tag:blogger.com,1999:blog-22973357.post903588402539258501..comments2023-09-27T07:44:19.769-04:00Comments on Sabine Hossenfelder: Backreaction: Do Complex Numbers Exist?Sabine Hossenfelderhttp://www.blogger.com/profile/06151209308084588985noreply@blogger.comBlogger126125tag:blogger.com,1999:blog-22973357.post-76735709094030784892021-07-08T07:05:22.713-04:002021-07-08T07:05:22.713-04:00Dear Sabine,
I wonder if this is like asking if ...Dear Sabine, <br /><br />I wonder if this is like asking if possibilities (or impossibilities) exist ...<br /><br />The possibility that the particle will exist at 'x' <br />and (logical and- as in the multiplication of 2 numbers) <br />the impossibility that it will exist anywhere else,<br />in the infinitesimally near future,<br />equals <br />the probability of the fact that the Lee Bloomquisthttps://www.blogger.com/profile/04391297278836440983noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-26677269109853429412021-03-16T23:22:54.188-04:002021-03-16T23:22:54.188-04:00You can also reduce problems in gravitation to 10 ...You can also reduce problems in gravitation to 10 coupled non-linear PDEs, but the content of the theory is in the idea that matter induces changes in the metric structure of spacetime, so the metric tensor as an algebraic object in a Riemann space becomes a physical thing, as real as the dielectric constant in paraffin. Just counting equations and solving specific problems is not enough - the drlhttps://www.blogger.com/profile/05424774416249451584noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-47260296921134731062021-03-16T14:59:03.491-04:002021-03-16T14:59:03.491-04:00There is a 3rd direct sense in which complex numbe...There is a 3rd direct sense in which complex numbers show up. You can think of Minkowski space as a projective space made metric by introducing an ideal domain in the Cayley-Klein sense (fundamental quadric). The ideal domain can be identified with the light cone. Same thing for Euclidean geometry, where the ideal domain can be identified with the points at infinity (celestial sphere). Such drlhttps://www.blogger.com/profile/05424774416249451584noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-78870996980103682352021-03-16T14:20:33.041-04:002021-03-16T14:20:33.041-04:00I amend my statement from "All calculations&q...I amend my statement from "All calculations" to "All arithmetic calculations". I agree that "calculations" is a broader term than that, although in an abstract way. JimVhttps://www.blogger.com/profile/10198704789965278981noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-64977008871810659912021-03-16T12:34:05.010-04:002021-03-16T12:34:05.010-04:00It's unfortunate these numbers were called &qu...It's unfortunate these numbers were called "imaginary", people now a days take it so literally.Catalinhttps://www.blogger.com/profile/06192244112905762189noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-45043474387144195742021-03-16T12:04:54.025-04:002021-03-16T12:04:54.025-04:00Also - Dirac eqn goes to Pauli eqn in the non-rel ...Also - Dirac eqn goes to Pauli eqn in the non-rel limit, which goes to Schroedinger eqn for the spinless limit, so you can trace the "i" in Schroedinger all the way back to spacetime geometry as encoded in the Dirac Clifford algebra, making it very real in the direct sense. <br /><br />-drldrlhttps://www.blogger.com/profile/05424774416249451584noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-73476873632033605832021-03-16T11:57:39.208-04:002021-03-16T11:57:39.208-04:00Hi Sabine, such things are fun, but the classical ...Hi Sabine, such things are fun, but the classical theory of diffraction is intractable without the essential appearance of the complex plane. No QM, just waves. You could argue that you are dealing with the Schroedinger equation for photons, but that would be retrograde history.<br /><br />-drldrlhttps://www.blogger.com/profile/05424774416249451584noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-14432856462127300762021-03-14T06:03:51.033-04:002021-03-14T06:03:51.033-04:00All calculations anyone has ever done, by pencil a...<i>All calculations anyone has ever done, by pencil and paper, abacus, slide rule (I could never get more than three significant figures from one), calculator, or computer have used only rational numbers; </i><br /><br />Not sure this is true. e^πi = -1. That calculation only works if e and pi are real. Scotthttps://www.blogger.com/profile/16914985126761335721noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-64514691579544173642021-03-13T00:46:22.207-05:002021-03-13T00:46:22.207-05:00Mozibur5:29 AM, March 12, 2021
Physics reduces al...Mozibur5:29 AM, March 12, 2021<br /><br />Physics reduces all observed phenomena to the quantum and GR, up to the precision of measurement and excluding a few open questions. This all-encompassing, mind-bogglingly successful ontological reduction is all you need to know on the topic of "ontology".<br />Remind me. Why are Newton and Einstein famous? For discovering general empirical Steven Evanshttps://www.blogger.com/profile/13898046706669437332noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-13069369971128854402021-03-12T12:52:28.927-05:002021-03-12T12:52:28.927-05:00All calculations anyone has ever done, by pencil a...All calculations anyone has ever done, by pencil and paper, abacus, slide rule (I could never get more than three significant figures from one), calculator, or computer have used only rational numbers; and the same for all physical measurements.<br /><br />The reason for the utility of calculus is that it is the limit of finite-difference equations as the minimum increment goes to zero, and JimVhttps://www.blogger.com/profile/10198704789965278981noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-61755781387408806862021-03-12T11:51:39.466-05:002021-03-12T11:51:39.466-05:00Don, I'm not that kind of electrical engineer ...Don, I'm not that kind of electrical engineer and know little about power distribution. These days I work in electronic design automation.Joehttps://www.blogger.com/profile/10968310390394517323noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-17206887093877222062021-03-12T10:52:06.392-05:002021-03-12T10:52:06.392-05:00"When I said "nothingness is not nothing..."When I said "nothingness is not nothingness per se", I was harking back to Parmenides and what he had to say about it"<br />I wasn't objecting (or agreeing for that matter), just reflecting from the perspective of Buddhist knowledge. As far as I can remember, I enjoyed Parmenides (it was some unfinished text). And he approached the indication to 'unspeakable' Vadimhttps://www.blogger.com/profile/17350813784317789818noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-36576257094440522682021-03-12T09:21:38.122-05:002021-03-12T09:21:38.122-05:00@ Joe,
If you have time, I have a little off topic...@ Joe,<br />If you have time, I have a little off topic curiosity here. Do you know of any studies of micro-voltage variation in the power grid. Could not find anything. Wonder what the signal looks like.<br />Thanks Don Fosterhttps://www.blogger.com/profile/04814669413022486958noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-16529580505765570732021-03-12T07:23:14.762-05:002021-03-12T07:23:14.762-05:00Steven Evans,
Thanks for answering, I see my anal...Steven Evans, <br />Thanks for answering, I see my analogy wasn't adequate. I got distracted by pondering 'how are different sorts of numbers real', although it's apparent how they function to describe real and theoretical phenomena. <br />I'm slowly learning how mathematics are used in physics.C Thompsonhttps://www.blogger.com/profile/01723392308309671498noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-64508063345246437792021-03-12T05:29:39.796-05:002021-03-12T05:29:39.796-05:00@Steven Evans:
Ontology is difficult, even the no...@Steven Evans:<br /><br />Ontology is difficult, even the nominalist case leads us to such difficult questions as the set of all sets and the like. <br /><br />Given that people like Newton and Einstein thought philosophy as important, I take your dismissal of philosophy as similar to your dismissal of super-symmetry, and which has nothing to do with philosophy, and every thing to do with physicsMoziburhttps://www.blogger.com/profile/11836761141351221660noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-66000322961177977522021-03-12T03:01:39.000-05:002021-03-12T03:01:39.000-05:00The key term in this respect is isomorphism. If tw...The key term in this respect is isomorphism. If two mathematical structures are isomorphic, they are mathematically equivalent. One can use one or another without a difference in underlying mathematics.<br /><br />For example, matrices 2x2 made from real a and b as below will be mathematically equivalent to complex numbers a + ib.<br /><br />a b<br />-b aEvgenii Rudnyihttps://www.blogger.com/profile/01535547902638172794noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-24536357481287784632021-03-12T02:32:12.603-05:002021-03-12T02:32:12.603-05:00Mozibur10:17 PM, March 11, 2021
I was responding ...Mozibur10:17 PM, March 11, 2021<br /><br />I was responding to C. Thompson's bot remark.<br /><br />I don't think the ontology is difficult. The complex numbers are precisely defined. They are useful for describing aspects of the physical world. In the application described in the blog post, it turns out they may even be essential, relative to the real numbers at least.<br />There are Steven Evanshttps://www.blogger.com/profile/13898046706669437332noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-12144128607133840602021-03-11T22:36:31.430-05:002021-03-11T22:36:31.430-05:00>But we don't have to use them. In most cas...>But we don't have to use them. In most cases we could do the calculation with real numbers. It's just more cumbersome.<br /><br />Since nature doesn't appear to allow arbitrary precision, we could just as well dispense with the reals and calculate only with rationals. That would be even more cumbersome as well. Imagine trying to work with calculus with only the rationals. And whatMoziburhttps://www.blogger.com/profile/11836761141351221660noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-43554692443007268432021-03-11T22:17:42.912-05:002021-03-11T22:17:42.912-05:00@Steven Evans:
I'm not putting spirituality i...@Steven Evans:<br /><br />I'm not putting spirituality into the complex numbers, but simply pointing out that the ontology of abstract thongs, such as numbers and words is a difficult one. Plato, resolved this as step in his intellective dialectic towards the One. If you're not keen about Platonist philosophy, thats fine with me. Plenty of people have been. <br /><br />Even for Moziburhttps://www.blogger.com/profile/11836761141351221660noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-45214264626194163602021-03-11T22:11:24.488-05:002021-03-11T22:11:24.488-05:00@Vadim:
When I said "nothingness is not noth...@Vadim:<br /><br />When I said "nothingness is not nothingness per se", I was harking back to Parmenides and what he had to say about it, which was that it couldn't be thought because it couldn't be actually referred to. This isn't the nothing that Hegel refers to and which I said was comparable to the sunyata of Buddhism. <br /><br />It's got nothing to do with ascetismMoziburhttps://www.blogger.com/profile/11836761141351221660noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-91068056219196078362021-03-11T20:12:13.024-05:002021-03-11T20:12:13.024-05:00What do you mean "represent complex numbers b...What do you mean "represent complex numbers by structures made from real numbers"?David Marcushttps://www.blogger.com/profile/07084520656051241766noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-24747782665134503692021-03-11T15:55:56.753-05:002021-03-11T15:55:56.753-05:00Hi Terry, yes, I think they have them, I think the...Hi Terry, yes, I think they have them, I think there is no choice but to trial and error and how much fantasy and mathematical intuition and not to trust classical concepts including time and space. Thanks .Luishttps://www.blogger.com/profile/05491803947570764962noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-66485545686909791952021-03-11T15:47:45.360-05:002021-03-11T15:47:45.360-05:00A complex number is equivalent to a pair of real n...A complex number is equivalent to a pair of real numbers. Any equation involving complex numbers can be converted to pairs of equations involving pairs of real numbers. I'm an electrical engineer by training. Complex numbers are are at the heart of signal processing and communication theory. Filter design is based on the analysis of poles and zeros on the complex plane; the amplitude and Joehttps://www.blogger.com/profile/10968310390394517323noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-80489149349715362942021-03-11T14:32:26.030-05:002021-03-11T14:32:26.030-05:00Thank you, Terry. Yet, for model reduction you sho...Thank you, Terry. Yet, for model reduction you should thank mathematicians, I have just applied their algorithms to engineering problems.Evgenii Rudnyihttps://www.blogger.com/profile/01535547902638172794noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-84888674267540069802021-03-11T11:48:19.885-05:002021-03-11T11:48:19.885-05:00Physics undergraduate proposes solution to quantum...Physics undergraduate proposes solution to quantum field theory problem<br /><br />More information: Jiani Fei et al. Nevanlinna Analytical Continuation, Physical Review Letters (2021).<br /><br />DOI: 10.1103/PhysRevLett.126.056402<br /><br />In examining this problem, Fei realized that to accurately convert quantum mechanic theories from imaginary to real numbers, physicists needed a class of inMatrix.ruhttps://www.blogger.com/profile/13043825547072634468noreply@blogger.com