Black Holes: #1 Falling In

This is the first in a short series on black holes and we start with the falling in.

Ever wondered what would happen if you had the nasty fate of falling into a black hole or what you would see happen if you were at a safe distance watching your friend fall in? Well read on and find out…

To set up the scene we need two characters (or observers as is the language of theoretical physics). I’ve always fantasised about interstellar travel and this site has two authors so i’ll indulge myself. Joe and Mekhi are orbiting a black hole at a safe distance in their spaceship. By safe distance I mean their spaceship is at a stable radius, far enough away from the center of the black hole such that it does not spiral inwards as a result of the hole’s immense gravitational pull. Mekhi has decided she wants to die in the most spectacular way possible, being engulfed by a black hole and Joe, for science’s sake, is very keen to see what happens to Mekhi as she falls in. So, she puts on her spacesuit on to stop her exploding prematurely, waves goodbye to her best friend and exits the spaceship.

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[Black Holes have a very large gravitational pull and as such can distort even the paths of photons passing by, in a process called ‘lensing’ causing them to be whipped into an orbit around the black hole which leads to this eerie surrounding glow.]

Right, let’s flash back to special relativity for a moment (get it?). Remember one of the consequences of moving extremely fast? Time dilation. (You can read more about it here). This means, an observer, who watches an other observer travel at a high proportion of the speed of light measures the time between their events to be longer than the travelling observer does. For example Mekhi is about run a race at a high proportion of light speed and she has  a stopwatch in her pocket. She starts the stopwatch when she starts running and stops it when she finishes the lap. Joe does the same, he starts the stopwatch when Mekhi starts running and stops it when she finishes the lap, all the while sitting still watching. The time measured on Mekhi’s stop watch will be less than the time measured on Joe’s. Remarkable but true, this is time dilation – a consequence of moving very fast. Now let’s get back to general relativity, which is the big theory in the case of Black Holes. Here’s the relevance –  time dilation is also a consequence of a gravitational fields. Time runs slower in stronger gravitational fields. If you’re close to a large gravitational mass, the field will be subsequently stronger and your clock will run slower than somebody’s who is not. For example if you spent all your life at the top of a skyscraper, your clock would run slightly (almost negligible but slightly) faster than someone on the ground (closer to the Earth’s center of mass i.e. a stronger gravitational field) – general relativity decides your pay off for enjoying such a wonderful view would be having a slightly shorter life.

So as Mekhi approaches the Black Holes she gets closer and closer to the Black Hole an object with a colossal mass and as such a colossal gravitational field. Think of each tick on Mekhi’s clock (that she carries with her) as an event. When Mekhi and Joe were together in the spaceship the time between Mekhi’s ticks would coincide with the time between Joe’s clicks.  But as she gets closer and closer to the black hole the time between Mekhi’s ticks/events, as measured by Joe, get further and further apart – time dilation. Now there is this special radius that every black hole has called the event horizon. It the radius (or distance) from the center of the black hole at which the gravitational pull is so strong that not even light can escape. The event horizon is determined purely by the mass of the black hole and is given by the equation: r = 2GM/c^2  Where r is the radius (distance), G is the gravitational constant, a fundamental universal constant, c is the speed of light and M is the mass of the black hole. So remember the ticks on Mekhi’s clock coincide with events in Mekhi’s experience for example the blinking of her eyelids or the kicking of her feet as she realises what she has done. As she gets closer and closer to the Black Hole the time Joe measures betweens these events gets longer and longer, it as though Joe essentially sees all Mekhi’s movements go in to hyper slow motion. Now how is Joe receiving this information? He is seeing her and how is he seeing her – he is seeing her through the transmission of photons which are carrying light from her towards him. Now here is the link with the event horizon part – when Mekhi crosses this radius during her fall the photons can no longer escape the gravitational pull and make it back to Joe. Joe cannot see the Mekhi who crosses the event horizon. Now, counterintuitively, it’s not that Mekhi disappears suddenly. The time as measured by Joe between her events just before she crossed the horizon became so so very dilated that he essentially sees her frozen image just before she crossed the point of no return. The light waves stretch to lower and redder frequencies and the image of Mekhi slowly dims and fades, over and out.

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[A depiction of the warping of space time around the center of a black hole. The gravitational pull becomes so strong that the center of the black hole results in a singularity where the laws of physics break down.]

Now what about Mekhi’s experience of this whole thing, after all she’s the one doing the travelling. Well Mekhi sails through the event horizon without experiencing anything different at all, she probably couldn’t even tell it was happening. In fact as she crosses she can still look back and see the spaceship and the region outside the black hole horizon as normal and she can probably also just about make out Joe’s horrified face through the spaceship window. Now if the black hole is a small one tidal forces can come into play here and the force on her feet (which are closer to  the center and hence experience a stronger gravitational pull)  may be significantly stronger than the force on her head and thus she would experience spaghettification – one of my favourite words in theoretical physics – where she gets stretched so much that she becomes elongated like a piece of spaghetti until eventually she gets torn in two. If the hole is small and this effect is quite large she will see a lot of warping of the light around her as well as she undergoes this gruesome process. However if the black hole is a larger one these tidal forces will be much weaker and she will go on her merry way sailing down to the center of the black hole without noticing much difference. Moral of the story if you’re going to go off galavanting in a black hole, choose a large one! So on she goes down the center where most likely she will be torn apart before she reaches the singularity. The singularity is the point at the center of the black hole where the spacetime has been warped so immensely, density and the gravity have become infinite and the laws of physics as we know them have disintegrated. If Mekhi remarkably reaches the singularity without being spaghettified her only reward will be being crushed to an infinite density… probably, the truth is we don’t have a clue what actually happens at the singularity because our laws of physics completely break down. There are theories in modern day theoretical physics that believe the gravitational field does increase as your get closer to the black hole’s core but then eventually reduce as if you’re coming out the other end of the black hole, into what could be a new universe, this hypothetical exit region has imaginatively been named a white hole. Though it’s very likely a meek human being would not survive the crushing forces of gravity before this point occurred.

Forthcoming posts in the series will delve into mysteries surrounding black holes such as the information loss problem and the black hole firewall paradox. Black holes have always been a source of many cosmic problems and the answer to the paradoxes surrounding them may help us answer some of the most pressing questions in theoretical physics, such as how to reconcile general relativity with quantum mechanics. For now however we stop here having explained what it looks like when an observer falls in and how this contradicts with what the observer themselves experiences. I’d much rather be the one on the spaceship after all…

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47 responses to “Black Holes: #1 Falling In

  1. As you say, as you approach a black hole you will speed in orbital velocity to the extent of time dilation. If you somehow have enough fuel to increase your momentum to gain a larger orbit and return to normal space, you will arrive sometime in the future you would not have traveled to in normal space. Therefore can a black hole be used as a time machine, and is that trip far enough into the future to make the experience worthwhile? Or would the centrifugal force in the orbital spin be fatal?

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    • Theoretically speaking this idea is possible yes – which is why time dilation was one of three theoretically consistent possibilities in my time travel post. To get rid of the complicated nature that comes with a black hole (where physics can get rather speculative) this same idea can be simulated with a very very heavy planet with a large gravitational pull. If two people sit in a spaceship orbiting the planet and one goes down to the surface (i.e a region where the gravitational field is much stronger) for what is a month as measured on his watch, when he returns back up to the spaceship he will find his companion has aged many more months or even years depending on the strength of the gravitational field! In a sense travelling into the future with respect to another observer… spooky stuff.

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      • The reason this interested me was that some things today might be useful to send with speed into the future if the far future becomes available. People with incurable diseases freeze themselves cryogenically in the hopes that in the future may provide cures. Stores of seeds or DNA are now preserved in the hopes a future culture will find them useful, Scientific hopes and speculations are put aside today for lack of information but if a time capsule could be managed to ship these hopes more rapidly into the far future secure from the devastating loss through time this stab into the darkness of time may have some kind of use for preserving knowledge. Descending into the destructive gravity of a huge planet or a black hole sounds a bit futile but if some procedure were discovered to send things more quickly far into the future it may be useful.

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      • Ah cryogenics, Joe is going to have a post up on this soon – keep an eye out! Indeed I like your idea however unfortunately, as far as I know, the only manner is which something like this is theoretically possible is time dilation so we would either need to find a way to transport people at a significant speed of light or take them close to a very strong gravitational field, which unless we find a way to harness gravity, is only achievable near masses on the scales of planets/black holes. Humanity might have to work harder on preserving knowledge the old fashioned way for now (though I think cyrogenics is a step in the right direction)

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      • The concept of access to the future even on a one way trip does have its fascinations. Way back in 1980 when I was back in New York a guy visited a new Apple users club when computers were just starting and offered to sell members Apple stock at a very low price. Nobody knew what would happen to the new computer market so nobody bought any but I often thought of how I might have become a millionaire if I had spent a couple of hundred dollars on the new stock. Just suppose a good business man made some chancy investments and then took a quick trip near a black hole to return quickly a couple of hundred years later to become astoundingly rich as his investment matured.

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  2. I am OBSESSED with space travel and the universe and could read/talk/watch tv about this ALL DAY. It’s so interesting to think about these theories and concepts, I will be looking forward to reading the next post of this!

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  3. As an artist I tend to think visually and the standard way to think of the effect of gravity visually is to use the rubber sheet model where a mass attraction is indicated, as in your diagram, as a weight resting on the rubber sheet and causing a depression in the sheet so that anything moving on that surface moves in curves restricted to the surface of the sheet. No doubt this conveys the proper feeling of what happens by reducing our three dimensional space to two dimensions which can be graphically represented. But what bugs me is that space as we know it is three dimensional and my mind refuses to think four dimensionally. That dent caused by gravity has a direction vertical to the surface of that sheet and I am curious, thinking four dimensionally, what is that vertical direction in actuality? Is it time or is it another direction altogether? Does a black hole point in a time direction and is the depth of the dent towards the future or the past or is it another dimension altogether?

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    • Yes I have always found that visualisation extremely helpful when thinking about spacetime and gravity and have reached the same troubles you have. Don’t beat yourself up about your mind refusing to think four dimensionally, the human mind resides in the three-dimensional world and to that world it is trapped. These thoughts however are excellent and I agree in thinking that time is the key here. In the mathematics of black holes the four coordinates are the three of space and the fourth of time, now the maths gets very weird once we go past the event horizon, in fact in some coordinate set-ups the spatial coordinates and the time coordinates actually swap roles. The mathematics tells us that the singularity at the centre of the black hole is actually not a place but a time, all particles will end up reaching it because they are moving ever forward to this point ‘the singularity’ in the future – so perhaps the depth of the dent can represent the direction towards the future! I confess I need to do some more reading about this – thank you for getting me thinking!

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  4. When I was a teenager back in 1940 I read a book by Sir James Jeans called “The Mysterious Universe¤” about much of Einstein’s theories and I was much frustrated by my high school science courses at Stuyvesant in Manhattan which mentioned none of the fascinating ideas. My best references were through some of the science fiction stories in Astounding SF by guys like Heinlein and Asimov. I began to assemble some sort of model from the birth of the universe towards the future as a kind of four dimensional onion where each skin layer was an instant in time and as one moved in normal time one more or less moved on one layer but as one sped up towards the speed of light a kind of centrifugal force threw one towards the future. Mass had a kind of fourth dimensional inertia so it slowed time. On that basis black holes were deep pockets into the past that moved very slowly into the future. The arrow of time is a kind of fourth dimensional wind that blows things into the future. Whether any of this has any relation to reality I cannot say. On the 4D block viewpoint our movement into the future is an illusion so my construction probably is way off course.

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    • On the 4D block viewpoint events can still be categorised as past & future given the reference point of the observer so the construction is not necessarily way off at all – in fact the block viewpoint of time may not even be correct as it is only the view of the universe as given by Special Relativity! Quantum Mechanics and even General Relativity in part, refute this idea and attempt to salvage a universal flow of time (I’ve been meaning to do a follow up post on this for a long time forgive me it will come!) Your model is very interesting – I would love to see a diagram of this four-dimensional onion idea to help me visualise is (though depicting a four-dimensional idea in two-dimensions isn’t an easy task I know!) Could you explain to me a little more the principles behind your idea?

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  5. and maybe……some big enough mass……someday would fall in the gravitational web of the black hole……and while the black hole devours the delicious matter……so of mekhi particles will be emitted…….and maybe form a mekhi planet in thousands of years…….
    if someone desires to be a planet someday……this could be tried…..
    and pardon my ignorance and courage……i obviously do not know what i am talkking about…….
    great post……..you have made the complex concepts very interesting!!! 🙂 🙂

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  6. Pingback: 3rd question: Does there exist a Divine Creator – Questiontime – Vragenuurtje·

  7. Pingback: Black Holes: #2 Glowing and Shrinking | Rationalising The Universe·

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