*Dr Toby Fagan asked the Naked Scientists:*

I've only recently discovered your programme on BBC's iPlayer, but I'm now an avid listener even if I am in County Durham at the moment!

I have a question about time dilation and black holes. I've got my head round most of the weirdness that happens with general and special relativity, with one exception. I'm sure I've heard this at least twice now, once I think from the nouveau majeste that is Dr Brian Cox, and on a downloaded lecture covering relativity and particle physics.

The bit I don't get is that they both seem to be saying that, to an outside observer, nothing can ever actually fall into a black hole since time slows so massively that time stops at the event horizon.

I get that a fixed light speed means time is variable, slowing as you approach the speed of light, and that something similar happens to distance (the lecture on relativity from Audible used an illustration along the lines of the twin paradox, one twin gets on board a space ship bound for a star 10 light years away, and their ship is capable of 0.8c as max velocity; for the twin who stays on earth, the ship is gone on a round trip lasting (10/0.8)x2 = 12.5 x 2 = 25 yrs; for the twin on the spaceship however he gives an experienced time of 7 yrs each way (no, I'm not working through the entire Lorentz transformation!), which then implies that to the twin on the spaceship they only travelled 5.6 light years each way); I get that gravity has a similar effect, such that time runs slower in a gravity well; I gather this has even been proven using atomic clocks that have been up in orbit around the Earth for a while.

Now, what I don't get, is what is supposed to happen when you approach a black hole.

What my understanding about it says, is that if you take the twins again, (one of whom possibly has a terminal illness or is feeling acutely suicidal, as they choose to fly a spaceship straight into a black hole, or maybe they just want to get into the record books, from the point of view of the twin who is outside the black hole, watching the dive, they will see the ship approaching the black hole at, presumably, some crushing rate of acceleration from the local gravity, and that the twin outside will see their twin's ship disappear as it crosses the event horizon; this will take place in an appropriately small amount of time which is dependent solely on the ship's starting distance from the black hole, and the initial speed of the ship and it's acceleration due to gravity as it approaches the black hole, in a more or less mechanistic manner.

For the twin who is actually falling *into* the black hole, all the relativistic stuff comes into play, and they experience a massive time dilation effect, so that for 1 second of their time, several minutes/hours/days/months/years could potentially pass for the outside observer; however this seems to then lead to the conclusion that, if time were to actually stop at the event horizon, the twin who is diving into the black hole never enters the black hole, since time has stopped, and to the external universe their ship will always be sitting just on boundary of the event horizon.

To my mind, this is patently nuts.

Surely regardless of the time dilation experienced by the one flying into the black hole, from the external view, they will approach the black hole at an accelerating rate until they disappear inside it; if this wasn't true, then how can Hawking quantum black holes radiate energy (if no time passes at the event horizon, how can anything be emitted?), and how can things like quasars exist since they are thought to be supermassive black holes giving off radiation as matter is sucked in; if time freezes and nothing ever enters the event horizon, how can quasars be sending out blasts of radio waves and other EM radiation? I would have thought the conclusion would end up being that the twin's final approach to the black hole is happening so fast that even though time slows nearly to zero, the actual amount of time that is needed to enter the black hole also becomes so tiny, that to the external observer, they disappear on cue...

I don't know if I've explained myself very well here, but I'm hoping you understand my question! I realise it may not be all that topical, but then again you did recently talk about making wormholes from exotic matter

Yours,

Toby

*What do you think?*