An interesting twist on chess is taking a position and attempting to deduce something about what must have occurred in the game previously. For example, has a promotion occurred or not?
What must have been white's last move?
I don't know whether there exist computer algorithms for solving these sort of problems - a brute force approach would probably be useless.
It's possible to construct quite interesting and non-trivial puzzles of this sort. The logician Raymond Smullyan's delightful book
The Chess Mysteries of Sherlock Holmes starts with some easy examples and builds up to some really mind boggling examples.
What I always found most intruiging about Go is the difficulty of initially grasping its rules, despite their beautiful simplicity. It was a while before I found a decent logically complete explanation of how the game works. I think it may be much harder computationally than chess due to its "topological" character - that is, to play well, one has to have an intuitive grasp of the way curves behave in the plane and so on, which is hard to give a computer but we are hard-wired with.
I was working in an MIT computer lab on my Ph.D thesis at the time, and had about a week to complete it, or 6 years work was down the pan. Imagine my surprise when the entire eastern seaboard blew a fuse. Luckily, Boston seemed to be spared most of the blackout. I remember half hoping it would give me an excuse to not have to finish it.
Dropzone for the C64 was pretty ace. And all those ungulate based Jeff Minter things (e.g. Iridis Alpha) were damn hard but good once you got the hang of it, and had the added bonus of titillation for those of us with a bovine fetish.
This doesn't test General Relativity anyway, in the sense that it doesn't rule out modifications to Einstein's equations, because it is only in the weak field regime. The pulsar spin down experiments have already pretty much made this satellite redundant. Only cosmology and black hole physics can really test GR.
Maybe the string theorists themselves don't know whether or not the information can be retrieved. The "a black hole has no hair" theorem is a result in classical general relativity. In string theory, apparently one can find solutions that look like black holes in some classical limit, but in fact have all the hair that is missing in the classical theory. But is there an analogue of the event horizon in string theory? (I always thought string theory was only done in flat spacetime anyway. How do they do it in Schwarzschild spacetime?) Any string mavens here?
I was a grad student at MIT, doing a PhD in physics. Every real scientist hated those media lab dicks, whose aim in life mainly seems to be hyping up their latest lame buzzword infested cranky inventions, and sucking up lots of cash that could be much better spent on some real stuff. What a wanker, I say.
I think both particles have to be indistinguishable for the composite to behave like a boson. It follows from quantum mechanics (what counts is whether the wavefunction is symmetric or anti-symmetric under particle exchange). Feel free to be bamboozled.
I think this is possibly a big step towards room temperature superconductivity. The point is that in normal (even high Tc) superconductors, the forces between the cooper pairs are rather weak, hence the need to cool to at least 70K or so to get the effect. In this fermionic stuff, the force is a little stronger (at least, this is claimed in the article). Thus it may be possible to design a material which uses the same principle as the fermionic gas but in the form of a solid material at say 300K (just as high Tc superconductors are essentially solid B-E condensates, more or less). BTW, I'm a cosmologist, not a condensed matter person, so I could be talking out of my arse.
By "jump" I assume you mean leap off the roof of the SUV you brought along with you. This would cause you to have a roughly parabolic orbit for a little while *in the frame which is plunging in free-fall with you into the hole*. Locally, you can always set up this free-fall frame. But in terms of the Schwarzschild coordinates, whatever you do, r decreases monotonically once you are inside the horizon. This is what I mean by one-way enforcement. Perhaps a way to convince yourself of this is to imagine a photon orbiting right at the horizon. If it were able to travel radially, even infinitesimally, it would escape. What do you think happens if someone shines a torch, radially outwards, just inside the horizon? Those photons do not travel outwards (not even an infinitesimal distance) - I guess they never leave the surface of the filament in the torch! Intuitively, the lightcones in the r-t plane have tipped inwards.
It's probably a lot cheaper - the article says that this microwave device is not more expensive than a mechanical drill. How much does a 500W laser cost?
Locally physics is always the same as good old flat space, you are just in free fall - but in a very strong gravitational field the tide (i.e. relative acceleration of two slightly displaced particles) is huge. But the black hole "really" manifests itself by disturbing the global *causal structure* of spacetime, by introducing a boundary (the singularity) on which certain geodesics (worldlines) terminate.
I repeat, a particle (massive or massless) inside the event horizon cannot travel radially outwards, even if you have an arbitrarily powerful rocket. If you don't believe me, consult any of a number of general realtivity texts (Introduction to GR by Schutz is very good, and the real thing is Gravitation by Misner, Thorne and Wheeler). The event horizon does mark a point of no return, but there is more to black holes than just the existence of a one membrane - the distortion of spacetime is extreme at all points inside the horizon.
that's completely wrong, you even have the wrong dimensions. (1/2 m v^2 is energy, not force)
From Newtonian mechanics of circular orbits we have:
mrw^2 = GMm/r^2
where m is mass of orbiting body, M is mass of central body, r is distance between them, w is angular velocity of orbiting body. Apply this to Earth/Sun system and star/black hole system, and one has:
r_star/r_sun =c uberoot(M_hole/M_sun)*cuberoot(w_earth/w_star)^2 With
They merge, emitting huge quantities of gravitational radiation in the process, and eventually settle down into a nice Kerr hole.
There is some hope that gravitational wave observatories like LIGO II and LISA will see the signature of these events (although they are expected to be rare - neutron star/neutron star, neutron star/black hole collisions are more frequent. Most people think these are the gamma ray bursts).
People are trying to figure out the expected waveform of the emitted radiation with numerical simulations, which are notoriously difficult.
The dark matter could be composed of mini black holes - but then one would expect them to be visible in the galactic halo since they would accrete matter and have jets etc. (The massive black holes at the galactic center are not nearly massive enough to solve the problem). Most cosmologists think it is probably composed of some exotic weakly interacting particles, e.g. axions.
Actually, that's not true - photons emitted from inside the event horizon *cannot* travel radially outwards. An observer who has passed through the horizon will see some photons coming from outside, and from points at larger radii, but absolutely nothing in the direction of the singularity.
The mass of the Milky Way is anout 10^11 solar masses, which is typical for a spiral (Andromeda is even bigger). This is all luminous mass. Very roughly, there is about 10 times more dark matter in the "halo" around the Milky Way.
But according to you, you will cross the event horizon in a relatively short time. This discrepancy between the times and distances that two different observers ascribe to the same events is fundamental in special and general relativity.
From Newtonian mechanics of circular orbits we have:
mrw^2 = GMm/r^2
where m is mass of orbiting body, M is mass of central body, r is distance between them, w is angular velocity of orbiting body. Apply this to Earth/Sun system and star/black hole system and one has:
According to the website the closest approach is 17 light hours. So perhaps the orbit is very eccentric.
By the way, the size of the event horizon is about 36 light seconds (easy to find if you know that the Schwarzschild radius of the Sun is about 3 km), or about a 13th of the distance from the Earth to the Sun. The star can hardly be described as "skirting the hole's event horizon" as stated in the BBC report.
Slashdot Mirror
An interesting twist on chess is taking a position and attempting to deduce something about what must have occurred in the game previously. For example, has a promotion occurred or not? What must have been white's last move? I don't know whether there exist computer algorithms for solving these sort of problems - a brute force approach would probably be useless. It's possible to construct quite interesting and non-trivial puzzles of this sort. The logician Raymond Smullyan's delightful book The Chess Mysteries of Sherlock Holmes starts with some easy examples and builds up to some really mind boggling examples.
What I always found most intruiging about Go is the difficulty of initially grasping its rules, despite their beautiful simplicity. It was a while before I found a decent logically complete explanation of how the game works. I think it may be much harder computationally than chess due to its "topological" character - that is, to play well, one has to have an intuitive grasp of the way curves behave in the plane and so on, which is hard to give a computer but we are hard-wired with.
I was working in an MIT computer lab on my Ph.D thesis at the time, and had about a week to complete it, or 6 years work was down the pan. Imagine my surprise when the entire eastern seaboard blew a fuse. Luckily, Boston seemed to be spared most of the blackout. I remember half hoping it would give me an excuse to not have to finish it.
Dropzone for the C64 was pretty ace. And all those ungulate based Jeff Minter things (e.g. Iridis Alpha) were damn hard but good once you got the hang of it, and had the added bonus of titillation for those of us with a bovine fetish.
This doesn't test General Relativity anyway, in the sense that it doesn't rule out modifications to Einstein's equations, because it is only in the weak field regime. The pulsar spin down experiments have already pretty much made this satellite redundant. Only cosmology and black hole physics can really test GR.
Screw that, wake me up when they bring out the flying car.
Maybe the string theorists themselves don't know whether or not the information can be retrieved. The "a black hole has no hair" theorem is a result in classical general relativity. In string theory, apparently one can find solutions that look like black holes in some classical limit, but in fact have all the hair that is missing in the classical theory. But is there an analogue of the event horizon in string theory? (I always thought string theory was only done in flat spacetime anyway. How do they do it in Schwarzschild spacetime?) Any string mavens here?
I was a grad student at MIT, doing a PhD in physics.
Every real scientist hated those media lab dicks, whose aim in life mainly seems to be hyping up their latest lame buzzword infested cranky inventions, and sucking up lots of cash that could be much better spent on some real stuff. What a wanker, I say.
I think both particles have to be indistinguishable for the composite to behave like a boson. It follows from quantum mechanics (what counts is whether the wavefunction is symmetric or anti-symmetric under particle exchange). Feel free to be bamboozled.
I think this is possibly a big step towards room temperature superconductivity. The point is that in normal (even high Tc) superconductors, the forces between the cooper pairs are rather weak, hence the need to cool to at least 70K or so to get the effect. In this fermionic stuff, the force is a little stronger (at least, this is claimed in the article). Thus it may be possible to design a material which uses the same principle as the fermionic gas but in the form of a solid material at say 300K (just as high Tc superconductors are essentially solid B-E condensates, more or less).
BTW, I'm a cosmologist, not a condensed matter person, so I could be talking out of my arse.
By "jump" I assume you mean leap off the roof of the SUV you brought along with you. This would cause you to have a roughly parabolic orbit for a
little while *in the frame which is plunging in free-fall with you into the hole*. Locally, you can always set up this free-fall frame. But in
terms of the Schwarzschild coordinates, whatever you do, r decreases monotonically once you are inside the horizon. This is what I mean by one-way enforcement. Perhaps a way to convince yourself of this is to imagine a photon orbiting right at the horizon. If it were able to travel radially, even infinitesimally, it would escape. What do you think happens if someone shines a torch, radially
outwards, just inside the horizon? Those photons do not travel outwards (not even an infinitesimal
distance) - I guess they never leave the surface of the filament in the torch! Intuitively, the lightcones in the r-t plane have tipped inwards.
It's probably a lot cheaper - the article says
that this microwave device is not more expensive
than a mechanical drill. How much does a 500W laser cost?
Locally physics is always the same as good old
flat space, you are just in free fall - but in a very strong gravitational field the tide (i.e. relative acceleration of two slightly displaced particles) is huge. But the black hole "really" manifests itself by disturbing the global *causal structure* of spacetime, by introducing a boundary (the singularity) on which certain geodesics (worldlines) terminate.
I repeat, a particle (massive or massless)
inside the event horizon cannot travel
radially outwards, even if you have an arbitrarily
powerful rocket. If you don't believe me,
consult any of a number of general realtivity
texts (Introduction to GR by Schutz is very good,
and the real thing is Gravitation by Misner, Thorne and Wheeler). The event horizon does
mark a point of no return, but there is more to black holes than just the existence of a one membrane - the distortion of spacetime is extreme
at all points inside the horizon.
that's completely wrong, you even have the wrong dimensions. (1/2 m v^2 is energy, not force)
From Newtonian mechanics of circular orbits we have:
mrw^2 = GMm/r^2
where m is mass of orbiting body, M is mass of central body, r is distance between them, w is angular velocity of orbiting body. Apply this to Earth/Sun system and star/black hole system, and one has:
r_star/r_sun =c uberoot(M_hole/M_sun)*cuberoot(w_earth/w_star)^2
With
M_hole = 3.6 * 10^6 M_sun
w_earth = 15.2 * w_star
this gives
r_star = 940.4 r_sun
= 7520 light minutes
= 125 light hours
According to the website the closest approach
is 17 light hours. So perhaps the orbit is very eccentric.
They merge, emitting huge quantities of
gravitational radiation in the process, and eventually settle down into a nice Kerr hole.
There is some hope that gravitational wave observatories like LIGO II and LISA will see the signature of these events (although they are expected to be rare - neutron star/neutron star, neutron star/black hole collisions are more frequent. Most people think these are the gamma ray bursts).
People are trying to figure out the expected waveform of the emitted radiation with numerical simulations, which are notoriously difficult.
The dark matter could be composed of mini black
holes - but then one would expect them to be
visible in the galactic halo since they would
accrete matter and have jets etc. (The massive
black holes at the galactic center are not
nearly massive enough to solve the problem).
Most cosmologists think it is probably composed
of some exotic weakly interacting particles,
e.g. axions.
Actually, that's not true - photons emitted
from inside the event horizon *cannot* travel
radially outwards. An observer who has passed
through the horizon will see some photons coming
from outside, and from points at larger radii,
but absolutely nothing in the direction of the
singularity.
The mass of the Milky Way is anout 10^11 solar masses, which is typical for a spiral (Andromeda is even bigger). This is all luminous mass.
Very roughly, there is about 10 times more
dark matter in the "halo" around the Milky Way.
But according to you, you will cross the event horizon in a relatively short time.
This discrepancy between the times and distances that two different observers
ascribe to the same events is fundamental in special and general relativity.
I've got a degree in physics from Cambridge
University. Good enough for you?
That's right mate.
I just checked the article on the Nature
website. It seems that the orbit
has a semi-major axis of 5.5 light *days*!
(which is almost what I got by assuming
a circular orbit).
Amazing that tidal forces haven't circularized
the bugger.
Assuming a football field is 100m long
(sorry, I'm British):
size of event horizon (36 light second)
= 100 million football fields
closest approach distance of star to hole
(17 light hours)
= 184 billions football fields
From Newtonian mechanics of circular orbits we have:
mrw^2 = GMm/r^2
where m is mass of orbiting body, M is mass of central body,
r is distance between them, w is angular velocity of orbiting
body. Apply this to Earth/Sun system and star/black hole system
and one has:
r_star/r_sun = cuberoot(M_hole/M_sun) * cuberoot(w_earth/w_star)^2
With
M_hole = 3.6 * 10^6 M_sun
w_earth = 15.2 * w_star
this gives
r_star = 940.4 r_sun
= 7520 light minutes
= 125 light hours
According to the website the closest approach
is 17 light hours. So perhaps the orbit is very
eccentric.
By the way, the size of the event horizon is
about 36 light seconds (easy to find if you know
that the Schwarzschild radius of the Sun is about
3 km), or about a 13th of the distance from the Earth to the Sun.
The star can hardly be described as "skirting the hole's event horizon"
as stated in the BBC report.