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    Riding A Long Train Down A Black Hole
    By Sascha Vongehr | May 15th 2012 04:41 AM | 9 comments | Print | E-mail | Track Comments
    About Sascha

    Dr. Sascha Vongehr [风洒沙] studied phil/math/chem/phys in Germany, obtained a BSc in theoretical physics (electro-mag) & MSc (stringtheory)...

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    Riding into a black hole is a fun mental exercise.  General relativity predicts* that an observer who falls freely into a large black hole will have no means with which she can establish whether she is at the event horizon, which is the radius below which there is no escape possible.  I explained this more detailed in Black Hole Duality: Not noticing crashing with light speed.  Nevertheless, many popular descriptions leave the feeling as if the event horizon is also locally, to the one who falls freely through it and his close surroundings that fall with her, a recognizable place.  This can be misleading in interesting ways and a thought experiment involving a train will clarify that such popular science descriptions must always be taken with great care.

    Imagine you and your friends sitting on a very long train.  Every wagon has one friend leaning out of his window.  There are perhaps a few hundred such wagons before you and a hundred still hanging behind the wagon in which you happen to travel.  The train is passing a station sign.  You and your friends previously agreed to raise your arms when you are exactly next to the sign.  And so, while riding the train, you watch the sign approach from very far away and whenever a friend passes it, you see him or her lifting their arms, one after the other until it is your turn.

    Now say the station sign was removed but you all calculated the time at which each would pass that sign, or say you all know for some other reason where the proper location of the sign is anyway (hole in the ground perhaps).  Now you cannot see the sign (and also not its hole in the ground from further away), but you still see how there is wagon after wagon having a friend raise his or her arms, until it is the one in front of you, and then you raise your arms, and then when you turn around, you see the one in the wagon behind you raise her arms, and so on.

    Now ride this train into a very large black hole.  Each friend has to raise his or her arms when they cross the event horizon.  What will you see?

    It may seem plausible that the situation is similar:  One friend after the other is seen to raise their hands.  But what you will see is quite disturbing if you are unprepared for it:

    All your friends in front of you raise their arms all “at the same time” together with you while those behind you do not yet raise their arms (making you appear to be special, although all friends are in pretty much the same situation)!

    Why is that?  Well, the light that is emitted backwards at the event horizon will stay right there at the event horizon.  In some sense, space “is rushing into the black hole” at the speed of light at the event horizon, thus, since the outwards emitted light is traveling inside that "in-rushing" space with the velocity of light, the two movements compensate each other and the light just stays at the same radius coordinate.  Whatever light is emitted backwards at the event horizon will be received exactly at the event horizon – it must be so because the light never goes anywhere else.

    Therefore, the light that any of your friends emitted/reflected while raising their arms when passing the event horizon will stay at the event horizon until your eyes pick it up when you are at the event horizon.  This holds for all the friends that fall in before you, so just when you raise your arms, you see them all raising their arms, every one in front of you as if in unison.  It looks like as if the event horizon is everywhere along the train in front of you, but not behind you, or as if the event horizon is rather a moment in time than a location (and these statements are true in some sense, but it is difficult to describe such properly without sounding nuts, so I won’t attempt it).

    I recommend thinking about it in order to weaken rigid concepts about time.  Also,it helps to see that a lot of popular descriptions of black holes are wrong.  If you and your friends fall into a large black hole, you will see the whole train in front of you and all its lights and perhaps hear the whistle.  Black holes are only black if nothing else fell inside for a while.

    One interesting issue is the following:  According to what I wrote, even just a few meters in front of the event horizon, you would still see the wagons in front of you as if nothing happened to them, although they are many meters in front of you and thus behind the event horizon.  They do not even look distorted or let alone shrunk to fit in between you and the horizon.  That is not yet a problem (just think about where the light you see was emitted), but it becomes a problem with extremely long trains.  My description cannot hold for arbitrarily long trains.

    What will you see if the train’s length is comparable to the black hole's radius?  This question touches on the fact that the singularity** is not so much inside of a black hole as it is the only possible future that can be had in the black hole.  However long the train, you will never see any wagons in front of you being destroyed.  Already at the event horizon, you saw your friends all only having come as far as the event horizon.  This “delay” or "distortion" becomes worse inside the black hole.  From your point of view, you will always be the first one of all your friends to hit the singularity!  Quantum solipsism is preempted by relativity theory!

    ***

    -------------------------------------

    * If the unification of quantum theory with gravity will only modify general relativity close to the curvature singularity** of the black hole, not already at its event horizon***.  Though this is not necessarily so and the issue is still an open question today, one aspect is certain:  Especially if the event horizon is fully described by relativity, it should for that very reason not be presented as something tangible.

    ** A singularity is something inside a model that tells us that the model does not properly describe the physics.  General relativity has singularities because it does not include quantum mechanics.  So, "singularity" in the above article is basically the middle of the black hole; I do not claim there are true singularities.

    *** We assume that general relativity does not break down as a description already close to the event horizons.  This may be wrong and in any case we need to consider very large black holes.  The maximum free fall time between event horizon and singularity in a massive hole like Sagittarius A* would only be 20.05 seconds!

    Comments

    If the light is not moving out of the black hole at the horizon, there should not be any perspective either. The hands you see raised in front of you as you cross are all at the same place as you. The image must appear compressed, no?

    vongehr
    According to general relativity, to a free falling observer, there is locally (locally = in a small space-time hyper-volume whose smallness depends on the size of the black hole and the resolution of the observers instruments) no difference between being far out in space or, say, at the event horizon. It is like Einstein's elevator thought experiment where you observe your feet while your elevator falls into a black hole. No distortion is visible - everything looks normal - this is the core of relativity.
    That is exactly the reason your "long train" goes astray: you invoke locallity arguments in a situation where signals reach you from afar. Do the math (a string of observers freely falling in a black hole metric) and you see that your long train presentation is inconsistent.

    vongehr
    It depends on the size of the black hole. The black hole in our galaxy is not very large - there are much more massive ones that allow half an hour before singularity. A usual train would thus hold as a local system in its whole length, since it is much smaller than the SS radius, so no distortions visible at the horizon.
    blue-green
    “A black hole has no hair” …. this Wheelerism was conceived before Hawking came up with some hairy radiation. So the phrase died ... It rose from its ashes when it was seen again that a black hole is like a fundamental particle with just a Mass, Charge, and Spin (and a few more exotic qualities) to pin it like a butterfly in a botanist's viewing case.

    Help me land on my feet ... What exactly is it with the DUALITIES from the macrocosm to the microcosm that map the physics of black holes onto the physics of fundamental particles whose properties have no spacial or temporal dependence? For a black hole, M, S and Q can change with time, however, the information content is devoid of particulars, whether it is built from toasters or trains; that's why it as hairless as the physics of elementary particles. Surely we are not going back to "as above so below" .... again. Show me the progress.

    vongehr
    It rose from its ashes
    How so? Black holes have lots of fine hair, just like a confused little kitty cat. I have no idea what you are talking about. Maybe you are confusing extremal black holes of string theory, those that (almost) have no event horizon anyway, and their similarity to fundamental particles of the standard model? And why no "as above so below"? You are not still hung up on the particle physicists' advertising that sold small distances as fundamental or are you? We have already reached the fundamental scale, it is h-bar, the action quantum. "Above" and "below" are relative and due to human obsession with hierarchies.
    blue-green
    I agree with h-bar action being an indivisible that cannot be physically split. As for the rest, well, I'd like to spell it out in more detail…. and yet …. summer rush is getting in the way. I'm sure readers would appreciate it if we both were less cryptic. I doubt that you or Hans can agree on what Wheeler meant by his no hair theorem. I'm not up to speed on what it means in its current incarnation. The apparition of a megalomaniac with a hairless cat in his lap gets in the way.
    vongehr
    In some dual description, the hair is the strings that are attached to the event horizon, much as I explained in my article on black hole duality and the one about gravity without singularities. Wheeler was talking about the black hole in as far as he understood QM, namely as only modifying the singularity without there being anything at all at the event horizon. That is a dual picture more useful as a description for the free falling observer.
    Very interesting article. Thank you Sascha :)