According to 1905 Relativity, a single material point must be always at rest
in [Relativity]
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From: Androcles on 20 May 2010 18:02 "harald" <hvan(a)swissonline.ch> wrote in message news:34620241-476e-4407-a7c7-2c5cc5427266(a)w3g2000vbd.googlegroups.com... Einsteins thoery does not prefer one inertial system over the other, it is not supporting your theory. ========================================== "It is essential to have time defined by means of stationary clocks in the stationary system, and the time now defined being appropriate to the stationary system we call it ``the time of the stationary system.'' tau = t * sqrt(1-v^2/c^2) is the time of the moving system. If the stationary system were not preferred, tau would equal t/sqrt(1-v^2/c^2) and moving clocks would run fast.
From: valls on 20 May 2010 18:17 On 20 mayo, 11:57, Darwin123 <drosen0...(a)yahoo.com> wrote: > 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 centre of mass inertial reference frame (CM) corresponding to a determined body set is a Newtonian concept developed long before 1905 Einstein. If the body set is composed by all parts of the real Earth (including today all GPS satellites and clocks), the corresponding CM, that I denote as ECI (between ), is the stationary system used by 1905 Einstein with its centre of mass (as all the rotating axis, including the poles) at rest. That CM is without any doubt a system of co-ordinates in which the Newtonian equations hold good (using 1905 Einstein literal words). The Earths surface is rotating in that CM with a determined angular velocity. I remember you that in the today GPS ECI, the I is for Inertial, but take into account that in 1905 the GPS doesnt exist yet. > 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. Of course not, because the Moon, the Sun, the Galaxy and the rest of the Universe do not belong to the CM body set (their masses are not taking into account when determining the CM centre of mass). With all respect, I think you are wrong when saying that Einstein is considering only the centripetal acceleration of the earth's surface. He is considering in first place the linear velocity v of the Earths equator, knowing that it is zero at the poles. An acceleration doesnt appear at all in any 1905 Relativity formula. > 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. The centripetal acceleration of the Earths equator is the unique one we need to consider here, and only owed to its relation with the linear velocity v. > 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. You are making references to concepts developed AFTER 1905 (like local measurements and general relativity), forgetting that the topic in this thread refers only to 1905 Relativity (any concept developed in its future must be mantained out). 1905 Einstein is NOT approximating the Earth surface as an inertial frame. Even having the linear velocity v of its equator a near to c value, 1905 Relativity formulas and procedures remain valid. The Earth is rotating in the stationary space corresponding to the considered centre of mass (CM) inertial frame. What 1905 Einstein does is to consider the moving system (the clock at the equator) with an instantaneous uniform velocity v, that is not uniform at all, because the clock is really centripetal accelerated. We can have here a uniform speed (scalar), but not a uniform velocity (vector). To convince about it, read the relevant text almost at the end of paragraph 4: If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the travelled clock on its arrival at A will be (1/2)tv^2/c^2 second slow. Then, 1905 Relativity can be applied with ANY moving system, not only a one moving with a uniform velocity. This is supported by the huge experimental evidence of today GPS (including clocks centripetal accelerated). RVHG (Rafael Valls Hidalgo-Gato)
From: valls on 20 May 2010 19:39 On 20 mayo, 16:43, harald <h...(a)swissonline.ch> wrote: > On May 20, 4:28 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: > > > > > 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. > > Good / so now you do consider a not so alone particle, and even not a > point if you want to establish time measurements at different places. > The use of a material point to model part of our Universe as a unique entity is inherent to Newtonian mechanics since its beginning. You cant formulate any mechanical law (included the universal gravitation one) without modelling first all bodies as material points. The 1684 Principia was published only after Newton could prove that an Earth modelled by a material point in its centre of mass provokes the same action as the real Earth on bodies at its surface and more far away. My alone material point at rest can be up to the whole Universe (if it can be proved composed by a finite quantity of bodies). With Einsteins definition of time, you can synchronize a clock at ANY point of the space corresponding to ANY centre of mass inertial frame. I dont understand the meaning of your even not a point. Please, clear me that in your next post. > > 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?). > > Following your arguments elsewhere, here we dont care about what you > think. Einsteins thoery does not prefer one inertial system over the > other, it is not supporting your theory. > Long before Einstein, to any body set correspond a unique centre of mass inertial frame. You never have more than one CM inertial frame to describe the same body set (the holding of Newtons laws is the cause). By the way, we are considering here only 1905 Relativity (and I was born long after that epoch). 1905 Einstein can support only 1905 Relativity. > Regards, > Harald > > > > > 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) RVHG (Rafael Valls Hidalgo-Gato)
From: Dono. on 20 May 2010 20:30 On May 20, 4:39 pm, va...(a)icmf.inf.cu wrote: > and I was born long after that epoch). Judging by your advanced level of senility, this isn't true.
From: Inertial on 20 May 2010 22:42
<valls(a)icmf.inf.cu> wrote in message news:c13b9123-0513-4072-8dc5-54557b8cfaf5(a)y12g2000vbr.googlegroups.com... > 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) Yeup .. do you think that is a problem? |