Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: AndroidNeox on 22/10/2013 22:00:08
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I've seen a number of Relativity thought experiments that use idealized rope in lowering an object (like Hawking's box of light/radiation) to the vicinity of an event horizon. What I'm not sure about is how the rope gets altered relativistically. If a light beam were to parallel the rope's path, the wavelength of the light would shorten as the light got deeper into the gravity well. Would the light be shortening with respect to the rope?
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As I understand it, to the distant observer, the wavelength of light increases the nearer the event horizon it originates, until it's in the infra-red and no longer visible. Consequently, an observer moving along the rope towards the EH should see this effect retreating ahead of him in that direction. This corresponds to the increasing tidal spaghettification as you approach the black hole. The effect would be as if spacetime were flowing into the BH like water down a plughole - although whether that's more than just an analogy, I couldn't say.
Of course, my understanding could be way off beam... ;)
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Sorry... I wasn't clear. I was imagining hanging the ideal rope down from a platform toward the event horizon and shining a light beam in parallel, downward. The light beam's wavelength will definitely shorten as it approaches the event horizon (zero wavelength at the event horizon). Time will slow. I think time will slow so that, for a local observer, the frequency of the light will appear unchanged, but I'm not positive.
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If a light beam were to parallel the rope's path, the wavelength of the light would shorten as the light got deeper into the gravity well. Would the light be shortening with respect to the rope?
I don't understand. Why do you think that the wavelength would shorten?
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Sorry... I wasn't clear. I was imagining hanging the ideal rope down from a platform toward the event horizon and shining a light beam in parallel, downward.
That's what I thought you meant. Seems to me, for the local observer, the light leaving his torch will appear unchanged, although the tidal gradient will mean it becomes more quickly red-shifted the closer he gets to the BH. The distant observer sees the local observer's time run slow and his light red-shifted.
The light beam's wavelength will definitely shorten as it approaches the event horizon (zero wavelength at the event horizon).
From who's viewpoint will it shorten?
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Sorry... I wasn't clear. I was imagining hanging the ideal rope down from a platform toward the event horizon and shining a light beam in parallel, downward.
That's what I thought you meant. Seems to me, for the local observer, the light leaving his torch will appear unchanged, although the tidal gradient will mean it becomes more quickly red-shifted the closer he gets to the BH. The distant observer sees the local observer's time run slow and his light red-shifted.
The light beam's wavelength will definitely shorten as it approaches the event horizon (zero wavelength at the event horizon).
From who's viewpoint will it shorten?
Light going down into a gravity well increases in frequency and shortens in wavelength. This process is reversed if the light is reflected back up, out of the gravity well.
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Sorry... I wasn't clear. I was imagining hanging the ideal rope down from a platform toward the event horizon and shining a light beam in parallel, downward. The light beam's wavelength will definitely shorten as it approaches the event horizon (zero wavelength at the event horizon). Time will slow. I think time will slow so that, for a local observer, the frequency of the light will appear unchanged, but I'm not positive.
Sorry... I got this mixed up. I'm imagining shining a laser parallel to the rope down toward a black hole. There's a mirror on the end of the rope and the light is reflected back up to where it started. If the mirror is stationary, the returning light should be the same frequency as it had originally.
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If the mirror is stationary, the returning light should be the same frequency as it had originally.
This may be the key. I usually see discussions about free-falling objects & observers.
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If the mirror is stationary, the returning light should be the same frequency as it had originally.
This may be the key. I usually see discussions about free-falling objects & observers.
That still doesn't help me with the rope, though.
Does the rope shorten along with the wavelength of the light?
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Is there a widely used definition of "idealized rope"? If not, please explain how the rope is idealized.
The rope I am imagining has zero mass, infinite strength and tensile modulus, and the light-travel time between its distance markers is constant in the reference frame of an imaginary observer clinging to the rope. Is that an accurate description of the rope in the thought experiment?
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I've seen a number of Relativity thought experiments that use idealized rope in lowering an object (like Hawking's box of light/radiation) to the vicinity of an event horizon. What I'm not sure about is how the rope gets altered relativistically. If a light beam were to parallel the rope's path, the wavelength of the light would shorten as the light got deeper into the gravity well. Would the light be shortening with respect to the rope?
It's my understanding that as you approach and cross the event horizon nothing particularly changes to the light you are observing. Even after crossing the event horizon you would still be able to see light from the outside coming in since it is acting as a kind of "one way" valve only allowing light in but not out. To an observer situated at some distance away, however, the light coming from you would be stretched and stretched to the point of becoming infrared and eventually stop being light at all and become radio waves, etc., which is why to an observer you would ultimately disappear. You would also appear to an observer to become ever increasingly slowed to the point where you would seem frozen although to you, nothing would seem different. This is because the closer you get to the event horizon the harder light has to work to overcome the tidal forces of the BH, taking longer than normal. Despite your "on board" clocks seeming normal if you could suddenly travel back to where the observer is sitting you would find they have aged much more than you because your time flowed relatively much slower than theirs. Another way to look at it is that at some point, when about to cross the event horizon, there will be a final photon that is able to escape the gravity of the BH, after which, all the photons will be trapped inside the BH at which point you will appear to an observer to be frozen, although in reality you keep going. I'm not quite clear on this point but we have to remember that a BH is not only sucking in material objects but space itself too, so presumably this contributes to the the slowing of light to reach an observer.
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It's my understanding that as you approach and cross the event horizon nothing particularly changes to the light you are observing.
That’s quite correct.
Even after crossing the event horizon you would still be able to see light from the outside coming in since it is acting as a kind of "one way" valve only allowing light in but not out.
That’s also quite correct. In fact the following article is all about this exact same thing - Stellar sky as seen from the vicinity of a black hole by Joachim Schastok, Michael Soffel, and Hanns Ruder, Am. J. Phys., 55(4), Apr. (1987)
To an observer situated at some distance away, however, the light coming from you would be stretched and stretched to the point of becoming infrared and eventually stop being light at all and become radio waves, etc., which is why to an observer you would ultimately disappear.
This is a very subtle point here. If you’ve fallen in past the event horizon then there’s no way the people outside the black hole can speak of them. Always occurring from outside the horizon. What you’ve just described here applies to observers outside the event horizon watching an object falling into the black hole, However from this point of view the falling object never reaches the event horizon.
You would also appear to an observer to become ever increasingly slowed to the point where you would seem frozen although to you, nothing would seem different. This is because the closer you get to the event horizon the harder light has to work to overcome the tidal forces of the BH, taking longer than normal.
Careful here. The light is overcoming the gravitational forces, not the tidal forces.
Despite your "on board" clocks seeming normal if you could suddenly travel back to where the observer is sitting you would find they have aged much more than you because your time flowed relatively much slower than theirs. Another way to look at it is that at some point, when about to cross the event horizon, there will be a final photon that is able to escape the gravity of the BH, after which, all the photons will be trapped inside the BH at which point you will appear to an observer to be frozen, although in reality you keep going.
Now you’ve lost me. There will never be a final photon that is able to escape the gravity of the BH. What led you to believe such a thing?
I'm not quite clear on this point but we have to remember that a BH is not only sucking in material objects but space itself too, …
Where did you get that idea? It’s news to me. In fact I can’t even imagine what it means.
…so presumably this contributes to the slowing of light to reach an observer.
No. Not at all. The slowing of light is due to the nature of the metric which itself is the description of the gravitational field. The component of interest is the one containing the gravitational field. If you wish to see the derivations for this please see http://home.comcast.net/~peter.m.brown/gr/c_in_gfield.htm
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I'm not quite clear on this point but we have to remember that a BH is not only sucking in material objects but space itself too, …
Where did you get that idea? It’s news to me. In fact I can’t even imagine what it means.
I'm assuming that Brian Cox knows what he is talking about:
http://www.bbc.co.uk/ science/space/universe/sights/black_holes/#p00frjln
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The URL you posted had a space in it which made it unworkable so I fixed it.
http://www.bbc.co.uk/science/space/universe/sights/black_holes/#p00frjln
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The URL you posted had a space in it which made it unworkable so I
http://www.bbc.co.uk/science/space/universe/sights/black_holes/#p00frjln
Thank you. Unfortunately, I'm using my iPad, which does not seem to display the URL for copying so I had to type it out in full myself.
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Is there a widely used definition of "idealized rope"? If not, please explain how the rope is idealized.
The rope I am imagining has zero mass, infinite strength and tensile modulus, and the light-travel time between its distance markers is constant in the reference frame of an imaginary observer clinging to the rope. Is that an accurate description of the rope in the thought experiment?
Yes, that's what I had in mind... infinitely strong & flexible but weightless.
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Pmb, there has to be a moment when light is no longer able to escape the pull of the black hole else why does the image of something that is about to cross the event horizon become frozen? If light continued to travel from such an object it would be seen as moving away.
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So, anybody here know how this will work?
Will the rope change length with light wavelength?
I can see how the two frames would be different... on the distant platform, the acceleration of gravity will be small. Hanging from the rope, the strength of gravity will be arbitrarily large.
The fact that there will be a last photon coming up from an object being lowered into the gravity well isn't relevant to the thought experiment. For example, we could have the guy that's hanging on the rope have a mirror. That way, the reflected light will be immune from the infinite redshift (the light will blue-shift on the way down and red-shift on the way up).
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Pmb, there has to be a moment when all light is no longer able to escape the pull of the black hole else why does the image of something that is about to cross the event horizon become frozen? If light continued to travel from such an object it would be seen as moving away.
This is explained by saying that all future light cones dip inside the event horizon - and that's why light which is aimed radially away from a falling object in a direction opposite the singularity then will not move outwards from the event horizon. I'll see if I can find it described in Exploring Blackl Holes - 2nd Ed. Taylor, et al
In the meantime see the last figure on
http://www.phy.syr.edu/courses/modules/LIGHTCONE/schwarzschild.html
The following diagram shows a foolish observer's worldline in the outside region, venturing into the black hole. This observer is periodically sending out light-pulses. However, notice that the closer our foolish observer gets, the longer it takes for his pulses to reach an outside observer. Before he reaches the event horizon, the observer can still return to the outer regions of the outside region... but the longer he waits, the longer it will take him to return.
Just after the foolish observer crosses the event horizon (at event u), his light-pulses never reach an outside observer. And since his light-pulses can't reach the outside, no particle (for example, his spaceship) can reach the outside.
Now, once inside, the light cones now direct him to the singularity. His life will soon be over: his worldline will end.
Does this help? I'm assuming that you know what light cones are, right?
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It's hard to know how much of a popular science programme is analogy and how much is hard physics, but Cox does explicitly say that space flows into the black hole with increasing velocity. It occurs to me that in that model the tidal force spahettification is due to the increasing 'stretching' of space, which should lead to the wavelength of infalling light lengthening... ;)
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Would the light be shortening with respect to the rope?
No. The reason for all of this confusion is a misunderstanding about gravitational redshift. Students of GR often make the mistake of thinking that the frequency of an EM wave changes as it moves through a gravitational wave wherein fact there is no change in frequency. In fact the energy of the photon doesn't change either.
See http://home.comcast.net/~peter.m.brown/gr/grav_red_shift.htm
Notice the conclusion arrived at after Eq. (2) -
Therefore the frequency of the light, as measured by any single observer, does not change as the light moves through the gravitational field!
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It's hard to know how much of a popular science programme is analogy and how much is hard physics, but Cox does explicitly say that space flows into the black hole with increasing velocity.
But where does it say that. I did a search on that page for the phase space flows and found nothing.
I then simplified it to search for "flow" and also found nothing.
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Would the light be shortening with respect to the rope?
No. The reason for all of this confusion is a misunderstanding about gravitational redshift. Students of GR often make the mistake of thinking that the frequency of an EM wave changes as it moves through a gravitational wave wherein fact there is no change in frequency. In fact the energy of the photon doesn't change either.
See http://home.comcast.net/~peter.m.brown/gr/grav_red_shift.htm
Notice the conclusion arrived at after Eq. (2) -
Therefore the frequency of the light, as measured by any single observer, does not change as the light moves through the gravitational field!
You're mistaken. Light dropping into a gravity well increases in energy... wavelength shortens/frequency increases.
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It's hard to know how much of a popular science programme is analogy and how much is hard physics, but Cox does explicitly say that space flows into the black hole with increasing velocity. It occurs to me that in that model the tidal force spahettification is due to the increasing 'stretching' of space, which should lead to the wavelength of infalling light lengthening... ;)
It works the other way. When spacetime is stretched (e.g. gravity well) objects in spacetime shrink and slow.
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It's hard to know how much of a popular science programme is analogy and how much is hard physics, but Cox does explicitly say that space flows into the black hole with increasing velocity. It occurs to me that in that model the tidal force spahettification is due to the increasing 'stretching' of space, which should lead to the wavelength of infalling light lengthening... ;)
A singularity is warping spacetime to a much greater degree than an ordinary mass, such as a star, therefore, I would have thought one could refer to spacetime crossing the event horizon and entering the singularity. Or is this misguided?
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But where does it say that. I did a search on that page for the phase space flows and found nothing.
I then simplified it to search for "flow" and also found nothing.
It's in the video clip at around 2:15; Cox is by a large waterfall and using the river & waterfall as an analogy, describing being unable to swim fast enough to stop being carried over the edge of the waterfall.
... Well it's the same close to a black hole, because space flows faster, faster and faster towards the black hole. Literally, this stuff [gestures around himself], my space that I'm in, flowing over the edge, into the black hole; and at the very special point, called the event horizon, space is flowing at the speed of light into the black hole...
Seems pretty explicit.
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A singularity is warping spacetime to a much greater degree than an ordinary mass, such as a star, therefore, I would have thought one could refer to spacetime crossing the event horizon and entering the singularity. Or is this misguided?
I'm not qualified to say. When I first heard this as the river & waterfall analogy, I assumed the analogy was just with the effects of gravity on matter falling towards a black hole. Subsequently I've seen several articles by people who should know (and now Cox's video) who talk of space literally 'flowing' into the black hole, moving at c at the event horizon, and continuing to accelerate past it (this sounds analogous to the expansion of space by dark energy, that causes the most distant galaxies to recede from us faster than c). In this case, I'd expect infalling light to be red-shifted due to the acceleration expanding or stretching of space towards the black hole and outgoing light (above the EH) also red-shifted climbing out of the gravity well.
I'm still not clear whether they're saying the acceleration due to gravity is actually physically equivalent to space flowing (i.e. the physics is the same), or whether it is simply an overblown analogy and a misuse of 'literally' (never mind what the OED says)...
I'd be grateful for an authoritative view on this.
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It's hard to know how much of a popular science programme is analogy and how much is hard physics, but Cox does explicitly say that space flows into the black hole with increasing velocity. It occurs to me that in that model the tidal force spahettification is due to the increasing 'stretching' of space, which should lead to the wavelength of infalling light lengthening... ;)
It works the other way. When spacetime is stretched (e.g. gravity well) objects in spacetime shrink and slow.
What works the other way? and from who's point of view? are you talking about stationary or infalling objects? in which directions or dimensions do they shrink?
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A singularity is warping spacetime to a much greater degree than an ordinary mass, such as a star, therefore, I would have thought one could refer to spacetime crossing the event horizon and entering the singularity. Or is this misguided?
I'm not qualified to say. When I first heard this as the river & waterfall analogy, I assumed the analogy was just with the effects of gravity on matter falling towards a black hole. Subsequently I've seen several articles by people who should know (and now Cox's video) who talk of space literally 'flowing' into the black hole, moving at c at the event horizon, and continuing to accelerate past it (this sounds analogous to the expansion of space by dark energy, that causes the most distant galaxies to recede from us faster than c). In this case, I'd expect infalling light to be red-shifted due to the acceleration expanding or stretching of space towards the black hole and outgoing light (above the EH) also red-shifted climbing out of the gravity well.
I'm still not clear whether they're saying the acceleration due to gravity is actually physically equivalent to space flowing (i.e. the physics is the same), or whether it is simply an overblown analogy and a misuse of 'literally' (never mind what the OED says)...
I'd be grateful for an authoritative view on this.
Language is always going to be inadequate to accurately describe physics because it is mathematics that describes the real way physicists talk about phenomena but not everyone is mathematically literate, therefore, analogies have to be used to give people some framework for understanding. I'm just an ordinary chap but it seems reasonable to me that if you accept Einstein's model of spacetime and how the curvature of it is distorted by mass then it seems logical to regard a singularity as a special case of an unusually large/infinite mass which, to be consistent with the aforementioned model, distorts timespace to to a much greater degree. So when Cox talks about space crossing into the black hole he's 'kind' of right and to be fair to him the presentation he was making is for popular viewing and as an introduction to the topic.
In regard to space, well, we know (or at least are told) that space is expanding at speeds greater than c out in the universe, therefore, problems about infinite mass don't seem to apply so it seems perfectly reasonable to be told that space is being pulled (probably the wrong term) into a black hole at the speed of light due to the immense gravitational power of the singularity.
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You're mistaken.
The proof that you're wrong is found at
http://home.comcast.net/~peter.m.brown/gr/grav_red_shift.htm
See Eq. (12) in that page. Other sources of proof, such as the American Journal of Physics, are quoted below.
Light dropping into a gravity well increases in energy... wavelength shortens/frequency increases.
This too is a common mistake. The frequency of light does not change as it moves through a gravitational field as reckoned by any single observer. It’s only when you later compare measurements made by observers located at different gravitational potentials does the spectral shift manifest itself.
You’re confusing the (locally measured) kinetic energy of a light (a photon) with its total energy which includes potential energy. The increase of the kinetic energy (locally measured blue shift) is compensated for a decrease in the photons potential energy. Some authors don’t like this description but its rigorous and accurate and agrees with observation.
Your mistake is not that uncommon though. Many people confuse spectral shift (aka the phenomena of gravitational redshift) with the “changing” of the “photon’s energy.” If you’re not that familiar with general relativity (GR) then you may only know the energy of a photon as its used in special relativity (SR) where the energy of the photon is all kinetic energy.
In GR any one observer will reckon the frequency of a beam of light to remain constant as if falls through a gravitational potential. See On the interpretation of the redshift in a static gravitational field by L.B. Okun, K.G. Selivanov, and V.L. Telegdi, Am. J. Phys., 68(2), Feb. (2000)
The change in a photon’s kinetic energy as it moves through a gravitational field means that when the energy is measured locally, i.e. at the same height, the photon is located then it has different values due to spectral shift caused by the gravitational field.
Recall the analogy from Newtonian gravity: If I drop a rock from the roof of my house then the energy of the rock will remain constant as it falls. Does that mean that the kinetic energy as measured by an observer at the same height as the rock will all measure the same kinetic energy? No, it doesn't.
The same thing holds for the energy of the photon as it moves through a gravitational field. This is proven in textbooks on general relativity. E.g. A Short Course in General Relativity – Second Edition by Foster and Nightingale, Springer, (1994). This is proved in section 4.3 Spectral Shift, pages 132 to 135.
If you don’t have that text then see the proof I wrote out under my website at http://home.comcast.net/~peter.m.brown/gr/grav_red_shift.htm
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... Well it's the same close to a black hole, because space flows faster, faster and faster towards the black hole. Literally, this stuff [gestures around himself], my space that I'm in, flowing over the edge, into the black hole; and at the very special point, called the event horizon, space is flowing at the speed of light into the black hole...
okay. I found it. It's described in the article
The River Model of Black Holes by Hamilton & Lisle, Am J. Phys., 76 (6), June 2008).
as well as in the new version of Exploring Black Holes - Second Version. I never heard of this before and I may get drive heaves after I learn about it. :)
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The River Model of Black Holes by Hamilton & Lisle, Am J. Phys., 76 (6), June 2008).
I found the paper (http://arxiv.org/pdf/gr-qc/0411060v2.pdf). They say it's a way to conceptualize stationary black holes via an intuitively appealing mental model - based on the Gullstrand-Painleve metric applied to the Schwartzchild geometry, which looks like ordinary flat space, but 'flowing radially inwards at the Newtonian escape velocity'. Apparently it's been used in undergraduate education classes with good results.
So, a way of looking at black holes that fits the maths and is easy to visualise. It becomes a bit odd for rotating black holes, because instead of an overall spiraling vortex, there is a twist, or shear of the metric, at each point of the flow. Interesting stuff.
One of the class questions asks what you see hovering near the event horizon and answers that you see incoming light blue-shifted because space is rushing towards you (so it's a doppler shift). If you are free-falling, it looks normal, though presumably as tidal forces increase, it will become slightly red-shifted as you are carried inwards faster than the space further out.
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It becomes a bit odd for rotating black holes, because instead of an overall spiraling vortex, there is a twist, or shear of the metric, at each point of the flow.
Are you familiar with frame dragging? This flowing stuff (which I'm totally ignorant about right now) sounds similar to frame dragging.
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Are you familiar with frame dragging? This flowing stuff (which I'm totally ignorant about right now) sounds similar to frame dragging.
Yes; I suppose they both refer to distortions of the spacetime metric, but the river model is based in an analogy for gravitational distortion; I don't know of an equivalent analogy for frame-dragging.
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Are you familiar with frame dragging? This flowing stuff (which I'm totally ignorant about right now) sounds similar to frame dragging.
Yes; I suppose they both refer to distortions of the spacetime metric, but the river model is based in an analogy for gravitational distortion; I don't know of an equivalent analogy for frame-dragging.
Distortion? I'll assume by that you mean spacetime curvature.
Frame-dragging doesn't neccesarily refer to spacetime curvature. To test this idea out one day I decided to see what would happen in I started out at rest in a frame of referance S in which there is uniform gravitational field (which has no spacetime curvature) in the z-direction. I then transformed to a frame of reference S' which was moving perpendicular to the field with uniform velocity. In that frame there is frame dragging. That means that if you were to drop an object from rest in S' it would be deflected.
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... Frame-dragging doesn't neccesarily refer to spacetime curvature. ...
That suggests frame dragging and the river model are not as similar as they might sound - but I'm at my depth limit here.
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It's hard to know how much of a popular science programme is analogy and how much is hard physics, but Cox does explicitly say that space flows into the black hole with increasing velocity. It occurs to me that in that model the tidal force spahettification is due to the increasing 'stretching' of space, which should lead to the wavelength of infalling light lengthening... ;)
It works the other way. When spacetime is stretched (e.g. gravity well) objects in spacetime shrink and slow.
What works the other way? and from who's point of view? are you talking about stationary or infalling objects? in which directions or dimensions do they shrink?
By working "the other way" I meant that when light (or anything else) passes into a region where spacetime is stretched, as in a gravity well, relative to another frame where spacetime is less stretched (or not stretched at all in the case of inertial reference frames) then the object (or wavelength of light) is observed to shrink and time is observed to slow. Time passes more slowly on Earth with respect to (WRT) an observer outside of our gravity well, maybe floating out in space. Because acceleration changes the nature of one's reference frame, an observer on Earth can see that time is passing more quickly for the observer out in space. In the case where there is no acceleration but two observers are moving WRT each other, they will both see that the other observer's clock is going more slowly than their local clock.
Anyway, when spacetime stretches, the objects in spacetime shrink and clocks slow.
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You're mistaken.
The proof that you're wrong is found at
http://home.comcast.net/~peter.m.brown/gr/grav_red_shift.htm
See Eq. (12) in that page. Other sources of proof, such as the American Journal of Physics, are quoted below.
Light dropping into a gravity well increases in energy... wavelength shortens/frequency increases.
This too is a common mistake. The frequency of light does not change as it moves through a gravitational field as reckoned by any single observer. It’s only when you later compare measurements made by observers located at different gravitational potentials does the spectral shift manifest itself.
Regardless of potential energy, the energy one would absorb by absorbing the photon will be greater if it's absorbed after dropping into a gravity well. Perhaps a brick falling a thousand feet has no more energy than a stationary one but it's kinetic energy is greater and its energy, from the perspective of a local observer, will be greater.
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So, back to the topic of this thread.
Does an ideal rope shorten just as a light beam's wavelength will shorten as it travels down into a gravity well?
I've been working on various thought experiments and it seems that it must.
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By working "the other way" I meant that when light (or anything else) passes into a region where spacetime is stretched, as in a gravity well, relative to another frame where spacetime is less stretched (or not stretched at all in the case of inertial reference frames) then the object (or wavelength of light) is observed to shrink and time is observed to slow. Time passes more slowly on Earth with respect to (WRT) an observer outside of our gravity well, maybe floating out in space. Because acceleration changes the nature of one's reference frame, an observer on Earth can see that time is passing more quickly for the observer out in space. In the case where there is no acceleration but two observers are moving WRT each other, they will both see that the other observer's clock is going more slowly than their local clock.
Ah, OK - General Relativity; I couldn't make out what you meant...
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That suggests frame dragging and the river model are not as similar as they might sound - but I'm at my depth limit here.
I dunno. :) I haven't read that paper yet.
I prefer not to comment on stuff until I have a solid understanding of the subject at hand. I've been busy today trying to order an entire new computer system for my new buisness and haven't had time to read that paper yet. I'd be more than happy to get back to you after I understand it to chat about it if you'd like?
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It seems to me that rather than trying to clarify things, you just like to nit-pick and argue.
But correcting errors is clarifying...
He's shown why he thinks what you said is mistaken. If you feel his proofs and arguments are wrong and the error is his, you just have to show how they're wrong. You can't both be right, but an assertion can't stand without some evidence, plausible argument or mathematical proof.
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... I'd be more than happy to get back to you after I understand it to chat about it if you'd like?
Yes, that would be helpful, thanks; it doesn't look that difficult.
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He's shown why he thinks what you said is mistaken. If you feel his proofs and arguments are wrong and the error is his, you just have to show how they're wrong. You can't both be right, but an assertion can't stand without some evidence, plausible argument or mathematical proof.
Actually not only did I prove it myself but I also provide several references to the physics literature were it's also proved. I gave an example from a popular GR text as well, i.e. the GR text by Foster and Nightingale
Perhaps he doesn’t have a single GR text to read. Therefore see
On the Interpretation of the Redshift in a Static Gravitational Field by Okun, et al, Am. J. Phys., 68(2), Feb 2000 - http://arxiv.org/abs/physics/9907017
The abstract reads
The classical phenomenon of the redshift of light in a static gravitational potential, usually called the gravitational redshift, is described in the literature essentially in two ways: on the one hand the phenomenon is explained through the behaviour of clocks which run the faster the higher they are located in the potential, whereas the energy and frequency of the propagating photon do not change with height. The light thus appears to be redshifted relative to the frequency of the clock. On the other hand the phenomenon is alternatively discussed (even in some authoritative texts) in terms of an energy loss of a photon as it overcomes the gravitational attraction of the massive body. This second approach operates with notions such as the "gravitational mass" or the "potential energy" of a photon and we assert that it is misleading. We do not claim to present any original ideas or to give a comprehensive review of the subject, our goal being essentially a pedagogical one.
This is also discussed in Exploring Black Holes - Second Edition by Taylor, Wheeler and Bertschinger in Chapter 4 Global Positioning System. This chapter is available online at http://www.eftaylor.com/exploringblackholes/GPS130923v4.pdf See page 4-3
The clock at the top of the tower emits two flashes radially downward (emission events A and B) differentially close together in global t-coordinate: dtAB. For the stationary tower clock, dr = 0 and dphi = 0, the metric tells us the corresponding wristwatch time lapse d H recorded on the tower clock: (#eq:1A)
dTH = (1 - 2M/rH)1/2 dtAB (dphi = 0; dr = 0) (4.2)
Figure 4.2 traces the radially-downward global worldlines of the two flashes emitted by the tower clock at events A and B. The Earth clock receives these flashes at events C and D with map t-coordinate separation dtCD. Map t-lapse Equation (4.1) tells us that these worldlines have identical slopes (the radial map speed of light has the same value) at every intermediate value of r-coordinate. As a result, the two worldlines are parallel at every radius on the map spacetime diagram, so the global t-coordinate separation between them maintains its initial value dtAB.
which is precisely what I explained to AndroidNeox to begin with.
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okay. I found it. It's described in the article
The River Model of Black Holes by Hamilton & Lisle, Am J. Phys., 76 (6), June 2008).
as well as in the new version of Exploring Black Holes - Second Version. I never heard of this before and I may get drive heaves after I learn about it. :)
And, also in the first version, Chapter "Inside the Black Hole." Page b-4.
It’s seem’s to be a metric for the coordinates of an infaller‘s frame.
In the infaller’s coordinate frame there is an ever decreasing r coordinate. That’s your ‘flowing space’.
From the 'distant' observer frame(not infaller's) the infaller doesn’t reach the horizon ‘as usual’. I may be misunderstanding this, so you better check-it out.
Infaller frame called raindrop/diver. :)
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So, the ideal rope shrinks just as the wavelength of infalling light does and the distance from any point in spacetime is infinitely far from the event horizon. Spacetime stretches infinitely as matter falls into a black hole, they are bottomless, and Einstein was right that event horizons cannot form (in finite time).
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It seems to me that rather than trying to clarify things, you just like to nit-pick and argue.
But correcting errors is clarifying...
He's shown why he thinks what you said is mistaken. If you feel his proofs and arguments are wrong and the error is his, you just have to show how they're wrong. You can't both be right, but an assertion can't stand without some evidence, plausible argument or mathematical proof.
The energy of the photon, considering its potential energy, which is irrelevant to observations, is unchanging but it's unhelpful just as the fact that the total universe has zero energy is useless for determining its local behavior. It would be relevant to a discussion of the nature of physical law and conservation symmetries but it's irrelevant to this topic.
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... Einstein was right that event horizons cannot form (in finite time).
The event horizon isn't a special place in terms of physical characteristics, it just happens to be where the escape velocity exceeds 'c'. For a large black hole, you could pass through it without noticing. Although I've heard that to an infalling observer, the event horizon always appears to remain ahead.
Did you mean the singularity?
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... Einstein was right that event horizons cannot form (in finite time).
The event horizon isn't a special place in terms of physical characteristics, it just happens to be where the escape velocity exceeds 'c'. For a large black hole, you could pass through it without noticing. Although I've heard that to an infalling observer, the event horizon always appears to remain ahead.
Did you mean the singularity?
No, I mean the event horizon. Gravitational collapsars, black holes, are inevitable but event horizons cannot form in finite time because the distance between any point in space and the event horizon is infinite. I asked about the ideal rope because it provides a thought experimental model to show this.
Since nothing can fall to an event horizon in finite time, none have formed yet and nothing has fallen through to a singularity.
Mass causes spacetime to stretch. As the matter that forms it falls into the gravity well, spacetime stretching approaches infinite. This is why an infalling object/observer will be seen to slow exponentially toward a halt and the infalling observer will see the external universe speed up.
If one compares the proper time for the infalling observer to that of an observer distant from the black hole, their time rate difference increases exponentially. By the time the infalling observer reaches the event horizon (which I agree isn't a 'thing' any more than the universe's observable horizon is... they're dependent on the observer's frame of reference) an infinite amount of time will pass for the external observer.
If you try using a slight modification on Hawking's model where he lowers a box of light to the vicinity of an event horizon and replace the box with a mirror, one can show it takes an infinite amount of rope to lower the mirror to the event horizon and that, by reflecting light off of the mirror, the distant observer can verify that the mirror has not passed beyond an event horizon.
A typical description of the infalling object/observer model is that while it appears the object has slowed to a halt, that's an illusion and it has fallen through the event horizon. Ignoring the fact that all of Relativity is based on how the universe appears and that presuming there could be a difference violates the basis of Einstein's thought experiments, there's a simple thought experiment to demonstrate the problem, here.
If the infalling observer has a mirror with him then the reflected light beam must stop being reflected if/when the mirror has passed the event horizon and fallen to the singularity. That means that the distant observer would see the reflected beam disappear while still seeing the mirror.
Presuming anything can fall to an event horizon, including the matter that initially caused the gravitational collapse, violates causality and the basic assumptions of Relativity.
Ask a physicist to present an actual calculated result based on Relativity for the amount of time it would take for some object to pass the event horizon and they won't be able to. These are conclusions without mathematical support and which are in direct violation of the assumptions Relativity is based on.
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Ask a physicist to present an actual calculated result based on Relativity for the amount of time it would take for some object to pass the event horizon and they won't be able to.
They will, given the relevant frame of reference (i.e. that of an infalling observer). See 'Falling into a black hole (http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html)' and '.. if I fell into a black hole (http://cosmology.berkeley.edu/Education/BHfaq.html#q3)':How long does the whole process take? Well, of course, it depends on how far away you start from. Let's say you start at rest from a point whose distance from the singularity is ten times the black hole's radius. Then for a million-solar-mass black hole, it takes you about 8 minutes to reach the horizon. Once you've gotten that far, it takes you only another seven seconds to hit the singularity. By the way, this time scales with the size of the black hole, so if you'd jumped into a smaller black hole, your time of death would be that much sooner.
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Ask a physicist to present an actual calculated result based on Relativity for the amount of time it would take for some object to pass the event horizon and they won't be able to.
They will, given the relevant frame of reference (i.e. that of an infalling observer). See 'Falling into a black hole (http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html)' and '.. if I fell into a black hole (http://cosmology.berkeley.edu/Education/BHfaq.html#q3)':How long does the whole process take? Well, of course, it depends on how far away you start from. Let's say you start at rest from a point whose distance from the singularity is ten times the black hole's radius. Then for a million-solar-mass black hole, it takes you about 8 minutes to reach the horizon. Once you've gotten that far, it takes you only another seven seconds to hit the singularity. By the way, this time scales with the size of the black hole, so if you'd jumped into a smaller black hole, your time of death would be that much sooner.
Neither of those links present the time it takes for the infalling observer to pass the event horizon, from the perspective of an external observer. This is because the time for the external observer is infinite. Only the time for the infalling observer is finite, but since that time rate slows exponentially, the infalling observer's proper time will not reach the 8 minute mark (from your example) until an infinite amount of time has passed externally.
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Neither of those links present the time it takes for the infalling observer to pass the event horizon, from the perspective of an external observer. This is because the time for the external observer is infinite.
That's what both the links say:
"So if you, watching from a safe distance, attempt to witness my fall into the hole, you'll see me fall more and more slowly as the light delay increases. You'll never see me actually get to the event horizon. My watch, to you, will tick more and more slowly, but will never reach the time that I see as I fall into the black hole."
"Penelope is sitting still at a safe distance, watching me fall into the black hole. What does she see?
Penelope sees things quite differently from you. As you get closer and closer to the horizon, she sees you move more and more slowly. In fact, no matter how long she waits, she will never quite see you reach the horizon."
Only the time for the infalling observer is finite, but since that time rate slows exponentially, the infalling observer's proper time will not reach the 8 minute mark (from your example) until an infinite amount of time has passed externally.
That's why it's such an interesting example; that the two equally valid but different frames of reference result in such entirely different experiences for the observers involved. For one (or all external observers), the fall takes an infinite time; for the other (the infaller), it takes a finite, relatively short time.
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That's why it's such an interesting example; that the two equally valid but different frames of reference result in such entirely different experiences for the observers involved. For one (or all external observers), the fall takes an infinite time; for the other (the infaller), it takes a finite, relatively short time.
Exactly. And this is why Einstein insisted event horizons cannot form.
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That's why it's such an interesting example; that the two equally valid but different frames of reference result in such entirely different experiences for the observers involved. For one (or all external observers), the fall takes an infinite time; for the other (the infaller), it takes a finite, relatively short time.
Exactly. And this is why Einstein insisted event horizons cannot form.
Not really; Einstein questioned the whole existence of black holes (see On a Stationary System With Spherical Symmetry Consisting of Many Gravitating Masses (http://www.cscamm.umd.edu/tiglio/GR2012/Syllabus_files/EinsteinSchwarzschild.pdf)):The essential result of this investigation is a clear understanding as to why the "Schwarzschild singularities" do not exist in physical reality. Although the theory given here treats only clusters whose particles move along circular paths it does not seem to be subject to reasonable doubt that more general cases will have analogous results. The "Schwarzschild singularity" does not appear for the reason that matter cannot be concentrated arbitrarily. And this is due to the fact that otherwise the constituting particles would reach the velocity of light.
Turns out he was wrong on this one. You can't always be right, even if you're Einstein.
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In 1938 Einstein thought rotations would hold matter out but later it was realized rotational energy would radiate as gravitational energy, if through no other means. He always insisted that event horizons cannot form.
There is no difference in Relativity between appearance and reality. It's not an illusion that objects in motion or under acceleration contract. It's not an illusion that time passes more slowly for clocks in motion or under acceleration. It's not an illusion that the infalling object slows to a virtual halt outside the event horizon. Spacetime is stretching without bound. It's a bottomless hole. There is absolutely no theoretical justification for presuming that, in this one case, reality does not obey the same rules it does for the rest of Relativity.
The model you present, where observable reality is “an illusion” that is causally irreconcilable with the “real” reality. It violates GR because it’s non-causal.
What the thought experiment shows us is not just what something will look like. It is the paths of information. It defines, for all observers, observable reality. And, observable reality has no causal violations.
Relativity isn't just a theory. It's a complete logical argument. It's a flawless set of statements. The rules Einstein used in developing the theories are essential to the reality of Relativity. It's not possible to use Relativity to argue that event horizons can form because their formation presumes reality does not follow the physical rules that Einstein relied on to develop it. All of Einsteins thought experiments he used to develop his theories from which he derived his equations depended upon the fact that physical reality is entirely consistent with its observable nature.
There are no viable arguments for asserting event horizons can form. If you know of any, I'd be interested in seeing them. Just an unending repetition of "because it's just so" isn't science. It wasn't until years after Einstein was dead that the idea sprang up and I can't find an explanation. Einstein would have stomped on it.
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There is no difference in Relativity between appearance and reality. It's not an illusion that objects in motion or under acceleration contract. It's not an illusion that time passes more slowly for clocks in motion or under acceleration. It's not an illusion that the infalling object slows to a virtual halt outside the event horizon. Spacetime is stretching without bound. It's a bottomless hole. There is absolutely no theoretical justification for presuming that, in this one case, reality does not obey the same rules it does for the rest of Relativity.
Yup, I agree with all that.
The model you present, where observable reality is “an illusion” that is causally irreconcilable with the “real” reality. It violates GR because it’s non-causal.
Ah, no. I explicitly said the two reference frames were equally valid, despite the apparently contradictory experiences. There is only one reality; different observers experience it differently.
There are no viable arguments for asserting event horizons can form. If you know of any, I'd be interested in seeing them. Just an unending repetition of "because it's just so" isn't science. It wasn't until years after Einstein was dead that the idea sprang up and I can't find an explanation. Einstein would have stomped on it.
Are you suggesting black holes can't exist? A black hole has an escape velocity > c. The event horizon is the distance from it at which the escape velocity becomes c. If event horizon can't form, you won't have a black hole...
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The model you present, where observable reality is “an illusion” that is causally irreconcilable with the “real” reality. It violates GR because it’s non-causal.
Ah, no. I explicitly said the two reference frames were equally valid, despite the apparently contradictory experiences. There is only one reality; different observers experience it differently.
There are no viable arguments for asserting event horizons can form. If you know of any, I'd be interested in seeing them. Just an unending repetition of "because it's just so" isn't science. It wasn't until years after Einstein was dead that the idea sprang up and I can't find an explanation. Einstein would have stomped on it.
Are you suggesting black holes can't exist? A black hole has an escape velocity > c. The event horizon is the distance from it at which the escape velocity becomes c. If event horizon can't form, you won't have a black hole...
Second comment, first: I agree that, under general relativity, black holes are inevitable. But, I am certain that the contemporary model of what black holes are (which includes event horizons and singularities) cannot form, in finite time.
Now, regarding causality. While observers in different reference frames inevitably don't see the world the same way, they can always agree on whether an event takes place. e.g. "Was the coin tossed and it came up heads?" They might not agree on time or location or even sequence for different events, they will agree on the events, themselves. This is fundamental to all science and natural philosophy: Causality.
For any matter to have yet fallen to an event horizon within our universe would not only violate the apparent and observable reality predicted by general relativity, but it would violate causality.
This is why I've proposed a thought experiment in which a mirror is dropped toward an event horizon and a laser beam is bounced off of it. If matter can actually fall through an event horizon, then there will be a point in time where the laser beam stops coming back but I can still see the mirror:
- If the beam can stop while the mirror appears to still hang there, then matter can fall to an event horizon and Relativity is fundamentally wrong.
- If the beam continues to return forever, though it will be redshifted by the motion of the falling mirror, which I could compensate for by perpetually increasing the source laser's frequency (but the returning light will not be shifted by gravity because it took a round-trip) then matter cannot fall to an event horizon and Relativity passes another test.