tag:blogger.com,1999:blog-13869903.post3163322626285398521..comments2021-05-08T11:27:06.192-05:00Comments on nanoscale views: SuperluminalityDouglas Natelsonhttp://www.blogger.com/profile/13340091255404229559noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-13869903.post-1566111843061704402007-08-28T21:01:00.000-05:002007-08-28T21:01:00.000-05:00Peter - The problem I have with your wording is th...Peter - The problem I have with your wording is that it implies that infinite bandwidth is required to send information. I'm pretty sure my phone line does not pass arbitrarily high frequency components. So, how does a signal with some kind of nonanalyticity pass through a finite bandwidth signal channel?Douglas Natelsonhttps://www.blogger.com/profile/13340091255404229559noreply@blogger.comtag:blogger.com,1999:blog-13869903.post-18385868689692373382007-08-26T20:48:00.000-05:002007-08-26T20:48:00.000-05:00Well, to be precise, there's no such thing as a si...Well, to be precise, there's no such thing as a signal that is ideally discontinuous. After all, there is <I>always</I> a finite rise time for any signal. A more precise statement of your realization is that every signal must occupy a finite (i.e., non-vanishing) bandwidth. In which case, the ratio of the bandwidth of the signal to the height of the potential barrier becomes relevant. And, indeed, this ratio need not be larger (or smaller) than unity, for real-world signals. But it cannot be zero, or infinite. I mean, on the face of it, it is clearly not true that all signals must contain arbitrarily high frequency components.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-13869903.post-79586746247437355162007-08-17T10:56:00.000-05:002007-08-17T10:56:00.000-05:00This subject is VERY interesting. It is remarkabl...This subject is VERY interesting. It is remarkable that the problem can be stated so simply, but still stump anyone from advanced undergraduate students to full professor.<BR/><BR/>Technically it is not even a quantum mechanics problem as identical issues can arise in EM transmission through undersized waveguides.<BR/><BR/>I made my own peace with the whole issue of superluminality and signaling etc. when realizing that "a signal" must constitute a difference from some background level and must also be something discontinuous in the time domain. A signal that isn't somehow discontinuous in time, isn't a signal at all. Discontinuity in the time domain means it is composed of arbitrarily high frequencies in the Fourier domain. These high frequencies, being arbitrarily high, are always above the barrier height, or cutoff frequency and so they propagate with c or the free particle velocity.Anonymousnoreply@blogger.com