QUESTION: how are the 4 dimensions actually used in physics math?
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From: BURT on 20 Mar 2010 18:47 On Mar 20, 3:39 pm, "Sue..." <suzysewns...(a)yahoo.com.au> wrote: > On Mar 20, 4:17 pm, JJ <sa...(a)temporaryinbox.com> wrote:> Hi all, > > > here is a question I wanted to ask about, regarding this concept of > > the Universe being 4-dimensional. > > > The question is, how is this 4-dimensionality reflected in mathematic > > equations used to solve physics problems? > > > For example, my understanding is (correct me if I am wrong) that > > before "time" was added as one of the dimensions, some of the > > calculations were done with just 3 dimensions and adding the dimension > > of time helped in solving some of the calculations. Are the dimensions > > in reflected in the equations as exponents of some kind? > > ============ > > > Thanks in advance, > > Does that violate causality ? :-) > > << 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 > > << 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 > > http://en.wikipedia.org/wiki/Complex_number > > "Space-time"http://farside.ph.utexas.edu/teaching/em/lectures/node113.html > > Sue... Time slows down while filling the curve of space in gravity. Mitch Raemsch
From: Uncle Al on 20 Mar 2010 19:28 JJ wrote: > > Hi all, > > here is a question I wanted to ask about, regarding this concept of > the Universe being 4-dimensional. > > The question is, how is this 4-dimensionality reflected in mathematic > equations used to solve physics problems? Special Relativity General Relativity particle physics' collisions. http://www.eftaylor.com/pub/projecta.pdf <http://www.public.asu.edu/~rjjacob/Lecture16.pdf> <http://relativity.livingreviews.org/Articles/lrr-2003-1/index.html> Relativity in the GPS system <http://relativity.livingreviews.org/open?pubNo=lrr-2003-1&page=node5.html> <http://unusedcycles.wordpress.com/2008/05/30/physics-of-gps-relativistic-time-delay/> Relativistic effects on orbital clocks <http://en.wikipedia.org/wiki/Hafele-Keating_experiment> <http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html> <http://metrologyforum.tm.agilent.com/pdf/flying_clock_math.pdf> http://metrologyforum.tm.agilent.com/cesium.shtml http://arxiv.org/abs/physics/0008012 Hafele-Keating Experiment > For example, my understanding is (correct me if I am wrong) that > before "time" was added as one of the dimensions, some of the > calculations were done with just 3 dimensions and adding the dimension > of time helped in solving some of the calculations. Are the dimensions > in reflected in the equations as exponents of some kind? The first GPS satellite was corrected for SR (velocity vs. ground) but not for GR (height above geoid). Some insubordinate engineer added an offset oscillator for GR correction against the four on-board atomic clocks. They built it, they launched it, and they fired it up. The first GPS satellite was a disaster. They kicked in the offset oscillator and it was accurate to 0.1 parts-per-billion. All subsequent GPS satellites were corrected for SR and GR both. One can only hope said engineer had the back door slam him in his butt as he was expelled from NASA for disobeying management and saving that first satellite. Proper employees follow their superiors' orders without question, <http://www.freerepublic.com/focus/f-news/979224/posts> 24 huge retaining bolts were not torqued down - or even inserted - when the tilt table tilted and the satellite succumbed to gravity's seductive lure. There was no base-bolting requirement in technicians' procedure sheets. Some ISO 900x jackass in front of a screen left out one line and $100 million worth of satellite fell 10 feet to the ground. A year of NASA inquiry concluded that nobody was to blame. Everybody down the Table of Command exactly following orders. No thoughtcrime! One would be curious to discover performance bonuses awarded. The Hubble mirror was deeply fucked. A tiny single crystal alumina hard end of a steel fiduciary rod was invisible during optical calibration. An old fart optician blew the whistle saying the rough grind could not be correct. He was fired. NASA saved a $million not testing the finished mirror. Once in orbit it was the most precise large optic ever fabricated, albeit inaccurately by about a diopter. Jury rigging and emplacing a fix cost at least $5 billion. The Hubble satellite is a Keyhole satellite pointed the other way. NASA could have started with the working answer for all systems. Keyholes don't burn through steering gyros. DON'T BE STUPID unless you are in management, where stupidity is the entry fee. -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz4.htm
From: Peter Webb on 20 Mar 2010 21:43 "JJ" <santa(a)temporaryinbox.com> wrote in message news:19df96bb-07b8-4b5e-b277-6c7f5b006cf9(a)q21g2000yqm.googlegroups.com... > Hi all, > > here is a question I wanted to ask about, regarding this concept of > the Universe being 4-dimensional. > > The question is, how is this 4-dimensionality reflected in mathematic > equations used to solve physics problems? > > For example, my understanding is (correct me if I am wrong) that > before "time" was added as one of the dimensions, some of the > calculations were done with just 3 dimensions and adding the dimension > of time helped in solving some of the calculations. Are the dimensions > in reflected in the equations as exponents of some kind? > > Thanks in advance, > You are bumping up against the concept of "dimension" which is not a very well defined term. In mathematics, it often means just some independent variable in a calculation (ie a "degree of freedom"). It does not necessarily mean spatial dimension. The dimension of "time" in a mathematical sense has existed in equations since before Newton. What Einstein did was say that the time dimension acted in many respects the same way as a length dimension (multiplied by the sqrt of -1). Whether that is a physical dimension or a mathematical dimension is really up to you. If it is a physical dimension it is not one in the same sense as the three physical dimensions you are used to. However, the time dimension behaves so similarly (almost identically) to space dimensions in so many formula in SR that the impression is that it is a very similar thing, if not quite the same.
From: Ste on 21 Mar 2010 04:18 On 20 Mar, 20:48, BURT <macromi...(a)yahoo.com> wrote: > > The universe is extened in the round surface of the 4th dimension. I do always wonder what people mean when they say "the 4th dimension is round". I find it's a statement almost devoid of meaning. If all it means is "history repeats itself", then it would be more meaningful to simply say that, rather than evoking "circular" physical imagery and leaving the reader to try and work out whether "round" is to be interpreted literally, or merely metaphorically (i.e. "history repeats itself"). Perhaps the reason physicists like to ask questions like "what shape is time" is because it gives a concrete mathematical veneer to the whole thing, and also makes the questions sound novel. Whereas if they simply asked the question "does history repeat", the question would seem so trite and philosophical.
From: Peter Webb on 21 Mar 2010 05:37
> > Perhaps the reason physicists like to ask questions like "what shape > is time" is because it gives a concrete mathematical veneer to the You know, I cannot imagine a physicist ever saying these words. So I googled them. There are 9 hits, none from scientists. Whatever questions physicists may like to ask, this is not one of them. |