Mathematics of spacetime , from spacetime wiki For physical reasons, a spacetime continuum is mathematically defined as a four-dimensional, smooth, connected Lorentzian manifold<http://en.wikipedia.org/wiki/Lorentzian_manifold> (*M*,*g*). This means the smooth Lorentz metric<http://en.wikipedia.org/wiki/Lorentz_metric> *g* has signature (3,1). The metric determines the geometry of spacetime, as well as determining the geodesics <http://en.wikipedia.org/wiki/Geodesic> of particles and light beams. About each point (event) on this manifold, coordinate charts <http://en.wikipedia.org/wiki/Coordinate_charts> are used to represent observers in reference frames. Usually, Cartesian coordinates (*x* ,*y*,*z*,*t*) are used. Moreover, for simplicity's sake, the speed of light *c* is usually assumed to be unity.
----------------------------------------------------------------------------------------------------------------------------------------- A reference frame (observer) can be identified with one of these coordinate charts; any such observer can describe any event *p*. Another reference frame may be identified by a second coordinate chart about *p*. Two observers (one in each reference frame) may describe the same event *p* but obtain different descriptions. ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Usually, many overlapping coordinate charts are needed to cover a manifold. Given two coordinate charts, one containing *p* (representing an observer) and another containing *q* (representing another observer), the intersection of the charts represents the region of spacetime in which both observers can measure physical quantities and hence compare results. The relation between the two sets of measurements is given by a non-singular<http://en.wikipedia.org/wiki/Non-singular>coordinate transformation on this intersection. The idea of coordinate charts as local observers who can perform measurements in their vicinity also makes good physical sense, as this is how one actually collects physical data—locally. For example, two observers, one of whom is on Earth, but the other one who is on a fast rocket to Jupiter, may observe a comet crashing into Jupiter (this is the event *p*). In general, they will disagree about the exact location and timing of this impact, i.e., they will have different 4-tuples (*x*,*y*,*z*,*t*) (as they are using different coordinate systems). Although their kinematic descriptions will differ, dynamical (physical) laws, such as momentum conservation and the first law of thermodynamics, will still hold. In fact, relativity theory requires more than this in the sense that it stipulates these (and all other physical) laws must take the same form in all coordinate systems. This introduces tensors<http://en.wikipedia.org/wiki/Tensors>into relativity, by which all physical quantities are represented. Geodesics are said to be time-like, null, or space-like if the tangent vector to one point of the geodesic is of this nature. The paths of particles and light beams in spacetime are represented by time-like and null (light-like) geodesics (respectively). Adrie I do not think that the dispute was meanigless or only verbal, the position from the squirrel towards the observer and vice-versa is always relative, never absolute,and are following the exact formulating that originated from general relativity ;... to observers , one in each reference frame, may describe the same event p but obtain different descriptions .James his story is mathematical science. I still think it is interesting to catch the squirrel. But i also agree that it is difficult to see for the non-math eye. I have a friend that is a theorethical physician, works at cern, i will ask his advice before i proceed. 2010/9/6 david buchanan <[email protected]> > > Magnus said to Adrie: > Ok, yes, I remember the squirrel. And yes, spatial statements like "around" > does of course depend on the observer's position, just like political > statements like right and left depend on some baseline in the middle. But > I'm not sure we can generalize those examples to all? other levels. I'm > probably not seeing what you want me to see here. > > > dmb butts in: > > As I understand it, the squirrel scene is not about differences in > perspective. It's supposed to illustrate the power of pragmatism to > distinguish the difference between a real dispute and one that's merely > verbal. The two camps seemed to be in disagreement about whether or not the > man ever got "around" the squirrel, even though they all agreed about what > actually happened. They all saw it happen and yet some said he did and some > said he didn't. Asked to settle the dispute, James wondered what practical > difference it made. By posing this question, the disputants realized that > they didn't really disagree about what happened. It's just that they were > using two different meanings of the term "around". Did the man get around > the squirrel? Some said yes and some said no but the only real difference > was in what they took "around" to mean. So their dispute was merely verbal > and therefore meaningless. > > Did the man ever catch the squirrel? Nope. Good thing too. Those things > bite and scratch like hell. You'd have to be nuts to catch a squirrel. > > > I haven't been following this thread, really, but something Einstein said > leapt to mind as I was going by the other day. He said something like, space > and time are not the stage on which the drama of the universe unfolds, they > are part of the drama. I think Hawking's idea that there was a singularity > prior to the big bang goes along quite nicely with that idea. If I > understand this picture, time and space and matter and energy are different > manifestations of the same thing and exist only in relation to one another, > as in E=Mc2, where mass is a certain amount of condensed energy. Just about > any equation is essentially a description of their relations. In that sense, > space and time are just as physical as matter, an equal feature of the same > fabric. It's a beautiful picture. The Big Bang is more like the Big > Unfolding. The singularity from which the whole universe exploded was not > some empty nothingness. It was more like all of reality folded in on itself > and packed into a tiny > suitcase small enough for a flea to carry in his hand. > > > In that singularity all the equations were perfectly balanced. It was a > perfect symmetry in every way such that there was no time or space or matter > or energy. Not yet. But, the story goes, something tipped it ever so > slightly, the symmetry was broken and BANG! We're in the midst of that > ongoing explosion at this moment. Watch your head! > > > > > > > > Magnus > > > > > > > > > > > > On 2010-09-06 11:46, ADRIE KINTZIGER wrote: > > > ah, okay Magnus, i will make a suggestion to set gravity aside for this > > > moment , and move on it later on, > > > > > > ok, i think it will become important, because it will show something > > > > > > I suppose you have the e-book lila, can you go to page 212-213, and > read the > > > squirrel part James introduced, and was recognised by pirsig? > > > > > > Than, if you re-read the parts we discussed on general relativity, > > > relativity, quantum physiks, the many worlds interpretation Hawing > > > is supporting as the momental mainstream science,pay special attention > to > > > the part is was pointing to as for the relative position of the > observer > > > > > > James , Pirsig, Einstein,Hawking all on 1 line, in a sequence of > recognised > > > patterns regarding reality. saying the same,it takes a visionair to > > > recognise a visionair > > > > > > i think it becomes important to list it up, sequentially. > > > and set it to be read in one artikel, will take us some time i guess, > its > > > only a proposal of course. > > > i'm still investigating this push-pull model of you, there seems to be > some > > > evidence, but very difficult to understand. > > > working on it, probably it is not in conflict with Hawkings idea's, or > > > general relativity, or supersymmetry > > > probably it resides in the supersymetry-model.it willt ake time, the > product > > > is there. > > > So can you read page 212-213, and recognise what James and Pirsig are > > > saying? > > > greetzz,Adrie > > > > > > 2010/9/6 Magnus Berg<[email protected]> > > > > > >> Hi Adrie > > >> > > >> Getting hard to distinguish the signals from all the noise around > here. > > >> Soon I'll start using Thunderbird's spam filter to cancel out the > worst. > > >> > > >> Anyway, I was able to read some of the links you sent yesterday. Very > > >> interesting, this geoid form vs the freatic surface. But I'm really > not sure > > >> if it can be used to hint either way on the gravity push/pull issue? > But > > >> perhaps that wasn't your intention? > > >> > > >> I also read the MWI page, at least parts of it. And even it sounds > very > > >> much like the quality event, I'm a little uncertain as to why it is > > >> important here? > > >> > > >> Magnus > > >> > > >> > > >> > > >> > > >> > > >> > > >> > > >> On 2010-09-05 15:10, ADRIE KINTZIGER wrote: > > >> > > >>> Okay , lets compare , for now to explore our the geoidform of the > earth,to > > >>> make it possible to crossrefer this geoid > > >>> to the freatic surface,the geoid shape is very important Magnus, can > you > > >>> read it carefully, and keep in mind that i want to compare the geoid > shape > > >>> with the freatic surface. > > >>> > > >>> http://en.wikipedia.org/wiki/Geoid > > >>> > > >>> > > >>> > > >>> And after that This will be the follow up, after we compared the > geoid > > >>> with > > >>> the freatic field. > > >>> > > >>> It will lead to a field making your interpretation on gravity as good > as > > >>> any > > >>> other scientifically projection, without conflicting other matters. > > >>> It is surely nessesary to avoid conflicting matters, otherwise we > will end > > >>> up in a non-existing meta-gravity, that serves no purpose > > >>> from the beginning. > > >>> All details matter. > > >>> > > >>> Okay , this will be the field i propose, The many worlds > interpretation, > > >>> parented by Stephen Hawking,but he is incorporating all quantum > physiks in > > >>> his model, and the conflicting matter i was mentioning earlier, about > the > > >>> relative/absolute position of the observer is in conflict with the > > >>> quantum-states supported by Hawking.In the Q P there is no absolute > > >>> position > > >>> unless proven. > > >>> But for now , you can find what i'm pointing towards, in this regard, > > >>> under > > >>> "Interpreting waveform or function collapse" > > >>> This will give the answer as to why its better to leave the absolute > > >>> position as observer.Hawking's copenhagen interpretation is > interwoven > > >>> with > > >>> that model,the relative model.the relative model is dynamical , the > > >>> absolute > > >>> is statical. > > >>> Your clever enough to find it yourself, and than read our earlier > matter > > >>> back. > > >>> I will come back on this later on, but i think its good to read > yourself > > >>> in > > >>> a little bit in advance. > > >>> Probably you will notice that Hawking allows multiple realitys and > > >>> explains > > >>> them, you will also notice that this material is not in conflict with > any > > >>> OTHER possible reality or history.Hawking merges all reality's. > > >>> But as i come to think about it, you were the only one brave and bold > > >>> enough > > >>> to step into Andy's code, and to recognise the embedded > > >>> idea within the formulation, so you are a very clever guy, i agree > that > > >>> the > > >>> model was very difficult to peel open. > > >>> > > >>> greetzz, Adrie > > >>> > > >>> > > >>> > > >>> > > >>> http://en.wikipedia.org/wiki/Many-worlds_interpretation > > >>> > > >>> > > >>> > > >>> > > >>> 2010/9/5 ADRIE KINTZIGER<[email protected]> > > >>> > > >>> No, i only meant to say, Magnus, that accelerating is not in > conflict > > >>>> with > > >>>> cooling down,and that there is evidence for the cooling down, > > >>>> I was clumsy. > > >>>> > > >>>> Adrie > > >>>> > > >>>> 2010/9/5 Magnus Berg<[email protected]> > > >>>> > > >>>> > > >>>>> Hi Adrie > > >>>>> > > >>>>> "ADRIE KINTZIGER"<[email protected]> wrote: > > >>>>> > > >>>>>> --quote,Magnus > > >>>>>> Another line of thought is what Horse mentioned the other day. If > > >>>>>> gravity > > >>>>>> comes from space, and space is expanding, then it should get > weaker > > >>>>>> with > > >>>>>> time. If we can find evidence that gravity was higher when the sun > and > > >>>>>> > > >>>>> our > > >>>>> > > >>>>>> planets formed, then that could be a smoking gun. But I doubt > anyone > > >>>>>> has > > >>>>>> searched for such evidence > > >>>>>> > > >>>>>> Yes , the universe is speeding up and cooling down at the same > time, > > >>>>>> > > >>>>> there > > >>>>> > > >>>>>> is evidence for the cooling down and sedating. > > >>>>>> This is not in conflict with accelerating speed. > > >>>>>> > > >>>>> > > >>>>> That was a bit unclear. Of course "speeding up" is not in conflict > with > > >>>>> "accelerating speed", they are the same thing. > > >>>>> > > >>>>> Did something I say make you think I thought something conflicted? > > >>>>> > > >>>>> Magnus > > >>>>> > > >>>>> > > >>>>> Moq_Discuss mailing list > > >>>>> Listinfo, Unsubscribing etc. > > >>>>> http://lists.moqtalk.org/listinfo.cgi/moq_discuss-moqtalk.org > > >>>>> Archives: > > >>>>> http://lists.moqtalk.org/pipermail/moq_discuss-moqtalk.org/ > > >>>>> http://moq.org/md/archives.html > > >>>>> > > >>>>> > > >>>> > > >>>> > > >>>> -- > > >>>> parser > > >>>> > > >>>> > > >>> > > >>> > > >>> > > >> Moq_Discuss mailing list > > >> Listinfo, Unsubscribing etc. > > >> http://lists.moqtalk.org/listinfo.cgi/moq_discuss-moqtalk.org > > >> Archives: > > >> http://lists.moqtalk.org/pipermail/moq_discuss-moqtalk.org/ > > >> http://moq.org/md/archives.html > > >> > > > > > > > > > > > > > Moq_Discuss mailing list > > Listinfo, Unsubscribing etc. > > http://lists.moqtalk.org/listinfo.cgi/moq_discuss-moqtalk.org > > Archives: > > http://lists.moqtalk.org/pipermail/moq_discuss-moqtalk.org/ > > http://moq.org/md/archives.html > > Moq_Discuss mailing list > Listinfo, Unsubscribing etc. > http://lists.moqtalk.org/listinfo.cgi/moq_discuss-moqtalk.org > Archives: > http://lists.moqtalk.org/pipermail/moq_discuss-moqtalk.org/ > http://moq.org/md/archives.html > -- parser Moq_Discuss mailing list Listinfo, Unsubscribing etc. http://lists.moqtalk.org/listinfo.cgi/moq_discuss-moqtalk.org Archives: http://lists.moqtalk.org/pipermail/moq_discuss-moqtalk.org/ http://moq.org/md/archives.html
