tag:blogger.com,1999:blog-5376628436133716219.post813746856181075300..comments2021-08-24T18:39:54.377-07:00Comments on Why I hate physics: Group Velocity vs Phase VelocityMarty Greenhttp://www.blogger.com/profile/17624084719249673373noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-5376628436133716219.post-84912789631404194962017-07-20T07:53:43.904-07:002017-07-20T07:53:43.904-07:00But it's the principle of stationary action, n...But it's the principle of stationary action, not necessarily least action. If you look at the trajectories which bend upwards, it's clear that a slight variation upwards will increase the action (faster and further) while a slight variation downwards will decrease the action (slower and closer). The action is not stationary.<br />Now if you do the same for a trajectory which bends downwards, the variation upwards will not change the action (more velocity compensates for less distance) and neither will a variation downwards (less velocity but more distance). So in this case the amplitudes of the nearby trajectories interfere constructively and that's what we will observe.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5376628436133716219.post-90692287291733207682013-05-14T05:44:04.095-07:002013-05-14T05:44:04.095-07:00I'm not sure I like the way I phrased that pas...I'm not sure I like the way I phrased that passage. If I leave out the phrase "...k=1, and then...", the offending phrase becomes "we can arbitrarily choose our units so the proportionality becomes exact". I think that's OK. The reason for the relation between w and k is that w (frequency) is proportional to energy, and k (wave number) is proportional to momentum. And energy is proportional to the square of momentum.Marty Greenhttps://www.blogger.com/profile/17624084719249673373noreply@blogger.comtag:blogger.com,1999:blog-5376628436133716219.post-83898869555649816342013-05-13T16:58:38.620-07:002013-05-13T16:58:38.620-07:00In your blog, you have an equation exp{j(kx-wt)}. ...In your blog, you have an equation exp{j(kx-wt)}. Then you went on to choose k = 1. So if you chose k = 1, then what's the meaning of the following equation where there magically appears w = k^2? That is, if you already chose k = 1, then how does that lead to the equation w = k^2?Kenny Lnoreply@blogger.comtag:blogger.com,1999:blog-5376628436133716219.post-16612913841666294522013-01-13T07:10:48.947-08:002013-01-13T07:10:48.947-08:00I'm glad you enjoyed the article, but I don...I'm glad you enjoyed the article, but I don't feel worthy of the praise you've given me. I'm going to assume you meant to say the concept of "group velocity" has become more clear, because "phase velocity" is the obvious thing. It's true that I introduced the not-so-obvious equation for group velocity, but then I proceeded to use that equation in a very mechanical way. I don't feel I explained why it worked. I might take that up on another day if I can think of a good way of explaining it. But this example definitely shows why it's something we have to be concerned about.Marty Greenhttps://www.blogger.com/profile/17624084719249673373noreply@blogger.comtag:blogger.com,1999:blog-5376628436133716219.post-50252569892018823112013-01-13T06:03:11.506-08:002013-01-13T06:03:11.506-08:00thanks for this article. the concept of phase velo...thanks for this article. the concept of phase velocity has now become more clearphysicshttp://physics-ref.blogspot.com/noreply@blogger.com