Dear Neil,
Thanks for your comments. Yes, it looks that your Essay is connected to my one. If you really find a way to distinguish quantum mixtures of the same density matrix this is also of fundamental importance for the black hole information paradox. I am going to read, comment and rate your Essay before the vanishing of the Community Rate's deadline.
Cheers,
Ch.
Christian,
First of all thank you for your enthusiastic comments here and at my own essay (/1610). I am flattered to get kudos from the current top-rated essayist. (That BTW is not surprising to me, considering that your essay most resembles a journal paper proposing an advance.) Sadly I have a bit of visual trouble reading your essay, perhaps my older pdf SW did not render it right (it has the scratchy look for me of "Ghostview" altho I downloaded the file itself.) I do note first that you recognize the importance to information issues of trying to resolve controversies over BH information representation and barriers. (This is something I remember as issue from back in early days of hearing "black holes have no hair" - ie, only mass, spin, and charge were considered to be residual, and then on to the "black hole wars" as you relate.) It is of course necessary to try and integrate QM issues into this imbroglio, despite our not having a proper theory of quantum gravity! Then Hawking's discovery about EH radiation knocked a wrench into everything. Yet you realize he should not be hero-worshiped, brilliant as he is (even Einstein and von Neumann made mistakes.)
You make good progress in relating all the above to evolution of the Schrödinger equation, use of DDF etc. It seems you are zeroing in on your main point when you aptly note how to evade the cruder density matrix view and recover genuine SE of a pure state. (My own essay refers to how we might distinguish mixtures with the same DM, against the common view that is not possible.) This you cap up in a money quote "The result agrees with the assumption by 't Hooft that Schrödinger equations can be used universally for all dynamics in the universe", also being the second person I've read to directly try to refute Hawking's claim about loss of information from a BH. IOW, another pathway to quantum spring!
Readers may find my own essay interesting since I explain how we could find out more about quantum states or mixtures than heretofore considered possible. This involves for example repeated interactions (akin to weak measurements) of a single photon, as well as how to distinguish e.g. random H, V polarization mixtures from random R, L mixtures. My essay is indeed related to yours, in that distinguishing such mixtures should profoundly impact the BH information paradox.
Congratulations on your placement in the contest! It is refreshing to see a rigorously argued contribution within accepted physical theory that bears on such broad issues.
My own essay was much more philosophically and generally focused, inquiring into the intersection of the foundations of mathematics, computer science, and physics, noting that often the laws of physics themselves seem to be implied by redundancies in information (gauge theories), which are unavoidable.
Christian,
My most sincere congratulations on your win. Now it's perhaps the judges turn to be under scrutiny. For such different essays it's astonishing the insight of the Coleman statement; "The career of a young theoretical physicist consists of treating the harmonic oscillator in ever-increasing levels of abstraction." was central for us both.
You also know from my AGN (BH) galaxy cyclic sequence work that I'm overjoyed by your cutting through the dense nonsense talked about black holes in recent decades. In fact I hope I can now convince you to cut deeper still to reach a simpler reality where all the matter/information accreted is simply accelerated, re-ionised and blasted back out as quasar jets, condensing fresh fermions from the QV to start the next cycle. The problems of re-ionisation, galaxy mass growth, kinetic decoupling etc. thereby also explained. I propose Coleman's statement then also applies to BH's.
FQXi has never had a better opportunity to fulfil it's remit and enable a (Q?) leap in the understanding of nature. So many theses agreed where the solutions lay, many not even in the top 40, that a major correlation job is required. Do you agree Tom Ray's (excellent I think) idea to compile a 'set of self similar sets'? The term 'herding cats' comes to mind, but is it beyond the wit of man? If the FQXi trustees retreat to doctrine then perhaps one of the title you edit?
Very best wishes for the final assessment.
Peter
Hi Jennifer,
Thank you very much for your kind words. I am honoured that you are working through the mathematical presentation of my paper. I see that you are among the Finalists. Congrats and let us cross the fingers for the final judgement by the FQXi expert panel of judges.
Cheers and Best of Luck in the Contest to you too,
Ch.
Hi Neil,
Thanks for your kind words. I see that you are among the Finalists. Congrats and let us cross the fingers for the final judgement by the FQXi expert panel of judges. I agree with your point of view that your Essay could have important implications on the BH information paradox because its distinguishing mixtures within the density matrix.
Cheers and good luck in the Contest,
Ch.
Dear Bram,
Thank you very much for your kind words. Although the deadline for the Community Rating vanished yesterday, I will be pleasured to read and comment your Essay in next days.
Cheers,
Ch.
Thank you again, Christian. I hope that judges appreciate the importance of papers proposing empirical tests, even if they remain thought experiments due to practical difficulties. Overall I found quite a variety of perspectives and levels of communication here. I do regret not participating in discussions as much as I maybe should have. Being busy and a spell of eye trouble slowed me down but I could have done more. (I did leave a detailed response to your questions at my own page.) Well I keep my fingers crossed too and also hope I get some kind of "amateur" recognition as the administrators were talking about. Yes, despite some significant study and handle on the subjects I am not a pro.
Congratulations for coming out on top!
Your essay certainly deserves kudos, Christian. I hope the expert judges agree with my assessment (and the accolades of the community) that it is indeed worthy of a prize.
Good Luck!
Jonathan
Dear Christian,
I congratulate you with all my heart with the first place in the first phase of the V International FQXi Essay Contest 2013!
I wish you continued success in your research and extensive organizational work for the good of the World Science!
Good summer holiday!
With great respect,
Vladimir
Hi Peter,
Thanks for your kind congrats. Have the same congrats from me also on your great result. I am going to have a deeper reading of your model of the AGN (BH) galaxy cyclic sequence after the end of my vacations, i.e. in September. I did not know Tom Ray's idea to compile a 'set of self similar sets'. I am going to read it in detail.
Very best wishes for the final assessment also to you,
Ch.
Dear Jonathan,
Thank you very much for your congrats and wishes. In the same way, I send you my best congrats and wishes for your excellent position in the final ranking of the Community Rate. Now let us cross the fingers for the final judgement by the FQXi experts panel. All the best for the final result.
Cheers,
Ch.
Hi Vladimir,
Thank you very much. Have my best congrats and wishes for your excellent position in the final ranking of the Community Rate and let us my best congrats and wishes for your excellent position in the final ranking of the Community Rate.
Good summer holiday also to you and all the best for the final result.
Cheers,
Ch.
Christian,
I'm afraid there's some misunderstanding. I think what Peter is referring to, is my proposed experiment to catalog a set of results dependent on the orientation of an apparatus emulating a primordial initial condition. This is basically the experimental interpretation of a scale invariant solution to the time-dependent Schrodinger equation. Annihilation of particle pairs which conserves angular momentum, without producing gamma radiation, implies a primary role for wavefunction in particle creation, with no loss of information.
Best,
Tom
