tag:blogger.com,1999:blog-22973357.post6731187369418702169..comments2023-09-27T07:44:19.769-04:00Comments on Sabine Hossenfelder: Backreaction: Understanding Quantum Mechanics #8: The Tunnel EffectSabine Hossenfelderhttp://www.blogger.com/profile/06151209308084588985noreply@blogger.comBlogger44125tag:blogger.com,1999:blog-22973357.post-66911109723744200362020-11-20T02:27:08.587-05:002020-11-20T02:27:08.587-05:00Hi Ajit,
Ok, thanks, I see now what you mean. I t...Hi Ajit,<br /><br />Ok, thanks, I see now what you mean. I thought you were talking about the tunneling part. Yes, I suspect that this comes from the boundary condition. You see, the boundary condition will try to push the value of the Gaussian down to zero somewhere off to the right, though actually it isn't zero. I guess I should have put the boundary farther away, but that'd have Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-21661627707557141102020-11-20T02:12:52.232-05:002020-11-20T02:12:52.232-05:00Oops. The left half is longer (~0.56), and the rig...Oops. The left half is longer (~0.56), and the right half is shorter (~0.44). --Ajit<br />Ajit R. Jadhavhttps://www.blogger.com/profile/02194541129055576042noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-73580783333879584662020-11-20T02:10:35.390-05:002020-11-20T02:10:35.390-05:00Hi Sabine,
Check out at 02.49 in the video. The p...Hi Sabine,<br /><br />Check out at 02.49 in the video. The peak is under your left palm. I took a screenshot and verified. While the absolute number of pixels would depend on the size of the window of the video when the screenshot was taken, it is clear that the x-axis extents of the left- and right halves of the profile, as measured at the bottom of the profile, are roughly in the 0.44 : 0.56 Ajit R. Jadhavhttps://www.blogger.com/profile/02194541129055576042noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-39403687704895072972020-11-20T00:42:14.313-05:002020-11-20T00:42:14.313-05:00Hi Ajit,
I am still not sure what asymmetry you m...Hi Ajit,<br /><br />I am still not sure what asymmetry you mean. Could you let me know what time in the video you are referring to so I can look into this? Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-41468561074953991072020-11-19T14:24:15.558-05:002020-11-19T14:24:15.558-05:00Sabine,
1. OK, I got it! I mean the travel to th...Sabine, <br /><br />1. OK, I got it! I mean the travel to the right. (Stupid me! Somehow, had got stuck in the special case of k_0 = 0 in my imagination, once I *began* with that case). <br /><br />2. Well, the profile in the video does seem to become asymmetric as it moves. Could be a numerical artifact, but guess it's best to leave the matter at that, because the overall picture *is* quiteAjit R. Jadhavhttps://www.blogger.com/profile/02194541129055576042noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-64923596902855512752020-11-19T13:55:39.810-05:002020-11-19T13:55:39.810-05:00Dr. Hossenfelder:
Is there some mass limit (or c...Dr. Hossenfelder: <br /><br />Is there some mass limit (or complexity limit) to tunneling? For example, can a water molecule tunnel through a physical barrier? Or is it impossible to make a physical barrier that thin?<br /><br />(I have long thought pancake syrup tunnels; I have no other explanation for how it can get everywhere.)Dr. A.M. Castaldohttps://www.blogger.com/profile/17988116835722393503noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-67480260665402399922020-11-19T12:51:28.956-05:002020-11-19T12:51:28.956-05:00My "code" isn't a code really, and i...My "code" isn't a code really, and it's in no condition to share. I'm not sure I understand your question, I just used the initial condition for a wave-packet with a non-vanishing momentum, that's why it travels to the right. I don't know why you think it's not symmetric. It should be. Maybe that's from the shading? The shading may not be symmetric. (It'sSabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-89108412810606132732020-11-19T12:21:12.524-05:002020-11-19T12:21:12.524-05:00Sabine,
Sorry to bother you again, but I've a...Sabine,<br /><br />Sorry to bother you again, but I've another question:<br /><br />If you didn't put infinite walls on the sides, then how come the peak ends up travelling in one direction (to the right)? <br /><br />...On second viewing of the video, looks like your wavefunction isn't symmetrical around the peak---it has a sharper drop on the right hand side. That can explain it.<brAjit R. Jadhavhttps://www.blogger.com/profile/02194541129055576042noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-15130716323997804722020-11-19T11:49:26.341-05:002020-11-19T11:49:26.341-05:00Hi Sabine,
1. Sure! Also see the PhET simulation....Hi Sabine,<br /><br />1. Sure! Also see the PhET simulation. You can try plane-waves in it.<br /><br />2. For pop-sci videos, the forward Euler is quite great! I vaguely recall that Chad Orzel used it for showing how precession (with nutation) arises, and Rhett Allain for demo'ing 3-body simulation, in their blog posts. <br /><br />(BTW, I always check out *others'* code first, before Ajit R. Jadhavhttps://www.blogger.com/profile/02194541129055576042noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-73923333321559908052020-11-19T10:38:32.395-05:002020-11-19T10:38:32.395-05:00I should think you have one or the other, graviton...I should think you have one or the other, gravitons or curvature; and the relationship between them is analogous to how the equations of fluid dynamics (e.g. Navier-Stokes and others) accurately describe the aggregate behavior of what are ultimately many trillions of discrete atoms; but (as we've seen even with QD) does not capture the behavior of individual particles.<br /><br />Meaning, Dr. A.M. Castaldohttps://www.blogger.com/profile/17988116835722393503noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-3684443265542311132020-11-19T10:28:35.134-05:002020-11-19T10:28:35.134-05:00Hi Ajit,
Thanks for pointing out, I hadn't se...Hi Ajit,<br /><br />Thanks for pointing out, I hadn't seen this app! I have really just dumbly forward integrated the Schr eq. Anything more sophisticated seemed to me an overkill given that I'd only need a few seconds of it. I did not put infinite walls on the side, and the Gaussian you see in my sim actually isn't exactly a Gaussian because it goes to zero at a point you can't Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-21763209787467415782020-11-19T10:14:43.733-05:002020-11-19T10:14:43.733-05:00To Engineers, i.e. people who know PDEs, the Fouri...To Engineers, i.e. people who know PDEs, the Fourier theory, and a bit about numerical solutions. I write this for you. (Sorry, laymen! I just don't know how to explain it *briefly* enough---and I have RSI.):<br /><br />See if this helps. (Sabine, could you please to chime in if I am describing it wrong somewhere.)<br /><br />---<br /><br />Explanatory Comments:<br /><br />A neat applet quiteAjit R. Jadhavhttps://www.blogger.com/profile/02194541129055576042noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-42915532899925140352020-11-19T08:37:52.433-05:002020-11-19T08:37:52.433-05:00Hi Dr A.M.,
Thanks, I appreciate the feedback! Fo...Hi Dr A.M.,<br /><br />Thanks, I appreciate the feedback! For some reason my own logic always sounds a lot clearer inside my head than it probably does to folks outside said head. (Anyone else ever feel that way?… :)<br /><br />>... Would you think that a non-zero probability of tunneling requires the leading edge of the wave packet to be on the other side of the barrier? (as opposed to withinTerry Bollingerhttps://www.blogger.com/profile/03915136249111338024noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-61858484137823199692020-11-18T10:18:29.254-05:002020-11-18T10:18:29.254-05:00Commonly tunnel effects are noticeable through dim...Commonly tunnel effects are noticeable through diminishing hustle and bustle.martenhttps://www.blogger.com/profile/02423871089614417690noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-76917194080242827862020-11-18T07:05:27.812-05:002020-11-18T07:05:27.812-05:00I have to wonder what happens to the portion of th...I have to wonder what happens to the portion of the wavefuction that was associated with the tunneled particle, but is reflected at the barrier and doesn’t continue with the particle? This, I imagine, impinges on the old debate whether the wavefunction is something real, or is just knowledge of the observer. My understanding is that the Copenhagen interpretation would fit in the latter categoryDavid Schroederhttps://www.blogger.com/profile/18048116250413347228noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-854241851332760272020-11-17T12:40:06.641-05:002020-11-17T12:40:06.641-05:00The tunnel effect can also be understood by the pa...The tunnel effect can also be understood by the particle model of Louis de Broglie; which means in a more classical way which is helpful for imagination and avoids much of the weirdness of QM.<br /><br />A potential wall in this context is realized by a field which repels the charges of the particle trying to pass. These field forces build the potential wall which the particle has to pass. This antooneohttps://www.blogger.com/profile/12559038212417783694noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-66806461381710834612020-11-17T08:14:27.710-05:002020-11-17T08:14:27.710-05:00John,
The potential of the barrier is an average ...John,<br /><br />The potential of the barrier is an average one. You do not actually know what was the potential at the exact time and place the particle was there. It might be the case it was low enough so that no violation of energy conservation is required.Andreihttps://www.blogger.com/profile/05519448415253342448noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1956247960197079112020-11-16T13:15:19.625-05:002020-11-16T13:15:19.625-05:00Referring to the last part of your video, I notice...Referring to the last part of your video, I noticed how the 2007 conjectures of Günter Nimtz - the superluminal tunneling of information and the violation of Special Relativity - can be debunked with a single stroke. kudos!rhkailhttps://www.blogger.com/profile/08396062602672163235noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-35294589601872635232020-11-16T11:17:36.970-05:002020-11-16T11:17:36.970-05:00Terry Bollinger: Wow, thanks, that is enlightening...Terry Bollinger: Wow, thanks, that is enlightening.<br /><br />If all that happened is the barrier introduced some skew in a non-infinite distribution and the leading edges are still the same, then I still see no reason for FTL angst. I'd expect the barrier to change the distribution somehow.<br /><br />I suppose there is some mystery, which might be resolved just by the math, as to why the Dr. A.M. Castaldohttps://www.blogger.com/profile/17988116835722393503noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-3880734951917553862020-11-16T08:54:16.432-05:002020-11-16T08:54:16.432-05:00As someone with an understanding of physics limite...As someone with an understanding of physics limited by not having the math involved, I still found this to be a very clarifying description of tunneling. Thanks, Dr. Hossenfelder!Friarhttps://www.blogger.com/profile/16907204457371629428noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-84001262226495490022020-11-16T04:27:49.872-05:002020-11-16T04:27:49.872-05:00Mathematically, Schrödinger's equation is akin...Mathematically, Schrödinger's equation is akin to a diffusion equation, and inaccurate in the context discussed here. A relativistic equation (Klein-Gordon or Dirac) should be used. The solutions could then actually have sharp edges instead of long tail precursors.<br /><br />Incidentally, the tunnel effect in the case of photons is adequately described by classical optics ("evanescentWernerhttps://www.blogger.com/profile/08502954437062856468noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-54790446321104139412020-11-15T17:14:21.775-05:002020-11-15T17:14:21.775-05:00>… How is a rubidium atom "classically vis...>… How is a rubidium atom "classically visible", and even if it were, isn't that measuring its position and therefore invalidating the experiment?<br /><br />It’s classically visible because it’s <i>inside</i> the apparatus. It’s hard to play with rubidium atoms that aren’t there! The game in experiments like this is that you let the location of the rubidium atom wave function Terry Bollingerhttps://www.blogger.com/profile/03915136249111338024noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-23623234355822836912020-11-15T17:06:21.126-05:002020-11-15T17:06:21.126-05:00Hi Dr A.M., nice to hear from you and I hope you a...Hi Dr A.M., nice to hear from you and I hope you are well!<br /><br />An answer in two parts:<br /><br />>… I thought the wave packet of a particle with indefinite position, as shown in the video, was a distribution with infinite tails.<br /><br />No. To be precise, such wave functions cannot even exist in the real universe. That’s because they would require infinite time and space to form Terry Bollingerhttps://www.blogger.com/profile/03915136249111338024noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-14335729405754618052020-11-15T12:22:14.196-05:002020-11-15T12:22:14.196-05:00“Thus in the scenario of "blasting tons of pa...“Thus in the scenario of "blasting tons of particles", I could theoretically associate different atomic elements with different answers, blast a ton of a particular kind of atom at the barrier, some which traverse it superluminally, and the receiver knows the intended message based upon the kind of atom received.”<br /><br />“That message could reasonably consist of 3 or 4 bits of David Schroederhttps://www.blogger.com/profile/18048116250413347228noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-89406475133626167972020-11-15T11:36:50.391-05:002020-11-15T11:36:50.391-05:00Sabine, thanks, I didn't make that connection....Sabine, thanks, I didn't make that connection.David Schroederhttps://www.blogger.com/profile/18048116250413347228noreply@blogger.com