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Author Topic: Question about Relativistic Thought Experiments  (Read 12316 times)

Offline dlorde

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Re: Question about Relativistic Thought Experiments
« Reply #25 on: 24/10/2013 10:45:22 »
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.
Quote from: Brian Cox
... 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.
 

Offline dlorde

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Re: Question about Relativistic Thought Experiments
« Reply #26 on: 24/10/2013 11:13:14 »
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.
« Last Edit: 24/10/2013 11:14:45 by dlorde »
 

Offline dlorde

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Re: Question about Relativistic Thought Experiments
« Reply #27 on: 24/10/2013 11:30:52 »
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?
 

Offline webplodder

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Re: Question about Relativistic Thought Experiments
« Reply #28 on: 24/10/2013 11:36:11 »
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.
« Last Edit: 24/10/2013 13:09:13 by webplodder »
 

Offline Pmb

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Re: Question about Relativistic Thought Experiments
« Reply #29 on: 24/10/2013 14:46:36 »
Quote from: AndroidNeox
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.

Quote from: AndroidNeox
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
« Last Edit: 24/10/2013 14:56:24 by Pmb »
 

Offline Pmb

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Re: Question about Relativistic Thought Experiments
« Reply #30 on: 24/10/2013 14:59:53 »
Quote from: Brian Cox
... 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. :)

 

Offline dlorde

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Re: Question about Relativistic Thought Experiments
« Reply #31 on: 24/10/2013 16:34:26 »
The River Model of Black Holes by Hamilton & Lisle, Am J. Phys., 76 (6), June 2008).
I found the paper. 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.
 

Offline Pmb

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Re: Question about Relativistic Thought Experiments
« Reply #32 on: 24/10/2013 16:44:08 »
Quote from: dlorde
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.
 

Offline dlorde

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Re: Question about Relativistic Thought Experiments
« Reply #33 on: 24/10/2013 20:01:15 »
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.
 

Offline Pmb

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Re: Question about Relativistic Thought Experiments
« Reply #34 on: 24/10/2013 20:11:56 »
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.
 

Offline dlorde

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Re: Question about Relativistic Thought Experiments
« Reply #35 on: 24/10/2013 20:21:07 »
... 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.
 

Offline AndroidNeox

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Re: Question about Relativistic Thought Experiments
« Reply #36 on: 24/10/2013 21:40:23 »
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.
 

Offline AndroidNeox

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Re: Question about Relativistic Thought Experiments
« Reply #37 on: 24/10/2013 21:47:17 »
Quote from: AndroidNeox
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.

Quote from: AndroidNeox
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.
« Last Edit: 26/10/2013 08:50:37 by CliffordK »
 

Offline AndroidNeox

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Re: Question about Relativistic Thought Experiments
« Reply #38 on: 24/10/2013 21:49:10 »
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.
 

Offline dlorde

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Re: Question about Relativistic Thought Experiments
« Reply #39 on: 24/10/2013 22:30:10 »
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...
 

Offline Pmb

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Re: Question about Relativistic Thought Experiments
« Reply #40 on: 24/10/2013 22:30:18 »
Quote from: dlorde
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?
 

Offline dlorde

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Re: Question about Relativistic Thought Experiments
« Reply #41 on: 24/10/2013 22:35:16 »
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.
« Last Edit: 24/10/2013 22:37:55 by dlorde »
 

Offline dlorde

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Re: Question about Relativistic Thought Experiments
« Reply #42 on: 24/10/2013 22:36:35 »
... 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.
 

Offline Pmb

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Re: Question about Relativistic Thought Experiments
« Reply #43 on: 25/10/2013 01:02:42 »
Quote from: dlorde
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
Quote
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
Quote
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.
« Last Edit: 25/10/2013 06:31:06 by Pmb »
 

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Re: Question about Relativistic Thought Experiments
« Reply #44 on: 27/10/2013 10:19:32 »
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. :)
« Last Edit: 27/10/2013 16:21:43 by beany »
 

Offline AndroidNeox

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Re: Question about Relativistic Thought Experiments
« Reply #45 on: 28/10/2013 17:52:56 »
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).
 

Offline AndroidNeox

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Re: Question about Relativistic Thought Experiments
« Reply #46 on: 28/10/2013 17:56:18 »
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.
 

Offline dlorde

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Re: Question about Relativistic Thought Experiments
« Reply #47 on: 28/10/2013 20:14:29 »
... 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?
 

Offline AndroidNeox

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Re: Question about Relativistic Thought Experiments
« Reply #48 on: 28/10/2013 21:59:34 »
... 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.
 

Offline dlorde

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Re: Question about Relativistic Thought Experiments
« Reply #49 on: 28/10/2013 22:47:12 »
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' and '.. if I fell into a black hole':
Quote from: berkeley.edu
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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Re: Question about Relativistic Thought Experiments
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