Value of g near a black hole (re-visited)

[Spin-Analyser]

Okay I kind of see, but if the in-faller were to get very close to the horizon (say one plank length away) and then move away, would that mean that they observed the previous in-fallers crossing the event horizon twice, once on the way towards it and them reemerging on the return journey?

 

[PAllen]

Okay I kind of see, but if the in-faller were to get very close to the horizon (say one plank length away) and then move away, would that mean that they observed the previous in-fallers crossing the event horizon twice, once on the way towards it and them reemerging on the return journey?

No. Until the moment the event horizon 'passes them' they sell all prior infallers as of before they passed the horizon. In my analogy, if the pink flash is 1 Planck length from the trailing observer:

- no earlier observer is seen to have flashed pink
- the trailing observer can still, in principle, accelerate away from the light, and without ever quite exceeding c, stay ahead of it: see Rindler Horizon.

At precisely the moment the flash reaches the trailing observer, all prior observer's flash pink, and no acceleration at all will catch light that has already passed.

Sufficiently locally, all 'near horizon' phenomena are accurately described by a passing flash of light - because the event horizon is a light like surface.

 

[Passionflower]

As long as an infaller is outside the horizon, they see prior infallers as they were closer to the horizon than they are. Note that distances perceived by this infaller are very different from the r coordinate value - there is "lot's of room".

You are wrong.

A free falling observer (free falling from infinity) will measure his distance to the EH to be exactly equal to r - rs (where rs is the event horizon).

Contrast this with a stationary observer close to EH he will measure his distance from the EH to be more than r - rs

 

[Spin-Analyser]

What if the in-faller stops one plank length away? They will see the event horizon as just in front of them, but also just in front of every other object that hasn't crossed the horizon yet but who are closer to the singularity than they are? This seems very paradoxical!

 

[PAllen]

You are wrong.

A free falling observer (free falling from infinity) will measure his distance to the EH to be exactly equal to r - rs (where rs is the event horizon).

Contrast this with a stationary observer close to EH he will measure his distance from the EH to be more than r - rs

I wasn't actually thinking of infalling from infinity. In these scenarios of changing mind at the last second, I think in terms of observers hovering near the horizon, then shutting off fuel. However, I failed to specify this, and certainly you are right about an infaller from infinity.

[Edit: this observation does clarify that I needn't have said anything about comparative distances, as it is not relevant to the main issues - see next post.]

 

[PAllen]

What if the in-faller stops one plank length away? They will see the event horizon as just in front of them, but also just in front of every other object that hasn't crossed the horizon yet but who are closer to the singularity than they are? This seems very paradoxical!

No, they will see earlier infallers a 'normal' distance away, as of before they passed the horizon. Think of it this way: if they could know where the horizon was just before it hit them, they would see earlier infallers at a distance such that they could deduce they must be already inside; however, if each earlier infaller had a watch, the image they would see on the watch would be of a moment just before each earlier infaller crossed the horizon. Think more about the passing flash of light example. Further, if at this last moment, they accelerated away frantically, they would never see the earlier infaller's watches reach their infall moment.

 

[Spin-Analyser]

So let me clarify.

1). It is perfectly possible to observe objects crossing the event horizon of a black hole.
2). It is not possible to observe them at a time after they reached the event horizon.

Think very carefully about your next answer.

 

[PAllen]

So let me clarify.

1). It is perfectly possible to observe objects crossing the event horizon of a black hole.
2). It is not possible to observe them at a time after they reached the event horizon.

Think very carefully about your next answer.

Both your statements are not quite right.

It is perfectly possible to see objects cross the horizon when you cross the horizon. It will be obvious (at that moment) that they crossed before you. Further, you can deduce for possible infallers ahead of you, that 'if they are still where they appear to be', and you know where the horizon is, they are inside the horizon. However, since you are seeing an 'old' image of them, you cannot tell if they made a last moment decision to escape (and thus are closer to you than they appear) unless you also make such a decision, and later see that they did. Further, as long as you remain outside the horizon, you cannot tell for sure whether they crossed or not.

 

[Spin-Analyser]

It is perfectly possible to see objects cross the horizon when you cross the horizon. It will be obvious (at that moment) that they crossed before you.

I'm talking about an observer who never reaches the horizon themselves. As they approach they will see objects crossing the event horizon, but they will be seeing them as they were before they reached the horizon?

 

[PAllen]

I'm talking about an observer who never reaches the horizon themselves. As they approach they will see objects crossing the event horizon, but they will be seeing them as they were before they reached the horizon?

Let's talk about a supermassive BH, and let's say you are following 10 feet behind your partner, approaching the horizon. Let's say you know exactly where it is all times (by computation and knowledge of the region). Let's say you fall to 3 feet from the horizon and stop. At this moment, it is possible to still see an image of your partner that looks 10 feet from you. Now consider two cases:

1) Your partner crossed the horizon. You will see their image fade to black, and their wristwatch will never quite reach the time they crossed the horizon.

2) Your partner stopped 1 foot from the horizon. Some time after you stop, you will see that your partner started accelerating to hover before you did, getting closer to you in the process, and are now stopped 2 feet away.


The closer to the horizon your partner makes decision (2), the longer before you can distinguish it from (1).

 

[Spin-Analyser]

1) Your partner crossed the horizon. You will see their image fade to black, and their wristwatch will never quite reach the time they crossed the horizon.

So if you are close enough to the horizon you can observe objects crossing it?

2) Your partner stopped 1 foot from the horizon. Some time after you stop, you will see that your partner started accelerating to hover before you did, getting closer to you in the process, and are now stopped 2 feet away.

They both hover just above the horizon. One of them turns off their engines. Does the other one see them disappear passed the horizon?

 

[PAllen]

So if you are close enough to the horizon you can observe objects crossing it?

This is getting repetitive. You are seeing an old image from before they crossed. It is from when they were still (in my prior example) 10 feet from you but right near the horizon. This light takes a while (up to forever) to reach you.

They both hover just above the horizon. One of them turns off their engines. Does the other one see them disappear passed the horizon?

The one that remains hovering sees the other one approach the horizon, effectively going black before reaching it. The image history here is quite different from tandem infallers. The image history (past world lines + light null paths) makes for the difference these cases.

 

[Passionflower]

Basically an observer can detect a signal from another observer who passed the event horizon if he passes the event horizon as well in time. He will observe the signal only after he passed the horizon himself.

An observer who never passes the event horizon cannot receive a signal from an observer passed the event horizon.

 

[Spin-Analyser]

This is getting repetitive. You are seeing an old image from before they crossed. It is from when they were still (in my prior example) 10 feet from you but right near the horizon. This light takes a while (up to forever) to reach you.

I'm just trying to be absolutely clear that you're saying you can see an object turn black, effectively crossing the horizon. But at this point you're still not sure if they reached the horizon or not? If they accelerated at the last moment they would presumably reappear from the others perspective after a time. And if they cross the horizon they would suddenly see all the other objects that had fell in earlier?

The one that remains hovering sees the other one approach the horizon, effectively going black before reaching it. The image history here is quite different from tandem infallers. The image history (past world lines + light null paths) makes for the difference these cases.

The one that remains hovering will see them approaching the horizon as they are falling towards the singularity, meaning the event horizon will always be falling in ahead of them?

 

[PAllen]

I'm just trying to be absolutely clear that you're saying you can see an object turn black, effectively crossing the horizon. But at this point you're still not sure if they reached the horizon or not? If they accelerated at the last moment they would presumably reappear from the others perspective after a time. And if they cross the horizon they would suddenly see all the other objects that had fell in earlier?

I think I will have to let someone else answer your questions after this. Somehow, I think I'm being clear and you get something quite different from what I said out of it. Someone else may express it in a way you get it.

Repeating yet again: You don't see them actually cross the horizon if you remain outside. No exception. The turning black is just a matter of infinite red shift and time dilation relative to you if you are hovering further away.

If they divert from crossing at the last minute, sometime before infinite redshift, you see them turn on their thrusters and (as in my tandem example) get closer to you (you having already hovered). All this is due to light delay. You never see turning fully black and reappearing[edit: you can see someone have arbitrarily close to infinite redshift, then approach you becoming less redshifted, even pass you]. Ultimately, after infinite time, you can infer they crossed if you never detect that they stopped and hovered.

Finally, yes, the moment you cross you see prior infallers as of the moment they crossed.

The one that remains hovering will see them approaching the horizon as they are falling towards the singularity, meaning the event horizon will always be falling in ahead of them?

I don't understand this at all. The one that is hovering simply sees the one that turns off thrusters fall towards the horizon, get redder, ultimately black, just outside the horizon. Nothing about the history from horizon to singularity can be seen by the one remaining outside.

 

[Spin-Analyser]

I think I will have to let someone else answer your questions after this. Somehow, I think I'm being clear and you get something quite different from what I said out of it. Someone else may express it in a way you get it.

Repeating yet again: You don't see them actually cross the horizon if you remain outside. No exception. The turning black is just a matter of infinite red shift and time dilation relative to you if you are hovering further away.

If they divert from crossing at the last minute, sometime before infinite redshift, you see them turn on their thrusters and (as in my tandem example) get closer to you (you having already hovered). All this is due to light delay. You never see turning fully black and reappearing[edit: you can see someone have arbitrarily close to infinite redshift, then approach you becoming less redshifted, even pass you]. Ultimately, after infinite time, you can infer they crossed if you never detect that they stopped and hovered.

Finally, yes, the moment you cross you see prior infallers as of the moment they crossed.

Then you can see objects crossing the horizon (because you're one plank length away and they're in front of you), so light is escaping from inside the horizon?

I don't understand this at all. The one that is hovering simply sees the one that turns off thrusters fall towards the horizon, get redder, ultimately black, just outside the horizon. Nothing about the history from horizon to singularity can be seen by the one remaining outside.

The bit I'm having trouble with is seeing distance between you (hovering a plank length above the horizon) and another object but niether of you have crossed the horizon. You could therefore move alongside the other observer and niether of you would have crossed the event horizon, so you can't have been next to the horizon in the first place?

 

[PAllen]

Then you can see objects crossing the horizon (because you're one plank length away and they're in front of you), so light is escaping from inside the horizon?

The bit I'm having trouble with is seeing distance between you (hovering a plank length above the horizon) and another object but niether of you have crossed the horizon. You could therefore move alongside the other observer and niether of you would have crossed the event horizon, so you can't have been next to the horizon in the first place?

I say "you never see x" . You respond: "Then you can see x". We will never get anywhere this way.

Classically, Planck length is irrelevant. Quantum mechanically, nobody knows. Take your pick depending on approach to a partial theory of quantum gravity: (a) there is nothing resembling a horizon (and surface of smallest visibility is smaller than EH as predicted by GR); (b) there is something that is not a horizon microscopically, but it looks a lot like it macroscopially; (c) there is a horizon, but with some difference in properties from the classical picture; (d) a horizon never forms and matter is always outside what would be the horizon radius.

I don't understand your second paragraph at all.

 

[Spin-Analyser]

Let me be clearer. You're saying you can observe light coming out to your eye from inside the horizon as you hover just above it (because you see distance between you and objects ahead of you), but you're seeing light that hasn't reached the horizon yet?

 

[PAllen]

Let me be clearer. You're saying you can observe light coming out to your eye from inside the horizon as you hover just above it (because you see distance between you and objects ahead of you), but you're seeing light that hasn't reached the horizon yet?

Nope, never said this, said the opposite several times. I said if you are outside, you only see light that was emitted outside as well. It may look like it comes from a distance such that if the object is still that distance from you it would be inside. But the light is old, from outside the horizon.

 

[Spin-Analyser]

It's old light from outside the horizon coming at you from inside the horizon of light that hasn't reached the horizon yet?

 

[PAllen]

It's old light from outside the horizon coming at you from inside the horizon of light that hasn't reached the horizon yet?

I give up. I write English, you twist into word soup.

 

[DrGreg]

It's old light from outside the horizon coming at you from inside the horizon of light that hasn't reached the horizon yet?

No, it's old light from outside the horizon that has never been inside the horizon.

If you and your partner are both falling into the black hole, then from your point of view, you and your partner are stationary and the event horizon is rushing towards you at the speed of light. You see your partner 10 feet in front of you at all times. The image you see has been delayed 10 nanoseconds; you see where your partner was 10 ns ago.

At exactly the moment you reach the event horizon (i.e. at a distance of zero, not a distance of 1 Planck length) you see, 10 feet in front of you, what your partner was doing 10 ns earlier, which was crossing the event horizon. (10 ns ago the event horizon was 10 ft in front of you, as was your partner.)

This illustrated in the left-hand spacetime diagram below.

If you decide at the last minute to brake and hover at a small fixed distance outside the event horizon, you see your partner's image slow down, red-shift and darken and never actually cross the horizon. This illustrated in the right-hand spacetime diagram below.

 

[Passionflower]

If you and your partner are both falling into the black hole, then from your point of view, you and your partner are stationary and the event horizon is rushing towards you at the speed of light. You see your partner 10 feet in front of you at all times.

Sorry but I cannot agree with this.
I think you are forgetting the tidal forces between them.

 

[PAllen]

Sorry but I cannot agree with this.
I think you are forgetting the tidal forces between them.

If you go back to the post I introduced this scenario, I specified a supermassive black hole. Tidal forces can be made as small as desired by making the mass large enough, as you have noted in other discussions.

 

[Spin-Analyser]

No, it's old light from outside the horizon that has never been inside the horizon.

If you and your partner are both falling into the black hole, then from your point of view, you and your partner are stationary and the event horizon is rushing towards you at the speed of light. You see your partner 10 feet in front of you at all times. The image you see has been delayed 10 nanoseconds; you see where your partner was 10 ns ago.

At exactly the moment you reach the event horizon (i.e. at a distance of zero, not a distance of 1 Planck length) you see, 10 feet in front of you, what your partner was doing 10 ns earlier, which was crossing the event horizon. (10 ns ago the event horizon was 10 ft in front of you, as was your partner.)

If you decide at the last minute to brake and hover at a small fixed distance outside the event horizon, you see your partner's image slow down, red-shift and darken and never actually cross the horizon. This illustrated in the right-hand spacetime diagram below.

As you approach you see objects in front of you crossing the horizon, and you're seeing light from the other side of the event horizon. When you move away the light from previous observers moves back across the event horizon. So what if you stop one plank length away from the horizon and the one in front of you never reached the horizon either? The event horizon is no longer in one place. If you moved alongside and hovered next to the one in front of you then you would still be outside the horizon. It doesn't work. The event horizon must be moving inwards at c, not outwards.

 

[PAllen]

As you approach you see objects in front of you crossing the horizon, and you're seeing light from the other side of the event horizon. When you move away the light from previous observers moves back across the event horizon.

Why do you do this? So far now, a dozen or more times, 3 of us have now told you this is false, in all different words, and clear beautiful pictures from Dr. Greg. You respond with the opposite of what everyone says. You never see light emitted from inside the horizon unless you are also at or inside the horizon. Every other part of your statement is false as well, and this has been explained multiple times.

I think this thread is dead.

 

[Spin-Analyser]

If there's distance between them and you are one plank length away from the horizon then 'As you approach you see objects in front of you crossing the horizon, and you're seeing light from the other side of the event horizon. When you move away the light from previous observers moves back across the event horizon'. I thought there was "plenty of room". The only other alternative is that they all pile up at the horizon.