tag:blogger.com,1999:blog-8883034.post1670922732793875788..comments2024-01-27T12:50:11.862+01:00Comments on atdotde: Causality issuesRoberthttp://www.blogger.com/profile/06634377111195468947noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-8883034.post-6797455898972387292007-10-30T10:29:00.000+01:002007-10-30T10:29:00.000+01:00John,thanks for your explanation. Since I wrote th...John,<BR/><BR/>thanks for your explanation. Since I wrote this post I also heard the claim that it's the high frequency limit of the group velocity which determines the propagation velocity (with the hand-waving argument that it's the infinite frequency part of a step that one uses to send the information). <BR/><BR/>Well, I should better have a look at the book you recommend. What do you say about causality in these k-essence type models? At least if you have two such scalar fields (with different background solutions) this should lead to causality violation. <BR/><BR/>There is also another paper: <BR/> k-Essence, superluminal propagation, causality and emergent geometry.<BR/>Eugeny Babichev (Gran Sasso & Moscow, INR) , Viatcheslav Mukhanov, Alexander Vikman (ASC, Munich & Munich U.) . LMU-ASC-54-07, Aug 2007. 34pp.<BR/>e-Print: arXiv:0708.0561 [hep-th]Roberthttps://www.blogger.com/profile/06634377111195468947noreply@blogger.comtag:blogger.com,1999:blog-8883034.post-77011304534796611322007-10-30T05:29:00.000+01:002007-10-30T05:29:00.000+01:00Actually, the technical term I should have used wa...Actually, the technical term I should have used was not "signal velocity" but "propagation velocity".John Baezhttps://www.blogger.com/profile/11573268162105600948noreply@blogger.comtag:blogger.com,1999:blog-8883034.post-71297890087174281522007-10-30T05:27:00.000+01:002007-10-30T05:27:00.000+01:00It's actually neither the wave nor the group veloc...It's actually neither the wave nor the group velocity that determines the speed at which signals can be sent! This is an <A HREF="http://groups.google.com/group/sci.physics.research/msg/d177e43f1d9cc98c?dmode=source" REL="nofollow">old chestnut</A>. Superluminal group velocities do occur in media with "anomalous dispersion"... but, <A HREF="http://www.nature.com/nature/journal/v406/n6793/full/406243a0.html" REL="nofollow">despite misguided worries</A>, what really matters is yet a third velocity: the <A HREF="http://www.mathpages.com/home/kmath210/kmath210.htm" REL="nofollow">signal velocity</A>. <BR/><BR/>The best book on this stuff is Leon Brilloin's <I>Wave Propagation and Group Velocity</I>, Academic Press, 1960. He worked it all out very nicely. It's a really fun book.<BR/><BR/>In particular, tachyons have signal velocity equal to c.<BR/><BR/>(By the way, you got some spam in your comments here.)John Baezhttps://www.blogger.com/profile/11573268162105600948noreply@blogger.comtag:blogger.com,1999:blog-8883034.post-14126305163782020742007-04-11T05:27:00.000+02:002007-04-11T05:27:00.000+02:00Hey, there is something even cooler to think about...Hey, there is something even cooler to think about. For instance, the tachyonic mode (hint) in the KG equation. Check out Coleman lectures on Acausality, they are awesome, unfortunately I couldnt find them on the web. <BR/><BR/>If we have the wrong sign for the mass in the KG Lagrangian we will get causality from the fact that the kinetic piece didnt change (flipping the mass sign of hte mass term) and the characteristic surfaces are thus the same. Nevertheless, the theory is acausal from the simple observation that the group velocity is larger than 1.<BR/><BR/>Why isnt this a contradiction??? ;)Anonymousnoreply@blogger.com