Minkowski Metric.
in [Relativity]
|
Prev: Infinite vs. instant
Next: It's a heatwave
From: Sue... on 25 May 2010 21:24 On May 25, 7:39 pm, eric gisse <jowr.pi.nos...(a)gmail.com> wrote: > ..@..(Henry Wilson DSc) wrote: > > I would like a relativist to explain why the distance term ct is imaginary > > in 4D 'spacetime'. > > It isn't. If you are hawking a book that smells a little like the book of Genesis to a Pope that isn't mixed up with little boys, a well placed blessing might make that sort of absurdity palatable to most of the flock. At the least it can ensure that book sales are not inhibited by religious dogma. But when the Pope is already has an ethical shadow over his credibility, members of the flock might be tempted to to test their catechism. If kneeling for 10 minutes of prayer does not produce the same results as a 10 minute stroll to the pub, then members of the flock might start to question the integrity of an embattled Father. There is a place for child molesters and a place for imaginary operators and little if any confidence that the present Pope can find those places. Sue.. > > Don't make stuff up, Ralph. > > > > > Does this imply that the whole theory is just a figment of Einstein's > > imagination? > > > Henry Wilson... > > > .......A relativist's IQ = his snipping ability. > >
From: Sue... on 26 May 2010 08:49 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 > > >> 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 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...
From: PD on 26 May 2010 12:04 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. 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. 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. 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." PD
From: Igor on 26 May 2010 13:35 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'. > > Does this imply that the whole theory is just a figment of Einstein's > imagination? > > Henry Wilson... > > .......A relativist's IQ = his snipping ability. And Mister Bullshit baits his hook once more...
From: Henry Wilson DSc on 26 May 2010 19:39
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..... Henry Wilson... ........A relativist's IQ = his snipping ability. |