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Thread: The original "frozen star" black hole interpretation is correct after all

  1. #1 The original "frozen star" black hole interpretation is correct after all 
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    The thing I've been trying to convey in our recent discussions is that you can gain understanding via a "back to basics" approach. You start by appreciating that time travel is a fantasy, then you look at what a clock really does and you note what Einstein said: the speed of light varies with position. You take small steps and check every inch of the way, and realise that you can understand how gravity works like never before: light curves because the speed of light varies with position, and matter falls down because of the wave nature of matter. It's different because it takes a "global" view rather than the local view, but you can't put your finger on why it's wrong. That's the idea anyway: you can't explain why it's wrong because it isn't. Then before you know it, you're faced with a new understanding of black holes.

    I think the most question re black holes is why doesn't the light get out? Imagine you’re standing on a planet shining a laser beam straight up into space. The light goes straight up, it doesn’t curve round, it doesn't slow down. Now imagine it’s a denser more massive planet. The light still goes straight up, it still doesn’t curve round, it still doesn't slow down. Let’s make it really massive: the light still goes straight up, it still doesn’t curve round, it still doesn't slow down. But when we make it so massive that it’s a black hole, all of a sudden light can’t escape. Why not?

    Some will tell you that the light curves round into the black hole. When you challenge that by saying the light didn’t start curving as we made the planet more and more massive, they’ll maybe say it’s because spacetime is curved. Then when you say spacetime is an static mathematical model, they’ll maybe fall back to the waterfall analogy. That’s where space is falling inwards so the light beam doesn’t make any progress. That’s badly misleading. In no sense is space falling inwards in a gravitational field. A gravitational field alters the motion of light through space, but it doesn’t suck space in. Because it’s a region of inhomogeneous space, like Einstein said. We can depict it like this:



    Optical clocks go slower when they’re lower because the space is different nearer the surface of a planet. We talk of gravitational time dilation, but there's no actual time going slower, it’s just light going slower when it’s lower, so the optical clocks go slower too. I know it sounds unfamiliar, but check out what Don Koks says in the Baez speed of light article:

    Quote Originally Posted by Don Koks
    "A curvature of rays of light can only take place when the velocity [Einstein means speed here] of propagation of light varies with position..."

    "In that sense, we could say that the 'ceiling' speed of light in the presence of gravity is higher than the 'floor' speed of light..."
    The crucial thing about gravitational time dilation, is that it is said to go infinite at the black hole event horizon, where the "coordinate" speed of light is said to be zero. That's the ultimate floor for the speed of light. An optical clock at the event horizon doesn’t tick because the speed of light there is zero. That’s why your laser beam doesn’t get out of the black hole. Not because of some mystical curvature, or because the sky’s falling in, but because at that location the light isn’t moving, so it doesn’t go up and it doesn’t get out because it is effectively “frozen”.

    You may be aware that black holes were originally called frozen stars. If you google on frozen star Oppenheimer you can find references to this. However if you google on frozen star and follow the links, what comes up is black hole along with a point singularity. It’s like history has been rewritten. It’s like the original “frozen star” has been airbrushed away, and replaced with something else. Something that doesn't make sense. See the picture below:


    Image credit: W H Freeman, publishers

    A guy called Jesse Mazer put it up on the internet a couple of years back when we were discussing all this. It’s a screenshot from Misner/Thorne/Wheeler, the "bible" of gravitation. It depicts Schwarzschild coordinates for a body falling into a black hole. See the dashed line up the middle? That’s the event horizon. See how to the right of it the curve goes up? Do you know where that’s headed? It’s headed to the end of time. Only it’s cut off vertically, and then it comes back down. Yes, according to MTW if you fall into a black hole, you go to the end of time and back in no time flat. That’s why you read about the elephant and the event horizon, where the elephant is in two places at once. Look horizontally across the picture above to appreciate that. It's the same kind of thing in Kevin Brown’s mathspages article the formation and growth of black holes where he talks about "future infinity", but at least he gives a bit of history. Have a read of this excerpt:

    Quote Originally Posted by Kevin Brown
    Incidentally, I should probably qualify my dismissal of the "frozen star" interpretation, because there's a sense in which it's valid, or at least defensible. Remember that historically the two most common conceptual models for general relativity have been the "geometric interpretation" (as originally conceived by Einstein) and the "field interpretation" (patterned after the quantum field theories of the other fundamental interactions). These two views are operationally equivalent outside event horizons, but they tend to lead to different conceptions of the limit of gravitational collapse.

    According to the field interpretation, a clock runs increasingly slowly as it approaches the event horizon (due to the strength of the field), and the natural "limit" of this process is that the clock just asymptotically approaches "full stop" (i.e., running at a rate of zero) as it approaches the horizon. It continues to exist for the rest of time, but it's "frozen" due to the strength of the gravitational field. Within this conceptual framework there's nothing more to be said about the clock's existence. This leads to the "frozen star" conception of gravitational collapse.

    In contrast, according to the geometric interpretation, all clocks run at the same rate, measuring out real distances along worldlines in spacetime. This leads us to think that, rather than slowing down as it approaches the event horizon, the clock is following a shorter and shorter path to the future. In fact, the path gets shorter at such a rate that it actually reaches (our) future infinity in finite proper time...
    Originally Kevin Brown referred to Wheeler for the "geometric interpretation" and to Weinberg for the "field interpretation". He changed this after I queried it with Weinberg, I'm not sure why, and IMHO no way would Einstein concur with the point singularity. But anyhow, the important point is that there's two interpretations, and the one that everybody thinks is right, isn't. And then to make things worse, they don't even know that there's this other interpretation. They think the interpretation they know about is "what GR says". Wherein the Schwarszchild singularity is a mere coordinate artefact. That's just got to be wrong. Light can't go slower than stopped. The local force of gravity relates to the local gradient in the coordinate speed of light, and since it can't go less than zero, there's no more gravitational force at the event horizon. When you fall into a black hole, everything goes slower and slower until it stops. Your clocks go slower and slower, and so do you. Some people then refer to Eddington–Finkelstein coordinates, even though "neither ever wrote down these coordinates", and even though you can't cancel out a stopped clock with a stopped observer. This observer is said to not see anything amiss, but that's just go to be wrong too. He doesn't see anything. Because the coordinate speed of light is zero. He ain't seen nothing yet, and he never ever will. His light is stopped, and because of the wave nature of matter, he’s stopped too. And because he can't go faster than light he isn’t going to fall any further. But other things can fall on top of him, such that he can't pass through the surface, but the surface can pass through him. So the frozen-star black hole grows like a hailstone, which is apt.

    Yes I know this goes against the grain of "all reference frames are equally valid", but if light doesn't move you don't have a reference frame. You have no way to measure distance or time, so the frozen-star is like the gravastar in that it features "a void in the fabric of space and time". See the black portion of this image or the image on the right here. That makes it more of a hole than the point-singularity black hole, and leads to some interesting consequences for cosmological inflation. And for firewalls too, but that's one for another day.
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    The thing I've been trying to convey in our recent discussions is that you can gain understanding via a "back to basics" approach.
    I completely agree. And the basics-approach is the distinction between local and global as it pertains to GR. It doesn't get any more basic than that !

    you can't explain why it's wrong because it isn't
    Indeed. Neither can you explain how to resolve a contradiction where no contradictions exist in the first place

    See the dashed line up the middle?
    See the labels on the axis ? That's a specific choice of how to label events in your space-time. Choose a different set of coordinates and the event horizon boundary ceases to be an asymptote. No choice you make is unique or in any way physically privileged, meaning no observer is physically privileged over any other observer - you declaring that Schwarzschild coordinates take precedence over any other choice means you choose to ignore both the principle of relativity, as well as the principle of general covariance, both of which are at the heart of what GR means.

    But anyhow, the important point is that there's two interpretations
    No - there is no interpretative layer here at all. The meaning of coordinate systems and the invariance of the laws of physics under changes of same are clear and unambiguous. The external observer never sees anything reaching the horizon, whereas the in-falling observer crosses it in finite proper time; you need to understand that this is not a contradiction at all, because neither one of these is in any way privileged.

    they don't even know that there's this other interpretation.
    Surely you are having a laugh here, right ? With all due respect, but if you think that people who have studied GR ( "they" ? ) are not aware of the infinite coordinate in-fall time as determined by an external observer, then you need to think again. And think very hard.

    Wherein the Schwarszchild singularity is a mere coordinate artefact.
    The Schwarzschild singularity at r=0 is demonstrably not a coordinate artefact. I don't know where you get that idea, but no one here has claimed such a thing. It is only the Schwarzschild coordinate chart that becomes singular at the event horizon.

    That's just got to be wrong.
    It is trivial to show that space-time is smooth and regular at the event horizon, and that it is only the Schwarzschild coordinates that become singular. So no, it is not wrong at all.

    Some people then refer to Eddington–Finkelstein coordinates, even though "neither ever wrote down these coordinates"
    Of course you can write these down, just Google it. And there are others that work just as well, such as Novikov coordinates, or the Kruskal-Szekeres chart, or Gullstrand-Painleve coordinates. They are all just different ways to label events in the same space-time.

    and even though you can't cancel out a stopped clock with a stopped observer.
    Except...no one ever sees the clock stopping, it's just something an external observer calculates, but no one ever measures. So what is there to cancel ?

    This observer is said to not see anything amiss, but that's just go to be wrong too.
    No, it's a trivial consequence of the fact that everyone experiences the same laws of physics.

    and because of the wave nature of matter,
    GR does not make reference to any quantum effects, never has and never will.

    Yes I know this goes against the grain of "all reference frames are equally valid"
    If you know that, then why do you present it as if it were fact in the hard physics section of this forum ? You are declaring a specific frame to be privileged, and hence you violate relativity and general covariance. That is not GR.

    but if light doesn't move you don't have a reference frame
    Exactly - that's why time is never infinitely dilated anywhere. There's a huge difference between what distant observers calculate, and what actually happens locally. Now combine this with the principles of relativity as well as general covariance, and there you go.
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    They are all just different ways to label events in the same space-time.
    To add to this - because they are all just different ways to label events in the same space-time, it is sufficient to show that the event horizon is non-singular in any one coordinate system. The same is not true for the r=0 singularity, because all coordinate systems become singular here. That is the principle of general covariance in action !
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    Quote Originally Posted by Markus Hanke View Post
    I completely agree. And the basics-approach is the distinction between local and global as it pertains to GR. It doesn't get any more basic than that!
    I thought we'd already agreed that GR tells the story from the "local" viewpoint, hence the c in



    And that we can gain further understanding by comparing notes as it were, and stepping back to get a "global" viewpoint where we look at more than one frame at once.

    Quote Originally Posted by Markus Hanke View Post
    Indeed. Neither can you explain how to resolve a contradiction where no contradictions exist in the first place
    There's a clear contradiction with the elephant and the event horizon. It's in two places at the same time. It can't be both. There's also a clear contradiction about where the infalling observer ends up. At the event horizon, or at the point singularity. It can't be both.

    Sorry, time for tea. To be continued.
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    Quote Originally Posted by Markus Hanke View Post
    See the labels on the axis? That's a specific choice of how to label events in your space-time. Choose a different set of coordinates and the event horizon boundary ceases to be an asymptote. No choice you make is unique or in any way physically privileged, meaning no observer is physically privileged over any other observer - you declaring that Schwarzschild coordinates take precedence over any other choice means you choose to ignore both the principle of relativity, as well as the principle of general covariance, both of which are at the heart of what GR means.
    I'm not ignoring any principles. Look at the wikipedia general covariance article and see where it says this:

    "Mathematically, the physical quantities must transform covariantly, that is, under a certain representation of the group of coordinate transformations between admissible frames of reference of the physical theory.[1] This group is referred to as the covariance group".

    What I'm saying is that there are no admissible frames of reference beyond the event horizon.

    Quote Originally Posted by Markus Hanke View Post
    No - there is no interpretative layer here at all. The meaning of coordinate systems and the invariance of the laws of physics under changes of same are clear and unambiguous. The external observer never sees anything reaching the horizon, whereas the in-falling observer crosses it in finite proper time; you need to understand that this is not a contradiction at all, because neither one of these is in any way privileged.
    Is the infalling observer stalled at the horizon or not? It's a definite contradiction Markus. Can I ask you to re-read time travel is a fantasy and think again about proper time. It's merely some accumulated display of some kind of regular cyclical motion local within the clock. And if your clock is looking like this to me:



    ...then your finite proper time hasn't occurred yet and never ever will.

    Quote Originally Posted by Markus Hanke View Post
    Surely you are having a laugh here, right ? With all due respect, but if you think that people who have studied GR ( "they" ? ) are not aware of the infinite coordinate in-fall time as determined by an external observer, then you need to think again. And think very hard.
    I'm not saying they're not aware of it, I'm saying they have failed to understand the significance of it. It comes back to your finite proper time hasn't occurred yet and never ever will wherein a solution is mathematically fine but physically invalid.

    Quote Originally Posted by Markus Hanke
    The Schwarzschild singularity at r=0 is demonstrably not a coordinate artefact. I don't know where you get that idea, but no one here has claimed such a thing.
    I meant the r=2m singularity at the event horizon. That's said to be a coordinate artefact. I say it's a genuine singularity.

    Quote Originally Posted by Markus Hanke
    It is trivial to show that space-time is smooth and regular at the event horizon, and that it is only the Schwarzschild coordinates that become singular. So no, it is not wrong at all.
    There is no space-time at the event horizon. Space-time is just an abstract mathematical thing that is totally static. The infalling observer is falling through space, not spacetime. So showing smooth space-time is just showing me some smooth map that does not reflect the true nature of the territory. Which ends at the event horizon, like this picture.

    Quote Originally Posted by Markus Hanke
    Of course you can write these down, just Google it. And there are others that work just as well, such as Novikov coordinates, or the Kruskal-Szekeres chart, or Gullstrand-Painleve coordinates. They are all just different ways to label events in the same space-time.
    And they all suffer from a logical fallacy wherein your proper time takes forever and is assumed to happen all fine and dandy when it hasn't happened yet and never ever will.

    Quote Originally Posted by Markus Hanke
    Except...no one ever sees the clock stopping, it's just something an external observer calculates, but no one ever measures. So what is there to cancel?
    The infinite gravitational time dilation wherein the clock has stopped. have a look at Gullstrand-Painleve coordinates on Wikipedia, remember what I said about proper time, and look at "Define a new time coordinate by ". That's defining away the fact that the clock stops. It just isn't physical.

    Quote Originally Posted by Markus Hanke
    No, it's a trivial consequence of the fact that everyone experiences the same laws of physics.
    The infinite gravitational time dilation means you stop experiencing anything.

    Quote Originally Posted by Markus Hanke
    GR does not make reference to any quantum effects, never has and never will.
    No problem. But electron diffraction is a fact. The wave nature of matter is a scientific certainty.

    Quote Originally Posted by Markus Hanke
    If you know that, then why do you present it as if it were fact in the hard physics section of this forum?
    It's like I said above. Because there is no reference frame beyond the event horizon. All admissible reference frames are equally valid.

    Quote Originally Posted by Markus Hanke
    You are declaring a specific frame to be privileged, and hence you violate relativity and general covariance. That is not GR.
    I'm not declaring a specific frame to be valid, I'm looking at all frames next to each other. The parallel-mirror gif shows you two, right there in the room you're in. Mentally add more until you get to the stopped gif above. The light can't go slower than stopped. Nor can anything else. So there's no concept of time any more, or distance, or events. Everything is frozen, everything is stopped.

    Quote Originally Posted by Markus Hanke
    Exactly - that's why time is never infinitely dilated anywhere. There's a huge difference between what distant observers calculate, and what actually happens locally. Now combine this with the principles of relativity as well as general covariance, and there you go.
    It's infinitely dilated at the event horizon. If it wasn't, the light could get out.
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  6. #6  
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    Quote Originally Posted by Farsight View Post
    It's in two places at the same time. It can't be both.
    But it's not. Where do you get the idea it's at different places at the same time? There is no such thing as universal time. No point inside the blackhole is simultaneous to any point outside the blackhole.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Quote Originally Posted by Markus Hanke
    To add to this - because they are all just different ways to label events in the same space-time...
    The map is not the territory. Things move through space, events happen in the real world. Spacetime is just an abstract static mathematical model. If light moves slower and slower as it approaches the region we call a black hole, and if it then stops, it's the end of events, and the end of spacetime too.

    Quote Originally Posted by Markus Hanke
    it is sufficient to show that the event horizon is non-singular in any one coordinate system...
    Do it, and I will show you where you dropped a stitch.

    Quote Originally Posted by Markus Hanke
    The same is not true for the r=0 singularity, because all coordinate systems become singular here.
    The point singularity is just a mathematical fantasy, Markus. Like time travel.
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    Quote Originally Posted by KJW View Post
    But it's not. Where do you get the idea it's at different places at the same time?
    From the Schwarzschild chart in the OP and from The elephant and the event horizon:

    Quote Originally Posted by New Scientist
    What happens when you throw an elephant into a black hole? It sounds like a bad joke, but it's a question that has been weighing heavily on Leonard Susskind's mind. Susskind, a physicist at Stanford University in California, has been trying to save that elephant for decades. He has finally found a way to do it, but the consequences shake the foundations of what we thought we knew about space and time. If his calculations are correct, the elephant must be in more than one place at the same time.
    Quote Originally Posted by KJW
    There is no such thing as universal time. No point inside the blackhole is simultaneous to any point outside the blackhole.
    See above where I referred to Gullstrand Painlevé coordinates? Imagine I drop a whole series of raindrops into a black hole, one after the other. You might claim that they all reach the central point-singularity in finite proper time. But then you also say no point inside the blackhole is simultaneous to any point outside the blackhole. That means they haven't reached the point-singularity yet. We could sit here for an hour, a year, a billion years, and it's still true.
    Last edited by Farsight; 06-26-2014 at 03:32 PM. Reason: URL error
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    Perhaps you could walk us through the calculation that you are explicitly using, Farsight?
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    I'm not using a calculation, I'm using logic and hard scientific evidence and paying attention to what Einstein said. It's like playing detective. When there's a so-called paradox, somebody has got something wrong, and you track back looking for clues checking all the axioms and assumptions. When you have eliminated the impossible, whatever remains, however improbable, must be the truth. The "frozen star" interpretation has to be the one that's right.
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    And I suppose you want someone else to do the math for you, yes?

    If you had the I.Q. of five bazilion gagilion, like your facade, you would be able to do the math yourself. Don't you think?

    :EDIT:

    A very long time ago, you called AlphaNumeric "Maths boy" with a derogatory slant. And since that time, you have provided no concrete mathematical description of whatever you say. So, in that case, PhysBang has made valid criticisms.
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    First, I wish to note that coordinate singularities are real. Consider polar coordinates. Their origin has a coordinate singularity. Consider also some common coordinates for a sphere: latitude and longitude. They have a coordinate singularity at each pole.

    Here's how to look for coordinate singularities. Find the curvature, and see what value it has at a coordinate singularity. A problem is that, in general, the curvature is a tensor: the Riemann tensor. One must find coordinate-invariant quantities from it. One can do it by taking inner products over indices when multiplying it by combinations of itself, the metric tensor, and the antisymmetric symbol. One can also do it by turning it into an eigensystem probllem, where the eigenvectors are antisymmetric 2-tensors. But if all its components vanish, then one does not have to go through that song-and-dance.

    Some time ago, I'd written a Mathematica notebook for doing differential geometry. I put it to work on these examples. Polar-coordinate plane: curvature = 0. Latitude-and-longitude sphere: curvature = 1. Schwarzschild metric: much more complicated.

    I did that eigenvalue trick on the Riemann tensor, and I found two eigenvalues with value 2M/r3 and four eigenvalues with value -M/r3, where r is the usual Schwarzschild-metric radial coordinate, where the circumference of a circle around the center is 2π*r. This is finite at r = 2M, the Schwarzschild radius or black-hole radius, so that metric only has a coordinate singularity there. However, the eigenvalues are infinite at the center, r = 0. So there is a real, physical singularity singularity, and not some artifact of some coordinate system.

    Quote Originally Posted by Farsight
    ... what Einstein said ... like Einstein said ...
    As if Albert Einstein was a prophet of revealed truth.
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    I'll work out mathematically what I talked about earlier.

    From a space's metric or vielbein, one can find its Riemann curvature tensor: Rijkl. That looks very coordinate-dependent, but there is a way to find coordinate-independent quantities from it. Use it in an eigensystem problem:
    Rijklxkl = r*xij

    for eigenvalues r and eigenvectors x. The eigenvectors ought to be antisymmetric 2-tensors. In fact, one can use a basis set of these to turn the Riemann tensor into a N*N matrix, where N = n(n-1)/2 for n dimensions. If finding the eigenvalues is too difficult, one can find Tr(R(k)) for powers k from 1 to N. They are related to the eigenvalues.
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    Ipetrich, I think in your original post you said you would avoid going too far over our heads. Can you also state please in English or failing that some pretty diagrams or short movie clips?
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    I'll try.

    Consider an ellipse. It has two axes, its longest one and its shortest one (Major / minor axis of an ellipse - Math Open Reference). You can extend this analysis to an arbitrary number of dimensions. A 3D ellipsoid has three axes, its longest one, a middle one, and its shortest one (Ellipsoid - Wikipedia). Notice that the lengths of those axes are independent of how you rotate the ellipse/ellipsoid.

    So, in a sense, I turn the curvature of a 4D space into a 6D ellipsoid, and I then find the lengths of its axes. I did that because changing coordinates is like rotation: it changes the directions of the axes but not their lengths.


    The axes' lengths are eigenvalues and the axes' directions are eigenvectors.

    BTW, I just did it with the Kerr metric, the metric of a rotating black hole. Two eigenvalues were -M/(r+i*a*μ)3, two were -M/(r-i*a*μ)3, one was 2M/(r+i*a*μ)3, one was 2M/(r-i*a*μ)3 in Boyer-Lindquist coordinates, where M = mass, a = (angular momentum)/M and μ = cos(θ). The event horizon has no physical singularity there also.
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    Nice try Ipetrich, appreciate the effort. I will put my mind to that one when I have had a good 9 hours kip!
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    Quote Originally Posted by lpetrich View Post
    ...First, I wish to note that coordinate singularities are real. Consider polar coordinates. Their origin has a coordinate singularity. Consider also some common coordinates for a sphere: latitude and longitude. They have a coordinate singularity at each pole.

    Here's how to look for coordinate singularities. Find the curvature, and see what value it has at a coordinate singularity. A problem is that, in general, the curvature is a tensor: the Riemann tensor. One must find coordinate-invariant quantities from it...
    You've missed the simplicity, lpetrich. What is sometimes called Riemann curvature is said to be the defining feature of a gravitational field, the second derivative of potential, and related to tidal force. Read the previous gravity thread to appreciate that you can depict Riemann curvature by plotting light-clock rates. That's like plotting the coordinate speed of light. This is zero at the event horizon, and it can't go lower than that. So that's the end of your chart. You've got a hole in it. A black hole. Like this:


    See Falling into a Black Hole sucks! – Starts With A Bang

    But this isn't just some coordinate singularity that you can transform away. You can't make a stopped clock tick by "adopting a new coordinate system". I know people talk about Kruskal-Szekeres coordinates and say you can, but you can't. Imagine if I put a frozen man in front of a stopped clock and told you that "in his frame he sees the clock ticking normally". You'd laugh me out of court.

    Quote Originally Posted by lpetrich
    As if Albert Einstein was a prophet of revealed truth.
    When we're talking about gravity, pay attention to what the guy said. Don't try to dismiss what he said on some specious grounds throwing out words like "prophet". Oh, and remember that the people who say Einstein was wrong are usually on the wrong side of the crackpot fence.


    Quote Originally Posted by Jilan
    Ipetrich, I think in your original post you said you would avoid going too far over our heads. Can you also state please in English or failing that some pretty diagrams or short movie clips?
    I'm afraid lpetrich has a habit of posting mathematics that people don't understand. Some people sometimes do this when they can't put up a convincing argument. Sometimes they have no intention of stating anything in plain English.
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    There's a difference between the time that a stationary observer will experience and the time that an infalling observer will experience. If one has experience with the math of general relativity, one can easily work it out. I've done it myself.
    Quote Originally Posted by Farsight
    I'm afraid lpetrich has a habit of posting mathematics that people don't understand.
    The mathematics used by Newton and Maxwell and Einstein and Minkowski and Feynman and ... Why did these supposed Prophets of Revealed Truth use lots of math?
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    Quote Originally Posted by Farsight View Post
    You've missed the simplicity, lpetrich.
    I prefer to say that lpetrish did not lie and say that there was simplicity where there wasn't simplicity.

    Read the previous gravity thread to appreciate that you can depict Riemann curvature by plotting light-clock rates.
    I can't see that anywhere in that thread. Perhaps somewhere you could actually show us an example of how you can describe a physical system using a plot of light-clock rates to do everything one would do with Riemann curvature? Or perhaps you would like us to take your pronouncements on faith?
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    (Einstein...)
    Quote Originally Posted by Farsight
    When we're talking about gravity, pay attention to what the guy said.
    What's so special about him? That's the sort of thing I mean when I say that you treat Einstein as a prophet of revealed truth. That does not mean that I automatically reject what he stated. Whether I accept it or not has nothing to do with him.

    Now to trying to explain the Riemann tensor. Parallel-transport a vector around a loop and compare it to how it started. To lowest order,

    Deviation in that vector = (Riemann tensor) . (vector) . (area of loop)

    So the Riemann tensor measures how much deviation a vector had.

    Here's a rather strong example of deviation by parallel transport. Start out at the North Pole with a vector pointing to 0d longitude. Go south along 0d longitude to the equator. The vector will be pointing south. Go east to 90d longitude. The vector will still be pointing south. Go north to the North Pole. The vector will point to 90d longitude. It has rotated 90 degrees.

    But on a flat surface, the vector will not change direction. Euclid's Fifth Postulate = zero curvature.
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    I thought we'd already agreed that GR tells the story from the "local" viewpoint
    We did, yet you keep ignoring that; you insist that the local viewpoint of a stationary far-away observer must be globally valid all the way down to the event horizon. That's exactly the problem with your claims.

    It's in two places at the same time.
    Huh ? There's no "same time" across extended regions in GR at all, so I don't understand what you are saying here.

    What I'm saying is that there are no admissible frames of reference beyond the event horizon.
    No, what you doing is declaring the external "bookkeeper" frame of a far-away observer to be global. You are saying that what the external observer calculates is what locally happens in a remote frame ( "time stops at the event horizon" ). That is what I mean when I say you don't seem to get the distinction between local and global.

    Is the infalling observer stalled at the horizon or not?
    No, he is not stalled. An external observer determines/calculates him to be "stalled", but it is not what locally happens in his frame. Again, that is not a contradiction.

    There is no space-time at the event horizon.
    Again - it is trivial to show that the manifold is smooth and continuous at the event horizon; there is no geodesic incompleteness there. You can't change that mathematical fact by ignoring it or declaring it to be unphysical.

    And they all suffer from a logical fallacy wherein your proper time takes forever
    There are no logical fallacies in any of these coordinate systems, and proper time never becomes infinite. Again, just claiming that this is the case is meaningless unless you can bring forward a proper mathematical argument.

    The infinite gravitational time dilation means you stop experiencing anything.
    You are now just going round and round in circles, continuously repeating the same sentences, even though a number of people here have attempted to explain to you the difference between coordinate time and local proper time.

    If it wasn't, the light could get out.
    You don't need "infinite gravitational time dilation" to prevent light from escaping some region.

    Do it, and I will show you where you dropped a stitch.
    Why do I need to do it again ? You already know that the event horizon is not a singularity in any of the coordinate systems other than Schwarzschild.

    I'm using logic and hard scientific evidence and paying attention to what Einstein said.
    To be perfectly honest with you, it seems to me like you are using neither. To me, you appear to be defending a personal opinion. Don't take it personally, but that is my genuine impression. If I was to ask you to substantiate any of your claims with sound mathematical reasoning, you wouldn't be able to - you would just say that these are meaningless abstractions. That is not logic, nor is it hard science - it's just an opinion.
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    Your efforts are appreciated Ipetrich, but all of these points have already been exhaustively explained to Farsight. He does not consider the mathematics of this to be physically meaningful, and hence rejects such arguments.
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    Farsight, allow me to draw a line under what has been said, and try a new approach by asking you a simple question - what would I ( or anyone else ) here have to do to show you the flaw in your understanding ? Please give an honest answer, because I don't know about you but I am genuinely trying to make you understand here. If there is nothing that I or anyone else could possible do in that regard ( i.e. your opinion is set in stone ), then please just be honest and say so - I would accept that and quite simply not invest any more time and effort in this, as there's plenty of other people here who can continue the discussion. If on the other hand you are prepared to listen to a specific line of reasoning, then state it, and I will do my best to explain it.

    I am happy to help out with any explanation on GR I am able to provide ( and I think that goes for others here too ), but I will also be quite honest with you and say that as things stand I am starting to loose interest in this discussion because all we seem to be doing is go round and round the same circles over and over again. If you are not actually prepared to at least consider that your understanding is flawed, then I'd much prefer you say so outright, and I will simply withdraw from this. If you are prepared to listen, then please give me some indication what I could do to explain it better, because right now I am out of ideas, and the round-and-round-in-circles thing is just a waste of time for me. It was enjoyable for a while, and I really do appreciate that you remained civil and mature all along, but we seem to have reached an impasse here now.

    I shall be awaiting your response to this before continuing.
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    Quote Originally Posted by Markus Hanke View Post
    Farsight, allow me to draw a line under what has been said, and try a new approach by asking you a simple question - what would I ( or anyone else ) here have to do to show you the flaw in your understanding?
    Just point out an error in the chain of logic:

    http://www.thephysicsforum.com/speci...l-fantasy.html
    http://www.thephysicsforum.com/speci...eed-light.html
    http://www.thephysicsforum.com/speci...elativity.html
    http://www.thephysicsforum.com/speci...after-all.html

    I started by saying clocks don't literally measure the flow of time, then said when a light clock goes slow the light goes slow, then gave an explanation of how gravity actually works, then applied that to the black hole scenario to draw a conclusion about two alternative interpretations.

    Quote Originally Posted by Markus Hanke View Post
    Please give an honest answer, because I don't know about you but I am genuinely trying to make you understand here. If there is nothing that I or anyone else could possible do in that regard ( i.e. your opinion is set in stone ), then please just be honest and say so - I would accept that and quite simply not invest any more time and effort in this, as there's plenty of other people here who can continue the discussion.
    I'm certainly listening, that's part of why I'm here, to get feedback. But I just don't seem to be hearing anything in the way of counterargument. You seem to be saying "what I've read in my textbook just can't be wrong" and not much else. Like I said on another thread, I'll read the thread again. I'll read them all to see if there's anything you've said that I should look at again.

    Quote Originally Posted by Markus Hanke View Post
    If on the other hand you are prepared to listen to a specific line of reasoning, then state it, and I will do my best to explain it.
    I'll get back to you after I've done some re-reading.

    Quote Originally Posted by Markus Hanke View Post
    I am happy to help out with any explanation on GR I am able to provide ( and I think that goes for others here too ), but I will also be quite honest with you and say that as things stand I am starting to loose interest in this discussion because all we seem to be doing is go round and round the same circles over and over again.
    Don't. Because this stuff takes you places. But for a break, why don't you start a thread on something that really really interests you, and I'll try to show you how it relates to what I've been saying.

    Quote Originally Posted by Markus Hanke
    If you are not actually prepared to at least consider that your understanding is flawed, then I'd much prefer you say so outright, and I will simply withdraw from this. If you are prepared to listen, then please give me some indication what I could do to explain it better...
    Like I said, I'll get back to you after I've done some re-reading. Maybe you'd like to do some too? Meanwhile do note that the forum is picking up some new members.
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    Quote Originally Posted by lpetrich View Post
    There's a difference between the time that a stationary observer will experience and the time that an infalling observer will experience. If one has experience with the math of general relativity, one can easily work it out. I've done it myself.
    The discussion concerns "non real solutions". You can't use maths to decide whether the maths gives a misleading impression.

    Quote Originally Posted by lpetrich View Post
    The mathematics used by Newton and Maxwell and Einstein and Minkowski and Feynman and ... Why did these supposed Prophets of Revealed Truth use lots of math?
    We know why they used maths, and we know about . The issue is what really happens when r0=r.

    Quote Originally Posted by lpetrich
    What's so special about him? That's the sort of thing I mean when I say that you treat Einstein as a prophet of revealed truth. That does not mean that I automatically reject what he stated. Whether I accept it or not has nothing to do with him.
    If Einstein said light curves because the speed of light varies with position, and if you can't see time flowing in a clock, and if an optical clock goes slower because the light goes slower, then you maybe might start to appreciate that you've been treating your textbook like a bible instead of thinking for yourself.

    Quote Originally Posted by lpetrich
    Now to trying to explain the Riemann tensor. Parallel-transport a vector around a loop and compare it to how it started. To lowest order,

    Deviation in that vector = (Riemann tensor) . (vector) . (area of loop)

    So the Riemann tensor measures how much deviation a vector had.

    Here's a rather strong example of deviation by parallel transport. Start out at the North Pole with a vector pointing to 0d longitude. Go south along 0d longitude to the equator. The vector will be pointing south. Go east to 90d longitude. The vector will still be pointing south. Go north to the North Pole. The vector will point to 90d longitude. It has rotated 90 degrees.
    It's all too abstract, and the North Pole stuff isn't relevant enough to gravity. Your explanation isn't great. You need to practice more. Start a thread, get some feedback, improve your explanation, repeat.

    Markus: sorry, I have to go. I'll look at your detailed post above tomorrow. But meanwhile do note that what I'm saying isn't just some personal opinion. I didn't invent those two GR interpretations, I didn't make up the Einstein quotes, and I didn't dream up what Don Koks said about the speed of light at the ceiling and the floor.
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    Quote Originally Posted by Farsight View Post
    You can't use maths to decide whether the maths gives a misleading impression.
    And yet you are using "logic" (which is the same sort of thing as maths - you certainly aren't using physics) to do the same thing.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Farsight, do we measure the speed of light locally in vacuum to be the c?

    Would it matter if our location differs when we measure the speed of light locally in vacuum?
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    (me) The mathematics used by Newton and Maxwell and Einstein and Minkowski and Feynman and ... Why did these supposed Prophets of Revealed Truth use lots of math?
    Quote Originally Posted by Farsight
    We know why they used maths ...
    Because they recognized that nonmathematical pontification does not get very far. That's why they did much better than the likes of Aristotle, who did not use much math. If you don't think that that is the reason, then tell us what you think their real reason was.
    Quote Originally Posted by Farsight
    If Einstein said light curves because the speed of light varies with position,
    Either he was making an analogy or he was just plain wrong. That sort of approach to his writings is what I mean by scriptural percussion.
    Quote Originally Posted by Farsight
    and if you can't see time flowing in a clock
    Why should one be able to do so? Is time supposed to be something that light can bounce off of?
    and if an optical clock goes slower because the light goes slower,
    The math doesn't work out that way.
    then you maybe might start to appreciate that you've been treating your textbook like a bible instead of thinking for yourself.
    Why is a textbook much worse than your mined quotes?

    (me on explaining the Riemann tensor...)
    Quote Originally Posted by Farsight
    It's all too abstract, and the North Pole stuff isn't relevant enough to gravity.
    Curvature is a rather general concept, and parallel transport is a way of measuring it that can be done from the inside, as it were.
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    Quote Originally Posted by KJW View Post
    And yet you are using "logic" (which is the same sort of thing as maths - you certainly aren't using physics) to do the same thing.
    I am using physics. What I've actually been doing is looking at the terms in expressions like E=mc² and then looking at the empirical evidence to examine what's actually there and what the terms really refer to.


    Quote Originally Posted by Beer w/Straw
    Farsight, do we measure the speed of light locally in vacuum to be the c?
    Yes.

    Quote Originally Posted by Beer w/Straw
    Would it matter if our location differs when we measure the speed of light locally in vacuum?
    Yes. See the two parallel-mirror light-clocks below? You locate yourself at the upper clock and measure the speed of light there. You measure it to be c. Then you move down to the lower clock and measure the speed of light there. You measure it to be c. But that's because whatever location you're at, you measure the speed of light using metres and seconds defined using the motion of light at your location.



    Please talk about the speed of light on this thread: http://www.thephysicsforum.com/speci...eed-light.html

    All: sorry, I have to go.
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    Quote Originally Posted by Farsight View Post
    I am using physics. What I've actually been doing is looking at the terms in expressions like E=mc² and then looking at the empirical evidence to examine what's actually there and what the terms really refer to.
    Again, you are either incredibly deluded or you are lying. Please relate your claims to something we can compare with empirical evidence: give us an example, even a toy one, where we can see Farsight-Physics at work.
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    I did say I'd reply to this:

    Quote Originally Posted by Markus Hanke View Post
    We did, yet you keep ignoring that; you insist that the local viewpoint of a stationary far-away observer must be globally valid all the way down to the event horizon. That's exactly the problem with your claims.
    It's just an extension of the parallel-mirror gif. You can see the lower clock going slower. If you had another clock below that, you'd see that going even slower. Take it to the limit and the clock at the event horizon is stopped.

    Quote Originally Posted by Markus Hanke View Post
    Huh ? There's no "same time" across extended regions in GR at all, so I don't understand what you are saying here.
    There's a "same time" in the room you're in. Take it to the limit.

    Quote Originally Posted by Markus Hanke View Post
    No, what you doing is declaring the external "bookkeeper" frame of a far-away observer to be global. You are saying that what the external observer calculates is what locally happens in a remote frame ( "time stops at the event horizon" ). That is what I mean when I say you don't seem to get the distinction between local and global.
    There aren't any frames. There's light moving through space and inside clocks, and observers seeing it or not.

    Quote Originally Posted by Markus Hanke View Post
    No, he is not stalled. An external observer determines/calculates him to be "stalled", but it is not what locally happens in his frame. Again, that is not a contradiction.
    Where does he fetch up? The event horizon or the central singularity? You can't have it both ways.

    Quote Originally Posted by Markus Hanke View Post
    Again - it is trivial to show that the manifold is smooth and continuous at the event horizon; there is no geodesic incompleteness there. You can't change that mathematical fact by ignoring it or declaring it to be unphysical.
    You can't make a stopped clock tick by changing a coordinate system. It isn't some physical thing. The clock is.

    Quote Originally Posted by Markus Hanke View Post
    There are no logical fallacies in any of these coordinate systems, and proper time never becomes infinite. Again, just claiming that this is the case is meaningless unless you can bring forward a proper mathematical argument.
    The time-dilation expression suffers from a breakdown at r=r0. You think it can be trivially fixed, but I say it can't. But I can't use maths to back that up.

    Quote Originally Posted by Markus Hanke View Post
    You are now just going round and round in circles, continuously repeating the same sentences, even though a number of people here have attempted to explain to you the difference between coordinate time and local proper time.
    I've explained that proper time is merely an abstract thing derived from the motion of light. And that when light doesn't move there isn't any. You can't make a stopped clock tick by switching to some neverneverland coordinate system which gaily ignores the significance of the future infinity and has the infalling observer going to the end of time and back. It's the height of absurdity, and yet you will not examine it.

    Quote Originally Posted by Markus Hanke
    You don't need "infinite gravitational time dilation" to prevent light from escaping some region.
    You need a "coordinate" speed of light of zero. Frozen light in a frozen star.

    Quote Originally Posted by Markus Hanke View Post
    Why do I need to do it again ? You already know that the event horizon is not a singularity in any of the coordinate systems other than Schwarzschild.
    Those coordinate systems are indulging in fantasy.

    Quote Originally Posted by Markus Hanke View Post
    To be perfectly honest with you, it seems to me like you are using neither. To me, you appear to be defending a personal opinion. Don't take it personally, but that is my genuine impression. If I was to ask you to substantiate any of your claims with sound mathematical reasoning, you wouldn't be able to - you would just say that these are meaningless abstractions. That is not logic, nor is it hard science - it's just an opinion.
    It's not just an opinion. Read the OP. I've got backup.
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    ...and the fringe claims keep on rolling.
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    Quote Originally Posted by Farsight View Post
    Those coordinate systems are indulging in fantasy.
    Can you please tell us which coordinate system is the correct one?

    In some places, you have said that the "real" coordinate system is the one in which the CMB is at rest. Are you now claiming that there is one black hole and the Schwarzchild metric around that one black hole is the real coordinate system? Or is there one special black hole? And in this case, what happens at other black holes? And if the CMB-rest coordinate system is real, then can you show what happens with regards to black holes in this coordinate system?
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    Quote Originally Posted by PhysBang View Post
    Can you please tell us which coordinate system is the correct one?
    No. But I can tell you that when the clock is stopped, any coordinate system that purports to make it tick again, is incorrect. I've said Kruskal-Szekeres coordinates effectively place a stopped observer in front of a stopped clock and declare that "in his frame" he sees it ticking normally. Even though he doesn't see anything at all.

    Quote Originally Posted by PhysBang
    In some places, you have said that the "real" coordinate system is the one in which the CMB is at rest.
    I haven't said that. I've said it provides a de-facto reference frame for the universe, but that it isn't an "absolute" reference frame in the GR sense.

    Quote Originally Posted by PhysBang
    Are you now claiming that there is one black hole and the Schwarzchild metric around that one black hole is the real coordinate system? Or is there one special black hole? And in this case, what happens at other black holes? And if the CMB-rest coordinate system is real, then can you show what happens with regards to black holes in this coordinate system?
    No. No. No. Pass. No. You need to look afresh at the distinction between "doesn't see anything unusual" and "doesn't see anything". Relate the gedanken GR observer at the event horizon to the gedanken SR observer moving at the speed of light. Neither see anything, ever.
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    Quote Originally Posted by Farsight View Post
    No. But I can tell you that when the clock is stopped,
    OK, so please walk us through an actual case.
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    Quote Originally Posted by Farsight View Post
    But I can tell you that when the clock is stopped, any coordinate system that purports to make it tick again, is incorrect. I've said Kruskal-Szekeres coordinates effectively place a stopped observer in front of a stopped clock and declare that "in his frame" he sees it ticking normally. Even though he doesn't see anything at all.

    ...

    Relate the gedanken GR observer at the event horizon to the gedanken SR observer moving at the speed of light. Neither see anything, ever.
    The metric provides the measure of distance for (infinitesimal) displacements in all directions, not just locations (points) in spacetime. In other words, the "tick-rate" of a clock depends on the motion of the clock, not just its location. Therefore, the unqualified statement that clocks stop at the event horizon is false. A clock passing through the event horizon does not stop in proper terms. For example, the clock on my desk continues to tick even though its trajectory in spacetime passes through various light-cones. That is, the clock on my desk and the light-cones share locations, but because the directions in spacetime differ (the velocities differ), the clock on my desk continues to tick.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Setting aside what we were saying about motion being relative, we would say that a fast-moving clock ticks slow. SR time dilation and all that. So a fast-moving clock at the event horizon ticks slower than a stationary clock at the event horizon. Which has a tick rate of zero!

    Quote Originally Posted by KJW
    Therefore, the unqualified statement that clocks stop at the event horizon is false. A clock passing through the event horizon does not stop in proper terms.
    See Kevin Brown's article for the two different interpretations. An optical clock at the event horizon doesn't tick because light is stopped. Because the speed of light there is zero. And a clock can't travel faster than light. So the clock can't pass through the event horizon.

    Quote Originally Posted by KJW
    For example, the clock on my desk continues to tick even though its trajectory in spacetime passes through various light-cones.
    Spacetime is an abstract thing, as is a light cone. IMHO it's important to focus on the things that are real and avoid being distracted by abstraction.
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    Quote Originally Posted by Farsight View Post
    See Kevin Brown's article for the two different interpretations. An optical clock at the event horizon doesn't tick because light is stopped. Because the speed of light there is zero. And a clock can't travel faster than light. So the clock can't pass through the event horizon.
    That is not what Brown writes. Brown also points out that your frozen star interpretation is inconcsistent with the available observations, so I'm not sure why you continue to site him.
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    Those coordinate systems are indulging in fantasy.
    Diffeomorphism invariance is the defining characteristic of tensors as geometric objects, and hence of the Einstein equations and thus GR as a whole. If you declare this to be wrong and unphysical, then you declare all of GR to be wrong and unphysical, and we no longer have a common ground to lead a meaningful discussion on.

    Markus: sorry, I have to go. I'll look at your detailed post above tomorrow.
    See above. I am still awaiting a reply to that post. Before I continue you on with this I would like to hear your thoughts first.
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    Quote Originally Posted by Farsight View Post
    Setting aside what we were saying about motion being relative, we would say that a fast-moving clock ticks slow. SR time dilation and all that. So a fast-moving clock at the event horizon ticks slower than a stationary clock at the event horizon. Which has a tick rate of zero!

    See Kevin Brown's article for the two different interpretations. An optical clock at the event horizon doesn't tick because light is stopped. Because the speed of light there is zero. And a clock can't travel faster than light. So the clock can't pass through the event horizon.
    The local speed of light is the same everywhere, including the event horizon. I strongly recommend that you examine the metric of the Schwarzschild blackhole so that you can avoid making mistakes such as the above. For example, SR doesn't apply in the way you are trying to apply it... the spacetime is curved and you are not examining the local physics.


    Quote Originally Posted by Farsight View Post
    Spacetime is an abstract thing, as is a light cone. IMHO it's important to focus on the things that are real and avoid being distracted by abstraction.
    A light-cone is no more abstract than the event horizon.
    Markus Hanke likes this.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    IMHO it's important to focus on the things that are real and avoid being distracted by abstraction.
    Proper time and proper lengths are real because it is what clocks and rulers physically measure - it gets no more "real" than that. Coordinate time and coordinate lengths on the other hand are not, yet you are attempting to afford them a special status, and then complain about a "contradiction" that is only of your own making.
    All in all you are absolutely right - it is important to focus on what is real, and that is proper measurements taken by physical instruments, all of which are completely independent of the chosen coordinates ( unlike coordinate measurements ); and in terms of proper measurements there are no infinities at the event horizon, nor are there any contradictions, any more than it is a contradiction that an Earth-bound observer sees an accelerometer in free fall accelerate towards him at 9.8 m/s^2 whereas the accelerometer itself reads exactly zero. That is precisely the difference between proper and coordinate measurements.
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    Quote Originally Posted by Duffield
    See Kevin Brown's article for the two different interpretations.
    You are shamelessly distorting what K. Brown is writing. This is a pattern with you.

    An optical clock at the event horizon doesn't tick because light is stopped. Because the speed of light there is zero. .
    False. The COORDINATE speed of light is zero, the speed of light is still c: .

    And a clock can't travel faster than light. So the clock can't pass through the event horizon
    Nonsense, the light is not "stopped", the clock doesn't need to travel faster than light in order to go through the EH. You are simply piling up your misconceptions.
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    Quote Originally Posted by Markus Hanke View Post
    Diffeomorphism invariance is the defining characteristic of tensors as geometric objects, and hence of the Einstein equations and thus GR as a whole. If you declare this to be wrong and unphysical, then you declare all of GR to be wrong and unphysical, and we no longer have a common ground to lead a meaningful discussion on.
    I'm not saying that. See general covariance on Wikipedia and note this: The essential idea is that coordinates do not exist a priori in nature, but are only artifices used in describing nature, and hence should play no role in the formulation of fundamental physical laws. Now take it a stage further and see a couple of lines further down: Albert Einstein proposed this principle for his special theory of relativity; however, that theory was limited to space-time coordinate systems related to each other by uniform relative motions only[clarification needed], the so-called "inertial frames." Einstein recognized that the general principle of relativity should also apply to accelerated relative motions. OK? Now what happens when there is no motion? The clock has stopped. Introducing a stopped observer is an artifice. Kruskal-Szekeres coordinates are an artifice. It ends up with the absurd claim that "in his frame" he sees the clock ticking normally. There is no motion in the clock, and no motion in the observer, but we are asked to believe that there is motion after all? That's wrong and unphysical. But general relativity isn't.

    Quote Originally Posted by Markus Hanke View Post
    See above. I am still awaiting a reply to that post. Before I continue you on with this I would like to hear your thoughts first.
    See post #31.

    Quote Originally Posted by Markus Hanke
    Proper time and proper lengths are real because it is what clocks and rulers physically measure - it gets no more "real" than that.
    A clock does not physically measure proper time. It features some kind of regular cyclical motion, which it effectively counts, displaying the cumulative total on some kind of register. And when the regular cyclical motion stops, the clock stops. Sticking a stopped observer in front of it won't get it going again.

    Quote Originally Posted by Markus Hanke
    Coordinate time and coordinate lengths on the other hand are not, yet you are attempting to afford them a special status, and then complain about a "contradiction" that is only of your own making.
    I'm not. I'm pointing out what's there. And saying a clock is stopped and not stopped is a patent contradiction.

    Quote Originally Posted by Markus Hanke
    All in all you are absolutely right - it is important to focus on what is real, and that is proper measurements taken by physical instruments, all of which are completely independent of the chosen coordinates
    Quite. And when the clock stops, motion stops, and measurement is at an end. Full stop. You cannot choose some different coordinates to make it start up again.

    Quote Originally Posted by Markus Hanke
    ( unlike coordinate measurements ); and in terms of proper measurements there are no infinities at the event horizon
    No. Just a zero.

    Quote Originally Posted by Markus Hanke
    nor are there any contradictions, any more than it is a contradiction that an Earth-bound observer sees an accelerometer in free fall accelerate towards him at 9.8 m/s^2 whereas the accelerometer itself reads exactly zero. That is precisely the difference between proper and coordinate measurements.
    There's no contradiction about whether that accelerometer is falling. And we all know that gravity is not a force in the Newtonian sense. When you're falling there's no force acting upon you. Instead you feel a force on your feet when you're standing on the ground.
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    Quote Originally Posted by Farsight
    Now what happens when there is no motion? The clock has stopped.
    False, the clock continues to tick at the standard rate of one second per second.
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    Quote Originally Posted by KJW
    The local speed of light is the same everywhere, including the event horizon. I strongly recommend that you examine the metric of the Schwarzschild blackhole so that you can avoid making mistakes such as the above.
    I haven't made a mistake. See what I said to Markus above. The mistake is thinking you can do a hop skippety jump to the end of time and back again in finite proper time. And in changing to Kruskal-Szekeres coordinates to invent motion by pretending a stopped observer sees a stopped clock ticking normally. The mistakes are in MTW:



    Quote Originally Posted by KJW
    For example, SR doesn't apply in the way you are trying to apply it... the spacetime is curved and you are not examining the local physics.
    I'm not applying SR, spacetime is an abstract thing, and I am examining the local physics. And I'm not just making all this stuff up. Remember what Kevin Brown said:

    According to the field interpretation, a clock runs increasingly slowly as it approaches the event horizon (due to the strength of the field), and the natural "limit" of this process is that the clock just asymptotically approaches "full stop" (i.e., running at a rate of zero) as it approaches the horizon. It continues to exist for the rest of time, but it's "frozen" due to the strength of the gravitational field. Within this conceptual framework there's nothing more to be said about the clock's existence. This leads to the "frozen star" conception of gravitational collapse.

    Yes, he sides with the other interpretation. But Einstein did say that light curves because the speed of light varies with position. And an optical clock goes slower when its lower. At the event horizon it stops.

    Quote Originally Posted by KJW
    A light-cone is no more abstract than the event horizon.
    I'm saying it is. Markus would say the event horizon is a mere artefact, something that doesn't really exist. I don't, because that optical clock can't go slower than stopped.

    * * * * *

    Quote Originally Posted by PhysBang View Post
    That is not what Brown writes. Brown also points out that your frozen star interpretation is inconcsistent with the available observations, so I'm not sure why you continue to site him.
    Kevin Brown refers to two interpretations. See the OP. He didn't say An optical clock at the event horizon doesn't tick because light is stopped. Because the speed of light there is zero. And a clock can't travel faster than light. So the clock can't pass through the event horizon. I said that.
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    Quote Originally Posted by Farsight
    Kevin Brown refers to two interpretations. See the OP. He didn't say An optical clock at the event horizon doesn't tick because light is stopped.
    Of course he didn't, he knows physics.

    Because the speed of light there is zero.
    False, the local speed of light at the EH is "c". You continue to confuse the coordinate speed of light with the local speed of light.

    So the clock can't pass through the event horizon. I said that.
    We all know what you said, it is a series of misconceptions. Contrary to your many misconceptions, the clock passes through the EH undisturbed. Not that it has any relevance on the discussion.
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    Farsight, the clock does pass through the event horizon in its local frame, ticking normally. However for it to be reckoned to pass through the event horizon from a distant observer frame would require it to go to the ends of time (and back if it could, which it can't) so a distant observer will reckon that it never goes past the event horizon. There is no paradox here if you accept time dilation. The time dilation just becomes infinite at the event horizon.
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    Quote Originally Posted by Farsight View Post
    I haven't made a mistake. See what I said to Markus above. The mistake is thinking you can do a hop skippety jump to the end of time and back again in finite proper time. And in changing to Kruskal-Szekeres coordinates to invent motion by pretending a stopped observer sees a stopped clock ticking normally.
    You seem to be under the illusion that the clocks in one system of coordinates are the same clocks in another system of coordinates. You also seem to be unaware that GR begins by abandoning the light clocks of SR and instead adopts arbitrary clocks that conform to the metric, not to the behavior of light. Using the behavior of coordinates solely to determine the operation of physical systems without some covariant physical laws is contrary to GR.
    But Einstein did say that light curves because the speed of light varies with position. And an optical clock goes slower when its lower. At the event horizon it stops.
    But it would be a contradiction that would in no way stain your character to simply cherry-pick Einstein quotations will avoiding all talk about why Brown rejects the field interpretation.

    The reason that Brown rejects the field interpretation is that it cannot be made consistent with observations. It is a requirement of physical theories that they be comparable to observation. It would be a contradiction that would in no way stain one's character if one were to claim to be doing physics yet never offer any way to compare their theories with observations.

    Kevin Brown refers to two interpretations. See the OP. He didn't say An optical clock at the event horizon doesn't tick because light is stopped. Because the speed of light there is zero. And a clock can't travel faster than light. So the clock can't pass through the event horizon. I said that.
    Yes, you definitely put words in Brown's mouth because you don't understand how coordinate systems work in GR.
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    Quote Originally Posted by Jilan View Post
    Farsight, the clock does pass through the event horizon in its local frame, ticking normally.
    That's what they say, Jilan. And that's what I'm challenging in this thread.

    Quote Originally Posted by Jilan
    However for it to be reckoned to pass through the event horizon from a distant observer frame would require it to go to the ends of time (and back if it could, which it can't) so a distant observer will reckon that it never goes past the event horizon.
    No problem with that. The distant observer says the coordinate speed of light is zero at the event horizon. And that it's an optical clock. So it stops ticking. And since nothing can move faster than light, it stops moving too. So we've got a motionless clock. Let's add a local observer. He's motionless too. Some will say that he sees himself pass through the event horizon along with the clock. But both he and the clock are motionless. And light. Light doesn't move to his eye. Electrochemical signals don't move in his brain. He doesn't see anything at all.

    Quote Originally Posted by Jilan
    There is no paradox here if you accept time dilation. The time dilation just becomes infinite at the event horizon.
    I do accept time dilation. When the time dilation is infinite the clock rate is zero. The clock stops. And sticking a similarly-stopped observer in front of it doesn't make it start ticking again.
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    Quote Originally Posted by PhysBang View Post
    You seem to be under the illusion that the clocks in one system of coordinates are the same clocks in another system of coordinates.
    It's no illusion. We drop a clock into a black hole. It's the same clock whatever coordinate system you use.

    Quote Originally Posted by PhysBang View Post
    You also seem to be unaware that GR begins by abandoning the light clocks of SR and instead adopts arbitrary clocks that conform to the metric, not to the behavior of light. Using the behavior of coordinates solely to determine the operation of physical systems without some covariant physical laws is contrary to GR.
    What Einstein said isn't contrary to GR. Light curves because the speed of light varies with position. Get used to it.

    Quote Originally Posted by PhysBang
    But it would be a contradiction that would in no way stain your character to simply cherry-pick Einstein quotations will avoiding all talk about why Brown rejects the field interpretation.
    He rejects it because he doesn't know that light curves because the speed of light varies with position. The whole point of this series of threads is to deliver a chain of logic in a step-by-step fashion that leads to rejection of the point-singularity.

    Quote Originally Posted by PhysBang
    The reason that Brown rejects the field interpretation is that it cannot be made consistent with observations.
    Not so! The two interpretations are the same in terms of what we can observe.

    Quote Originally Posted by Physbang
    It is a requirement of physical theories that they be comparable to observation. It would be a contradiction that would in no way stain one's character if one were to claim to be doing physics yet never offer any way to compare their theories with observations.
    We can see optical clocks go slower when they're lower, and we can't see time flowing in them or anywhere. What I've said is perfectly consistent with observation.
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    the time dilation is only relative between the frames. It's only the observer outside the black hole that reckons the clock stops. The speed of light it constant in all frames of reference to the local observer.
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    I'm afraid that's a fallacy, Jilan. Think of infinite time dilation in the SR context. Time dilation would be infinite if you were travelling through space at c. Whereupon you don't see light moving at c. You don't see anything. Ever.
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    Quote Originally Posted by Duffield
    The distant observer says the coordinate speed of light is zero at the event horizon.
    It is mainstream physics that proves this:



    At the EH so .

    You can find this in most introductory textbooks.

    And that it's an optical clock.
    False.


    So it stops ticking.
    Also false. And it stays false no matter how many times you repeat it.
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    Consider these four metrics. I'll use c = G = 1, and signature -+++, both common in the professional literature.
    Using

    for the angular part,





    The coordinate speed of radially-moving light is different in each one of them. Does that mean that they are physically different solutions?
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    Light follows null geodesics, so , by making the LHS equal to zero and by dividing by we obtain different expressions for . From a physics point of view this means.....absolutely nothing!
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    Quote Originally Posted by Farsight View Post
    I'm afraid that's a fallacy, Jilan. Think of infinite time dilation in the SR context. Time dilation would be infinite if you were travelling through space at c. Whereupon you don't see light moving at c. You don't see anything. Ever.
    There is nothing special about the event horizon from a local perspective, at least that's what most sources say.
    http://courses.washington.edu/bbbtea.../Lecture18.pdf
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    Yes, that's what most sources say. This and the previous threads are my attempt to explain why they're wrong. Note this on slide 7:

    At r = 2m, i.e. on the event horizon, this velocity becomes zero – free-falling objects come to a stand-still!

    And yet on the same slide the lecture talks about the infalling observer falling through the event horizon.


    Quote Originally Posted by lpetrich
    Consider these four metrics. I'll use c = G = 1...
    Which means you've gone wrong from the off. The coordinate speed of light is zero and your optical clock is stopped. So saying c=1 is totally missing the trick.

    Quote Originally Posted by x0x
    Light follows null geodesics...
    A geodesic is an abstract line in a mathematical model. Light doesn't curve because it follows a null geodesic, it curves because the speed of light varies with position. That's what Einstein said. Take it to the limit for a black hole, and you have a frozen-star black hole.
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    Quote Originally Posted by Farsight View Post
    A geodesic is an abstract line in a mathematical model.
    What are you using to claim that the speed of light at the event horizon is zero?
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Infinite gravitational time dilation. Or "the coordinate speed of light is zero". Or the simple fact that the light can't get out. When you stand on the surface of a massive body with your laser pointed straight up, the light doesn't curve round or slow down or fall back*. Then make the body more and more massive until you've got yourself a black hole. The light doesn't curve round or slow down or fall back. But the light doesn't get out. Because it's stopped.

    * Rather counterintuitively, light speeds up as it ascends. If it didn't, optical clocks wouldn't go slower when they're lower.
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    Quote Originally Posted by Farsight View Post
    Infinite gravitational time dilation. Or "the coordinate speed of light is zero". Or the simple fact that the light can't get out. When you stand on the surface of a massive body with your laser pointed straight up, the light doesn't curve round or slow down or fall back*. Then make the body more and more massive until you've got yourself a black hole. The light doesn't curve round or slow down or fall back. But the light doesn't get out. Because it's stopped.

    * Rather counterintuitively, light speeds up as it ascends. If it didn't, optical clocks wouldn't go slower when they're lower.
    I'll rephrase:

    Quote Originally Posted by KJW View Post
    Quote Originally Posted by Farsight View Post
    A geodesic is an abstract line in a mathematical model.
    What are you using to claim that the speed of light at the event horizon is zero?
    What are you using to claim anything about blackholes?
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Quote Originally Posted by Duffield
    Yes, that's what most sources say. This and the previous threads are my attempt to explain why they're wrong.
    Actually you are wrong, you have been wrong for years.

    Light doesn't curve because it follows a null geodesic, it curves because the speed of light varies with position.
    That can't be, Farsight. What "curves" is the velocity. Nothing to do with speed. Time for you to stop posturing as a "physicist" and for an introductory class in kinematics.

    and you have a frozen-star black hole.
    There is no such thing.
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    Quote Originally Posted by KJW View Post
    What are you using to claim anything about blackholes?
    An understanding of how gravity actually works. A gravitational field is a region of space where the speed of light varies with position. It goes slower when its lower. The vertical light beam goes faster and faster as it ascends. So the only way light can't get out is if its initial speed is zero.

    Try explaining yourself why the light can't get out. When you can't, perhaps you'll appreciate where I'm coming from.
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    Quote Originally Posted by x0x View Post
    ...That can't be, Farsight. What "curves" is the velocity...
    Not so. Have a read of this article on the Baez website.

    "Einstein talked about the speed of light changing in his new theory. In his 1920 book "Relativity: the special and general theory" he wrote: "... 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 [...] cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity [Einstein means speed here] of propagation of light varies with position." This difference in speeds is precisely that referred to above by ceiling and floor observers."

    The article was updated by Don Koks this year. An earlier version written by Philip "vixra" Gibbs and Steve Carlip contained some confusion. It said this in the general relativity section:

    "Since Einstein talks of velocity (a vector quantity: speed with direction) rather than speed alone, it is not clear that he meant the speed will change, but the reference to special relativity suggests that he did mean so. This interpretation is perfectly valid and makes good physical sense..."

    Nothing wrong with that. But then the article said this:

    "but a more modern interpretation is that the speed of light is constant in general relativity".

    The interpretation has changed. Einstein said the speed of light changes, but that's not what's taught any more. And the last line of the article said this:

    "Finally, we come to the conclusion that the speed of light is not only observed to be constant; in the light of well tested theories of physics, it does not even make any sense to say that it varies."

    The article contradicted itself. Most unfortunate. But fortunately Don Koks has done a good job on the revised article.
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    You see, Duffield , this is what happens when you try doing physics by quote cherry picking, as you have been doing for years. The hilarious thing is that you have no understanding of what you are reading.

    But then the article said this:

    "but a more modern interpretation is that the speed of light is constant in general relativity".
    Yes, this is the mainstream interpretation. Still holds. Better you get with the program, John.
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    Quote Originally Posted by Farsight View Post
    It's no illusion. We drop a clock into a black hole. It's the same clock whatever coordinate system you use.
    Yes, but that clock isn't the clock of a coordinate system.
    What Einstein said isn't contrary to GR. Light curves because the speed of light varies with position. Get used to it.
    You are avoiding what I said in a way that does not stain your character. You seem not to understand Einstein's point about "mollusks": the clocks of coordinate systems are not clocks, they are assigned coordinates in order to sync with a chosen metric. In order to predict the behavior of clocks, one needs to apply covariant laws of physics. In your favorite coordinates, the mathematics breaks down at one point and is not able to provide a physical description. This is not the case with all coordinate systems.

    Of course, perhaps you can demonstrate that what happens in your preferred coordinate system is what happens in all coordinate systems?
    He rejects it because he doesn't know that light curves because the speed of light varies with position. The whole point of this series of threads is to deliver a chain of logic in a step-by-step fashion that leads to rejection of the point-singularity.
    So you should be able to show us the mathematical details that describe a black hole using your special VSL theory. If you can't then it seems that you have been telling us mistakes that do not stain your character.
    Not so! The two interpretations are the same in terms of what we can observe.
    Either you are mistaken because you did not read Brown, or you are mistaken in a way that does not stain your character, because Brown writes, "Nevertheless, if mass accumulates near the exterior of a black hole's event horizon the gravitational radius of the combined system must eventually increase far enough to encompass the accumulated mass, leading unavoidably to the conclusion that matter from the outside must reach the interior, and it must do so in a way that is perceptible in finite coordinate time for a distant observer, which seems to directly conflict with Item 2 (and certainly seems inconsistent with the "frozen star" interpretation)." He also writes, "Therefore, if the "frozen star" interpretation gave equivalent predictions for all externally observable phenomena, and was logically consistent, it would probably be the preferred view. The question is, does the concept of a "frozen star" satisfy those two conditions? We saw above that the idea of a frozen star as an empty region around which matter "bunches up" outside an event horizon isn't viable, because if nothing ever passes from the exterior to the interior of an event horizon (in finite coordinate time) we cannot accommodate infalling matter. Either the event horizon expands or it doesn't, and in either case we arrive at a contradiction unless the value of m inside the horizon increases, and does so in finite coordinate time."

    Perhaps you believe that we have not seen matter falling into black holes. If so, then you have the burden of telling us what observations you think are relevant to black holes and the operation of black holes prevents them from producing phenomena of the type observed.

    We can see optical clocks go slower when they're lower,
    That's not true: we can only infer this. By your standard for looking at clocks, we should not believe that they go slower because we cannot see them go slower.
    and we can't see time flowing in them or anywhere. What I've said is perfectly consistent with observation.
    You have the advantage of not being entirely correct there because you have not said anything about how your theory relates to observations. Until you lay out actual physics, your fantasies about physics will not face any test about consistency with observations. If you identify your theory with the one discussed by Brown, then you do face the problem that your theory seems to be inconsistent with the observation that matter falls into black holes.
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    Quote Originally Posted by Farsight View Post
    Yes, that's what most sources say. This and the previous threads are my attempt to explain why they're wrong. Note this on slide 7:

    At r = 2m, i.e. on the event horizon, this velocity becomes zero – free-falling objects come to a stand-still!

    And yet on the same slide the lecture talks about the infalling observer falling through the event horizon.
    .
    Farsight, did you see that the first part is describing it from the viewpoint of the distant observer, whereas the second part is from the viewpoint do the free-falling object? Can you see the distinction, because it's absolutely crucial!
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    (Me earlier: Consider these four metrics. I'll use c = G = 1...)
    Quote Originally Posted by Farsight
    Which means you've gone wrong from the off. The coordinate speed of light is zero and your optical clock is stopped. So saying c=1 is totally missing the trick.
    You ought to take up that complaint with people who do professional work involving general relativity -- and also special relativity, for that matter. Setting c = 1 is a *very* common convention there. Einstein did that also, so if his writings are Holy Writ, then doing so is completely orthodox.

    I'll now give the coordinate speed of radially-moving light for each of the four metrics.





    So by Farsight's argument, those metrics are physically distinct, since light moves at different speeds in them. But they are not. The metrics I'd posted are different versions of the Schwarzschild metric, with different definitions of the radial coordinate.

    Quote Originally Posted by x0x
    Light follows null geodesics...
    Quote Originally Posted by Farsight
    A geodesic is an abstract line in a mathematical model. Light doesn't curve because it follows a null geodesic, it curves because the speed of light varies with position. That's what Einstein said. Take it to the limit for a black hole, and you have a frozen-star black hole.
    A very theologian-like argument. Hunt down some convenient quote in a sacred book, ignore contrary context and contrary quotes, and declare that whoever denies what that quote supposedly demonstrates denies revealed truth. Also, what makes Einstein's writings Holy Writ?
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    Quote Originally Posted by lpetrich View Post
    (Me earlier: Consider these four metrics. I'll use c = G = 1...)

    You ought to take up that complaint with people who do professional work involving general relativity -- and also special relativity, for that matter. Setting c = 1 is a *very* common convention there. Einstein did that also, so if his writings are Holy Writ, then doing so is completely orthodox.

    I'll now give the coordinate speed of radially-moving light for each of the four metrics.





    So by Farsight's argument, those metrics are physically distinct, since light moves at different speeds in them. But they are not. The metrics I'd posted are different versions
    Hi Ipetrich, I am intrigued as to what these four different metrics represent. You say they are different versions, can you explain how they differ. This is all quite new to me!
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    Those metrics differ by their definition of the radial coordinate. It's possible to convert any one of them to another one of them with an appropriate redefinition of that coordinate.

    The radial coordinate in my fourth version is sometimes called the "tortoise" coordinate:


    where r is the traditional Schwarzschild radial coordinate.

    Here are some more versions of the Schwarzschild metric.

    Lemaître:

    where


    Gullstrand-Painlevé:

    where


    Eddington-Finkelstein:
    Ingoing:

    Outgoing:


    Kruskal-Szekeres:

    where
    exterior:

    interior:


    The radial factors are essentially

    using the tortoise coordinate.


    These versions are notable for lacking a coordinate singularity at r = 2M, the event-horizon radius.
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    why is there a need for the different versions?
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    Quote Originally Posted by Ipetrich
    A very theologian-like argument. Hunt down some convenient quote in a sacred book, ignore contrary context and contrary quotes, and declare that whoever denies what that quote supposedly demonstrates denies revealed truth. Also, what makes Einstein's writings Holy Writ?
    Duffield (Farsight) has been doing this for years, he has a PhD in this.
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    Quote Originally Posted by Jilan View Post
    why is there a need for the different versions?
    Different coordinates have different advantages and trade-offs, basically, and highlight different features of the manifold.

    The Schwarzschild coordinates are adapted to the spherical and time symmetries of the manifold, and correspond in a natural way to ordinary polar coordinates in the limit , but are singular at . Ingoing Eddington-Finkelstein coordinates are convenient for analysing radially ingoing light rays, and cover a larger region of the manifold than Schwarzschild (they include the region with the future singularity), but the time symmetry is less apparent. Their main theoretical value is in showing that ingoing geodesics can traverse the event horizon and reach the singularity at . Outgoing Eddington-Finkelstein coordinates are basically time-reversed versions of the ingoing E-F coordinates, and are convenient for analysing radially outgoing light rays. They do not cover the region leading to the future singularity (instead, they include a region leading from a "white hole" singularity in the past, which is unphysical for astronomical black holes, as this region of spacetime is replaced by the interior of the parent star).

    Kruskal-Szekeres coordinates are especially important in the study of the Schwarzschild solution, because they cover the maximal analytic extension of the solution. In other words, they are well-defined for the regions covered by all the other coordinate systems mentioned so far, and any other system that you could come up with. They also cover a region not described by any of the systems above, a second asymptotically flat spatial region that exists "on the other side" of the black hole; this is connected to our ordinary spatial region by a wormhole (a.k.a. the Einstein-Rosen bridge), and to the best of my knowledge was the first wormhole solution of GR discovered (though it is a bit boring as wormholes go; the wormhole is not physically traversable, and would not even be present in black holes formed from actual stars).
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    They are not really "different versions", they are all transforms of the same version.
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    Thanks btr and x0x. So they are versions of the same thing with a different choice of coordinates then? So how would that lead the the coordinate speed of light differing between them as in post #67?
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    Quote Originally Posted by Jilan View Post
    Thanks btr and x0x. So they are versions of the same thing with a different choice of coordinates then? So how would that lead the the coordinate speed of light differing between them as in post #67?
    In concept, it's the same as the situation you get in Special Relativity (and even in Galilean Relativity). If you describe the path of the particle through space with coordinates , the coordinate velocity is given by the quantities ; so, if you use different coordinates you'll get different values for the coordinate velocity components.

    In Special Relativity, you typically (but not always) work in inertial reference frames. When you do so, you find that the coordinate speed (the magnitude of the coordinate velocity) for a photon is always . If you work in non-inertial reference frames, the coordinate speed of photons is not necessarily (and not even necessarily the same in every direction at a given point, depending on how the coordinates are set up). In General Relativity this is pretty much unavoidable, as there are no globally-defined inertial reference frames unless spacetime is flat (in which case you just have SR).

    Nevertheless, even in GR, at any event in spacetime it is always possible to define a coordinate system (e.g. Riemann normal coordinates) such that the coordinate speed of light is in all directions at that particular event, and differs by only small amounts at neighbouring events, just as you can introduce a coordinate system on any point of a spherical surface in which geodesics (great circles) look locally like straight lines; the manifolds are "locally flat". In fact you can do better; for any given observer's world-line you can define a coordinate system (Fermi normal coordinates) which has that same property for all events along the world-line.
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    Thanks btr and x0x. So they are versions of the same thing with a different choice of coordinates then? So how would that lead the the coordinate speed of light differing between them as in post #67?
    Look again at post 67. What did Ipetrich do? He used the fact that light follows null geodesics, so he made . He then divided the RHS by , neglected all the rotational terms in order to obtain the purely radial speed . I did this earlier for Schwarzschild coordinates. Let me do it again:

    1. Start with the metric
    2. Use the fact that light follows null geodesics
    3. Neglect the rotational term
    4. Divide by and get . This is the COORDINATE speed of light.

    It is non-constant (varies with r).
    No one uses it in any experiment (despite "Physicist"'s claims that it is used in the Shapiro delay).
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    Thanks btr and x0x, I Think I can see the point that Iptrich was making in post #54 now.
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    You are welcome.
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    See post #31.
    I don't see how this addresses my original post 23, other than to say that you would come back to it later, which you haven't done yet. I simply wanted to know whether or not there is anything we could do to show you the error in your understanding, or whether your opinion is set in stone. If you go back to my original post I have also explained why I think it is important to obtain an answer to that question.
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    Quote Originally Posted by Farsight View Post
    I haven't made a mistake.
    You have. Hmmm... where do I begin? You are mistaken about the nature of the event horizon. For one thing, you have failed to recognise that there are no local properties of the spacetime that can identify the event horizon. In other words, the spacetime at the event horizon is locally just like the spacetime anywhere else, and this includes the speed of light. You are also mistaken in the belief that the observations of a distant observer are complete and that spacetime doesn't continue beyond what the distant observer can observe. For example, a constantly accelerated observer in flat spacetime has a horizon that is at a distance of below him, and he cannot observe the spacetime beyond that even though it exists for inertial observers. Another mistake is the belief that clocks actually slow down... they don't. Two clocks that have traversed different paths in spacetime may differ in the elapsed time, but this should not be regarded as saying anything about the rate of the clocks.


    Quote Originally Posted by Farsight View Post
    a clock runs increasingly slowly as it approaches the event horizon (due to the strength of the field)
    This statement suffers from the serious problem that the observed rate of a clock does not depend on the strength of the gravitational field at the location of the clock. The location of the event horizon of a blackhole is not determined by the spacetime curvature. Massive blackholes have a much lower spacetime curvature at the event horizon than much smaller blackholes.


    Quote Originally Posted by Farsight View Post
    The mistake is thinking you can do a hop skippety jump to the end of time and back again in finite proper time. And in changing to Kruskal-Szekeres coordinates to invent motion by pretending a stopped observer sees a stopped clock ticking normally.
    You say "changing to Kruskal-Szekeres coordinates" as if Schwarzschild coordinates have preferred status from which any change is to lesser coordinates.


    Quote Originally Posted by Farsight View Post
    I'm not applying SR
    You said "SR time dilation and all that" in the relevant quote.


    Quote Originally Posted by Farsight View Post
    I am examining the local physics
    You're not. You're using the observations of a distant observer to say what happens to an observer falling towards the event horizon.


    Quote Originally Posted by Farsight View Post
    I'm saying it is. Markus would say the event horizon is a mere artefact, something that doesn't really exist. I don't, because that optical clock can't go slower than stopped.
    How does "optical clock can't go slower than stopped" mean that the event horizon exists? Light-cones do exist. For example, the past light-cone from a given event is the set of all locations in spacetime that are visible from the given event, and the future light-cone from a given event is the set of all locations in spacetime at which the given event is visible. With what justification can you say that the event horizon exists?
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Farsight,

    Here is a problem you may find interesting to analyse, if you have not encountered it before.

    Imagine we'd never heard of Schwarzschild or black holes, but had recently discovered the following solution of the vacuum field equations:


    where is some constant. You can see that as the metric becomes the Minkowskian metric (in polar coordinates), and there appears to be some kind of singularity at the spatial origin . My questions are (a) how do we find out over what range of the coordinates the solution is physically applicable, and (b) how do we determine the fate of a test particle heading radially towards or away from the origin in this spacetime?
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    I found the solution, though I won't give it away. I'd written a Mathematica notebook on differential geometry for GR some time ago, and I put it to work for this problem.
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    Can you email it, please!

    My university primarily uses Maple and it's really hard to look for information on forums regarding Mathemitica. I've got some books, but it can overwhelming when there is so much else I have to do.

    I'd personally love to learn how to program it. I've done a bit for Newtonian physics. Tried to for Maxwel's equations. But I feel like I'm putting effort in the wrong place and wasting time. (Mathematica 9)
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    Quote Originally Posted by BwS
    I'd personally love to learn how to program it. I've done a bit for Newtonian physics. Tried to for Maxwel's equations. But I feel like I'm putting effort in the wrong place and wasting time. (Mathematica 9)
    You don't need any package to solve this problem. It is not very difficult to solve it by hand. I will post the solution after Farsight admits he doesn't know how to solve it.
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    It's not to solve the problem, it's I want to see the Mathematica notebook.

    But please do anyway
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    As soon as Farsight admits he doesn't know how to solve it.
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    Arbitrary...
















    Then I'd punch in F

    and automatically get an answer 4.002*10^-4 N
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    Let me be a bit clearer....

    In a finite mathematics course I actually should have got 100% but they only gave a 98% for protocol, but I did so well because I was screwing with Mathematica to see if I had the right answers and doing it in various different ways to be sure. I feel you can learn better if you can already know you have the wrong answer.

    I love Mathematica!

    (And of course Mathematica isn't allowed in an exam.)
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    You're not. You're using the observations of a distant observer to say what happens to an observer falling towards the event horizon.
    Yes, this is the key. Farsight, you do not appear to understand the crucial difference between local and global ( or equivalently the global relationship between local frames ) - a fact evidenced by your assertion that you can examine local physics using the metric of a far-away observer, which of course doesn't work. So long as you cannot get your mind around this, there will be no moving forward for this discussion, but only an endless going around in circles. In light of this, I would appreciate if you could comment on my question in post 79.
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    Quote Originally Posted by lpetrich View Post
    I found the solution, though I won't give it away. I'd written a Mathematica notebook on differential geometry for GR some time ago, and I put it to work for this problem.
    Quote Originally Posted by x0x View Post
    You don't need any package to solve this problem. It is not very difficult to solve it by hand. I will post the solution after Farsight admits he doesn't know how to solve it.
    Please allow Farsight to work through it and ask questions if he wants to. The journey is more important than the destination, in this instance.

    Thanks.
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    As to my Mathematica differential-geometry notebook, I'd have to have an e-mail address to send it to. I haven't yet put it up on my personal site.
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    I will PM you later.

    No hurry.
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    Sorry, I seem to have missed quite a few posts here. I'll try to catch up:

    Quote Originally Posted by PhysBang View Post
    You are avoiding what I said in a way that does not stain your character. You seem not to understand Einstein's point about "mollusks": the clocks of coordinate systems are not clocks, they are assigned coordinates in order to sync with a chosen metric. In order to predict the behavior of clocks, one needs to apply covariant laws of physics. In your favorite coordinates, the mathematics breaks down at one point and is not able to provide a physical description. This is not the case with all coordinate systems.
    I say the mathematics does provide a physical description, which is that the clock stops. I also say that what isn't a physical description is that this stopped clock carries on ticking in the frame of a stopped observer.

    Quote Originally Posted by PhysBang
    Of course, perhaps you can demonstrate that what happens in your preferred coordinate system is what happens in all coordinate systems?
    No I can't. But I can point to contradictions as to what happens to the infalling observer. He's either motionless at the event horizon or he isn't.

    Quote Originally Posted by PhysBang
    So you should be able to show us the mathematical details that describe a black hole using your special VSL theory. If you can't then it seems that you have been telling us mistakes that do not stain your character.
    It isn't my special VSL theory, and you know about Schwarzschild coordinates. It was Einstein who said the speed of light varies with position. All I'm saying is that there's two GR interpretations and the one that people think is wrong is the one that's right.

    Quote Originally Posted by PhysBang
    Either you are mistaken because you did not read Brown, or you are mistaken in a way that does not stain your character, because Brown writes, "Nevertheless, if mass accumulates near the exterior of a black hole's event horizon the gravitational radius of the combined system must eventually increase far enough to encompass the accumulated mass, leading unavoidably to the conclusion that matter from the outside must reach the interior, and it must do so in a way that is perceptible in finite coordinate time for a distant observer, which seems to directly conflict with Item 2 (and certainly seems inconsistent with the "frozen star" interpretation)."
    I've said already: the black hole grows like a hailstone. A water molecule doesn't pass through the surface of the hailstone. But it gets buried by other water molecules. The surface passes through it.

    Quote Originally Posted by PhysBang
    He also writes, "Therefore, if the "frozen star" interpretation gave equivalent predictions for all externally observable phenomena, and was logically consistent, it would probably be the preferred view. The question is, does the concept of a "frozen star" satisfy those two conditions? We saw above that the idea of a frozen star as an empty region around which matter "bunches up" outside an event horizon isn't viable, because if nothing ever passes from the exterior to the interior of an event horizon (in finite coordinate time) we cannot accommodate infalling matter. Either the event horizon expands or it doesn't, and in either case we arrive at a contradiction unless the value of m inside the horizon increases, and does so in finite coordinate time."
    The event horizon grows just as a hailstone grows.

    Quote Originally Posted by PhysBang
    Perhaps you believe that we have not seen matter falling into black holes. If so, then you have the burden of telling us what observations you think are relevant to black holes and the operation of black holes prevents them from producing phenomena of the type observed.
    I'll talk about Freidwardt Winterberg's firewall in another thread.

    Quote Originally Posted by PhysBang
    That's not true: we can only infer this. By your standard for looking at clocks, we should not believe that they go slower because we cannot see them go slower.
    It is true. We really can see optical clocks go slower when they're lower. See this David Wineland interview and note this:

    "But nowadays the precision of the clocks is such that we have to worry, when we compare clocks, if one clock in one lab is 30 centimeters higher than the clock in the other lab, we can see the difference in the rates they run at. And this is an extremely small effect that we haven't had to worry about before."

    Quote Originally Posted by PhysBang
    You have the advantage of not being entirely correct there because you have not said anything about how your theory relates to observations. Until you lay out actual physics, your fantasies about physics will not face any test about consistency with observations. If you identify your theory with the one discussed by Brown, then you do face the problem that your theory seems to be inconsistent with the observation that matter falls into black holes.
    It isn't my theory, it's one of two GR interpretations.
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    Quote Originally Posted by Jilan View Post
    Farsight, did you see that the first part is describing it from the viewpoint of the distant observer, whereas the second part is from the viewpoint do the free-falling object? Can you see the distinction, because it's absolutely crucial!
    Yes of course. And something else that's crucial is what actually happens. If there are any paradoxes or contradictions, something is badly wrong.
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    Quote Originally Posted by Markus Hanke View Post
    I don't see how this addresses my original post 23, other than to say that you would come back to it later, which you haven't done yet. I simply wanted to know whether or not there is anything we could do to show you the error in your understanding, or whether your opinion is set in stone.
    Just show me the evidence that the speed of light is truly constant. I've shown you the evidence that it isn't, and given you the Einstein quotes, and I've attempted to get you to examine why the light doesn't get out of a black hole. But you don't seem to have taken any of it seriously. Presumably because it's at odds with what you think you know.

    Quote Originally Posted by Markus Hanke
    If you go back to my original post I have also explained why I think it is important to obtain an answer to that question.
    I'll have another look:

    Quote Originally Posted by Markus Hanke
    Farsight, allow me to draw a line under what has been said, and try a new approach by asking you a simple question - what would I ( or anyone else ) here have to do to show you the flaw in your understanding? Please give an honest answer, because I don't know about you but I am genuinely trying to make you understand here. If there is nothing that I or anyone else could possible do in that regard ( i.e. your opinion is set in stone ), then please just be honest and say so - I would accept that and quite simply not invest any more time and effort in this, as there's plenty of other people here who can continue the discussion. If on the other hand you are prepared to listen to a specific line of reasoning, then state it, and I will do my best to explain it.
    As above. Show me the evidence. Give me the argument. I've shown you that there is no literal time flowing through a clock. I've argued that a clock "clocks up" some kind of regular cyclical motion. If the clock goes slower, it's because that motion goes slower. And then I've referred to optical clocks and the variable speed of light and how gravity actually works. Then we take it to the limit for a black hole and examine why the light doesn't get out. Only you aren't really participating in the discussion, you're keeping it at arm's length.

    Quote Originally Posted by Markus Hanke
    I am happy to help out with any explanation on GR I am able to provide ( and I think that goes for others here too ), but I will also be quite honest with you and say that as things stand I am starting to loose interest in this discussion because all we seem to be doing is go round and round the same circles over and over again. If you are not actually prepared to at least consider that your understanding is flawed, then I'd much prefer you say so outright, and I will simply withdraw from this.
    I've prepared a number of threads that provide a chain of logic. You haven't broken it. You can't show me where my understanding is flawed.

    Quote Originally Posted by Markus Hanke
    If you are prepared to listen, then please give me some indication what I could do to explain it better, because right now I am out of ideas, and the round-and-round-in-circles thing is just a waste of time for me. It was enjoyable for a while, and I really do appreciate that you remained civil and mature all along, but we seem to have reached an impasse here now. I shall be awaiting your response to this before continuing.
    I'm sorry Markus, but I am listening. And I'm not hearing the evidence or the argument that counters my own.
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    Quote Originally Posted by Farsight
    It isn't my special VSL theory,
    I prefer to take responsibility for what I advocate. President Harry Truman famously had a sign on his desk saying "The Buck Stops Here".
    Quote Originally Posted by Farsight
    and you know about Schwarzschild coordinates.
    Yes I do. I also know about various coordinate transformations. I illustrated them in some other posts here.
    Quote Originally Posted by Farsight
    It was Einstein who said the speed of light varies with position.
    Argument by scriptural percussion.
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    Quote Originally Posted by Farsight
    It isn't my theory, it's one of two GR interpretations.
    After a brief respite, Duffield is back to his favorite pastime, trolling.
    Or, as Ipetrich aptly calls it: "Argument by scriptural percussion".
    Given the amount of bandwidth and the memory footprint Duffield chews up with his inane posts, I suggest that the administrators start charging him per word, the website would be far in the black.
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    Quote Originally Posted by KJW View Post
    You have. Hmmm... where do I begin? You are mistaken about the nature of the event horizon. For one thing, you have failed to recognise that there are no local properties of the spacetime that can identify the event horizon. In other words, the spacetime at the event horizon is locally just like the spacetime anywhere else, and this includes the speed of light.
    Spacetime is not space. It's an abstract mathematical thing. And as Physicist was saying in the VSL thread the speed of light through space varies. Saying the event horizon is like anywhere else is just an assertion.

    Quote Originally Posted by KJW View Post
    You are also mistaken in the belief that the observations of a distant observer are complete and that spacetime doesn't continue beyond what the distant observer can observe.
    Spacetime is a static mathematical model. The distant observer says gravitational time dilation goes infinite, the infalling light clock stops ticking, and the coordinate speed of light goes to zero. Saying that the local observer continues to see his clock ticking normally contradicts what the distant observer sees. Whatever happens happens. Two different versions of what happened is a paradox.

    Quote Originally Posted by KJW
    For example, a constantly accelerated observer in flat spacetime has a horizon that is at a distance of below him, and he cannot observe the spacetime beyond that even though it exists for inertial observers.
    The observer accelerates through space. And if you keep on accelerating him such that he's going at c and is subject to infinite time dilation, he doesn't see everything happening as normal "in his frame". He doesn't see his clock ticking normally. He doesn't see anything. Not ever.

    Quote Originally Posted by KJW
    Another mistake is the belief that clocks actually slow down... they don't. Two clocks that have traversed different paths in spacetime may differ in the elapsed time, but this should not be regarded as saying anything about the rate of the clocks.
    Clocks actually do slow down. They don't actually "traverse different paths in spacetime".

    Quote Originally Posted by KJW
    This statement suffers from the serious problem that the observed rate of a clock does not depend on the strength of the gravitational field at the location of the clock.
    It depends on gravitational potential. The strength of the gravitational field relates to the gradient in the potential.

    Quote Originally Posted by KJW
    The location of the event horizon of a blackhole is not determined by the spacetime curvature. Massive blackholes have a much lower spacetime curvature at the event horizon than much smaller blackholes.
    I know. There's no spacetime curvature at the event horizon. The coordinate speed of light is zero, it can't go any lower.

    Quote Originally Posted by KJW
    You say "changing to Kruskal-Szekeres coordinates" as if Schwarzschild coordinates have preferred status from which any change is to lesser coordinates.
    Just a figure of speech. The important issue is that you can't make a stopped clock tick by adopting a different coordinate system.

    Quote Originally Posted by KJW
    You're not. You're using the observations of a distant observer to say what happens to an observer falling towards the event horizon.
    Yes, that's the frozen-star interpretation.

    Quote Originally Posted by KJW
    How does "optical clock can't go slower than stopped" mean that the event horizon exists?
    It's something physical. Light stops and so does everything. There are no events. There is no motion. And so no way of defining space or time.

    Quote Originally Posted by KJW
    Light-cones do exist. For example, the past light-cone from a given event is the set of all locations in spacetime that are visible from the given event, and the future light-cone from a given event is the set of all locations in spacetime at which the given event is visible.
    A light cone is an abstract thing.

    Quote Originally Posted by KJW
    With what justification can you say that the event horizon exists?
    Because black holes exist. They are very small, and very massive, and very black. Light can't get out. And the reason is that the speed of light there is zero.
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    Quote Originally Posted by btr View Post
    Imagine we'd never heard of Schwarzschild or black holes, but had recently discovered the following solution of the vacuum field equations:


    where is some constant. You can see that as the metric becomes the Minkowskian metric (in polar coordinates), and there appears to be some kind of singularity at the spatial origin . My questions are (a) how do we find out over what range of the coordinates the solution is physically applicable, and (b) how do we determine the fate of a test particle heading radially towards or away from the origin in this spacetime?
    I don't know, btr. This is something like isotropic coordinates, but what does it matter? The fate of the test particle is whatever it is. You can't change its fate by switching to some other coordinate system.
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    Quote Originally Posted by Markus Hanke View Post
    Yes, this is the key. Farsight, you do not appear to understand the crucial difference between local and global ( or equivalently the global relationship between local frames ) - a fact evidenced by your assertion that you can examine local physics using the metric of a far-away observer, which of course doesn't work. So long as you cannot get your mind around this, there will be no moving forward for this discussion, but only an endless going around in circles. In light of this, I would appreciate if you could comment on my question in post 79.
    See above. I think you're still missing the crucial point that local to you, in the room you're in, there's a gradient in the speed of light that causes the lower NIST optical clock to go slower, and causes your pencil to fall down. If there was no gradient in the speed of light there would be no gravitational field. A curvature of rays of light can only occur when the speed of light varies with position. Physicist tried to tell you this. You need to take it on board instead of saying it's meaningless, then apply it to black holes and think hard about why the light doesn't get out.
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