On Tuesday, January 15, 2019 at 12:10:23 AM UTC, Philip Thrift wrote: > > > > On Monday, January 14, 2019 at 5:52:39 PM UTC-6, agrays...@gmail.com > wrote: >> >> >> >> On Monday, January 14, 2019 at 11:41:15 PM UTC, Philip Thrift wrote: >>> >>> >>> >>> On Monday, January 14, 2019 at 4:58:52 PM UTC-6, agrays...@gmail.com >>> wrote: >>>> >>>> >>>> >>>> On Monday, January 14, 2019 at 10:27:19 AM UTC, Philip Thrift wrote: >>>>> >>>>> >>>>> >>>>> On Monday, January 14, 2019 at 2:53:53 AM UTC-6, agrays...@gmail.com >>>>> wrote: >>>>>> >>>>>> >>>>>> >>>>>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote: >>>>>>> >>>>>>> >>>>>>> >>>>>>> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote: >>>>>>> >>>>>>> This means, to me, that the arbitrary phase angles have absolutely >>>>>>> no effect on the resultant interference pattern which is observed. But >>>>>>> isn't this what the phase angles are supposed to effect? AG >>>>>>> >>>>>>> >>>>>>> The screen pattern is determined by *relative phase angles for the >>>>>>> different paths that reach the same point on the screen*. The >>>>>>> relative angles only depend on different path lengths, so the overall >>>>>>> phase >>>>>>> angle is irrelevant. >>>>>>> >>>>>>> Brent >>>>>>> >>>>>> >>>>>> The Stackexchange links affirm the existence of interference for >>>>>> *relative* phase angles, but say nothing about different path >>>>>> lengths, which is the way I've previously thought of interference. So I >>>>>> remain confused on the subject of quantum interference and its relation >>>>>> to >>>>>> relative phase angles. AG >>>>>> >>>>> >>>>> >>>>> Each path going to screen has a UCN* (unit complex number). For screen >>>>> locations that get their paths with UCNs that are in the same general >>>>> direction (as a vector in the complex plane, angle or phase), the sum of >>>>> those UCNs will be a complex number with a big length. For other screen >>>>> locations, the path UCNs when summed will cancel each other out. Hence >>>>> the >>>>> light and dark lines on the screen. >>>>> >>>>> * UCN: unit complex numbers [ >>>>> https://en.wikipedia.org/wiki/Circle_group ] >>>>> >>>>> "In mathematics, the circle group, denoted by T, is the multiplicative >>>>> group of all complex numbers with absolute value 1, that is, the unit >>>>> circle in the complex plane or simply the unit complex numbers." >>>>> >>>>> - pt >>>>> >>>> >>>> Thanks, but I don't think you understand the issue I raised. I >>>> discussed two ways to apply relative phases, which results in different >>>> probabilities. AG >>>> >>> >>> I don't how "relative" helps with anything, but a phase is what it is: >>> >>> A physical basis for the phase in Feynman path integration >>> >>> https://arxiv.org/abs/quant-ph/0411005 >>> >>> - pt >>> >> >> The Stackexchange links illustrate global vs relative phases. AG >> > > I don't have any more to add, but relative phases are covered in an > introduction to the PI. > > Path Integral Methods and Applications > > https://arxiv.org/abs/quant-ph/0004090 > > These lectures are intended as an introduction to the technique of path > integrals and their applications in physics. > > - pt >

The inconsistency, if it exists, occurs in Wave Mechanics, not PI formulation. AG > >>> >> -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.