Minkowski Metric.
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From: Henry Wilson DSc on 26 May 2010 19:44 On Wed, 26 May 2010 05:49:48 -0700 (PDT), "Sue..." <suzysewnshow(a)yahoo.com.au> wrote: >On May 26, 4:27�am, ..@..(Henry Wilson DSc) wrote: >> On Wed, 26 May 2010 10:55:08 +1000, "whoever" <whoe...(a)whereever.com> wrote: >> >"Sue..." <suzysewns...(a)yahoo.com.au> wrote in message >> >news:5f53e198-d84d-4446-9a4e-24f643898e6c(a)j27g2000vbp.googlegroups.com... >> >> On May 25, 6:09 pm, ..@..(Henry Wilson DSc) wrote: >> >>> I would like a relativist to explain why the distance term ct is >> >>> imaginary in >> >>> 4D 'spacetime'. >> >> >> I am a just a Methodist and only for six days out of the >> >> week but I will try to answer your question. >> >> >> I say it is 1 hour to Paris. >> >> You say it is 1 kilometre to Paris. >> >> >> We are both correct if we are in a Renault moving >> >> toward Paris at 1 kilometre per hour. >> >> >> Do our statements imply that time and space are interchangeable? >> >> Of course not. They imply that we are in a Renault moving >> >> toward Paris at 1 kilometre per hour. >> >> >> The imaginary operator allows us to work with our >> >> motion graphically while preserving the difference >> >> in temporal and spatial displacement. >> >http://en.wikipedia.org/wiki/Complex_number >> >> >> << the four-dimensional space-time continuum of the >> >> theory of relativity, in its most essential formal >> >> properties, shows a pronounced relationship to the >> >> three-dimensional continuum of Euclidean geometrical space. >> >> In order to give due prominence to this relationship, >> >> however, we must replace the usual time co-ordinate t by >> >> an imaginary magnitude >> >> >> � sqrt(-1) >> >> >> ct proportional to it. Under these conditions, the >> >> natural laws satisfying the demands of the (special) >> >> theory of relativity assume mathematical forms, in which >> >> the time co-ordinate plays exactly the same r�le as >> >> the three space co-ordinates. >> >http://www.bartleby.com/173/17.html >> >> >> That says little more than 'nature pays no attention to >> >> our cleaver grid systems and they better have a way to keep >> >> space and time separated or they will break down.' >> >> >>> Does this imply that the whole theory is just a figment of Einstein's >> >>> imagination? >> >> >> It is just as imaginary as the capacitor banks that reduce >> >> the losses in transmitting power to your home. If you think it >> >> isn't "real" just make your house look more reactive and >> >> read the results on your power bill. >> >http://en.wikipedia.org/wiki/Reactive_power#Real.2C_reactive.2C_and_a... > >http://www.energytechpro.com/Demo-IC/Basic_Electricity/Distribution.htm I know all about complex numbers and AC theory. Now answer the question. How can the negative sign be justified? Why isn't the metric just: s^2 = (vt)^2 + (ct)^2 >> >> Sue... >> >> >As a nice change, you've managed to post a relevant link and say something >> >sensible. � >> >> She �didn't. >> She never does. > >Nine out ten ostriches that can write >'irrelevant to my delusions' >will surely vouch for that. > > >> >> If vt is less than ct, as SR says it must be, then s is imaginary. Why? How? > >Motoring along in your cabriolet it makes no difference >whether you say: > >Clocks are imaginary rods. > > or > >Rods are imaginary clocks. > ><< if you know about complex numbers you will notice that >the space part enters as if it were imaginary > >R2 = (ct)2 + (ix)2 + (iy)2 + (iz)2 = (ct)2 + (ir)2 > >where i^2 = -1 as usual. This turns out to be the essence >of the fabric (or metric) of spacetime geometry - that >space enters in with the imaginary factor i relative to >time. >> >http://www.aoc.nrao.edu/~smyers/courses/astro12/speedoflight.html Yes we know that. I'm asking someone to justify it. >But you can't say clocks and rods are *really* >the same because: > ><< * the invariance of physical systems with respect > to spatial translation (in other words, that the laws > of physics do not vary with locations in space) gives > the law of conservation of linear momentum; > * invariance with respect to rotation gives the law > of conservation of angular momentum; > * invariance with respect to time translation gives > the well-known law of conservation of energy >> >http://en.wikipedia.org/wiki/Noether%27s_theorem#Applications > > >Sue... > > Henry Wilson... ........A relativist's IQ = his snipping ability.
From: Henry Wilson DSc on 26 May 2010 19:54 On Wed, 26 May 2010 09:04:22 -0700 (PDT), PD <thedraperfamily(a)gmail.com> wrote: >On May 25, 5:09�pm, ..@..(Henry Wilson DSc) wrote: >> I would like a relativist to explain why the distance term ct is imaginary in >> 4D 'spacetime'. >> >> Does this imply that the whole theory is just a figment of Einstein's >> imagination? � >> > >A couple of comments. >1. It isn't a distance term. It's the time component, converted into >units meters with the conversion factor c. It is the distance a ray of light moves wrt its source in time t. >2. It *isn't* an imaginary number in 4D spacetime. In spacetime with >metric signature +--- or -+++, all the components are real numbers (in >the mathematical sense of "real number", not your bonehead >misconstrual). There is a way to make the spacetime signature LOOK >Cartesian (that is, with signature ++++ ) by using an imaginary number >for the time component, but it certainly isn't native to spacetime's >geometry. What justification is there in subtracting the distance light move in time t from the distance an object moves? That's what this is all about. I cannot see any physical connection. >3. An imaginary number is not a fictitious number, contrary to your >bonehead misconstrual. Imaginary and real numbers are classes of >numbers, both of which are commonly instantiated in real life. >Electrical engineers, for example, use designs calculated with >imaginary numbers all the time, and the devices built per those >designs work very well, thank you. I am very familiar with AC theory. It has nothing whatsoever to do with this. >This should be the point where you get embarrassed and say to >yourself, "Well, perhaps I should read something, on the off chance >that it will at least slow me from saying something equally boneheaded >tomorrow." I have yet to find any justification for the minus sign in the metric. Obviously I am wasting my time asking anyone here for a reason. >PD Henry Wilson... ........A relativist's IQ = his snipping ability.
From: whoever on 26 May 2010 20:08 "Henry Wilson DSc" <..@..> wrote in message news:89crv5psf93t3687iif8c44treu8d3kc86(a)4ax.com... > On Wed, 26 May 2010 02:39:04 -0700, eric gisse <jowr.pi.nospam(a)gmail.com> > wrote: > >>..@..(Henry Wilson DSc) wrote: >> >>[...] >> >>> If vt is less than ct, as SR says it must be, then s is imaginary. Why? >>> How? >> >>Now tell us what 's' is and why this matters. > > Oh sorry, I thought you knew something about this subject..... So .. you tell us what YOU think 's' means, and why YOU think it matters. Or don't you know what you think? --- news://freenews.netfront.net/ - complaints: news(a)netfront.net ---
From: eric gisse on 26 May 2010 20:34 ...@..(Henry Wilson DSc) wrote: > On Wed, 26 May 2010 02:39:04 -0700, eric gisse <jowr.pi.nospam(a)gmail.com> > wrote: > >>..@..(Henry Wilson DSc) wrote: >> >>[...] >> >>> If vt is less than ct, as SR says it must be, then s is imaginary. Why? >>> How? >> >>Now tell us what 's' is and why this matters. > > Oh sorry, I thought you knew something about this subject..... I want to hear you explain it in your own words without having someone explain it to you first. Can you do that? > > > Henry Wilson... > > .......A relativist's IQ = his snipping ability.
From: eric gisse on 26 May 2010 20:54
...@..(Henry Wilson DSc) wrote: [...] > I have yet to find any justification for the minus sign in the metric. Since you can't even comprehend Einstein's 1905 paper, what's the significance of you not understanding its' geometric formulation? > Obviously I am wasting my time asking anyone here for a reason. Obviously. But you've invested ten years of time into asking this newsgroup to teach you, so why stop now? > >>PD > > > Henry Wilson... > > .......A relativist's IQ = his snipping ability. |