## The Say of the Week July 17, 2007

Posted by dorigo in games, humor, science.

Alla partenza: sensazione simile a quella che si proverebbe cadendo in un buco nero

(At the start: sensation similar to what one would feel falling in a black hole)

[Paola de Carolis, Il Corriere della Sera, July 17th, 2007, in a diagram describing the 18′ swim of Lewis Gordon Pugh, who dove in -1.5 degree artic waters].

The writer would deserve to be addressed as Walter Matthau did once: “You are so imbecile that at a World Championship of imbeciles you would get second place. Why second ? Because you are such an imbecile…”

1. nc - July 17, 2007

I heard about Stephen Hawking claiming that a person diving into a black hole would be stretched into a long fibre, like a piece of spaghetti under tension. That sounds a very painful, but surely someone falling in a black hole wouldn’t feel anything because it would be faster than the human nervous reaction time?

The event horizon radius of the black hole (which you will fall into) is R = 2GM/c^2. Then the acceleration due to gravity at that distance is (assuming that the Newtonian approximation is OK as a first estimate):

a = MG/R^2
= MG/[2GM/c^2]^2
= (c^4)/(4GM).

Hence, for a black hole with 1 kg mass the acceleration due to gravity at the event horizon may be on the order

a = 3*10^43 ms^{-2}.

For other black hole masses, the acceleration is inversely proportional to the mass. But the figure is immense for all conceivable black hole sizes.

A person would therefore feel no pain at all since he or she would be accelerated rapidly and would not have time for the pain signals to move along the nerves to the brain. I think that this result holds good, regardless of the starting distance from the black hole. If you start a long distance away in comparison to the event horizon radius, the effect of different accelerations acting between between your head and feet – due to their different distances from the black hole – may well be trivial. It depends on the details of the mass of the black hole. But generally, a person falling at a large distances will just be in freefall. It’s only when you are close enough that the acceleration is immense, stretching begins between the part of you closest to the black hole centre and the part furthest away.

2. dorigo - July 17, 2007

Hey Nigel,

thanks for computing this for the rest of us. I feel relieved to know it would be painless!

As the old lady sitting in the front row at the conference on star evolution: “Excuse me, did you say the sun will blow up and burn and engulf the Earth in what, five million years ?” “Oh, no, lady, five billion years!” “Ah, whew! What a relief!”

Cheers,
T.

3. tulpoeid - July 17, 2007

If you like science fiction (and even if you don’t) I strongly strongly recommend Poul Anderson’s short story “Kyrie”. It is one of the most badly written (sic) and most ingenious stories around, and it deals with a paradoxical fact about falling in a black hole (I try to avoid spoilers). And yes, it is related to nc’s comment. Read it!

4. dorigo - July 18, 2007

Thank you tulpoeid, I do like science fiction, and I will try to read the story you mention.
Cheers,
T.

5. Fred - July 19, 2007

Hi Tommaso,

Here is a link to an MP3 audio recording from a sci-fi website radio show you may download of the story. It has a nice intro text and audio wise.

http://www.hour25online.com/Hour25_Previous_Shows_2001-2.html#kyrie_2001-02-16

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