Question on Spacetime dilation.
in [Relativity]
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From: Androcles on 17 Dec 2008 00:24 "Tom Roberts" <tjroberts137(a)sbcglobal.net> wrote in message news:5Y%1l.6930$pr6.5959(a)flpi149.ffdc.sbc.com... > harry wrote: >> At increased speed, clock frequency decreases ("time dilation") and >> lengths of objects (but NOT widths) shrink. > > That is a VERY poor statement. So poor it is tantamount to being wrong. > When you say "clock frequency decreases" or "lengths of objects shrink", > one naturally interprets those phrases as pertaining to the objects > themselves, which is just plain wrong. It is one's MEASUREMENTS of such > properties that change with relative motion, not the objects themselves. > > While you alluded to this in your next sentence, that is insufficient to > prevent the reader from interpreting your words incorrectly. > > Insufficient precision is the underlying cause of much of the confusion > around here. As it indicates insufficient precision in thought, it > behooves you to think and write more accurately. > > > Tom Roberts Got that, van lintel? The ruler shrinks along with the rod it is MEASURING and it behoves you to shut your lying mouth. Only Roberts can interpret Einstein's stupidity correctly, you make very POOR just plain wrong idiot statements and should lie more accurately, you are confusing things around here.
From: harry on 17 Dec 2008 02:01 "Tom Roberts" <tjroberts137(a)sbcglobal.net> wrote in message news:5Y%1l.6930$pr6.5959(a)flpi149.ffdc.sbc.com... > harry wrote: >> At increased speed, clock frequency decreases ("time dilation") and >> lengths of objects (but NOT widths) shrink. Note: that was a clarification to Ken, in view of his erroneous title. > That is a VERY poor statement. So poor it is tantamount to being wrong. > When you say "clock frequency decreases" or "lengths of objects shrink", > one naturally interprets those phrases as pertaining to the objects > themselves, which is just plain wrong. The fact is that you cannot prove your claim AND YOU KNOW IT - a number of famous physicists argued this and I accept their arguments. > It is one's MEASUREMENTS of such properties that change with relative > motion, not the objects themselves. > While you alluded to this in your next sentence, that is insufficient to > prevent the reader from interpreting your words incorrectly. It's certainly NOT due to me that people are misled into thinking that (the measurements of) "space shrinks". As Bell demonstrated, such poor thinking leads to big errors. Note: my next sentence was: "And of course, all such measurements are "relative". > Insufficient precision is the underlying cause of much of the confusion > around here. As it indicates insufficient precision in thought, it > behooves you to think and write more accurately. Thanks for the emphasis on my clarifying sentence - and there's no inaccuracy in my thinking. :-) Harald
From: harry on 17 Dec 2008 03:44 "Ken S. Tucker" <dynamics(a)vianet.on.ca> wrote in message news: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 *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
From: Ken S. Tucker on 17 Dec 2008 07:07 Hi Alen, et al. On Dec 16, 7:23 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) Yes that looks right to me. > 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! You can write it in the form > using g_uv, and it works mathematically, with > g_uvs being 1 and -1, but all this doesn't really > mean anything of any significance physically. > Alen "significance physically" It seems 4D spacetime is becoming deeply ingrained into our equations, possibly underestimating there complexity. Ken S. Tucker
From: Ken S. Tucker on 17 Dec 2008 07:19
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. > *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 Ken |