'm standing) purely aesthetic, and you haven't even given us anything equal to GR to use in its place (you won't provide the mathematical model, remember).

What I've given you is Einstein quotes and scientifc evidence to demonstrate that the speed of light varies with gravitational potential. Previously on another thread I objected to the infalling observer who notices nothing unusual, which doesn't match the original frozen-star black hole description where the speed of light goes to zero, wherein he ends up noticing nothing. It's not a matter of believing in GR so much as understanding where MTW GR presents an incorrect interpretation such as the Kruskal-Szekeres coordinates which hop over the end of time.

No, I'm taking you at your own word. You said, quite explicitly, that you did not want to provide a mathematical model. This particular sub-issue is technically not even one of the scientific evidence; it's one of logical self-consistency and your refusal to provide adequate information for us to assess your proposal.

I've provided scientific evidence, mathematics can't make up for that, and it can't make the speed of light not vary with gravitational potential. You don't need any units or coordinate system to know that one beam of light is going faster than the other:

Yes, because relativity+ includes elements that GR doesn't cover. Hence the plus sign.[/url]Right. So when you were saying you were merely presenting GR as Einstein originally intended, you were mistaken.

Not at all. This conversation concerns black holes and the speed of light varying with gravitational potential. The relativity+ aspects such as the wave nature of matter are incidental and have only arisen in response to particular questions.

The principle of equivalence - understood correctly - is indeed exact. Saying "it's a principle" as though it were only meant as an approximation or guideline is laughable. In GR, spacetime is locally Lorentzian flat, and as far as the clocks in my thought-experiment go, the deviations we expect due to tidal forces can be made negligible with an appropriate experimental setup.

It isn't exact. When you discard the Reimann curvature you've moved from a gravitational field to a simulcrum achieved via acceleration that you can transform away. It's like what I said to theprestige about the hill. If you take a small portion of it and say it's locally flat, then take another small portion and say that's locally flat too, and then repeat for all small portions, you've now got a flat hill. You haven't got a hill any more. You've thrown away the very feature that made it a hill. I have to go, but note that the usual pictures of curved spacetime are showing you Riemann curvature. The curvature of "the rubber sheet" is the Riemann curvature.

"FGR" or "Relativity+" is something only you are arguing for. Furthermore, only you have written a book about it and argued about it with such tenacity for such a length of time on so many internet forums.

I'm arguing for relativity. It's the sleeping beauty of contemporary physics. And I'm doing my bit for physics because this is important. More imporatant than you know. Must dash.

 

[sol invictus]

I'm in agreement with Einstein.

You're lying. Why? Everyone knows it - so what's the point?

We all know that accelerating through space doesn't actually create a gravitational field. Things fall down in your cabin as per the principle of equivalence, but there is no gravitational field generated around a rocket. Stop clutching at straws.

...the man in the chest will thus come to the conclusion that he and the chest are in a gravitational field...
Ought we to smile at the man and say that he errs in his conclusion? I do not believe we ought if we wish to remain consistent.......the Γ^τ_μν...are the components of the gravitational field.

 

[ctamblyn]

Check back through the thread, I came in at post #59 on page 2, objecting to the waterfall analogy.
(...snip...)

The waterfall analogy (which, by the way, is an excelleny analogy) is not something forced on you by "MTW" GR (i.e. standard GR), it is a separate issue entirely and thus irrelevant to my original question of empirical evidence.

You still cannot find any empirical evidence which shows GR is wrong and FGR is right.

What I've given you is Einstein quotes and scientifc evidence to demonstrate that the speed of light varies with gravitational potential.

None of which shows GR is wrong.

You still cannot find any empirical evidence which shows GR is wrong and FGR is right.

Previously on another thread I objected to the infalling observer who notices nothing unusual, which doesn't match the original frozen-star black hole description where the speed of light goes to zero, wherein he ends up noticing nothing. It's not a matter of believing in GR so much as understanding where MTW GR presents an incorrect interpretation such as the Kruskal-Szekeres coordinates which hop over the end of time.

Then present some actual evidence that the predictions of GR are incorrect with regard to black holes, instead of merely asserting it again. Shows us experimental data that shows that infalling observers do not reach the singularity in finite proper time. Show us that real black holes are "frozen stars". You can't, as I said before.

You still cannot find any empirical evidence which shows GR is wrong and FGR is right.

I've provided scientific evidence, mathematics can't make up for that, and it can't make the speed of light not vary with gravitational potential. You don't need any units or coordinate system to know that one beam of light is going faster than the other:

Every one of the observed results you have brought to the table is in accord with the predictions GR.

You still cannot find any empirical evidence which shows GR is wrong and FGR is right.

Not at all.

Yes, actually. If FGR/relativity+ is (as you claim) a superset of GR then you were mistaken to say that you were merely presenting GR. Not to mention the fact that FGR actually contradicts GR on some points.

This conversation concerns black holes and the speed of light varying with gravitational potential. The relativity+ aspects such as the wave nature of matter are incidental and have only arisen in response to particular questions.

It's not at all incidental. Without your idiosyncratic picture of fundamental particles you have no way of understanding why strong-interaction clocks, weak-interaction clocks and electromagnetic-interaction clocks remain synchronised. In GR it is a consequence of the EEP, in FGR it depends on your model of matter.

It isn't exact.
(...snip...)

Yes, it is. You have misunderstood what "local" means. I suppose that's a technicality which you can be forgiven for. However, the same can't be said for your misunderstanding of the word "negligible". I made it clear that we could select an experimental set-up where the effect of tidal forces is negligible, and now you are invoking tidal forces as a possible get-out. I'm afraid that just won't do.

I'll reword my statement to make it clearer to you: a loss of synchronisation greater than the tiny, immeasurable amount that would be expected on the basis of tidal forces would show the EEP, and hence GR, is false.

I'm arguing for relativity. It's the sleeping beauty of contemporary physics.

What you're arguing for is FGR/relativity+ as laid out in your book; it is your own personal view of the world, different from both SR and GR. Nor is what you are claiming merely a superset of GR, since it contradicts GR on several points. Neither SR nor GR depends on specific and experimentally unsupported models of matter as FGR/relativity+ does. Neither SR nor GR says that gravity is the result of the vacuum impedance varying from point to point as FGR/relativity+ does.

And I'm doing my bit for physics because this is important. More imporatant than you know.

That sounds ever so dramatic. Please, elaborate.

 

[Ziggurat]

Good. Now we're getting somewhere. But learn this, and learn it well: we don't need any coordinates to see that the speed of light varies with gravitational potential:

[qimg]http://www.physicsdiscussionforum.org/download/file.php?id=60[/qimg]

Your example relies on a particular choice of reference frame, and implied coordinates to go along with it. So yes, actually, you DO need coordinates to see that.

But we do need the motion of light to define the second and the metre. Then we use them to measure the local speed of light, and thus regardless of how fast it's moving, we always say that the local speed of light is 299,792,452 metres per second. Then we use our seconds and metres, via our rods and clocks, to define the abstract thing we call a coordinate system. So do not allow the assertion that "in some coordinate systems the speed of light is constant" blind you to the very real fact that the speed of light really does vary with gravitational potential.

Obviously not. I'm afraid all your example shows is that the meter got bigger. You didn't consider that possibility, did you? That's right: the bottom light ray isn't actually moving slower, you just drew it wrong: the bottom clock has expanded.

See, your foolproof logic doesn't actually prove what you think it proves. There are alternative interpretations which match observation just as well.

No, I think maths is a vital tool for physics.

And yet, you don't know how it works and refuse to use it or even learn it.

But I also think some people come out with gibberish like infalling space and neverneverland, then defend it by hiding behind mathematical expressions where they will not list the terms and they will not say what the expression represents. They abuse mathematics to dismiss scientific evidence that challenges their cargo-cult assertions.

You know, when people do the math wrong, it's not hard to demonstrate that they're doing it wrong. And the best way to do that is with math. Other than the fact that coordinate transformations offend your sensibilities, you don't have any actual substantive objection to them. If they were invalid, you could demonstrate why by using math. But you can't. So there is no reason, other than your intuition, for why we should reject such coordinate transforms.

Wake up Zig. If you zoom past an asteroid, it doesn't move at all.

Sure it does. It zooms past me.

It doesn't fall towards some other asteroid just because you're going by.

Who ever said it was falling towards some other asteroid? ALL asteroids are simply falling down. Down, in this case, isn't towards some fixed point. Down is just the opposite direction from where I'm accelerating. And the asteroid I zoom past is most definitely falling down in that direction. Hell, as long as the velocity isn't relativistic, it will even trace out the nice parabolic trajectories we all studies in freshman physics.

Everything in the universe isn't falling down. You're just moving through the universe, that's all.

And what's the difference? You say that like these are mutually contradictory statements. But the whole point is that they aren't. And again, the only objection you have on offer is that it offends your sensibilities.

And I'm the one lashing out am I? Zig, I'm in agreement with Einstein. Get used to it.

Yes, Farsight, you are the one lashing out. And no, you are not in agreement with Einstein. That has been demonstrated time and time again here.

Stop elevating mathematical abstraction above reality. You're in space, not spacetime.

You have it backwards. We are in spacetime, NOT space.

If you see light curving it's because you're changing your speed, or the light is. It's that simple.

Changing my speed relative to what? Well, the only sensible answer is relative to an inertial reference frame. And you're correct: light curves in my reference frame if my reference frame is accelerating relative to an inertial reference frame.

But that's exactly what my reference frame is doing if it's stationary in a gravitational field: it's accelerating relative to the inertial in-falling reference frame. So again: no difference between light curving in a gravitational field and light curving in an accelerated reference frame. Because the two are the same thing.