Re: Quantum Interference and the Plentitude
Russell Standish wrote: On Mon, Jan 07, 2008 at 02:48:35PM +0100, Mirek Dobsicek wrote: If quantum mechanics was done using a real-valued Hilbert space, you simply don't get wavelike interference patterns. To my knowledge, you don't get interference patterns for *positive* real-valued Hilbert space, but for real-valued Hilbert space you do. Check http://mina4-49.mc2.chalmers.se/~dobsicek/PhDThesis.pdf on page 39 for a quick review and references. Sincerely, Mirek Thanks for the info - I will take a look, when I'm on top of a few things. However, I'm not sure what you mean by positive real Hilbert space, as the positive real numbers do not form a field. I can only guess you mean some kind of non-Hilbert space generalisation, a bit like my non-Hilbert space non-commutative division ring gadgets I've alluded to in the past. Hi Russel, you are right, a *positive* real Hilbert space is a wrong term. However, the point of my comment was to express a belief that your sentence If quantum mechanics was done using a real-valued Hilbert space, you simply don't get wavelike interference patterns. is not correct. But of course, QM as physical framework and as derived from experiments goes with complex numbers. Best, Mirek --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Quantum Interference and the Plentitude
On Mon, Jan 21, 2008 at 03:31:20PM +0100, Mirek Dobsicek wrote: Hi Russel, you are right, a *positive* real Hilbert space is a wrong term. However, the point of my comment was to express a belief that your sentence If quantum mechanics was done using a real-valued Hilbert space, you simply don't get wavelike interference patterns. is not correct. But of course, QM as physical framework and as derived from experiments goes with complex numbers. Best, Mirek Yes, of course. And in fact given that the naive OM measure usually chosen and discussed is a positive measure, putting this into the theory of observations framework would give a theory without interference effects and the like. My point is still valid about the need for complex measure, but you have added an important correction. As I point out in ToN (and Why Occams Razor) complex measures are more general than real measures, so Occams razor should choose these over positive measures. And this is what is seen experimentally. My concern, of course, is that more general measures exist than complex measures. Hence this raises the intriguing possibility that a more general measure (such as quaternions for instance) might give rise to different physics than standard QM that could be experimentally tested for. If found, these would be mind-blowing. If not found, this raises the question of why complex measures are preferred over quaternions, say. The trouble is that at present, I'm all fingers and thumbs over manipulating division rings, as I'm not familiar with them, only their vector space cousins. Cheers -- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://www.hpcoders.com.au --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Quantum Interference and the Plentitude
On Mon, Jan 07, 2008 at 02:48:35PM +0100, Mirek Dobsicek wrote: If quantum mechanics was done using a real-valued Hilbert space, you simply don't get wavelike interference patterns. To my knowledge, you don't get interference patterns for *positive* real-valued Hilbert space, but for real-valued Hilbert space you do. Check http://mina4-49.mc2.chalmers.se/~dobsicek/PhDThesis.pdf on page 39 for a quick review and references. Sincerely, Mirek Thanks for the info - I will take a look, when I'm on top of a few things. However, I'm not sure what you mean by positive real Hilbert space, as the positive real numbers do not form a field. I can only guess you mean some kind of non-Hilbert space generalisation, a bit like my non-Hilbert space non-commutative division ring gadgets I've alluded to in the past. Cheers -- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://www.hpcoders.com.au --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Quantum Interference and the Plentitude
Le 14-janv.-08, à 17:20, Günther Greindl a écrit : Hi, Very interesting thesis Mirek. I have download it, and will certainly try to dig a bit more on it some week-ends. I second that. For christmass, I asked my girlfrind to give me The Wisdom of Insecurity, Computability: An Introduction to Recursive Function Theory, and Godel's Theorem: An Incomplete Guide to Its Use and Abuse, so these books might precede the Fabric :-) Good books all. If you like Watts book (and also if you don't ;-) I also recommend The Tao is silent by Raymond Smullyan (who you probably know from his logic stuff). That's a very nice book indeed. And in the same vein (and price) there is 5000 BC, quite interesting (and taoist) too. Smullyan is dead, and I am not sure I will ever know if Raymond Smullyan was aware of the computationalist links between his technical books in self-reference logic, and his more philosophical writings. One of his last books Who Knows? seems to me to witness he was not really aware of those links, and not so much open to the comp hyp or even Church's thesis, but who knows? After all, in 5000 BC he said about Mechanism that a self-pessimist could say I am a machine? what a pity, I knew I was not much: bad news for me, and a self-optimist could say Me? A machine? this shows machine can be as much as I am: good news for them. ... Something like that. Talking about Smullyan's books, I recall that Forever Undecided is a recreational (but ok ... not so easy, nor really recreational) introduction to the modal logic G (the one Solovay showed to be a sound and complete theory for the Godel-Lob (Gödel, Löb, or Goedel, Loeb) provability/concistency logic. G is the key for the math in the TOE approach I am developing. The logic G is the entry for all arithmetical Plotinian Hypostases. Search on Knight and/or Knaves in the archive for preceding discussion about Smullyan's Forever Undecided, and references. I must say I love also very much his How to Mock a Mocking Bird?, which is a rather good introduction (imo) to the SK-combinators. Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Quantum Interference and the Plentitude
Le 11-janv.-08, à 17:32, Mirek Dobsicek a écrit : Very interesting thesis Mirek. I have download it, and will certainly try to dig a bit more on it some week-ends. Thanks, hopefully you will find something interesting in there. I see you don't cite Everett, which indeed is not necessary for the practice of quantum computing. But your presence in this list could mean that you are open to many-worlds ideas, or everything-like theories. I would like to know, if you don't mind, your opinion on Everett, Deutsch ..., and perhaps about interpretation of QM in general Well yes, my opinion about QM is not well established yet. Me too. My certainly revisable opinion is that QM confirms the many comp histories we have to suspect below our level of substitution. I have jumped to the field of quantum computing three years ago. I had no previous knowledge on the topic nor I did know any quantum physics. I had been playing with the C compiler mostly in the past. Due to relatively short time in the quantum world, I have so far used QM only as a tool - 'shut up and calculate' interpretation. I am always a bit astonished that people can do that, but of course most of the time we have not really the choice. Personally I have still some problem to use my brain without instruction manual. It happened relatively recently, that I was searching the web for buddhist philosophy reading and found James Higgo's Four reasons why you don’t exist. Approximately at the same time I saw a lot of Everett related articles thanks to the 50th anniversary. So I bought Deutsch's Fabric of Reality. It led me to the Fabric-of-Reality mailing list and that took me to the Everything-list. Here I saw your UDA - (QM) - MWI and all these things together attracted me a lot. I think, I can say that I am pretty much open minded. It often seems to me that I keep a 'superposition' of all what I see and read. I don't abandom some forks, I just change the amplitudes. Like me you are a bit like a dovetailer ... It's all right but not necessarily easy with publish or perish sort of principles. I hardly ever insist on something, I am rarely sure, I think this is a mark of the serious scientist mind, and, well I can justify that it has to be the main feature of the sound lobian scientist, but I guess we will have perhaps some opportunity to elaborate on that later. I don't try to push 'good' and 'bad' far apart from each other. As far as you can distinguish a cup of coffee from a venomous spider ... But I agree that some Good/Bad, even True/False separation is a bit like the Chinese Ying-Yang where there is always pieces of Ying in the Yang, and Yang in the Ying. I like when I climb on a steep vertical wall I think that the interview of a lobian machine can be considered as a shortcut in the fundamental sciences, but then it could be a bit too much steep, especially for those who lack a bit of computer science. and life is hard and simple at the same time. Well said. Regarding MWI ... I have not read the original Everett paper yet. I expected to get most of his ideas from the Fabric of Reality, but alas in this book I got stuck at the strange frog seeing individual photons. I am not sure why you are stuck there. If you are really stuck there don't hesitate to discuss this on the FOR list. It seemed to me too much scientific-popular reading and I did not get back to the book so far. For christmass, I asked my girlfrind to give me The Wisdom of Insecurity, Computability: An Introduction to Recursive Function Theory, and Godel's Theorem: An Incomplete Guide to Its Use and Abuse, so these books might precede the Fabric :-) I see you believe more in your girlfriend than in Santa Klaus! Did she find Alan Watts' the wisdom of insecurity? About books I never know really what books I should suggest. Logicians like to write many beautiful books. If you like and appreciate the subject matter of Cutland's Computability: An Introduction to Recursive Function Theory, then you could think about asking your girlfriend to find the bible by Hartley ROGERS. (ref in my thesis). About the S K programming language, I guess some people have recognize the Shoenfinkel-Curry combinators. More on this in my old combinators Uuu, new excercises and I am still reading the DIAGONAL post from 31.12.2007. I guess this one: http://www.mail-archive.com/everything-list@eskimo.com/msg14107.html Please, take all your time, and don't hesitate to ask precisions or to make any comments. I prefer now to be sure people have a deep grasp of what is a Universal Machine and Church Thesis before jumping to the theology of the lobian entity. It means I am still living in the previous year, it is good, who wants to be old :-) Take all the time you want, but not slower! I have planned the Main Comp-Everything Exam for the year 789,144 :) Happy new years! Bruno
Re: Quantum Interference and the Plentitude
Hi, Very interesting thesis Mirek. I have download it, and will certainly try to dig a bit more on it some week-ends. I second that. For christmass, I asked my girlfrind to give me The Wisdom of Insecurity, Computability: An Introduction to Recursive Function Theory, and Godel's Theorem: An Incomplete Guide to Its Use and Abuse, so these books might precede the Fabric :-) Good books all. If you like Watts book (and also if you don't ;-) I also recommend The Tao is silent by Raymond Smullyan (who you probably know from his logic stuff). Regards, Günther -- Günther Greindl Department of Philosophy of Science University of Vienna [EMAIL PROTECTED] http://www.univie.ac.at/Wissenschaftstheorie/ Blog: http://dao.complexitystudies.org/ Site: http://www.complexitystudies.org --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Quantum Interference and the Plentitude
Very interesting thesis Mirek. I have download it, and will certainly try to dig a bit more on it some week-ends. Thanks, hopefully you will find something interesting in there. I see you don't cite Everett, which indeed is not necessary for the practice of quantum computing. But your presence in this list could mean that you are open to many-worlds ideas, or everything-like theories. I would like to know, if you don't mind, your opinion on Everett, Deutsch ..., and perhaps about interpretation of QM in general Well yes, my opinion about QM is not well established yet. I have jumped to the field of quantum computing three years ago. I had no previous knowledge on the topic nor I did know any quantum physics. I had been playing with the C compiler mostly in the past. Due to relatively short time in the quantum world, I have so far used QM only as a tool - 'shut up and calculate' interpretation. It happened relatively recently, that I was searching the web for buddhist philosophy reading and found James Higgo's Four reasons why you don’t exist. Approximately at the same time I saw a lot of Everett related articles thanks to the 50th anniversary. So I bought Deutsch's Fabric of Reality. It led me to the Fabric-of-Reality mailing list and that took me to the Everything-list. Here I saw your UDA - (QM) - MWI and all these things together attracted me a lot. I think, I can say that I am pretty much open minded. It often seems to me that I keep a 'superposition' of all what I see and read. I don't abandom some forks, I just change the amplitudes. I hardly ever insist on something, I am rarely sure, I don't try to push 'good' and 'bad' far apart from each other. I like when I climb on a steep vertical wall and life is hard and simple at the same time. Regarding MWI ... I have not read the original Everett paper yet. I expected to get most of his ideas from the Fabric of Reality, but alas in this book I got stuck at the strange frog seeing individual photons. It seemed to me too much scientific-popular reading and I did not get back to the book so far. For christmass, I asked my girlfrind to give me The Wisdom of Insecurity, Computability: An Introduction to Recursive Function Theory, and Godel's Theorem: An Incomplete Guide to Its Use and Abuse, so these books might precede the Fabric :-) About the S K programming language, I guess some people have recognize the Shoenfinkel-Curry combinators. More on this in my old combinators Uuu, new excercises and I am still reading the DIAGONAL post from 31.12.2007. It means I am still living in the previous year, it is good, who wants to be old :-) Have a nice weekend, Mirek --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Quantum Interference and the Plentitude
Le 07-janv.-08, à 14:48, Mirek Dobsicek a écrit : If quantum mechanics was done using a real-valued Hilbert space, you simply don't get wavelike interference patterns. To my knowledge, you don't get interference patterns for *positive* real-valued Hilbert space, but for real-valued Hilbert space you do. Check http://mina4-49.mc2.chalmers.se/~dobsicek/PhDThesis.pdf on page 39 for a quick review and references. Very interesting thesis Mirek. I have download it, and will certainly try to dig a bit more on it some week-ends. I see you don't cite Everett, which indeed is not necessary for the practice of quantum computing. But your presence in this list could mean that you are open to many-worlds ideas, or everything-like theories. I would like to know, if you don't mind, your opinion on Everett, Deutsch ..., and perhaps about interpretation of QM in general About the S K programming language, I guess some people have recognize the Shoenfinkel-Curry combinators. More on this in my old combinators posts: http://www.mail-archive.com/everything-list@eskimo.com/msg05920.html http://www.mail-archive.com/everything-list@eskimo.com/msg05949.html http://www.mail-archive.com/everything-list@eskimo.com/msg05953.html http://www.mail-archive.com/everything-list@eskimo.com/msg05954.html http://www.mail-archive.com/everything-list@eskimo.com/msg05955.html http://www.mail-archive.com/everything-list@eskimo.com/msg05956.html http://www.mail-archive.com/everything-list@eskimo.com/msg05957.html http://www.mail-archive.com/everything-list@eskimo.com/msg05958.html http://www.mail-archive.com/everything-list@eskimo.com/msg05959.html http://www.mail-archive.com/everything-list@eskimo.com/msg05961.html But people could try to solve the problem without looking at this, or just ask me. Those interested in quantum programming language could search for quantum lambda calculus. Lambda calculus, the original universal system proposed by Church, and which is at the origin of Church thesis, has some deep advantages concerning the idea of building quantum programming languages. Have a nice week-end, Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Quantum Interference and the Plentitude
If quantum mechanics was done using a real-valued Hilbert space, you simply don't get wavelike interference patterns. To my knowledge, you don't get interference patterns for *positive* real-valued Hilbert space, but for real-valued Hilbert space you do. Check http://mina4-49.mc2.chalmers.se/~dobsicek/PhDThesis.pdf on page 39 for a quick review and references. Sincerely, Mirek --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Quantum Interference and the Plentitude
Both Russell Standish's Theory of Nothing and Wei Dai's really simple interpretation of quantum mechanics suggest that the mere existence of all possible states is all that is needed to explain quantum mechanics. While I can understand how it would leads to unpredictability I was wondering how is quantum interference accommodated? Thanks, Jason --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Quantum Interference and the Plentitude
I'm not sure how Wei Dai would answer this, but this is where it comes from in my theory: Interference, along with most of the other weird aspects of quantum mechanics is a direct result of the measure of observer moments being complex. If quantum mechanics was done using a real-valued Hilbert space, you simply don't get wavelike interference patterns. So why is the OM measure complex and not positive real (like most people assume). Because it can be - complex measures are more general than real valued ones. A real valued measure would require an explanation. Unfortunately, so does a complex valued one, as measures can be even more general than complex valued - see the concept of spectral measure. I suspect division has an important role in order to get real probabilities as ratios of OM measures, and whilst there are still a number of division algebras that can be deployed as measures, possibly the division has to commutative, which would leave just the complex numbers. Alternatively, perhaps the use of these more general spectral measures give exactly the same result as using a complex-valued measure. It would be interesting to develop alternative QM formulations using modules over division rings rather than vector spaces to see if there would be any physically measurable effect of (say) relaxing the requirement of commutivity of multiplication. Alas, this is well out of my comfort zone, so I'll have to pass the baton on to some other foolhardy individual. Cheers On Thu, Dec 20, 2007 at 08:18:59PM -0800, Jason wrote: Both Russell Standish's Theory of Nothing and Wei Dai's really simple interpretation of quantum mechanics suggest that the mere existence of all possible states is all that is needed to explain quantum mechanics. While I can understand how it would leads to unpredictability I was wondering how is quantum interference accommodated? Thanks, Jason -- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://www.hpcoders.com.au --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
