If black holes destroyed information, [Hawking/black-body] radiation, containing no information, would be the end of the story.
Um, no.
Maximal entropy = maximum number of corresponding microstates. The universe is in just one of those microstates, not any of the others, so in selecting that microstate the Hawking radiation does actually represent an real flow of information.
Classically, every system can always be viewed as being in one microstate. Then there is no such thing as entropy. Obviously, that would be a confused and useless view.
For a given amount of energy radiated, a black body spectrum represents the great possible entropy. I'm not sure whether you have confused yourself, or one of us has confused the other and we actually are in agreement. (I'm reasonably certain I have not confused myself!)
If this is enough to guarantee that the Second Law of thermodynamics is obeyed, as the previous poster suggested, ie that
Entropy rate of the Hawking radiation + change in entropy of the black hole > all the entropy of particles falling into the black hole
then there's no really fundamental reason why the whole thing shouldn't be compatible with a more fine-detailed, deterministic quantum description for the whole process.
Except for that unitarity problem (and the superfluous word "rate" and the fact that it's greater than or equal, because the incoming energy may also be black-body), this is correct. And assigning to the black hole an entropy equal to 1/4 its surface area (times enough c's, G's, k's and h-bar's to make the units work out) makes the formula correct.
Black holes are generally detected by the X-rays emitted by the matter falling into the black hole not by Hawking radiation. I think Hawking radiation would be at a much lower intensity.
Much, much, much lower!
The Hawking radiation is completely specified by its temperature, which is inversely proportional to the mass of the black hole. If the black hole's mass is more than around 1% of the Earth's mass (or 20 billionths of the sun's), its temperature is colder than the cosmic background radiation. It's actually gaining mass from the background faster than it loses mass by radiating. The universe has to get quite a bit colder before solar- and galactic-mass black holes start evaporating!
Look at it this way: if all the matter in the universe were condensed into a black hole which in doing so destroyed all the information about that matter, the universe would be less entropic than before the black hole consumed everything.
That is exactly wrong. Black holes radiate (no pun intended) a black-body spectrum, which is a spectrum of maximal entropy. This had been proven several different ways by the mid-seventies. If black holes destroyed information, which radiation, containing no information, would be the end of the story. (Pun intended, this time.) However,...
In QM, physical processes are represented by "unitary operators", which cannot destroy information. If you're familiar with Liousville's theorem in classical mechanics, it's a bit like that.
Not really. He was a famous name, so they got him to write a letter to the president. That was the extent of his essential involvement.
The bombs could have been designed without understanding that well-known unit-conversion formula* between matter and energy, since the fission process and its products were understood.
[*] That's all "E equals m c squared" is, a conversion between different units.
It turns out it is cheaper (and faster) to put it on magnetic storage and fly it from London to Los Angeles than it is to try and move it over the Internet.
When you have your own wavelengths across the Atlantic, as from, say, Geneva CH to Chicago US, and can light them up at 10Gb/s, you're going to be far faster than a Concorde with that Terabyte!
Fermilab is moving dozens of terabytes a day into and out of mass storage. It's the perfect place to handle this camera's output.
At the risk of slashdotting my new host, here's my geeky take on How to Lose Less at Video Poker...
I read it. You advocate keeping a kicker with a pair to increase the expected payback. You made one important mistake, due to your unfounded "don't look beyond the next card" dogma.
If you keep just the pair, and the first of the three new cards doesn't match it, now you can consider it your kicker and get all the same chances of two-pair while enjoying a 50% greater chance of three of a kind.
sorry but roulette with just picking the color gives your 50% odds of winning. That's pretty damn good and pretty much the best you can expect of any form of gambling. (payout is lower though)
Bzzzt! Thank you for playing.
Or at least, that's what the casino will say to you if you believe this. There's the little matter of the one (Europe) or two (USA) green spaces on the wheel!
Poker, Blackjack or other such games are the only sort of gambling I would be remotely willing to participate in...
I don't regard poker as gambling. To date, it's a nearly certain small income. If I ever play with players better than I am, I'll have to regard it as tuition money.
It's interesting, but on firefox on a gigaherz machine, it crawls. Alpha blending is pretty, but damn slow -- web designers really need to avoid it for anything that moves and has to be re-composed frequently.
Which gigahertz machine? In Firefox - or Safari - on my 1.00 GHz powerbook, there is no perceptible slowing.
"Gentelmen, I give you the year's supply of water we used to have!"
A fluid-optic system was the Maguffin of an Asimov story, which was itself a sequel to another story.
I can only come up with the Russian title at the moment.. "?????????" I think it was. "Anniversary"? Yeah, that must be it.
(Ugh, that cyrillic doesn't preview well at all. Transliterating: "Godovshchina."
How much does the weather affect the signal quality of satellite TV reception?
Aside from local broadcast channels, how do you think the Cable outfit gets the signals they send down your wire?
From satellites!
I drive past the local cable baron's antenna farm every workday. They use bigger dishes, so they can withstand a bit more rain fade, but I do see weather-related signal loss on their system. Often it looks just like the problems in the FUD ads they show against satellite TV.
Of course it does. You get an ionosphere from having your atmosphere hit by solar radiation. Mars, at 1.5 AU from the sun, gets almost half as much radiation (to a given area) as the earth does.
More information.
I'll take the risk of looking stupid and ask the musical question: Why should the expiration of a certificate cause an increase in traffic to a CRL server? Once a certificate has expired its revocation status is irrelevant. Revocation lists exist solely to cancel a key before its certificate expires.
Or is it merely that some software automatically calls the mothership for new information on expiration, and the hostname of the mothership happens to start with "crl"?
(Antidisclaimer: I operate five private CAs and delude myself that I basically understand this stuff.)
Maybe people wouldn't steal movies so much if cell phones, morons, etc didn't keep making noise in the theater
I think the theater where I saw RotK a week ago was a radio dead zone (Faraday caged or some such thing). When I came out to the lobby, my (silenced!) pager vibrated with a message time-stamped two hours old.
Do they mean there will come a day when one can download a 700MB Linux iso in less than 5 minutes? If my math is correct that's a 2333.3 kbps download speed!
Where I sit, I can order 3Mb/s down, 256kb/s up right now for US$50 a month. But I'm thinking of splurging on the 10Mb/s up/down offering from the same provider.
If you're entering a country, they have just about any rights they feel like having.
Fair enough. But the context here is the United States, which has a Constitution which explicitly states [...] The authority of TSA screeners is limited to making sure that I'm not carrying a hazardous item.
Yes. That applies to domestic travel. Entering the country (by any mode of travel), there's a no-man's-land before you clear customs where you do not have the full rights of a legal resident or visitor.
Traveling within the US, a warrantless demand for inspection of your files or your dead-tree matter would set off constitutional alarm bells no judge would be deaf to.
Since the TSA came in, I've been overall pleased with the situation - most of the people I've encountered have been pleasant,...
Last year at the x-ray station my son, aged 6 at the time, asked me what sorts of things you weren't supposed to have. I said I'd tell him later and that elicited a smile from the baggage-inspector droid.
You allowed someone to look at secure FILES on your system? What on earth made you think they had the right, or the authority for that matter, to look at FILES? They can physically inspect your system, but they do not have any right to search your laptops electronic contents.
If you're entering a country, they have just about any rights they feel like having. The UK used to demand that you boot your incoming laptop from their magic floppy disk which was somehow supposed to detect pornography. It doesn't seem to happen any more. Can't imagine why, nope, nuh-uh.
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For a given amount of energy radiated, a black body spectrum represents the great possible entropy. I'm not sure whether you have confused yourself, or one of us has confused the other and we actually are in agreement. (I'm reasonably certain I have not confused myself!)
Except for that unitarity problem (and the superfluous word "rate" and the fact that it's greater than or equal, because the incoming energy may also be black-body), this is correct. And assigning to the black hole an entropy equal to 1/4 its surface area (times enough c's, G's, k's and h-bar's to make the units work out) makes the formula correct.
Much, much, much lower!
The Hawking radiation is completely specified by its temperature, which is inversely proportional to the mass of the black hole. If the black hole's mass is more than around 1% of the Earth's mass (or 20 billionths of the sun's), its temperature is colder than the cosmic background radiation. It's actually gaining mass from the background faster than it loses mass by radiating. The universe has to get quite a bit colder before solar- and galactic-mass black holes start evaporating!
That is exactly wrong. Black holes radiate (no pun intended) a black-body spectrum, which is a spectrum of maximal entropy. This had been proven several different ways by the mid-seventies. If black holes destroyed information, which radiation, containing no information, would be the end of the story. (Pun intended, this time.) However, ...
In QM, physical processes are represented by "unitary operators", which cannot destroy information. If you're familiar with Liousville's theorem in classical mechanics, it's a bit like that.
Not really. He was a famous name, so they got him to write a letter to the president. That was the extent of his essential involvement.
The bombs could have been designed without understanding that well-known unit-conversion formula* between matter and energy, since the fission process and its products were understood.
[*] That's all "E equals m c squared" is, a conversion between different units.
Back in '77 I once spent 3 or 4 minutes trying to get the key to work in the door of the wrong white '67 Mustang.
When you have your own wavelengths across the Atlantic, as from, say, Geneva CH to Chicago US, and can light them up at 10Gb/s, you're going to be far faster than a Concorde with that Terabyte!
Fermilab is moving dozens of terabytes a day into and out of mass storage. It's the perfect place to handle this camera's output.
No, they have to shout about stiffer penalties, and making it a separate crime to use a Foo in the commission of a Bar.
What they are saying is, in a career of making laws, they've never gotten it right yet.
And Alvarez's lab tech had a platinum wedding ring.
Platinum is hardened with Iridium. It doesn't take much rub-off to give the tiny amounts needed ...
I read it. You advocate keeping a kicker with a pair to increase the expected payback. You made one important mistake, due to your unfounded "don't look beyond the next card" dogma.
If you keep just the pair, and the first of the three new cards doesn't match it, now you can consider it your kicker and get all the same chances of two-pair while enjoying a 50% greater chance of three of a kind.
Bzzzt! Thank you for playing.
Or at least, that's what the casino will say to you if you believe this. There's the little matter of the one (Europe) or two (USA) green spaces on the wheel!
I don't regard poker as gambling. To date, it's a nearly certain small income. If I ever play with players better than I am, I'll have to regard it as tuition money.
"Gentelmen, I give you the year's supply of water we used to have!" A fluid-optic system was the Maguffin of an Asimov story, which was itself a sequel to another story. I can only come up with the Russian title at the moment .. "?????????" I think it was. "Anniversary"? Yeah, that must be it.
(Ugh, that cyrillic doesn't preview well at all. Transliterating: "Godovshchina."
From satellites!
I drive past the local cable baron's antenna farm every workday. They use bigger dishes, so they can withstand a bit more rain fade, but I do see weather-related signal loss on their system. Often it looks just like the problems in the FUD ads they show against satellite TV.
There's not just the trade balance, there are also the questions of customs & immigration
Or is it merely that some software automatically calls the mothership for new information on expiration, and the hostname of the mothership happens to start with "crl"?
(Antidisclaimer: I operate five private CAs and delude myself that I basically understand this stuff.)