tolove said:
Anyone read a good books lately that were related to physics/mathematics? I'm thinking history books, or things of that sort.
I've recently finished reading "Black Hole Wars," by Leonard Susskind. I liked it quite a lot. It was a very nice mixture of history, anecdote, and information.
Yes, "
Black Hole Wars," by Susskind was good.
It inspired me to calculate the displacement of an object as a function of time that one, I'll call him "Bob," would measure if Bob was right up next to the event horizon of a large [supermassive, for example] black hole (imagine Bob was suspended from above by a long cable), and and Bob dropped an object (call it "Alice"), allowing the object (Alice) to free-fall into the black hole.
The displacement of the object I came up with is:
x' = d \left[ 1 - \mathrm{sech} \left( \frac{c}{d} \tau \right) \right]
where
x': displacement of object [Alice] away from stationary observer [Bob] as measured by the observer [Bob].
c: speed of light.
d: distance of stationary observer [Bob] to the event horizon. (Not the distance to the center of black hole! it is assumed that d \ll r).
\tau: time, as measured by the stationary observer [Bob].
\mathrm{sech}(): hyperbolic secant function.
According to the equation, the object [Alice] will approach the event horizon, but never actually cross it (as measured from the observer's [Bob's] frame of reference).
And note that the stationary observer feels an acceleration (from the cable suspending him) of g = c^2/d. With that, it can be shown through series expansion that the displacement reduces to x' = \frac{1}{2}g \tau^2 for small \tau, agreeing with Newtonian mechanics (at small times, before things get relativistic)!
(This also ignores the mass of Alice and any spacetime curvature caused by Alice's mass; it is assumes Alice has negligible mass. Also, quantum effects are ignored.)
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Anyway, back to the topic. I recommend
"
Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics," by John Derbyshire.
and
"
The Drunkard's Walk: How Randomness Rules Our Lives," by Leonard Mlodinow.
