Galilean transformation equations
in [Relativity]
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From: eric gisse on 20 Jun 2010 15:04 Inertial wrote: [...] You are arguing with a guy who doesn't understand the symbols he's using. C'mon.
From: PD on 21 Jun 2010 17:19 On Jun 18, 9:38 pm, rbwinn <rbwi...(a)gmail.com> wrote: > On Jun 18, 11:02 am, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > > On Jun 18, 11:18 am, rbwinn <rbwi...(a)gmail.com> wrote: > > > > On Jun 18, 8:44 am, PD <thedraperfam...(a)gmail.com> wrote: > > > > > On Jun 17, 5:47 pm, rbwinn <rbwi...(a)gmail.com> wrote: > > > > > > On Jun 17, 1:06 pm, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > > On Jun 13, 8:31 am, rbwinn <rbwi...(a)gmail.com> wrote: > > > > > > > > x'=x-vt > > > > > > > y'=y > > > > > > > z'=z > > > > > > > t'=t > > > > > > > > Experiment shows that a clock in moving frame of reference S' is > > > > > > > slower than a clock in S which shows t. According to theGalilean > > > > > > > transformation equations, that slower clock does not show t'. Time on > > > > > > > the slower clock has to be represented by some other variable if the > > > > > > >Galileantransformation equations are to be used. We call time on the > > > > > > > slow clock in S' by the variable n'. > > > > > > > We can calculate time on the slow clock from theGalilean > > > > > > > transformation equations because we know that it shows light to be > > > > > > > traveling at 300,000 km per second in S'. Therefore, if > > > > > > > |x'|=300,000 km/sec(n') and |x| =300,000km/sec(t), then > > > > > > > > cn'=ct-vt > > > > > > > n'=t(1-v/c) > > > > > > > > We can now calculate orbits of satellites and planets without > > > > > > > the problems imposed by the Lorentz equations and their length > > > > > > > contraction. For instance, the speed of earth in its orbit around the > > > > > > > sun is 29.8 km/sec. While a second of time takes place on earth, a > > > > > > > longer time is taking place on the sun. > > > > > > > > n'(earth)=t(sun)(1-v/c) > > > > > > > 1 sec..=t(sun)(1-29.8/300,000) > > > > > > > t(sun)=1.0001 sec. > > > > > > > > Since the orbit of Mercury was the proof used to verify that > > > > > > > Einstein's equations were better than Newton's for gravitation, we > > > > > > > calculate how time on earth compares with time on Mercury. > > > > > > > > n'Mercury=t(sun)(1-v(Mercury)/c) > > > > > > > n'(mercury)=1.0001sec(1-47.87 km/sec/ > > > > > > > 300,000km/sec) > > > > > > > n'(Mercury)=.99994 sec > > > > > > > > So a second on a clock on earth is .99994 sec on a clock on > > > > > > > Mercury. The question now is where would this put the perihelion of > > > > > > > Mercury using Newton's equations? > > > > > > > Amazing to see you back, Robert. Even more amazing to find that you've > > > > > > done a reset and started with the very same nonsense you've put out > > > > > > for years and years. I would have thought that you would have learned > > > > > > something. > > > > > > > So you are claiming that for clocks A and B, where B is moving > > > > > > relative to A and runs slower than A, then A is measuring time (as > > > > > > denoted by the quantity t), but B is not measuring time (as denoted by > > > > > > the quantity t'). > > > > > > > The problem of course is that A is moving relative to B and runs > > > > > > slower than B. Your conclusion consistently would be that B is > > > > > > measuring time but A is not. > > > > > > > Therefore, according to you, A is measuring time and not measuring > > > > > > time, and B is measuring time and not measuring time. > > > > > > > PD > > > > > > You are confusing measurement of time with transformation of > > > > > coordinates. Time can be measured about any way imaginable. > > > > > Coordinates can be transformed only with t' and t. > > > > > t and t' stand for *measured* time, Robert. > > > > It really helps to know what the variable stand for in an algebraic > > > > expression. > > > > > You can always write down any old algebraic expression and say that > > > > it's true. It's when you try to associate the variables in the > > > > algebraic expression with physical quantities that it becomes physics, > > > > and then the truth of the expression isn't a matter of algebra any > > > > more. It's a matter whether when you actually take measured values of > > > > those physical quantities and stick them in, the equality holds or > > > > not. If you stick measured values in and the equality doesn't hold, > > > > then the algebraic expression may be algebraically fine but physically > > > > worthless. > > > > > Under some circumstances, such as in ordinary welding applications, if > > > > you use theGalileantransformation and check whether the measured > > > > values yield an equality, you find that the precision of the > > > > measurement is low enough that the equality holds. In this case, theGalileantransformation is "good enough". > > > > > But in a large number of other circumstances, which are probably of > > > > little interest to welders, the precision is high enough or the > > > > circumstances sufficiently different, then the equality no longer > > > > holds. And then theGalileantransformation is no good. > > > > > PD > > > > It does not seem to occur to you that you are measuring time two > > > different ways in S'. > > > But I'm not. I'm measuring it with a clock. > > > I don't make measurements with a transformation, Robert. > > Measurements are made with instruments, not transformations. > > If you have the right transformation, it will tell you what the > > relationship will be between the measurement in S and the measurement > > in S'. If you have the wrong transformation, it will not tell you the > > right relationship. It's so simple that a welder would understand it. > > > > First, you are measuring time by the motion of > > > S' relative to S. TheGalileantransformation equations account for > > > this. The time used to compute the velocity is t, the time in S. > > > Second, you are measuring time by the transitions of a cesium isotope > > > molecule, which get slower the faster S' is moving. You claim that > > > the way to resolve this difference is to say that the slower clock > > > shows the same speed as the faster clock in S and compensate by having > > > a length contraction. > > > I say that the correct way to resolve the difference is to say > > > that a slower clock will show a higher speed. That is what reality > > > would dictate. No, we do not want reality, say scientists. We want > > > to live in a fantasy world. > > > OK, live in a fantasy world. > > > I do not care if you live in a fantasy world. Why should you > > > care if I use the correct equations? > > > I don't care at all if you use the correct equations, Robert. You do > > as you please. If you want to use theGalileantransformations, please > > be my guest. We physicists will use them when it is appropriate to use > > them, given the sensitivity of the measurements being made and the > > observational circumstances, and will use others when it is > > appropriate to use the others. It seems to work better that way. > > Well, that is wonderful, PD. It is nice to see you becoming so > tolerant. Now, with regard to the motion of S' relative to S, were > you aware that measurement of this motion constitutes what is known as > a clock? No, it is not. It REQUIRES a clock. It does not constitute a clock. > If S' is moving at 10 feet per minute, what would be the time when > S' has moved 20 feet? > See, you could put 2 minutes at 20 feet, 3 minutes at 30 feet, and > so on, and you would have a working clock. First you need the clock to establish that it is moving at 10 feet per minute, no? > Then with regard to t', since t' equals t, But it doesn't. Moreover, the distances between the marks are not the same in S and S'. They may be 10 feet apart in S, but they're not 10 feet apart in S'. > you could put a mark on > S' and marks every ten feet in S and keep time the same way. I know > how amazing this concept must seem to a scientist. It is described by > the Galilean transformation equations.- Hide quoted text - > > - Show quoted text -
From: PD on 21 Jun 2010 17:20 On Jun 17, 5:47 pm, rbwinn <rbwi...(a)gmail.com> wrote: > On Jun 17, 1:06 pm, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > > On Jun 13, 8:31 am, rbwinn <rbwi...(a)gmail.com> wrote: > > > > x'=x-vt > > > y'=y > > > z'=z > > > t'=t > > > > Experiment shows that a clock in moving frame of reference S' is > > > slower than a clock in S which shows t. According to the Galilean > > > transformation equations, that slower clock does not show t'. Time on > > > the slower clock has to be represented by some other variable if the > > > Galilean transformation equations are to be used. We call time on the > > > slow clock in S' by the variable n'. > > > We can calculate time on the slow clock from the Galilean > > > transformation equations because we know that it shows light to be > > > traveling at 300,000 km per second in S'. Therefore, if > > > |x'|=300,000 km/sec(n') and |x| =300,000km/sec(t), then > > > > cn'=ct-vt > > > n'=t(1-v/c) > > > > We can now calculate orbits of satellites and planets without > > > the problems imposed by the Lorentz equations and their length > > > contraction. For instance, the speed of earth in its orbit around the > > > sun is 29.8 km/sec. While a second of time takes place on earth, a > > > longer time is taking place on the sun. > > > > n'(earth)=t(sun)(1-v/c) > > > 1 sec.=t(sun)(1-29.8/300,000) > > > t(sun)=1..0001 sec. > > > > Since the orbit of Mercury was the proof used to verify that > > > Einstein's equations were better than Newton's for gravitation, we > > > calculate how time on earth compares with time on Mercury. > > > > n'Mercury=t(sun)(1-v(Mercury)/c) > > > n'(mercury)=1.0001sec(1-47.87 km/sec/ > > > 300,000km/sec) > > > n'(Mercury)=.99994 sec > > > > So a second on a clock on earth is .99994 sec on a clock on > > > Mercury. The question now is where would this put the perihelion of > > > Mercury using Newton's equations? > > > Amazing to see you back, Robert. Even more amazing to find that you've > > done a reset and started with the very same nonsense you've put out > > for years and years. I would have thought that you would have learned > > something. > > > So you are claiming that for clocks A and B, where B is moving > > relative to A and runs slower than A, then A is measuring time (as > > denoted by the quantity t), but B is not measuring time (as denoted by > > the quantity t'). > > > The problem of course is that A is moving relative to B and runs > > slower than B. Your conclusion consistently would be that B is > > measuring time but A is not. > > > Therefore, according to you, A is measuring time and not measuring > > time, and B is measuring time and not measuring time. > > > PD > > You are confusing measurement of time with transformation of > coordinates. Time can be measured about any way imaginable. > Coordinates can be transformed only with t' and t.- Hide quoted text - A time coordinate is what is *measured* in that frame, Robert. It really does help to know what the terms mean.
From: rbwinn on 21 Jun 2010 20:23 On Jun 21, 2:19 pm, PD <thedraperfam...(a)gmail.com> wrote: > On Jun 18, 9:38 pm, rbwinn <rbwi...(a)gmail.com> wrote: > > > > > > > On Jun 18, 11:02 am, PD <thedraperfam...(a)gmail.com> wrote: > > > > On Jun 18, 11:18 am, rbwinn <rbwi...(a)gmail.com> wrote: > > > > > On Jun 18, 8:44 am, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > On Jun 17, 5:47 pm, rbwinn <rbwi...(a)gmail.com> wrote: > > > > > > > On Jun 17, 1:06 pm, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > > > On Jun 13, 8:31 am, rbwinn <rbwi...(a)gmail.com> wrote: > > > > > > > > > x'=x-vt > > > > > > > > y'=y > > > > > > > > z'=z > > > > > > > > t'=t > > > > > > > > > Experiment shows that a clock in moving frame of reference S' is > > > > > > > > slower than a clock in S which shows t. According to theGalilean > > > > > > > > transformation equations, that slower clock does not show t'. Time on > > > > > > > > the slower clock has to be represented by some other variable if the > > > > > > > >Galileantransformation equations are to be used. We call time on the > > > > > > > > slow clock in S' by the variable n'. > > > > > > > > We can calculate time on the slow clock from theGalilean > > > > > > > > transformation equations because we know that it shows light to be > > > > > > > > traveling at 300,000 km per second in S'. Therefore, if > > > > > > > > |x'|=300,000 km/sec(n') and |x| =300,000km/sec(t), then > > > > > > > > > cn'=ct-vt > > > > > > > > n'=t(1-v/c) > > > > > > > > > We can now calculate orbits of satellites and planets without > > > > > > > > the problems imposed by the Lorentz equations and their length > > > > > > > > contraction. For instance, the speed of earth in its orbit around the > > > > > > > > sun is 29.8 km/sec. While a second of time takes place on earth, a > > > > > > > > longer time is taking place on the sun. > > > > > > > > > n'(earth)=t(sun)(1-v/c) > > > > > > > > 1 sec.=t(sun)(1-29.8/300,000) > > > > > > > > t(sun)=1.0001 sec. > > > > > > > > > Since the orbit of Mercury was the proof used to verify that > > > > > > > > Einstein's equations were better than Newton's for gravitation, we > > > > > > > > calculate how time on earth compares with time on Mercury. > > > > > > > > > n'Mercury=t(sun)(1-v(Mercury)/c) > > > > > > > > n'(mercury)=1.0001sec(1-47.87 km/sec/ > > > > > > > > 300,000km/sec) > > > > > > > > n'(Mercury)=.99994 sec > > > > > > > > > So a second on a clock on earth is .99994 sec on a clock on > > > > > > > > Mercury. The question now is where would this put the perihelion of > > > > > > > > Mercury using Newton's equations? > > > > > > > > Amazing to see you back, Robert. Even more amazing to find that you've > > > > > > > done a reset and started with the very same nonsense you've put out > > > > > > > for years and years. I would have thought that you would have learned > > > > > > > something. > > > > > > > > So you are claiming that for clocks A and B, where B is moving > > > > > > > relative to A and runs slower than A, then A is measuring time (as > > > > > > > denoted by the quantity t), but B is not measuring time (as denoted by > > > > > > > the quantity t'). > > > > > > > > The problem of course is that A is moving relative to B and runs > > > > > > > slower than B. Your conclusion consistently would be that B is > > > > > > > measuring time but A is not. > > > > > > > > Therefore, according to you, A is measuring time and not measuring > > > > > > > time, and B is measuring time and not measuring time. > > > > > > > > PD > > > > > > > You are confusing measurement of time with transformation of > > > > > > coordinates. Time can be measured about any way imaginable. > > > > > > Coordinates can be transformed only with t' and t. > > > > > > t and t' stand for *measured* time, Robert. > > > > > It really helps to know what the variable stand for in an algebraic > > > > > expression. > > > > > > You can always write down any old algebraic expression and say that > > > > > it's true. It's when you try to associate the variables in the > > > > > algebraic expression with physical quantities that it becomes physics, > > > > > and then the truth of the expression isn't a matter of algebra any > > > > > more. It's a matter whether when you actually take measured values of > > > > > those physical quantities and stick them in, the equality holds or > > > > > not. If you stick measured values in and the equality doesn't hold, > > > > > then the algebraic expression may be algebraically fine but physically > > > > > worthless. > > > > > > Under some circumstances, such as in ordinary welding applications, if > > > > > you use theGalileantransformation and check whether the measured > > > > > values yield an equality, you find that the precision of the > > > > > measurement is low enough that the equality holds. In this case, theGalileantransformation is "good enough". > > > > > > But in a large number of other circumstances, which are probably of > > > > > little interest to welders, the precision is high enough or the > > > > > circumstances sufficiently different, then the equality no longer > > > > > holds. And then theGalileantransformation is no good. > > > > > > PD > > > > > It does not seem to occur to you that you are measuring time two > > > > different ways in S'. > > > > But I'm not. I'm measuring it with a clock. > > > > I don't make measurements with a transformation, Robert. > > > Measurements are made with instruments, not transformations. > > > If you have the right transformation, it will tell you what the > > > relationship will be between the measurement in S and the measurement > > > in S'. If you have the wrong transformation, it will not tell you the > > > right relationship. It's so simple that a welder would understand it. > > > > > First, you are measuring time by the motion of > > > > S' relative to S. TheGalileantransformation equations account for > > > > this. The time used to compute the velocity is t, the time in S. > > > > Second, you are measuring time by the transitions of a cesium isotope > > > > molecule, which get slower the faster S' is moving. You claim that > > > > the way to resolve this difference is to say that the slower clock > > > > shows the same speed as the faster clock in S and compensate by having > > > > a length contraction. > > > > I say that the correct way to resolve the difference is to say > > > > that a slower clock will show a higher speed. That is what reality > > > > would dictate. No, we do not want reality, say scientists. We want > > > > to live in a fantasy world. > > > > OK, live in a fantasy world. > > > > I do not care if you live in a fantasy world. Why should you > > > > care if I use the correct equations? > > > > I don't care at all if you use the correct equations, Robert. You do > > > as you please. If you want to use theGalileantransformations, please > > > be my guest. We physicists will use them when it is appropriate to use > > > them, given the sensitivity of the measurements being made and the > > > observational circumstances, and will use others when it is > > > appropriate to use the others. It seems to work better that way. > > > Well, that is wonderful, PD. It is nice to see you becoming so > > tolerant. Now, with regard to the motion of S' relative to S, were > > you aware that measurement of this motion constitutes what is known as > > a clock? > > No, it is not. It REQUIRES a clock. It does not constitute a clock. > > > If S' is moving at 10 feet per minute, what would be the time when > > S' has moved 20 feet? > > See, you could put 2 minutes at 20 feet, 3 minutes at 30 feet, and > > so on, and you would have a working clock. > > First you need the clock to establish that it is moving at 10 feet per > minute, no? > > > Then with regard to t', since t' equals t, > > But it doesn't. Moreover, the distances between the marks are not the > same in S and S'. They may be 10 feet apart in S, but they're not 10 > feet apart in S'. > > > > > you could put a mark on > > S' and marks every ten feet in S and keep time the same way. I know > > how amazing this concept must seem to a scientist. It is described by > > theGalileantransformation equations.- Hide quoted text - > > > - Show quoted text - They are ten feet apart if that is where I put them. So what are you saying now, that only a scientist is allowed to put marks ten feet apart?
From: rbwinn on 21 Jun 2010 20:24
On Jun 21, 2:20 pm, PD <thedraperfam...(a)gmail.com> wrote: > On Jun 17, 5:47 pm, rbwinn <rbwi...(a)gmail.com> wrote: > > > > > > > On Jun 17, 1:06 pm, PD <thedraperfam...(a)gmail.com> wrote: > > > > On Jun 13, 8:31 am, rbwinn <rbwi...(a)gmail.com> wrote: > > > > > x'=x-vt > > > > y'=y > > > > z'=z > > > > t'=t > > > > > Experiment shows that a clock in moving frame of reference S' is > > > > slower than a clock in S which shows t. According to theGalilean > > > > transformation equations, that slower clock does not show t'. Time on > > > > the slower clock has to be represented by some other variable if the > > > >Galileantransformation equations are to be used. We call time on the > > > > slow clock in S' by the variable n'. > > > > We can calculate time on the slow clock from theGalilean > > > > transformation equations because we know that it shows light to be > > > > traveling at 300,000 km per second in S'. Therefore, if > > > > |x'|=300,000 km/sec(n') and |x| =300,000km/sec(t), then > > > > > cn'=ct-vt > > > > n'=t(1-v/c) > > > > > We can now calculate orbits of satellites and planets without > > > > the problems imposed by the Lorentz equations and their length > > > > contraction. For instance, the speed of earth in its orbit around the > > > > sun is 29.8 km/sec. While a second of time takes place on earth, a > > > > longer time is taking place on the sun. > > > > > n'(earth)=t(sun)(1-v/c) > > > > 1 sec.=t(sun)(1-29.8/300,000) > > > > t(sun)=1.0001 sec. > > > > > Since the orbit of Mercury was the proof used to verify that > > > > Einstein's equations were better than Newton's for gravitation, we > > > > calculate how time on earth compares with time on Mercury. > > > > > n'Mercury=t(sun)(1-v(Mercury)/c) > > > > n'(mercury)=1.0001sec(1-47.87 km/sec/ > > > > 300,000km/sec) > > > > n'(Mercury)=.99994 sec > > > > > So a second on a clock on earth is .99994 sec on a clock on > > > > Mercury. The question now is where would this put the perihelion of > > > > Mercury using Newton's equations? > > > > Amazing to see you back, Robert. Even more amazing to find that you've > > > done a reset and started with the very same nonsense you've put out > > > for years and years. I would have thought that you would have learned > > > something. > > > > So you are claiming that for clocks A and B, where B is moving > > > relative to A and runs slower than A, then A is measuring time (as > > > denoted by the quantity t), but B is not measuring time (as denoted by > > > the quantity t'). > > > > The problem of course is that A is moving relative to B and runs > > > slower than B. Your conclusion consistently would be that B is > > > measuring time but A is not. > > > > Therefore, according to you, A is measuring time and not measuring > > > time, and B is measuring time and not measuring time. > > > > PD > > > You are confusing measurement of time with transformation of > > coordinates. Time can be measured about any way imaginable. > > Coordinates can be transformed only with t' and t.- Hide quoted text - > > A time coordinate is what is *measured* in that frame, Robert. It > really does help to know what the terms mean. So how did you "measure" time, PD? With an hourglass, with the sun, with the moon, with a waterclock? You must have done it some way. |