tag:blogger.com,1999:blog-22973357.post5102245342353378637..comments2018-04-26T04:25:47.847-04:00Comments on Backreaction: PS on The Mathematical UniverseSabine Hossenfelderhttps://plus.google.com/111136225362929878171noreply@blogger.comBlogger39125tag:blogger.com,1999:blog-22973357.post-50723597365196227112007-10-18T10:16:00.000-04:002007-10-18T10:16:00.000-04:00Hi Neil:the platitude that "magnitude in wave func...Hi Neil:<BR/><BR/><I>the platitude that "magnitude in wave function does not matter, only the squared amplitude" is wrong</I> It is correct, wave-function is the complete wave-function including superpositions. If you superpose two pure states then their individual amplitudes do of course matter. I don't know why you think there is a 'wrong' platidute'.<BR/><BR/>Hi Arun:<BR/><BR/>Yeah sure. The Beehttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-61876609729614387622007-10-17T01:40:00.000-04:002007-10-17T01:40:00.000-04:00Bee wrote: Complex numbers are without doubt an us...Bee wrote: <EM>Complex numbers are without doubt an useful tool to deal with phase differences. However, in electrodyn you can do without, even if inconvenient. Not so in QM.</EM><BR/><BR/>Why not? I'm reading de Broglie's 1937 book, and while some of it is dated, it remains clear that for the people of that time, complex numbers only appeared as a way to represent a wave. They were not "magical"Christophe de Dinechinhttps://www.blogger.com/profile/15212549796119667462noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-43760492199565533702007-10-16T21:29:00.000-04:002007-10-16T21:29:00.000-04:00Since I see chatting about interference, here's a ...Since I see chatting about interference, here's a reminder, that the platitude that "magnitude in wave function does not matter, only the squared amplitude" is wrong! The amplitude is important if it interferes with the amplitude of another wave or part of the same wave. (Hey, do photons ever interfere with other photons, or only themselves?)<BR/><BR/>BTW, another reminder about those even more Neil'https://www.blogger.com/profile/04564859009749481136noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-45030252800465422712007-10-16T18:15:00.000-04:002007-10-16T18:15:00.000-04:00Hi Bee,Complex numbers, phase and zitterbewegung o...Hi Bee,<BR/><BR/>Complex numbers, phase and zitterbewegung or "oscillatory motion" may all be synonymous <BR/>terms.<BR/><BR/>David Hestenes, 'The Kinematic Origin of Complex Wave Functions' may be correct.<BR/><BR/>http://modelingnts.la.asu.edu/pdf/Kinematic.pdf<BR/><BR/>There is also Donghui Xu, 'Hannay angle in an LCR circuit with time-dependent inductance, capacity and resistance", that Doughttps://www.blogger.com/profile/07643919214761722345noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-68274189358928051212007-10-16T17:46:00.000-04:002007-10-16T17:46:00.000-04:00Umm, yes, and no, Bee. Phase info in QM is delicat...Umm, yes, and no, Bee. Phase info in QM is delicate and easily destroyed. That is why it doesn't easily show up in our experiments. On the other hand, if you reply to this over a Wi-fi connection, it is probably using phase shift keying or some such - phase information pervades life (and so more real, somehow).<BR/><BR/>Does phase have anything to do with complex numbers, or are two real Arunhttps://www.blogger.com/profile/03451666670728177970noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-90825675531162722792007-10-16T15:46:00.000-04:002007-10-16T15:46:00.000-04:00Hi Arun:err, apologies. But then I don't get your ...Hi Arun:<BR/><BR/>err, apologies. But then I don't get your point? Weren't you trying to argue that phases in qm are essentially the same as in classical ed ("Phase is very real classically"), while I was trying to say phase differences don't necessarily have something to do with complex numbers, it's just more convenient to handle with them? Best,<BR/><BR/>B.Beehttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-25369995258532867942007-10-16T15:02:00.000-04:002007-10-16T15:02:00.000-04:00Bee:The mystery of the double slit experiment is n...Bee:<I>The mystery of the double slit experiment is not the interference itself - you get these (phase differences) for classical waves. The mystery is that you get the interferences for single particles. That brings us back to the wave-particle problem, i.e. quantum mechanics.</I><BR/><BR/>I thought I said that.<BR/><BR/>Arun:<I>The phases do show up, as cos() or sin(). The whole mysterious Arunhttps://www.blogger.com/profile/03451666670728177970noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-3378847241975682942007-10-16T13:37:00.000-04:002007-10-16T13:37:00.000-04:00Bee wrote: The real numbers are a field as well, b...Bee wrote: <EM>The real numbers are a field as well, but unlike R, C is algebraically closed. You get the multiplication law if you require i^2 = -1, in addition to being a field, there's no ambiguity in that.</EM><BR/><BR/>This is how you get complex numbers in mathematics, but I don't think this is how you get them in physics.<BR/><BR/>Why do we use real numbers to measure distances? Because Christophe de Dinechinhttps://www.blogger.com/profile/15212549796119667462noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-11135548108964013012007-10-16T13:24:00.000-04:002007-10-16T13:24:00.000-04:00Plato wrote: That's a cop out if I ever heard one....Plato wrote: <EM>That's a cop out if I ever heard one.:)It's the very act of infinite regress that we would know what is "self evident."</EM><BR/><BR/>No, it's just pointing out the difference between "describing" and "explaining". If I open my hand and you see an apple fall from it, you can describe the movement of the apple using Newton's gravitation law. You cannot explain why the apple fell. Christophe de Dinechinhttps://www.blogger.com/profile/15212549796119667462noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-48042153492639093312007-10-16T11:33:00.000-04:002007-10-16T11:33:00.000-04:00Hi Stefan,Sorry that I was so sloppy with mentioni...Hi Stefan,<BR/><BR/>Sorry that I was so sloppy with mentioning the 'funny multiplication law'. The complex numbers are, as you say, a field, i.e. a vector space with a multiplication (among elements of the space, not a scalar multiplication, the vector space already has this). The multiplication has, roughly spoken, to work with the addition of the vector space (associative). The real numbers Beehttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-25081953218272417762007-10-15T22:30:00.000-04:002007-10-15T22:30:00.000-04:00Bee,About those pesky imaginariesI think that the ...Bee,<BR/>About those pesky imaginaries<BR/><BR/>I think that the real problem here is not that the imaginary numbers are more “imaginary” than the reals, but that the reals are less “real” than we imagine. We think of reals as being more concrete because we get used to putting them on a line, and because they look more like the natural “counting” numbers. Associating any numbers with distances,CapitalistImperialistPighttps://www.blogger.com/profile/17523405806602731435noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-83598012350786331442007-10-15T21:53:00.000-04:002007-10-15T21:53:00.000-04:00In his work "An Imaginary Tale", Paul Nahin says a...In his work "An Imaginary Tale", Paul Nahin says a number of amusing things about the square root of -1. Here's one that's especially amusing:<BR/><BR/>"The intimate connection of the square root of -1 to physical reality is still not always appreciated, however, even by educated people who claim to know quite a bit about math. Consider, for example, these words from celebrity intellectual Cynthianoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-64156517798885715052007-10-15T21:03:00.000-04:002007-10-15T21:03:00.000-04:00If you think the complex numbers are weird (and I ...If you think the complex numbers are weird (and I remember my sense of awe, looking at my sister's math textbook when I was 8 or 9), then you should get a really big kick out of the "surreal numbers" and such as that. Check it out. I still don't know if I can really get on board with that.Neil'https://www.blogger.com/profile/04564859009749481136noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-9370371343763931812007-10-15T20:15:00.000-04:002007-10-15T20:15:00.000-04:00Hi Bee,The Arun comment of 7:16 PM, October 14, 20...Hi Bee,<BR/><BR/>The Arun comment of 7:16 PM, October 14, 2007 is very close to the likely insight of the misnomer “imaginary numbers” by Leibniz [or whomever] as I understand this concept.<BR/><BR/>“Invisible numbers” is probably a more appropriate term since these numbers are detectable but not visible.<BR/><BR/>Paul J Nahin [PhD EE, former chair, now emeritus UNH-US] has an easy to read Doughttps://www.blogger.com/profile/07643919214761722345noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-61437716895827889032007-10-15T18:42:00.000-04:002007-10-15T18:42:00.000-04:00The mystery is rather why phases disappear in obse...<I>The mystery is rather why phases disappear in observable quantities.</I><BR/><BR/>The phases do show up, as cos() or sin(). The whole mysterious two-slit experiment is about how phases show up, even when only one particle is transiting the interference apparatus.Arunhttps://www.blogger.com/profile/03451666670728177970noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-91326349147957694972007-10-15T17:18:00.000-04:002007-10-15T17:18:00.000-04:00Dear Bee, Well, you can talk about im and re part ...Dear Bee,<BR/><BR/><I> Well, you can talk about im and re part instead of course, and understand C as vector space with a funny multiplication law</I><BR/><BR/>but this funny multiplication law for pairs of real numbers seems somehow to "exist" in nature - in the sense that it provides an economic description of the relation among quantities measured by real numbers? Then, the question is perhapsstefanhttps://www.blogger.com/profile/09495628046446378453noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-77880575097031250602007-10-15T17:15:00.000-04:002007-10-15T17:15:00.000-04:00Hi Thomas,polarized light is crying out to be desc...Hi Thomas,<BR/><BR/><I>polarized light is crying out to be described with complex numbers.</I><BR/><BR/>that reminds me... there is a way to describe <A HREF="http://en.wikipedia.org/wiki/Polarization#Parameterizing_polarization" REL="nofollow">polarised light by complex two-dimensional vectors</A>, related to the the Stokes parameters, and there is this connection with the Poincaré spherestefanhttps://www.blogger.com/profile/09495628046446378453noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-84100114152264630052007-10-15T15:18:00.000-04:002007-10-15T15:18:00.000-04:00Regarding the Cambridge intro to geometric algebra...Regarding the Cambridge intro to geometric algebra (GA). I would guess that everyone else in the industry has also read all these things at one time or another. Looking at it again, a couple things come to mind:<BR/><BR/>(1) Adding scalars to vectors and the like. This is more natural to elementary particle physicists than other branches, especially if they think about stuff like the V-A and theCarlBrannenhttps://www.blogger.com/profile/17180079098492232258noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-76054643573183053572007-10-15T13:33:00.000-04:002007-10-15T13:33:00.000-04:00Arun,You're saying classical phase implies complex...Arun,<BR/><BR/>You're saying classical phase implies complex numbers? Get real!Kris Kroghhttp://www.psych.ucsb.edu/people/researchers/krogh/index.phpnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-42690565438700173622007-10-15T13:17:00.000-04:002007-10-15T13:17:00.000-04:00Hi Who: got me ;-)Hi Who: got me ;-)Beehttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-46075541634997398422007-10-15T13:16:00.000-04:002007-10-15T13:16:00.000-04:00Dear Arun:A vector space comes by definition with ...Dear Arun:<BR/><BR/>A vector space comes by definition with a multiplication law with a scalar. What you need for a complex structure is an multiplication among elements of the space. You can get multiplication with a real number out of addition, but what you actually need is multiplication with a complex number. <BR/><BR/>Sure, phase differences exist, and as I said above complex numbers are Beehttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-39845393441596647992007-10-15T12:51:00.000-04:002007-10-15T12:51:00.000-04:00Dear Bee,Similarly we don't need multiplication, r...Dear Bee,<BR/><BR/>Similarly we don't need multiplication, repeated addition will do :)<BR/><BR/>Phase is very real classically, listen to your FM radio and think about it :)Arunhttps://www.blogger.com/profile/03451666670728177970noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-8060437429723494652007-10-15T09:33:00.000-04:002007-10-15T09:33:00.000-04:00Not just electrical circuits - polarized light is ...Not just electrical circuits - polarized light is crying out to be described with complex numbers. Two components at right angles and one has a magnitude and phase with respect to the other.<BR/><BR/>As for quantum mechanics - even though individual phases are unobservable, they crop up very often when one has a system with more than one particle or parameter. Aharonov-Bohm, Berry, ...<BR/><BR/>Thomas Dnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-45213971104717430062007-10-15T08:04:00.000-04:002007-10-15T08:04:00.000-04:00"So, it might take some more while, but I'll keep ..."So, it might take some more while, but I'll keep it in mind. Best,<BR/>"<BR/><BR/>Thanks!<BR/><BR/>ps I note the care with which you avoided the word "time" in that sentence....Dr Whonoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-2706850158388701512007-10-15T07:44:00.000-04:002007-10-15T07:44:00.000-04:00Dear Arun:Complex numbers are without doubt an use...Dear Arun:<BR/><BR/>Complex numbers are without doubt an useful tool to deal with phase differences. However, in electrodyn you can do without, even if inconvenient. Not so in QM. Well, you can talk about im and re part instead of course, and understand C as vector space with a funny multiplication law, but you don't get rid of the complexity.<BR/><BR/>Hi Dr. Who,<BR/><BR/>I do requests... Beehttps://www.blogger.com/profile/06151209308084588985noreply@blogger.com