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Offline AndroidNeox

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Question about Relativistic Thought Experiments
« on: 22/10/2013 22:00:08 »
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?


 

Offline dlorde

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Re: Question about Relativistic Thought Experiments
« Reply #1 on: 22/10/2013 22:12:23 »
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... ;)
 

Offline AndroidNeox

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Re: Question about Relativistic Thought Experiments
« Reply #2 on: 22/10/2013 22:23:08 »
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.
 

Offline Pmb

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Re: Question about Relativistic Thought Experiments
« Reply #3 on: 22/10/2013 22:47:44 »
Quote from: AndroidNeox
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?
« Last Edit: 22/10/2013 22:50:44 by Pete »
 

Offline dlorde

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Re: Question about Relativistic Thought Experiments
« Reply #4 on: 22/10/2013 22:50:25 »
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. 

Quote
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?
 

Offline AndroidNeox

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Re: Question about Relativistic Thought Experiments
« Reply #5 on: 23/10/2013 00:08:12 »
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. 

Quote
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.
 

Offline AndroidNeox

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Re: Question about Relativistic Thought Experiments
« Reply #6 on: 23/10/2013 00:11:03 »
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.
 

Offline dlorde

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Re: Question about Relativistic Thought Experiments
« Reply #7 on: 23/10/2013 00:31:43 »
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.
 

Offline AndroidNeox

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Re: Question about Relativistic Thought Experiments
« Reply #8 on: 23/10/2013 02:19:34 »
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?
 

Offline Phractality

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Re: Question about Relativistic Thought Experiments
« Reply #9 on: 23/10/2013 04:51:18 »
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?
 

Offline webplodder

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Re: Question about Relativistic Thought Experiments
« Reply #10 on: 23/10/2013 15:57:32 »
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.
 

Offline Pmb

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Re: Question about Relativistic Thought Experiments
« Reply #11 on: 23/10/2013 18:34:03 »
Quote from: webplodder
It's my understanding that as you approach and cross the event horizon nothing particularly changes to the light you are observing.
Thatís quite correct.

Quote from: webplodder
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.
Thatís 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)

Quote from: webplodder
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 youíve fallen in past the event horizon then thereís no way the people outside the black hole can speak of them. Always occurring from outside the horizon. What youíve 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.

Quote from: webplodder
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.

Quote from: webplodder
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 youíve 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?




Quote from: webplodder
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, Ö
Where did you get that idea? Itís news to me. In fact I canít even imagine what it means.

Quote from: webplodder
Öso 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
 

Offline webplodder

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Re: Question about Relativistic Thought Experiments
« Reply #12 on: 23/10/2013 20:14:17 »




Quote from: webplodder
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, Ö
Quote
Where did you get that idea? Itís news to me. In fact I canít 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

 

Offline Pmb

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Re: Question about Relativistic Thought Experiments
« Reply #13 on: 23/10/2013 20:22:00 »
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
 

Offline webplodder

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Re: Question about Relativistic Thought Experiments
« Reply #14 on: 23/10/2013 20:37:41 »
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.
 

Offline AndroidNeox

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Re: Question about Relativistic Thought Experiments
« Reply #15 on: 23/10/2013 20:38:04 »
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.
 

Offline webplodder

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Re: Question about Relativistic Thought Experiments
« Reply #16 on: 23/10/2013 20:43:08 »
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.
 

Offline AndroidNeox

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Re: Question about Relativistic Thought Experiments
« Reply #17 on: 23/10/2013 20:47:25 »
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).
 

Offline Pmb

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Re: Question about Relativistic Thought Experiments
« Reply #18 on: 23/10/2013 21:00:19 »
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

Quote
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?
« Last Edit: 23/10/2013 21:05:17 by Pmb »
 

Offline dlorde

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Re: Question about Relativistic Thought Experiments
« Reply #19 on: 23/10/2013 21:07:17 »
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... ;)
 

Offline Pmb

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Re: Question about Relativistic Thought Experiments
« Reply #20 on: 23/10/2013 21:16:34 »
Quote from: AndroidNeox
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) -
Quote
Therefore the frequency of the light, as measured by any single observer, does not change as the light moves through the gravitational field!
 

Offline Pmb

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Re: Question about Relativistic Thought Experiments
« Reply #21 on: 23/10/2013 21:19:14 »
Quote from: dlorde
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.
 

Offline AndroidNeox

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Re: Question about Relativistic Thought Experiments
« Reply #22 on: 23/10/2013 22:31:28 »
Quote from: AndroidNeox
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) -
Quote
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.
 

Offline AndroidNeox

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Re: Question about Relativistic Thought Experiments
« Reply #23 on: 23/10/2013 22:33:09 »
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.
 

Offline webplodder

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Re: Question about Relativistic Thought Experiments
« Reply #24 on: 24/10/2013 10:15:18 »
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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Re: Question about Relativistic Thought Experiments
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