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| Tags: contraction, length, measurements, possible |
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#1
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Friends,
In a separate thread titled 'Is length contraction of a rod real or perspective???', it is being argued that the length contraction of a rod observed by moving observers is only apparent and not real. The analysis given below shows that this apparent contraction actually does not affect the length measurements in any way. Coordinate Systems: The cardinal idea responsible for the invention of coordinate systems by Descartes consists of the assumption that to each real number there corresponds a unique point on a straight line. We choose a straight line X and a point O on it, which we call the origin. We choose a point A and call the length of the line segment OA, the unit length. Next we pick up any point P on this line X, as shown in the figure and take the ratio of the lengths of the line segments OP and OA. Let this ratio OP/OA be equal to x. The number x is called the coordinate of P. ......O...........A............................... ...P............. X The association of the set of points P on coordinate line X with the set of real numbers x, constitutes a coordinate system of the one-dimensional SPACE, once the notion of certain 'unit length' OA has been defined. Therefore, when we say that the coordinate of point P is x, it implies that the ratio OP/OA be equal to x. The distance OP or the length of line segment OP is associated with the coordinate x as OP = x.OA = x times unit length OA If OA is defined to be 1 meter then OP = x meters Now let us consider a pole of length L and a small standard rod of unit length Lu as shown below such that the pole is laid parallel to X-axis of a suitable coordinate system K0. ...... Lu ............................... L Suppose the unit length Lu is of one meter. Then to determine the length L of the pole in meters, we have to carry out a measurement process something like the one illustrated below. [For the sake of argument we may assume that this measurement process is automated and keeps getting repeated all the time.] ...... 1 ............................... L ..... 2 ............................... L ..... 3 ............................... L ..... 4 ............................... L ..... 5 ............................... L ..... 6 ............................... L This measurement shows that the length L of the pole is 6 meters. This can also be expressed as the ratio of L/Lu . L/Lu = 6 or, L = 6 Lu = 6 meters. Now let us imagine that this pole is observed from some far away location from where the objects appear to be much smaller in size. Even from this far away location the measured length of the pole is still found to be 6 meters. Next let us imagine that this pole is being observed from inertial reference frames K1, K2, K3 etc in relative uniform motion along X-axis of K0. For all observers in relative uniform motion wrt the pole, the lengths L and Lu will *appear* to be shorter (say L' and Lu') by their respective gamma factors. But the length of the pole measured with the standard meter rod is still found to be 6 meters since the ratio of the apparent lengths L' and Lu' is still the same L'/Lu' =6. Therefore it can be safely concluded that the length of a 6 m pole measured with a standard meter rod as per SI standards, will be found to be the same 6 m when observed from any inertial reference frame K1, K2, K3 etc. in relative uniform motion. This shows that the assertion of SR regarding contraction of length measurements of physical objects when observed from reference frames in relative uniform motion is *wrong* and just a facade. GSS |
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#2
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Space Interferometry Mission as a Test of Lorentz Length Contraction http://renshaw.teleinc.com/papers/simiee2/simiee2.stm Abstract--A basic tenet of special relativity is the concept of length contraction seen by an observer in motion. Lorentz contraction, which changes the apparent location of a light source, combines with aberration, which changes the apparent direction to the source, producing a variety of effects. While aberration has been confirmed, Lorentz contraction has never been tested directly, due to the generally negligible size of the effect. As the earth orbits the sun, Lorentz contraction offsets the apparent position of a distant source by as much as 18 micro-arcseconds (mas) per degree of separation. This offset is in addition to that caused by aberration. The Space Interferometry Mission, due for launch in 2005, promises a resolution of +/- 1 mas in a field of view of one degree, allowing for the first time the direct confirmation of Lorentz length contraction, one-hundred years after the introduction of Einstein's special theory of relativity in 1905. Space Interferometry Mission http://planetquest.jpl.nasa.gov/SIM/sim_index.cfm |
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#3
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Sorry, Dirk Vdm
I corrected the original illustration because it was not showing properly. As far as accented meters is concerned, I consider the standard meter as the 'standard' as per SI standards. It is not possible to regard it as changeable as per apparent observations and still consider it as a 'standard'. GSS |
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#4
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"GSS" wrote in message ups.com... Sorry, Dirk Vdm I corrected the original illustration because it was not showing properly. As far as accented meters is concerned, I consider the standard meter as the 'standard' as per SI standards. And first you call it Lu and a bit later you call it Lu'. It is not possible to regard it as changeable as per apparent observations and still consider it as a 'standard'. But first you call it Lu and a bit later you call it Lu'. Now, make the exercise I gave you: It does not show "that the assertion of SR regarding length contraction of physical objects when observed from reference frames in relative uniform motion is *wrong* and just a facade." It shows something else. Exercise: what does it show? Dirk Vdm |
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#5
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On Sat, 18 Mar 2006 11:04:46 -0800, GSS wrote:
Friends, In a separate thread titled 'Is length contraction of a rod real or perspective???', it is being argued that the length contraction of a rod observed by moving observers is only apparent and not real. The analysis given below shows that this apparent contraction actually does not affect the length measurements in any way. I'm not sure what a "length measurement" is in the context of a rod moving by me; the best I can do is to affix two lights to the rod and measure the time between light pulses generated by the rod (which leads to one measurement), or affix two mirrors to the rod and measure the time between light pulses generated by me (which leads to another). Either way, one has to be very careful on how one performs the measurement, as one is beset by two problems. [1] The rod is moving, if the lights do not flash. [2] The lights may or may not be synchronized if they flash. Light speed, after all, is not infinite; this was known even in Galileo's time (and Galileo came up with a surprisingly good figure for lightspeed even back then; the main problem was that the distance to Jupiter was not quite right). A proper theoretical calculation using this space-time equivalence would result in the following. Since you're already using O and A I'm going to have to alter my notation a bit; let O be the non-moving observer, as before, with coordinate system (x_O, t_O)_O; the moving rod will be M in this variant, with coordinate system (x_M, t_M)_M; the relationship will be the Lorentz, as hypothesized by SR: x_M = (x_O - v * t_O)*g t_M = (t_O - v * x_O/c^2)*g and therefore x_O = (x_M + v * t_M)*g t_O = (t_M + v * x_M/c^2)*g where g = 1/sqrt(1-v^2/c^2), as usual. This also means that (x_O,t_O)_O = ( (x_O - v*t_O)*g, (t_O - v*x_O/c^2)*g)_M (x_M,t_M)_M = ( (x_M + v*t_M)*g, (t_M + v*x_M)/c^2)*g)_O If the lights are not flashing then one is essentially trying to measure two events, with one event being (0,t_M)_M and the other being (L, t'_M)_M for some values t_M and t'_M. For convenience we set t_M = 0; this immediately yields t_O = 0 as well in the Lorentz. For various reasons, however, t'_M is not necessarily zero without a lot of work. If O allows the rod to pass over him, then t'_O is nonzero anyway (it takes time for the second endpoint to move over the observer, after all), and therefore trying to set t'_M = 0 is slightly pointless. Since O is forever locked to his origin, one is essentially solving the equation x'_O = 0 with x'_M = L This gives t'_M = -L/v and t'_O = (-L/v + v*L/c^2)*g = (L/v)(-1 + v^2/c^2)*g = -L/(vg). Since v is ostensibly known the rod has effectively shrunk in this measurement scenario. If the lights *are* flashing then we are measuring two times from flash events at (0,0)_M and (L,0)_M. This means t_M = t'_M = 0. However, t'_O is *not* zero, but vgL/c^2. Since x'_O = gL O cannot observe this directly but must wait abs(x'_O/c) = x'_O/c time units for the flash to reach him (SR assumes lightspeed is c everywhere). Total time between flashes is therefore (gL/c + vGL/c^2) = (gL/c)*(1+v/c) = (L/c)*sqrt(1+v/c)/sqrt(1-v/c), and in this scenario the rod is now *longer*. If we are using mirrors and a single (radar/lidar) flash from (0,0)_O = (0,0)_M, then in M-space the flash to the far endpoint can be rendered (L,L/c)_M = ( (L+vL/c)*g, L/c+vL/c^2)*g)_O. The time it takes O to see the second flash is therefore simply twice the value (L/c + vL/c^2)*g = (L/c)*sqrt(1+v/c)/sqrt(1-v/c) again. Weird goings-on, to be sure. Coordinate Systems: The cardinal idea responsible for the invention of coordinate systems by Descartes consists of the assumption that to each real number there corresponds a unique point on a straight line. We choose a straight line X and a point O on it, which we call the origin. We choose a point A and call the length of the line segment OA, the unit length. Next we pick up any point P on this line X, as shown in the figure and take the ratio of the lengths of the line segments OP and OA. Let this ratio OP/OA be equal to x. The number x is called the coordinate of P. .....O...........A................................ ..P............. X The association of the set of points P on coordinate line X with the set of real numbers x, constitutes a coordinate system of the one-dimensional SPACE, once the notion of certain 'unit length' OA has been defined. Therefore, when we say that the coordinate of point P is x, it implies that the ratio OP/OA be equal to x. The distance OP or the length of line segment OP is associated with the coordinate x as OP = x.OA = x times unit length OA If OA is defined to be 1 meter then OP = x meters Now let us consider a pole of length L and a small standard rod of unit length Lu as shown below such that the pole is laid parallel to X-axis of a suitable coordinate system K0. ..... Lu .............................. L Suppose the unit length Lu is of one meter. Then to determine the length L of the pole in meters, we have to carry out a measurement process something like the one illustrated below. [For the sake of argument we may assume that this measurement process is automated and keeps getting repeated all the time.] ..... 1 .............................. L ..... 2 .............................. L ..... 3 .............................. L ..... 4 .............................. L ..... 5 .............................. L ..... 6 .............................. L This measurement shows that the length L of the pole is 6 meters. This can also be expressed as the ratio of L/Lu . L/Lu = 6 or, L = 6 Lu = 6 meters. Now let us imagine that this pole is observed from some far away location from where the objects appear to be much smaller in size. Even from this far away location the measured length of the pole is still found to be 6 meters. Next let us imagine that this pole is being observed from inertial reference frames K1, K2, K3 etc in relative uniform motion along X-axis of K0. For all observers in relative uniform motion wrt the pole, the lengths L and Lu will *appear* to be shorter (say L' and Lu') by their respective gamma factors. But the length of the pole measured with the standard meter rod is still found to be 6 meters since the ratio of the apparent lengths L' and Lu' is still the same L'/Lu' =6. Therefore it can be safely concluded that the length of a 6 m pole measured with a standard meter rod as per SI standards, will be found to be the same 6 m when observed from any inertial reference frame K1, K2, K3 etc. in relative uniform motion. It turns out that, if both rods are moving, both are contracted by the same amount. One can observe the measurement method from a number of spots and one will still get the same result; the problem is that the measurement is being conducted from the *stationary* rod's reference frame. This is valid but problematic in establishing what the length of the rod is in the *moving* reference frame. This shows that the assertion of SR regarding contraction of length measurements of physical objects when observed from reference frames in relative uniform motion is *wrong* and just a facade. No, it simply means that your measurement is not doing what you seem to think it is doing. GSS -- #191, It's still legal to go .sigless. |
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Dirk Vdm wrote:
.... But first you call it Lu and a bit later you call it Lu'. Let me repeat the relevant part of my post for clarification. [Coordinate Systems: The cardinal idea responsible for the invention of coordinate systems by Descartes consists of the assumption that to each real number there corresponds a unique point on a straight line. We choose a straight line X and a point O on it, which we call the origin. We choose a point A and call the length of the line segment OA, the unit length. Next we pick up any point P on this line X, as shown in the figure and take the ratio of the lengths of the line segments OP and OA. Let this ratio OP/OA be equal to x. The number x is called the coordinate of P. ......O...........A............................... ...P............. X The association of the set of points P on coordinate line X with the set of real numbers x, constitutes a coordinate system of the one-dimensional SPACE, once the notion of certain 'unit length' OA has been defined. Therefore, when we say that the coordinate of point P is x, it implies that the ratio OP/OA be equal to x. The distance OP or the length of line segment OP is associated with the coordinate x as OP = x.OA = x times unit length OA If OA is defined to be 1 meter then OP = x meters Now let us consider a pole of length L and a small standard rod of unit length Lu as shown below such that the pole is laid parallel to X-axis of a suitable coordinate system K0. ...... Lu ............................... L ] Let us imagine that this pole is observed from some far away location from where the objects *appear* to be much smaller in size say Lu' and L'. Even from this far away location the measured length of the pole is still found to be the same. Mind you here Lu' and L' are the apparently reduced sizes because of the observation from a long distance. Lu' is still the meter rod even though it *appears* to be smaller in size. Similarly let us imagine that this pole is being observed from inertial reference frames K1, K2, K3 etc in relative uniform motion along X-axis of K0. For all observers in relative uniform motion wrt the pole, the lengths L and Lu will *appear* to be shorter (say L' and Lu'). But the length of the pole measured with the standard meter rod is still found to be the same since this measurement just depicts the ratio of L' and Lu'. Here we are essentially talking about the *measurement reading* as per standard notions. Now, make the exercise I gave you: It does not show "that the assertion of SR regarding length contraction of physical objects when observed from reference frames in relative uniform motion is *wrong* and just a facade." It shows something else. Exercise: what does it show? No, it still shows that the assertions of SR regarding length contraction of physical objects when observed from reference frames in relative uniform motion is *wrong* and just a facade. Two prominent justifications for this observation are : (a) As shown above the coordinate x of a point P is just a *ratio* of two length segments, namely OP and OA. In SR this *ratio* representing the coordinate x is claimed to transform to x' in moving coordinate system. This is logically and fundamentally *wrong*. Possibly under certain situations, as for example while observing from a distance, the length segments OP and OA might *appear* to be shorter but their ratio just cannot change. (b) The second postulate of SR depicts a fundamentally and logically wrong assumption that the speed of light in vacuum is the same constant c in all reference frames in relative uniform motion. This assumption is built in to the following relation involving space-time interval dS, (dS)^2 = (dx)^2 + (dy)^2 + (dz)^2 - (c.dt)^2 = (dx')^2 + (dy')^2 + (dz')^2 - (c.dt')^2 Just to comply with this wrong assumption, the notion of time as an absolute measure of change has been sacrificed in SR, leading to wrong notions of relative time and consequent wrong notions of length contractions. This wrong assumption has given rise to such fundamentally absurd convictions among SR followers that they really believe that the time intervals *dt* of a standard atomic clock will be seen to be *different* in each of the infinitely many reference frames in relative motion!! In my opinion it is a matter of shame on the collective intelligence of Humanity that such absurd notions of SR are still lingering on in this 21st century. All that just for defending one wrong assumption!!! GSS |
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#7
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"GSS" wrote in message ups.com... Dirk Vdm wrote: ... But first you call it Lu and a bit later you call it Lu'. Let me repeat the relevant part of my post for clarification. There is no need to repeat it, so I snip it up to the point where you went wrong. [snip] Similarly let us imagine that this pole is being observed from inertial reference frames K1, K2, K3 etc in relative uniform motion along X-axis of K0. For all observers in relative uniform motion wrt the pole, the lengths L and Lu will *appear* to be shorter (say L' and Lu'). But the length of the pole measured with the standard meter rod is still found to be the same since this measurement just depicts the ratio of L' and Lu'. So the length is not 10 meters, but 10 "accented-meters" If you measure a thing that is moving with respect to yourself, then you are supposed to compare with *your* measuring rod, not with some rod that is flying with the object you are measuring. Here we are essentially talking about the *measurement reading* as per standard notions. In your scheme you first compare with Lu. Then you compare with Lu'. That is not a standard. Now, make the exercise I gave you: It does not show "that the assertion of SR regarding length contraction of physical objects when observed from reference frames in relative uniform motion is *wrong* and just a facade." It shows something else. Exercise: what does it show? No, it still shows that the assertions of SR regarding length contraction of physical objects when observed from reference frames in relative uniform motion is *wrong* and just a facade. Two prominent justifications for this observation are : (a) As shown above the coordinate x of a point P is just a *ratio* of two length segments, namely OP and OA. In SR this *ratio* representing the coordinate x is claimed to transform to x' in moving coordinate system. And that x' is not the ratio of L'/Lu'. This is logically and fundamentally *wrong*. Indeed, it is definitely logically and fundamentally *wrong*. It is also not what SR says. I have seen many blatant misconceptions of SR on this forum, but this must be the most stupid one ever. My very sincere congratulations. Possibly under certain situations, as for example while observing from a distance, the length segments OP and OA might *appear* to be shorter but their ratio just cannot change. (b) The second postulate of SR depicts a fundamentally and logically wrong assumption that the speed of light in vacuum is the same constant c in all reference frames in relative uniform motion. If you call something that is observed over and over during the last 150 years "a fundamentally and logically wrong assumption", that is of course your business. But since you seem to be such an ignorant and arrogant imbecile, I will not bother attempting to explain. Surely *that* you must understand. This assumption is built in to the following relation involving space-time interval dS, (dS)^2 = (dx)^2 + (dy)^2 + (dz)^2 - (c.dt)^2 = (dx')^2 + (dy')^2 + (dz')^2 - (c.dt')^2 Just to comply with this wrong assumption, the notion of time as an absolute measure of change has been sacrificed in SR, leading to wrong notions of relative time and consequent wrong notions of length contractions. This wrong assumption has given rise to such fundamentally absurd convictions among SR followers that they really believe that the time intervals *dt* of a standard atomic clock will be seen to be *different* in each of the infinitely many reference frames in relative motion!! In my opinion it is a matter of shame on the collective intelligence of Humanity that such absurd notions of SR are still lingering on in this 21st century. All that just for defending one wrong assumption!!! You sound like Thomas Smid in disguise. Dirk Vdm |
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#8
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"Sam Wormley" schreef in bericht news:H%YSf.35334$oL.15374@attbi_s71... Space Interferometry Mission as a Test of Lorentz Length Contraction http://renshaw.teleinc.com/papers/simiee2/simiee2.stm Abstract--A basic tenet of special relativity is the concept of length contraction seen by an observer in motion. This is a very interesting document, but it also raises certain issues. 1. IMO in the document two different "types" of length contraction are discussed: Object length related and Distance related. 2. In figure 3 Length contraction of a moving train is discussed. The observer is stationary or resting. (Object length related) 3. In Figure 1 the distance between telephone poles is discussed. Observation point of view is the train, which has a speed v. The background, the poles are "fixed". In figure 5 length contaction based on the distance between stars is discussed. Observation point of view is the Earth and is in motion. The background, the stars are "fixed". (Distance related) 4. At page 144 "Subtle is the Lord" by Abraham Pais is written: "The question whether the Lorentz contraction does or does not exist is confusing. It does not "really" exist in so far as it does not exist for an observer who moves with the rod; it "really" exists, however, in the sense, that it can as a matter of principle be demonstrated by a resting observer". 5. IMO what the SIM does is to demonstrate length contration based on distance, in this particular case distance between stars. That is not what is discussed in the above mentioned quotation which discusses length contraction of an object. Length Contraction based on the distance between the poles and the distance between the stars, IMO if observed by a moving observer, represents more a vissible illusion and is not real and not physical related. 6. Above figure 3, in order to test length contraction of the train, there is written: "that a different set of contacts is required". I agree with that. This is in agreement with the coments I made in the thread: "Is length contraction of a rod real or perspective???" which raises two issues with "relativity of simultaneity" and a moving train. For an overview see: http://users.pandora.be/nicvroom/sim...y.htm#remarks2 Nicolaas Vroom http://users.pandora.be/nicvroom/ Space Interferometry Mission http://planetquest.jpl.nasa.gov/SIM/sim_index.cfm |
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#9
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GSS wrote: Friends, In a separate thread titled 'Is length contraction of a rod real or perspective???', it is being argued that the length contraction of a rod observed by moving observers is only apparent and not real. The analysis given below shows that this apparent contraction actually does not affect the length measurements in any way. Coordinate Systems: The cardinal idea responsible for the invention of coordinate systems by Descartes consists of the assumption that to each real number there corresponds a unique point on a straight line. We choose a straight line X and a point O on it, which we call the origin. We choose a point A and call the length of the line segment OA, the unit length. Next we pick up any point P on this line X, as shown in the figure and take the ratio of the lengths of the line segments OP and OA. Let this ratio OP/OA be equal to x. The number x is called the coordinate of P. .....O...........A................................ ..P............. X The association of the set of points P on coordinate line X with the set of real numbers x, constitutes a coordinate system of the one-dimensional SPACE, once the notion of certain 'unit length' OA has been defined. Therefore, when we say that the coordinate of point P is x, it implies that the ratio OP/OA be equal to x. The distance OP or the length of line segment OP is associated with the coordinate x as OP = x.OA = x times unit length OA If OA is defined to be 1 meter then OP = x meters Now let us consider a pole of length L and a small standard rod of unit length Lu as shown below such that the pole is laid parallel to X-axis of a suitable coordinate system K0. ..... Lu .............................. L Suppose the unit length Lu is of one meter. Then to determine the length L of the pole in meters, we have to carry out a measurement process something like the one illustrated below. [For the sake of argument we may assume that this measurement process is automated and keeps getting repeated all the time.] ..... 1 .............................. L ..... 2 .............................. L ..... 3 .............................. L ..... 4 .............................. L ..... 5 .............................. L ..... 6 .............................. L This measurement shows that the length L of the pole is 6 meters. This can also be expressed as the ratio of L/Lu . You'll note this procedure works ONLY if L is laying still on the ground, so that you have the freedom to pick up Lu and move it around. You'll note that this procedure breaks immediately if L is moving. This means that this procedure must be modified somehow to accomodate moving lengths. And this is where the fun begins. PD L/Lu = 6 or, L = 6 Lu = 6 meters. Now let us imagine that this pole is observed from some far away location from where the objects appear to be much smaller in size. Even from this far away location the measured length of the pole is still found to be 6 meters. Next let us imagine that this pole is being observed from inertial reference frames K1, K2, K3 etc in relative uniform motion along X-axis of K0. For all observers in relative uniform motion wrt the pole, the lengths L and Lu will *appear* to be shorter (say L' and Lu') by their respective gamma factors. But the length of the pole measured with the standard meter rod is still found to be 6 meters since the ratio of the apparent lengths L' and Lu' is still the same L'/Lu' =6. Therefore it can be safely concluded that the length of a 6 m pole measured with a standard meter rod as per SI standards, will be found to be the same 6 m when observed from any inertial reference frame K1, K2, K3 etc. in relative uniform motion. This shows that the assertion of SR regarding contraction of length measurements of physical objects when observed from reference frames in relative uniform motion is *wrong* and just a facade. GSS |
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#10
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"Nicolaaas Vroom" schreef in bericht ... "Sam Wormley" schreef in bericht news:H%YSf.35334$oL.15374@attbi_s71... Space Interferometry Mission as a Test of Lorentz Length Contraction http://renshaw.teleinc.com/papers/simiee2/simiee2.stm Abstract--A basic tenet of special relativity is the concept of length contraction seen by an observer in motion. This is a very interesting document, but it also raises certain issues. 1. IMO in the document two different "types" of length contraction are discussed: Object length related and Distance related. 5. IMO what the SIM does is to demonstrate length contration based on distance, in this particular case distance between stars. That is not what is discussed in the above mentioned quotation which discusses length contraction of an object. Length Contraction based on the distance between the poles and the distance between the stars, IMO if observed by a moving observer, represents more a vissible illusion and is not real and not physical related. 6. Above figure 3, in order to test length contraction of the train, there is written: "that a different set of contacts is required". I agree with that. This is in agreement with the coments I made in the thread: "Is length contraction of a rod real or perspective???" which raises two issues with "relativity of simultaneity" and a moving train. For an overview see: http://users.pandora.be/nicvroom/sim...y.htm#remarks2 Nicolaas Vroom http://users.pandora.be/nicvroom/ In the above mentioned post I made some remarks pointing out a difference between length contraction of a physical object versus space i.e. the distance between two objects. IMO length contraction is only possible in the first case. As such SIM, because it observes the position of stars, what ever the explanation is, IMO it does not prove length contraction. Any comments ? Nicolaas Vroom |
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