Question on Spacetime dilation.
in [Relativity]
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From: Ken S. Tucker on 17 Dec 2008 07:27 Hi XXein .... On Dec 16, 4:44 pm, xxein <xxe...(a)bellsouth.net> wrote: > xxein: Before I address you I must give kudos to Harry. Better check with Harry's wife. > Ken. Why do you screw around with math instead of physical logic? Because when I'm ordered by law to fill out my tax return, I need to know arithmetic, the tax man may accept Zen if I take a perpuatual oath of poverty, which is close! .... > I try to remain your friend. Of course you are. Ken S. Tucker
From: harry on 17 Dec 2008 07:56 "Ken S. Tucker" <dynamics(a)vianet.on.ca> wrote in message news:a588e951-6110-47ba-949f-ba5a9006f6b7(a)i18g2000prf.googlegroups.com... > Hi Harald. > > On Dec 17, 12:44 am, "harry" <harald.NOTTHISvanlin...(a)epfl.ch> wrote: >> "Ken S. Tucker" <dynam...(a)vianet.on.ca> wrote in >> messagenews:f747df81-0ff7-4b0d-9a2c-4688eae724de(a)c36g2000prc.googlegroups.com... >> >> > Hi Harald. >> >> > On Dec 16, 12:52 pm, "harry" <harald.vanlintelButNotT...(a)epfl.ch> >> > wrote: >> >> Just a little comment on the title! >> >> "Spacetime" doesn't dilate (except perhaps in cosmology - but I doubt >> >> that >> >> that is what you meant). >> >> > The quantity "ds" is often called the "spacetime >> > interval". >> >> Such an interval is a number, corresponding to a measurement of distances >> and durations. >> >> > I'm hoping to see how others (you too) >> > would solve the problem I posted. >> >> Sorry I can't help you with GRT (or maybe I could, but I'm really not >> skilled in GRT - definitely not in GRT notations). >> >> > What I want to do is draw the 4 differentials >> > (dx^0, dx_0, dx_1, dx^1) on a 0,1 diagram with >> > ds as well. >> >> >> At increased speed, clock frequency decreases ("time dilation") and >> >> lengths >> >> of objects (but NOT widths) shrink. And of course, all such >> >> measurements >> >> are >> >> "relative". >> >> > Can that be diagrammed? >> >> Well yes - the effects are illustrated in standard (SRT) space-time >> diagrams >> (but for sure you know that, thus I'm not sure what you really mean). >> These >> picture the (stress free*) length of moving objects as measured with >> standard rulers, as well as time intervals on moving clocks as measured >> with >> standard clocks. See for example the diagrams here*: >> http://en.wikipedia.org/wiki/Minkowski_diagram#Time_dilation > > From that ref, is this figure, > http://en.wikipedia.org/wiki/File:Minkowski_diagram_-_constancy_of_the_speed_of_light.png > that shows evidence of nonorthogonality and a break-out to covariant and > contravariant > projections. I'm still not too sure what you mean. Perhaps the presentation? There are roughly two ways of drawing such diagrams; just keep in mind that it's never more than a graphic representation of the math related to measurements. - One presentation, as in that article, is symmetrical at the price of all non-orthogonal axes - One is asymmetrical but the reference axes are orthogonal. The (older) presentation and a discussion of both is given in the paragraph just above Time dilation (Minkowski diagram in special relativity): "For the graphical translation it has been taken into account that the scales on the inclined axes are different from the Newtonian case described above. To avoid this problem it is recommended that the whole diagram be deformed in such a way that the scales become identical for all axes, eliminating any need to stretch or compress either axis." >> *Note: quite some misunderstanding occurs due to poor phrasings such as >> in >> the above article that says that "the space itself is contracted", and >> Bell >> corrected that with his spaceship >> example:http://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox >> Harald > > Thanks for the ref's. > Seasons Greetings Happy holidays, Harald
From: Alen on 17 Dec 2008 08:29 On Dec 17, 2:43 pm, Eric Gisse <jowr...(a)gmail.com> wrote: > On Dec 16, 6:23 pm, Alen <al...(a)westserv.net.au> wrote: > > > On Dec 17, 6:57 am, "Ken S. Tucker" <dynam...(a)vianet.on.ca> wrote: > > > > A clock (in K) moving at 0.8c (relative to K') is > > > dilated 0.6 by t' = t*sqrt(1 - v^2/c^2), so that > > > t'=(0.6)*t. > > > > In GR that is generalized to be, > > > > ds^2 =g_uv dx^u dx^v , {u,v=0,1,2,3}, > > > > and then by association equatable to > > > > = dx_u dx^u , > > > > = dx_0 dx^0 + dx_i dx^i , {i=1,2,3} , Eq.(1). > > > > I expect I should then obtain, > > > > dt' = ds = (0.6) dt, Eq.(2). > > > > What differential coefficients should be subbed > > > into Eq.(1) to yield Eq.(2)? > > > > TIA > > > Regards > > > Ken S. Tucker > > > c^2dt'^2 = c^2dt^2 -dx^2 -dy^2 -dz^2 > > = c^2dt^2 -ds^2 > > = c^2dt^2(1 - v^2/c^2) > > so > > dt' = (1/g)dt, where g = 1/sqrt(1 - v^2/c^2) > > > I say, of course, that these are time dilation > > equations only, and that the first equation has > > been misinterpreted as a metric equation for > > 100 years now! > > Except it is a metric equation, regardless of your ability to > understand. Won't you lot be surprised when you all have to eventually face the prospect that it might not be a metric equation after all!! It is certainly a wonderful metric, enthralling and magical, almost, since it produces such a vast arsenal of replies against anyone who might think to doubt it. It has captivated the minds of the most eminent physicists for an entire century. It might possibly turn out to have been the most fertile falsehood science has ever produced. Alen
From: Ken S. Tucker on 17 Dec 2008 11:50 Hi Harald On Dec 17, 4:56 am, "harry" <harald.NOTTHISvanlin...(a)epfl.ch> wrote: > "Ken S. Tucker" <dynam...(a)vianet.on.ca> wrote in messagenews:a588e951-6110-47ba-949f-ba5a9006f6b7(a)i18g2000prf.googlegroups.com... > > On Dec 17, 12:44 am, "harry" <harald.NOTTHISvanlin...(a)epfl.ch> wrote: > >> "Ken S. Tucker" <dynam...(a)vianet.on.ca> wrote in > >> messagenews:f747df81-0ff7-4b0d-9a2c-4688eae724de(a)c36g2000prc.googlegroups.com... > > >> > On Dec 16, 12:52 pm, "harry" <harald.vanlintelButNotT...(a)epfl.ch> > >> > wrote: > >> >> Just a little comment on the title! > >> >> "Spacetime" doesn't dilate (except perhaps in cosmology - but I doubt > >> >> that > >> >> that is what you meant). > > >> > The quantity "ds" is often called the "spacetime > >> > interval". > > >> Such an interval is a number, corresponding to a measurement of distances > >> and durations. > > >> > I'm hoping to see how others (you too) > >> > would solve the problem I posted. > > >> Sorry I can't help you with GRT (or maybe I could, but I'm really not > >> skilled in GRT - definitely not in GRT notations). > > >> > What I want to do is draw the 4 differentials > >> > (dx^0, dx_0, dx_1, dx^1) on a 0,1 diagram with > >> > ds as well. > > >> >> At increased speed, clock frequency decreases ("time dilation") and > >> >> lengths > >> >> of objects (but NOT widths) shrink. And of course, all such > >> >> measurements > >> >> are > >> >> "relative". > > >> > Can that be diagrammed? > > >> Well yes - the effects are illustrated in standard (SRT) space-time > >> diagrams > >> (but for sure you know that, thus I'm not sure what you really mean). > >> These > >> picture the (stress free*) length of moving objects as measured with > >> standard rulers, as well as time intervals on moving clocks as measured > >> with > >> standard clocks. See for example the diagrams here*: > >>http://en.wikipedia.org/wiki/Minkowski_diagram#Time_dilation > > > From that ref, is this figure, > >http://en.wikipedia.org/wiki/File:Minkowski_diagram_-_constancy_of_th... > > that shows evidence of nonorthogonality and a break-out to covariant and > > contravariant > > projections. > > I'm still not too sure what you mean. Perhaps the presentation? There are > roughly two ways of drawing such diagrams; just keep in mind that it's never > more than a graphic representation of the math related to measurements. > - One presentation, as in that article, is symmetrical at the price of all > non-orthogonal axes > - One is asymmetrical but the reference axes are orthogonal. Yes, one can convert imaginary to nonorthogonal. > The (older) presentation and a discussion of both is given in the paragraph > just above Time dilation (Minkowski diagram in special relativity): > "For the graphical translation it has been taken into account that the > scales on the inclined axes are different from the Newtonian case described > above. To avoid this problem it is recommended that the whole diagram be > deformed in such a way that the scales become identical for all axes, > eliminating any need to stretch or compress either axis." Understood. > >> *Note: quite some misunderstanding occurs due to poor phrasings such as > >> in > >> the above article that says that "the space itself is contracted", and > >> Bell > >> corrected that with his spaceship > >> example:http://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox > >> Harald > > > Thanks for the ref's. > > Seasons Greetings > > Happy holidays, > Harald Well, for now I'm leaning toward unmoderated forums. I see your posts in SPF are being rejected because you may have said something that CF finds threatening to his "teleconnection" theory, I see SPF going down the tubes, because CF dominates all the other moderators, and has a serious rake (up his ...) and agenda. Oh well, SPF was experimental. Regards Ken S. Tucker
From: harry on 17 Dec 2008 12:13
Hi Ken, "Ken S. Tucker" <dynamics(a)vianet.on.ca> wrote in message news:a9fd67c3-1282-4478-aca0-48bfa1fef236(a)i18g2000prf.googlegroups.com... > Hi Harald [...] >> I'm still not too sure what you mean. Perhaps the presentation? There are >> roughly two ways of drawing such diagrams; just keep in mind that it's >> never >> more than a graphic representation of the math related to measurements. >> - One presentation, as in that article, is symmetrical at the price of >> all >> non-orthogonal axes >> - One is asymmetrical but the reference axes are orthogonal. > > Yes, one can convert imaginary to nonorthogonal. > >> The (older) presentation and a discussion of both is given in the >> paragraph >> just above Time dilation (Minkowski diagram in special relativity): >> "For the graphical translation it has been taken into account that the >> scales on the inclined axes are different from the Newtonian case >> described >> above. To avoid this problem it is recommended that the whole diagram be >> deformed in such a way that the scales become identical for all axes, >> eliminating any need to stretch or compress either axis." > > Understood. > >> >> *Note: quite some misunderstanding occurs due to poor phrasings such >> >> as >> >> in the above article that says that "the space itself is contracted", >> >> and >> >> Bell corrected that with his spaceship example: >> >> http://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox >> >> Harald >> >> > Thanks for the ref's. >> > Seasons Greetings >> >> Happy holidays, >> Harald > > Well, for now I'm leaning toward unmoderated > forums. I see your posts in SPF are being > rejected because you may have said something > that CF finds threatening to his "teleconnection" > theory, I see SPF going down the tubes, because > CF dominates all the other moderators, and has > a serious rake (up his ...) and agenda. > > Oh well, SPF was experimental. > Regards > Ken S. Tucker I doubt that you would have been allowed to post that on SPF, in contrast to what CF is allowed to post there. ;-) Regards, Harald |