tag:blogger.com,1999:blog-13869903.post8554179916957537259..comments2021-05-08T11:27:06.192-05:00Comments on nanoscale views: Black holes, information, and "fire walls"Douglas Natelsonhttp://www.blogger.com/profile/13340091255404229559noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-13869903.post-13332978601037190412013-03-11T11:53:24.590-05:002013-03-11T11:53:24.590-05:00Douglas Natelson is fascinating person. free antiv...Douglas Natelson is fascinating person. <a href="http://freeantivirusdownloadx.com" rel="nofollow">free antivirus download</a>Free Antivirus Downloadhttp://freeantivirusdownloadx.comnoreply@blogger.comtag:blogger.com,1999:blog-13869903.post-85709941945374820952013-02-21T22:24:47.305-06:002013-02-21T22:24:47.305-06:00The entanglement picture is one way to look at the...The entanglement picture is one way to look at the paradox, but there's another way which AMPS initially talk about in their paper and which I find more intuitive. <br /><br />The first thing is the claim that quantum mechanics always works, hence a pure state always evolves into a pure state (unitary time evolution). Now, if we have a system in pure state which collapses into a black hole and eventually evaporates away via Hawking radiation, the total radiation would have to be in a pure state, which means if we take a subsystem it will be entangled with the rest of the system. (This is a common theme when we talk about entanglement entropy in condensed matter systems.)<br /><br />Now if I look at the Hawking radiation, I can define a small subsystem to be the radiation emitted in the last few moments of the black hole, with the rest of the system being everything that was emitted before. The fact that the small subsystem is entangled with the rest of the subsystem means that measuring the rest of the subsystem, one can know the state of the small subsystem. Hence, an observer measuring the early radiation will know what to expect in a particular mode of the late radiation. <br /><br />Now let's say an observer does measure the early state, and hence knows that the a particular mode of the late radiation is a specific energy eigenstate in his frame of reference for some operator that he can define. If the observer now decides to jump into the black hole, the mode he should be seeing is a energy eigenstate for an observer at rest. But for a quantum field theory in curved spacetime, the eigenstate for an observer at rest is a linear superposition of various frequency states for an accelerated observer. (This, in fact, is the origin of Hawking radiation as well as the Unruh effect.)<br /><br />Hence, as the state is an energy eigenstate for an observer at rest, the infalling observer will see quanta at all frequencies, and hence, will also see high energy (frequency) quanta as claimed by AMPS. This is the notion of so called "firewall".<br /><br />I wonder if this explanation was somewhat clearer than the entanglement argument! <br /><br />PS : The arguments across the horizon are not entirely "unphysical" as both sides of the horizon are accessible to an infalling observer, and if the infalling observer sees no drama at the horizon, that inevitably implies the entanglement across horizon in the frame of reference of an observer at rest w.r.t. the black hole. That simply follows from the fact that field operators for infalling observer are Bogoliubov transforms of the operators for the observer at rest. Vatsalhttps://www.blogger.com/profile/03028551668122345758noreply@blogger.comtag:blogger.com,1999:blog-13869903.post-87585289905267799702013-01-13T22:51:35.933-06:002013-01-13T22:51:35.933-06:00If not by theological means, how else are string t...If not by theological means, how else are string theorists supposed to make a living?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-13869903.post-33401541104908568722013-01-12T06:59:30.088-06:002013-01-12T06:59:30.088-06:00"... almost theological ..." According t..."... almost theological ..." According to Martinus Veltman, “If we do away with the experiments, science becomes religion. From that moment on it won’t be the facts that count when we are trying to determine what’s true, but the opinions of someone’s who’s been elected pope. … Theoretical physics is not worth anything until the laboratory has shown that it’s correct.”<br />Quoted from Bennie Mols’s blog, Feb 8. 2008, “Theory of Everything of Nothing – An exchange of views on string theory”<br />I say that the string theorists and quantum gravitational theorists have unfortunately ignored the work of Vera Rubin and Mordehai Milgrom. Rubin and Milgrom are correct, and the string theorists have made a huge mistake.David Brownhttps://www.blogger.com/profile/10537922851243581921noreply@blogger.comtag:blogger.com,1999:blog-13869903.post-24538009579231213322013-01-12T04:45:15.511-06:002013-01-12T04:45:15.511-06:00http://arxiv.org/pdf/1207.3123.pdf “Black Holes: C...http://arxiv.org/pdf/1207.3123.pdf “Black Holes: Complementarity or Firewalls”David Brownhttps://www.blogger.com/profile/10537922851243581921noreply@blogger.com