Minkowski Metric.
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From: Sue... on 26 May 2010 20:57 On May 26, 7:44 pm, ..@..(Henry Wilson DSc) wrote: > On Wed, 26 May 2010 05:49:48 -0700 (PDT), "Sue..." <suzysewns...(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 rôle 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. Others have offered numerous examples in science and engineering that justifies complex numbers. The specific sign that you refer to is justified by the fact that rods are not really clocks even if we can sometimes use them that way. <<Note that space-time cannot be regarded as a straightforward generalization of Euclidian 3-space to four dimensions, with time as the fourth dimension. The distribution of signs in the metric ensures that the time coordinate $x^4$ is not on the same footing as the three space coordinates. Thus, space-time has a non-isotropic nature which is quite unlike Euclidian space, with its positive definite metric. According to the relativity principle, all physical laws are expressible as interrelationships between 4-tensors in space-time. >> http://farside.ph.utexas.edu/teaching/em/lectures/node113.html Sue... > > > > >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: eric gisse on 26 May 2010 20:58 ...@..(Henry Wilson DSc) wrote: [...] > How can the negative sign be justified? > Why isn't the metric just: s^2 = (vt)^2 + (ct)^2 ....because SR isn't Euclid. [...]
From: Henry Wilson DSc on 26 May 2010 21:52 On Wed, 26 May 2010 17:57:25 -0700 (PDT), "Sue..." <suzysewnshow(a)yahoo.com.au> wrote: >On May 26, 7:44�pm, ..@..(Henry Wilson DSc) wrote: >> On Wed, 26 May 2010 05:49:48 -0700 (PDT), "Sue..." <suzysewns...(a)yahoo.com.au> >> wrote: >> >> >> 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. > >Others have offered numerous examples in science >and engineering that justifies complex numbers. > >The specific sign that you refer to is justified >by the fact that rods are not really clocks >even if we can sometimes use them that way. The specific sign is negative simply because einstein said v can never exceed c. In other words the whole theory is circular. ><<Note that space-time cannot be regarded >as a straightforward generalization of >Euclidian 3-space to four dimensions, with >time as the fourth dimension. The distribution >of signs in the metric ensures that the >time coordinate $x^4$ is not on the same >footing as the three space coordinates. >Thus, space-time has a non-isotropic nature >which is quite unlike Euclidian space, with >its positive definite metric. According to >the relativity principle, all physical laws >are expressible as interrelationships >between 4-tensors in space-time. >> >http://farside.ph.utexas.edu/teaching/em/lectures/node113.html A length in 4D is just the vector sum of the squares. Time is not related to space in any way. >Sue... > Henry Wilson... ........A relativist's IQ = his snipping ability.
From: Henry Wilson DSc on 26 May 2010 21:52 On Wed, 26 May 2010 17:58:31 -0700, eric gisse <jowr.pi.nospam(a)gmail.com> wrote: >..@..(Henry Wilson DSc) wrote: > >[...] > >> How can the negative sign be justified? >> Why isn't the metric just: s^2 = (vt)^2 + (ct)^2 > >...because SR isn't Euclid. We know what SR is.....plain bullshit [......] >[...] Henry Wilson... ........A relativist's IQ = his snipping ability.
From: eric gisse on 26 May 2010 22:20
...@..(Henry Wilson DSc) wrote: > On Wed, 26 May 2010 17:58:31 -0700, eric gisse <jowr.pi.nospam(a)gmail.com> > wrote: > >>..@..(Henry Wilson DSc) wrote: >> >>[...] >> >>> How can the negative sign be justified? >>> Why isn't the metric just: s^2 = (vt)^2 + (ct)^2 >> >>...because SR isn't Euclid. > > We know what SR is.....plain bullshit Is there something about my answer that you did not understand? Why can't you discuss SR honestly without spazzing over it? You've spent ten years so far, calm the hell down and read a book about it. What do you have to lose? > > [......] > >>[...] > > > Henry Wilson... > > .......A relativist's IQ = his snipping ability. |