According to 1905 Relativity, a single material point must be always at rest
in [Relativity]
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From: valls on 20 May 2010 12:28 On 20 mayo, 08:50, harald <h...(a)swissonline.ch> wrote: > On May 20, 3:19 pm, va...(a)icmf.inf.cu wrote: > > > In his first Relativity paper (30June1905), after declaring the ether > > superfluous, Einstein considers a material point at rest. He uses a > > system of Cartesian coordinates in which the equations of Newtonian > > mechanics and Euclidean geometry hold good. If the massive body is > > alone (and then without a Newtonian gravitational force acting on it), > > it must remains forever at rest in its own centre of mass inertial > > frame. > > RVHG (Rafael Valls Hidalgo-Gato) > > If it were alone, yes. But then a theory about relative motion of > reference systems would certainly be superfluous. ;-) > But who says that the material point must be always alone? Consider the Solar System centre of mass inertial reference frame (SS) and the GPS ECI one. The last can be modelled as a material point that is not alone (is part of the SS one). As a huge experimental evidence put out of any doubt, you can model the SS as a single material point at rest, describing later the Earth (ECI) movement in the SS without any problem at all. In a similar way, all GPS satellite movements (including the ground clock ones) can be described in an ECI modelled as a single material point at rest. Do you consider yet superfluous a theory about relative motion of reference systems? Note that the moving system must be always part of the stationary system, and a stationary system moving with respect to a moving system at rest is nothing more that a huge absurd (do you remember Ptolomys Sun going around the Earth?). At the end of paragraph 4 in the referred 1905 Einsteins paper, you can find already the ECI (the rotating Earth with a centre of mass at rest) with the moving system (clock at the equator) forming part of it. > Cheers, > Harald RVHG (Rafael Valls Hidalgo-Gato)
From: Darwin123 on 20 May 2010 12:32 On May 20, 9:19 am, va...(a)icmf.inf.cu wrote: > In his first Relativity paper (30June1905), after declaring the ether > superfluous, Einstein considers a material point at rest. He uses a > system of Cartesian coordinates in which the equations of Newtonian > mechanics and Euclidean geometry hold good. If the massive body is > alone (and then without a Newtonian gravitational force acting on it), > it must remains forever at rest in its own centre of mass inertial > frame. > RVHG (Rafael Valls Hidalgo-Gato) Yes it does. So? Conservation of momentum applies in both Galilean and Lorentz invariant systems. "An object at rest tends to stay at rest unless acted on by some external force." That is Newton's first law. It is good in any inertial frame.
From: Darwin123 on 20 May 2010 12:57 On May 20, 12:28 pm, va...(a)icmf.inf.cu wrote: > On 20 mayo, 08:50, harald <h...(a)swissonline.ch> wrote:> On May 20, 3:19 pm, va...(a)icmf.inf.cu wrote: At the > end of paragraph 4 in the referred 1905 Einsteins paper, you can find > already the ECI (the rotating Earth with a centre of mass at rest) > with the moving system (clock at the equator) forming part of it. > Ahh, now I see what you are driving at. Einstein is referring to the ECI as an inertial frame, when it is obviously not an inertial frame. The center of the earth orbits the sun, and the sun orbits the center of the Milky Way. Einstein is analyzing an experiment on the surface of the earth, considering only the centripetal acceleration of the earth's surface. The contributions of the earth's orbit around the sun, and the suns orbit around our galaxy, is not considered. I don't think this is a true mistake. Einstein was making a rather obvious approximation. For many purposes, the ECI is an approximate inertial frame. For the experiments that Einstein was suggesting, the ECI is effectively an inertial frame. I don't think Einstein was suggesting the ECI is precisely The best way to see that the ECI is approximately an inertial frame is to calculate the various contribution to the acceleration of the surface of the earth. One can measure this component with either a Foucault pendulum or a Sagnac interferometer. So the earths surface is definitely not an inertial frame. Einstein does not analyze the earth's surface as an inertial frame because it has a rather noticeable acceleration. So the earth's surface, with respect to special relativity, can't be considered an inertial frame. The surface of the earth is spinning relative to the earths pole. This spin causes the largest component of acceleration. The centripetal acceleration. You can easily calculate the acceleration due to spin as g_Spin=v_Surface^2/r_earth where g_Spin is the centripetal acceleration of the earth in the ECI, V_Surface is the velocity of the surface at a surface point, and r_Earth is the distance of the surface point from the spin axis. The acceleration measured by accelerometers (the Foucault pendulum and the Sagnac interferometer) is mostly g_Spin. However, there is also centripetal accleration from the orbit of the earth around the sun. g_Solar=v_Solar^2/r_Solar, where the meaning of the variables is rather obvious. Furthermore, there is an orbit of the sun around the galaxy. g_Galaxy=v_Galaxy^2/r_Galaxy. If you calculate the different components, you will find 0<g_Galaxy<<g_Solar<<g_Spin At the current level of accelerometer technology, only g_Spin can be detected with an accelerometer. So for all practical purposes, the ECI is an inertial frame. However, since 0<g_Galaxy<<g_Solar, one can not consider the center of the earth precisely still. The motion of the ECI can't be measured with an accelerometer, it can be detected by astronomical measurements. Einstein referred to these types of measurements as nonlocal. His postulates of general relativity only apply to local measurements. The measurements performed by Galileo are nonlocal. So sorry. Galileo is still considered correct, even in the post Einstein world. Even Galileo knew that one could approximate the earth as stationary for certain experiments. However, these are only approximations. The ECI is not exactly an inertial frame.
From: mpc755 on 20 May 2010 13:43 On May 20, 12:10 pm, va...(a)icmf.inf.cu wrote: > On 20 mayo, 08:30, mpc755 <mpc...(a)gmail.com> wrote: > > > On May 20, 9:19 am, va...(a)icmf.inf.cu wrote: > > > > In his first Relativity paper (30June1905), after declaring the ether > > > superfluous, Einstein considers a material point at rest. He uses a > > > system of Cartesian coordinates in which the equations of Newtonian > > > mechanics and Euclidean geometry hold good. If the massive body is > > > alone (and then without a Newtonian gravitational force acting on it), > > > it must remains forever at rest in its own centre of mass inertial > > > frame. > > > RVHG (Rafael Valls Hidalgo-Gato) > > > Einstein did not say the aether was superfluous. Einstein said an > > absolutely stationary space was superfluous. > > >http://en.citizendium.org/wiki/Ether_%28physics%29 > > > 'The introduction of a "luminiferous aether" (Lichtäther) will prove > > to be superfluous inasmuch as the view here to be developed will not > > require an "absolutely stationary space" provided with special > > properties, nor assign a velocity vector to a point of the empty space > > in which electromagnetic processes take place.' > > > Space is not absolutely stationary. > > And who is saying that it is? Following your own reference, 1905 > Einstein considers the ether superfluous because he identifies it with > an absolutely stationary space that he not requires. I don't care if > you or any other after 1905 (including Einstein himself) has a > different opinion. The topic of this thread refers only to 1905 > Relativity. > > RVHG (Rafael Valls Hidalgo-Gato) Einstein does not consider the aether to be superfluous. You are missing the 'inasmuch' part of the following: 'The introduction of a "luminiferous aether" (Lichtäther) will prove to be superfluous inasmuch as the view here to be developed will not require an "absolutely stationary space"' Einstein is not saying the aether is superfluous. Einstein is saying an absolutely stationary space is superfluous. Einstein's following quote shows the need for an aether: 'Ether and the Theory of Relativity by Albert Einstein' http://www-groups.dcs.st-and.ac.uk/~history/Extras/Einstein_ether.html "According to the general theory of relativity space without ether is unthinkable" Einstein goes so far as to discuss a state of the aether: "the state of the former is at every place determined by connections with the matter and the state of the ether in neighbouring places" Einstein declines to discuss what this state is: "disregarding the causes which condition its state." The cause which conditions its state is its displacement by matter.
From: mpc755 on 20 May 2010 13:46
On May 20, 1:43 pm, mpc755 <mpc...(a)gmail.com> wrote: > On May 20, 12:10 pm, va...(a)icmf.inf.cu wrote: > > > > > On 20 mayo, 08:30, mpc755 <mpc...(a)gmail.com> wrote: > > > > On May 20, 9:19 am, va...(a)icmf.inf.cu wrote: > > > > > In his first Relativity paper (30June1905), after declaring the ether > > > > superfluous, Einstein considers a material point at rest. He uses a > > > > system of Cartesian coordinates in which the equations of Newtonian > > > > mechanics and Euclidean geometry hold good. If the massive body is > > > > alone (and then without a Newtonian gravitational force acting on it), > > > > it must remains forever at rest in its own centre of mass inertial > > > > frame. > > > > RVHG (Rafael Valls Hidalgo-Gato) > > > > Einstein did not say the aether was superfluous. Einstein said an > > > absolutely stationary space was superfluous. > > > >http://en.citizendium.org/wiki/Ether_%28physics%29 > > > > 'The introduction of a "luminiferous aether" (Lichtäther) will prove > > > to be superfluous inasmuch as the view here to be developed will not > > > require an "absolutely stationary space" provided with special > > > properties, nor assign a velocity vector to a point of the empty space > > > in which electromagnetic processes take place.' > > > > Space is not absolutely stationary. > > > And who is saying that it is? Following your own reference, 1905 > > Einstein considers the ether superfluous because he identifies it with > > an absolutely stationary space that he not requires. I don't care if > > you or any other after 1905 (including Einstein himself) has a > > different opinion. The topic of this thread refers only to 1905 > > Relativity. > > > RVHG (Rafael Valls Hidalgo-Gato) > > Einstein does not consider the aether to be superfluous. You are > missing the 'inasmuch' part of the following: > > 'The introduction of a "luminiferous aether" (Lichtäther) will prove > to be superfluous inasmuch as the view here to be developed will not > require an "absolutely stationary space"' > > Einstein is not saying the aether is superfluous. Einstein is saying > an absolutely stationary space is superfluous. > > Einstein's following quote shows the need for an aether: > > 'Ether and the Theory of Relativity by Albert Einstein'http://www-groups.dcs.st-and.ac.uk/~history/Extras/Einstein_ether.html > > "According to the general theory of relativity space without ether is > unthinkable" > > Einstein goes so far as to discuss a state of the aether: > > "the state of the former is at every place determined by connections > with the matter and the state of the ether in neighbouring places" > > Einstein declines to discuss what this state is: > > "disregarding the causes which condition its state." > > The cause which conditions its state is its displacement by matter. Einstein's 'first' paper is all about the aether: http://www.worldscibooks.com/etextbook/4454/4454_chap1.pdf |