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Einstein (1905) Absurdities

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Subject: 1. Purpose Einstein violated simple logic (many times), common sense, the basic principles of analytic geometry, vector algebra, and elementary measurement theory in deriving the transfor- matin equations at the heart of Special Relativity. We explicate many of his absurdities. In all cases we are discussing his 1905 paper in which he presented the derivation of SR. We are using the Dover edition of "The Principle of Relativity" in which the title page is on p-35. By the way, our frequently asked question - often asserted as fact - is in one form or another: Isn't Special Relativity silly? ----------------------------------------------------------- Note: Everywhere in this document, we use @ to represent the curly deltas used for partial derivatives. Einstein used the curly deltas. -----------------------------------------------------------
Subject: 2. Table of Contents 1. Foreword and Intent 2. Table of Contents 3. The light direction absurdity. 4. The really strange and marvelous magical gamma absurdity. 5. The amazing transverse gamma absurdity. 6. The time increases as distance decreases absurdity. 7. Simultaneity and Measurement Prologue. 8. The data scale degradation absurdity. 9. The absolute simultaneity SR transforms. 10. The Relativistic Maxwell absurdity. 11. The Twins Paradox absurdity. 12. The "how does an absurd SR work" non-absurdity. 13. The "strange effects of nothing" absurdities. 14. The "lasting effects of no effect" absurdity. 15. The "brag about your absurdities" absurdity. 16. Einstein's anti-simultaneity argument. 17. A straightforward pro-simultaneity argument.
Subject: 3. The light direction absurdity. Having derived his differential equation and subse- uent tau function based on light moving in both directions, he then substitutes - for t - an expression for time that is valid only for one light direction. This creates a transform formula that could be valid only for one direction. Substituting the opposite direction expression is just as invalid, and results in a diff- erent transform for x to x'. ----------------------------------------------------------- At one point, Einstein attains a formula for what we'll call X', the transformed x; it is based on the tau equation he got from from his differential equation: X' = c*tau = ac(t-vx'/(cc-vv)). He then returns to the time arguments of his unknown tau functions, where he had t=x'/(c-v). He substitutes this expression into the X' formula above, to get: X' = accx'/(cc-vv). Remembering that Einstein's model, his unknown tau functions, his differential equation, and resultant tau function are all about light going BOTH directions, we see that using the time expression for just one light direction is an error, and time in the other direction, t=x'/(c+v), is just as valid, - which is to say not at all valid. The algebra works out just a bit differently: X' = ac(x'/(c+v)-vx'/(cc-vv)). = ac(x'(c-v)-vx')/(cc-vv) = ac(cx'-vx'-vx')/(cc-vv) = ac(cx'-2vx')/(cc-vv). QED. Einstein's derivation of the x' transform is invalid by reduction to the absurd; the transform depends on the direction of the light movement in the time term substituted for t in the X'=c*tau equation, an absolute violation of the principles of Special Relativity. It is one thing to realize that an expression in one case differs from the other, but a very different thing to let your one and only transform formula's derivation depend on an arbitrary choice of just one light direction.
Subject: 4. The really strange and marvelous magical gamma absurdity. Perhaps the most marvelous thing about Einstein's Special Relativity derivation is the math he used to get from his tau function in t and x' to his tau=f(t,x) transform. [We let his a=phi(v)=1, as he concludes later.] [1] tau = (t-vx'/(cc-vv)). [2] tau = (t-vx/cc)/sqrt(1-(v/c)^2). First of all, to get to [2], we certainly have to rid [1] of x'. x'=x-vt. [3] tau = (t-v(x-vt)/(cc-vv)) = (tcc-tvv-vx-vvt)/(cc-vv) = (tcc - vx)/(cc-vv) Now, divide numerator and denominator on the right by cc: [4] tau = (t-vx/cc)/(1-vv/cc). There's only one way to get [2] from [4]. Let tau<>tau, a logical absurdity in this situation; Einstein has proceeded far beyond tau the unknown function. The only unknown is a, which he later says is phi(v)=1. And if it is legal to get [2] by multiplying only one side by sqrt(1-vv/cc), then it is also correct to multiply only one side by (1-vv/cc), and get the galilean transform. Or to multiply one side by pi and get "t and -vx/cc are really circle diameters" transforms. [You know, the circumference of a circle is Pi*diameter?] But in all cases - both the absurd Einsteinian and Pi transforms - it is not legal to treat only one side of an equation in a non-identity fashion. The left side of the tau function would not be tau, but gamma*tau or Pi*tau. The appearance of gamma is just as magically marvelous in the X' transform (we used X' for the moving system x value coordinate, remember?): X' = ccx'/(cc-vv). = (ccx-ccvt)/(cc-vv) = (x-vt)/(1-vv/cc). Not X' = (x-vt)/sqrt(1-vv/cc).
Subject: 5. The amazing transverse gamma absurdity. Gamma=1/sqrt(1-vv/cc) (he called it beta, but tradition now calls it gamma) appeared magically in Einstein's t' and x' transforms, replacing the mundane 1/(1-vv/cc) without cause, reason, or justification. But Einstein did cause it to appear in expressions for the transformed y and z axes. All he had to do was say light movement along these transverse axes was at the rate sqrt(cc-vv). Remember, the (c-v) and (c+v) expressions Einstein used were not due to non-c light velocity, but due to the movement of objects toward which the light was moving. That condition does not hold in the y and z directions in his derivation. "In an analogous manner we find, by considering rays moving along the other two axes, that Y' = c*tau = ac(t-vx'/(cc-vv)) when t=y/sqrt(cc-vv), x'=0." When x'=0, we find that Y' = c*tau = act, just as every SRian in the universe agrees. In any case, the t=y/sqrt(cc-vv) line is the full, ridiculous justification Einstein gives for the existence of the expression sqrt(1-vv/cc). Ridiculous? Sure, x'=0 is a rather small subset of the possibilities for x'; how do you generalize to the full range of the universe from x'=0? And there is not even the hint of a justification for replacing (1-vv/cc) with its square root in his time and space (x) transforms. QED: Einstein's SR time transform derivation is invalid by reduction to the absurd: it is eithered based on the premise that x'=0 and not x'<>0, or based on nothing.
Subject: 6. The time increases as distance decreases absurdity. Einstein uses his distance to the mirror x' with which to derive the differential equation and tau function from which he derives the t' and x' transforms of Special Rela- tivity. The greater that distance, the more time it takes for the light to travel either direction, and roundtrip. But Einstein concludes that the slope of tau wrt the dist- ance to the mirror is the inverse of the slope wrt the time it takes. Einstein's x' is the distance to the mirror, which also defines the distance back to the source at the moving origin. This distance shows up in the time expressions in his un- known tau functions, and when differentiated wrt x' gives a value of 1.00, proving that the x' of the @tau/@x' term is indeed the distance to the mirror and not the other x' in his model (yes, there are two; the other is the location of the light and/or the clock in use at the time). The greater the distance, the greater time it takes for light to cover the total and part-wise distances. But Einstein's differential equation and his resultant tau equation say that although tau increases when the distance increases, tau decreases when time increases, and vice versa. His differential equation is: (@tau/@x') + (v/(cc-vv))(@tau/@t) = 0. We put the two terms on opposite sides: (@tau/@x') = - (v/(cc-vv))(@tau/@t). Thus, either v must always be negative or the slope of tau with respect to x' is the negative of the slope of tau with respect to t. Yet, his model - for that very x' - is that x' and v together fully define t, and that the time - with a constant v, which is how Einstein treated v - increases as x' increases. This aburdity is repeated in his immediately consequent tau function: tau = a(t-vx'/(cc-vv)). There can be no doubt that the x' in the differential equation and the resultant tau function are the x' that is the distance to the mirror. When he different- iates the time expressions in his unknown taus wrt x', the slope of that distance x' is 1 wrt to the differen- tiating x'. QED, by reduction to the absurd, his derivation of the SR transformations is nonsense. It is based on a model in which tau increases with a greater x' and/or a greater t - t being an increasing function of an increasing x' - but Einstein's conclusion is that tau increases with one when it decreases with the other. Objection: But, you say, you said there were two x' usages. Surely the tau at the time the light returns to the moving origin, at location L=0, is later than the tau when light reaches the mirror at L=x'. That's a negative relationship. OK. That is saying tau is an obvious inverse function of the location coordinate. But the tau at emission is surely less than at either of the other occasions, and its L is zero also, making it a direct function of the location coordinate, by the same argument.
Subject: 7. Simultaneity and Measurement Prologue. Einstein - and Special Relativity - not only mixes apples and oranges, but treats indepen- dent variables as dependent variables, and vice versa. One of the first things a child learns about algebra is to not add apples and oranges. Special Relativity adds apples and orangutans. Apples and oranges are at least both fruit, so you could add them and get a fruit total. But Special Relativity adds space and time, and does so without justification. Yes, there is a derivation process (with some of the absurdities outlined above) but in no way does that derivation specify any reason why one should treat time and space as dimensions similar enough to add them up together. Yes, the units in the transform equations that mix the two together are compatible, but it is not a set of compatible measures that are con- sidered a four-D coordinate system. It is not space and ct that are the four axes, it is space and t. Should we also consider heat and space similar dimensions because a balloon will rise to greater heights as its gasses warm up? Should we also consider velocity and distance similar measures because we can multiply the one by time and get distance? That's identical to the math that makes time and space suppos- edly compatible measures. ----------------------------------------------- The worst thing about mixing time and space as does SR, is that there is no macro-world evidence whatsoever that time can ever be a dependent variable, which is what the SR transforms make of it. A dependent variable is one that you can control indirectly, through control of other variables. You can REALLY control how great a distance you go by choosing to move for only some certain time period at the given velocity and then not going further than that distance. But you can NEVER control how long a time you 'go', no matter what you do, unless you consider suicide as accomplishing that control. Time is not a dependent variable, but when you decide that t'=g(t-xv/cc), you are saying time is just such a dependent variable. -------------------------------------------------- But it is only by imagining that time is a dependent variable - that you can add it somehow with space - that allows SR to imagine its transforms are rotations and not translations. Imagine x as the verticle axis on your graph, time as the horizontal axis. If x'=gx-gvt is just moving the x-axis to the right, more and more as time goes by, then the transformation is just a shift in the axis with no implication that x (space) and time are the same stuff. If x'=gx-gvt is a rotation, as SR says, then the graphical equivalent is to tilt the x-axis somewhat toward the horizontal, somehow becoming part time and part space.
Subject: 8. The data scale degradation absurdity. The SR transforms and the Galilean transforms both convert good, ratio scale data to inferior interval scale data. The effect is corrected, allowed for, when the transforms are conducted on the generalized coordinate forms specified by analytic geometry - and vector algebra, for that matter - but SR refuses to do it right. The consequence is the appearance that simultaneity does not hold across inertial frames, and the consequence of that is the Twins Paradox absurdity. Both sets of transforms are 'translations' - lateral movements of an axis, increasing over time in these caes - but with the SR transform also containing a rescaling. It is the translation term, -vt in the x transform to x', and -xv/cc in the t transform to t', that degrades the ratio scale data to interval scale data. SR likes to consider its transforms just rotations, however, and in the case of 'good' rotations, ratio scale data quality is indeed preserved, but SR violates the conditions of good rotations; they are not rigid rotations and they don't appropriately rescale all the axes that must be rescaled to preserve compati- bility. The proof is in the pudding, and the pudding is the combination of simple tests of the transformations. We can tell if the transformed data are ratio scale or interval. Ratio scale data are like absolute Kelvin. A measure- ment of zero means there is zero quantity of the stuff being measured. Ratio scale data support add- ition, subtraction, multiplication, and division. The test of a ratio scale is that if one measure looks like twice as much as another, the stuff being measured is actually twice as much. With absolute Kelvin, 100 degrees really is twice the heat as 50 degrees. 200 degrees really is twice as much as 100. Interval scale data are like relative Celsius, which is why your science teacher wouldn't let you use it in gas law problems. There is only one mathematical operation interval scales support, and that has to be between two measures on the same scale: subtraction. 100 degrees relative (household) Celsius is not twice as much as 50; we have to convert the data to absolute Kelvin to tell us what the real ratio of termperatures is. However, whether we use absolute Kelvin or relative Celsius, the difference in the two temperature readings is the same: 50 degrees. Thus, if we know the real quantities of the 'stuff' being measured, we can tell if two measures are on a ratio scale by seeing if the ratio of the two measures is the same as the ratio of the known quant- ities. If a scale passes the ratio test, the interval scale test is automatically a pass. If the scale fails the ratio test, the interval scale test becomes the next in line. It isn't just the bare differences on an interval scale that provides the test, however. Differences in two interval scale measures are ratio scale, so it is ratios of two differences that tell the tale. Let's do some testing, and remember as we do that our concern is for whether or not the data are messed up, not with 'reasons', excuses, or avoidance. ------------------------------------------------------ Are we going to take a transformed length and see whether that length fits ratio or interval scale definitions? Of course, not. Interval scale data are ratio after one measure is subtracted from another. That is the major reason the SR transforms can be used in science. Let there be three rods, A, B, C, of length 10, 20, 40, respectively. These lengths are on a known ratio scale, our original x-axis, with one end of each rod at the origin, where x=0, and the other end at the coordinate that tells us the correct lengths. Note that these x-values are ratio scale only because one end of each rod is at x=0. That may remind you of the correct way to use a ruler or yard/meter-stick: put the zero end at one end of the thing you are measuring. Put the one mark there instead of the zero, and you have interval scale measures. Let a,b,c be x' at v=.7071c, t=0. Let A',B',C' be x' at v=.7071c, t=10. g=sqrt(1-(.7071)^2)=.7071. A B C a b c A' B' C' ---------------- -------------------- --------------------- 10 20 40 14.14 28.28 56.57 4.14 18.28 46.57 ---------------- -------------------- --------------------- B/A = 2 b/a = 2 B'/A' = 4.42 C/A = 4 c/a = 4 C'/A' = 11.25 C/B = 2 c/b = 2 C'/B' = 2.55 C-A = 10 b-a = 14.14 B'-A' = 14.14 C-A = 30 c-a = 32.52 C'-A' = 42.42 C-B = 20 c-b = 28.28 C'-B' = 28.28 (C-A)/(B-A) = 3 (c-a)/(b-a) = 3 (C'-A')/(B'-A') = 3 (C-B)/(B-A) = 2 (c-b)/(b-a) = 2 (C'-B')/(B'-A') = 2. The results show that the primed data (a,b,c) are ratio scale as we'd expect since the vt term is zero. The ratios b/a, etc, are the same as the known ratio scale ratios, B/A, etc. When vt=0 the data are still ratio scale, but the rescaling is why the differences (b-a, etc) are not the same as before transform. The simple ratios prove the data still ratio, and the ratios of differences [(c-a)/(b-a), etc] just support that finding. When vt<>0, the data (A',B',C') are no longer ratio scale, which is why the simple ratios now differ from both the original and vt=0 data. However, the ratios of differences show us that the data do satisfy the one mathematical operation of subtraction, the differences thus being shown to be ratio scale. If you do not understand that the above data table proves that the SR transforms did indeed degrade the ratio scale to interval scale, please study it until you understand. --------------------------------------------------- If we remember that the only effect of gamma=g is to rescale the data, we realize that the above results and conclusions also apply to the galilean transform. As we said in the introduction of this Subject, use of the generalized cartesian coordinate form corrects the interval scale problem. Using this form for the galilean transformation upgrades the traditional, incompetent, non-invariant transform of laws/equations up to invariant (so to speak) invariance. To test the results of the use of the generalized cartesian coordinate form, with (x-x0) instead of just (x), we can again let the SR version stand in for both the galilean and SR results. Here, our unprimed data were with x0=0. Let a,b,c be x' at v=.7071c, t=0. Let A',B',C' be x' at v=.7071c, t=10. g=sqrt(1-(.7071)^2)=.7071. a'= b'= c'= A B C x0 (A-x0)' (B-x0)' (C-x0)' x0' ---------------- -------------------------------- 10 20 40 0 14.14 28.28 56.57 -10 ---------------- -------------------------------- B/A = 2 b'/a' = 2 C/A = 4 c'/a' = 4 C/B = 2 c'/b' = 2 C-A = 10 b'-a' = 14.14 C-A = 30 c'-a' = 42.42 C-B = 20 c'-b' = 28.28 (C-A)/(B-A) = 3 (c'-a')/(b'-a') = 3 (C-B)/(B-A) = 2 (c'-b')/(b'-a') = 2. The above data table shows us that focusing on (x-x0), instead of just plain x, will give us ratio scale data in any equation the transforms are applied to. Use of the generalized coordinate form verifies the interval nature of the transforms. Just as one x' subtracted from another on the same scale is a ratio scale result, just so does subtracting x0' from every x' create a ratio scale result. There is absolutely nothing about the SR transform derivation that says to not use the generalized coordinate form, absolutely nothing to gain by insisting - so to speak - on using interval scale data in your equations. To do so is absolutely absurd. Doing so is a sufficient cause of the obvious simultaneity problem of Special Relativity, which is itself the cause of the absurd Twins Paradox mess.
Subject: 9. The absolute simultaneity SR transforms. Above we have shown that there is a problem with Einstein's idea that simultaneity is not absolute across inertial frames. Here, we add one more demonstration, based on insisting on use of the generalized cartesian coordinate form in our transformed equations, as a means of avoiding data degradation from ratio scale to interval scale. Using analytic geometry's obvious (x-x0) form, where x0 is an important 'anchor' or 'centroid' such as a circle center, we apply the SR transforms, x'=gx-gvt, and t'=gt-gxv/cc. (a) (x'-x0')=[ g(x-vt) - g(x0-vt) ] = g(x-x0); this shows (1) that the transform is thus a rescaled invariant, and (2) one x transforms to only one x', regardless of t. (b) (t'-t0')=[ g(t-vx/cc) - g(t0-vx/cc) ] = g(t-t0); this shows (1) that the transform is thus a rescaled invariant, and (2) one t transforms to only one t', regardless of x. (c) therefore any pair of points (xa,tc), (xb,tc) transform to one and only one (xa',tc') and (xb',tc') pair, which shows that time transformed intervals do not depend on location and therefore absolute simultaneity holds. (d) therefore any pair of points (xc,ta), (xc,tb) transform to one and only one (xc',ta') and (xc',tb') pair, which shows that spatial transformed intervals do not depend on time, and therefore absolute spatial congruence holds.
Subject: 10. The Relativistic Maxwell absurdity. When True Believer crackpots are shown the simple demonstration that the galilean transform on generalized cartesian coordinates is invariant, their first defense is usually an incredibly stupid "x0'=x0, because the coordinate of a circle center, or point of emission, etc, is a constant and can't be transformed." The last defense is "but Maxwell's equations are not invariant under that coordinate transform." When asked just what magic occurs in Maxwell that would prevent the simple algebra (x'-x0')=[ (x-vt)-(x0-vt) ]=(x-x0) from working, and when asked them for a demonstration, they will never do so, however many hundreds of times their defense is asserted. The reason may help you understand part of Einstein's 1905 paper in which he gave us his absurd Special Relativity derivation: THERE ARE NO COORDINATES IN THE EQUATIONS TO BE TRANSFORMED. Einstein gave the electric force vector as E=(X,Y,Z) and the magnetic force vector as B=(L,M,N), where the force components in the direction of the x axis are X and L, Y and M are in the y direction, Z and N in the z direction. Those values are not, however, coordinates, but values very much like acceleration values. BTW, the current fad is that E and B are 'fields', having been 'force fields' for a while, after being 'forces'. So, when Einstein says he is applying his coordinate transforms to the Maxwell form he presented, he is either delusive or lying. (a) there are no coordinates in the transform equations he gives us for the Maxwell transforms, where B=beta=1/sqrt(1-(v/c)^2): X'=X. L'=L. Y'=B(Y-(v/c)N). M'=B(M+(v/c)Z). Z'=B(Z+(v/c)M). N'=B(N-(v/c)Y). X is in the same direction as x, but is not a coordinate. Ditto for L. They are not locations, coordinates on the x-axis, but force magnitudes in that direction. Similarly for Y and M and y, Z and N and z. (b) the v of the "coordinate transforms" are in Maxwell before any transform is imposed; Einstein's transform v is the velocity of a coordinate axis, not the velocity of a particle, which is what was in the equation before he touched it. (c) if they were honest Einsteinian transforms, they'd be incompetent. The direction of the particle's movement is x, which means it is X and L that are supposed to be transformed, not Y and M, and Z and N. And when SR does transform more than one axis, each axis has its own velocity term; using the v along the x-axis as the v for a y-axis and z-axis transform is thus trebly absurd: the axes perpendicular to the motion are not changed according to SR, the v used is not their v, and the v is not a transform velocity anyway. (d) as everyone knows, the effect of E and B are on the particle's velocity, which is a speed in a particular direction. Both the speed and direction are changed by E and B, but v - the speed - is a constant in SR. As absurd as are the previously demonstrated Einsteinian blunders, this one transcends error and is an incredible example of True Believer delusion propagating over decades. The equations can be put in a coordinate dependent form, where one or more E or B component is expressed as a function of location, but internal to those functions each coordinate may be put in gemeralized coordinate form and transformed. Invariantly, of course. ------------------------------------------------------------- The SR crackpots don't know what coordinates are. The various things they call coordinates include coordin- nates, but also include a variety of other quantities. ------------------------------------------------------ 1. One may express coordinates in a one-axis-at-a-time manner [like x^2+y^2=r^2] but it is the use of vector notation that shows us what is going on. In vector notation the triplet x,y,z [or x1,x2,x3, whatever] represents the three spatial coordinates, but there are so-called basis vectors that underlie them. Those may be called i,j,k. Thus, what we normally treat as x,y,z is a set of three numbers TIMES a basis vector each. 2. These e*i, f*j, g*k products can have a lot of meanings. If e, f, j are distances from the origin of i,j,k then e*i, f*j, g*k are coordinates: distances in the directions of i,j,k respectively, from their origin. That makes the triplet a coordinate vector that we describe as being an x,y,z triplet; perhaps X=(x,y,z). The e*i, f*j, g*k products could be directions; take any of the other vectors described above or below and divide the e,f,g numbers by the length of the vector [sqrt(e^2+f^2+g^2)]. That gives us a vector of length=1.0, the e,f,g values of which show us the direction of the original vector. That makes the triplet a direction vector that we describe as being an x,y,z triplet; perhaps D=(x,y,z). The e*i, f*j, g*k products could be velocities; take any of the unit direction vectors described above and multiply by a given speed, perhaps v. That gives a vector of length v in the direction specified. That makes the triplet a velocity vector that we describe as being an x,y,z triplet; perhaps V=(x,y,z). Each of the three values, e,f,g, is the velocity in the direction of i,j,k respectively. The e*i, f*j, g*k products could be accelerations; take any of the unit direction vectors described above and multiply by a given acceleration, perhaps a. That gives a vector of length a in the direction specified. That makes the triplet an acceleration vector that we describe as being an x,y,z triplet; perhaps A=(x,y,z). Each of the three values, e,f,g, is the acceleration in the direction of i,j,k respectively. The e*i, f*j, g*k products could be forces (much like accel- erations); take any of the unit direction vectors described above and multiply by a given force, perhaps E or B. That gives a vector of length E or B in the direction specified. That makes the triplet a force vector that we describe as being an x,y,z triplet; perhaps E=(x,y,z) or B=(x,y,z). Each of the three values, e,f,g, is the force in the direction of i,j,k respectively. Einstein's - and Maxwell's - E and B are not coordinate vectors. ============================================================ There is another variety of intellectual befuddlement that misinforms the idea that Maxwell isn't invariant under the galilean transform: confusions about velocities. Velocities With Respect to Coordinate Systems. ----------------------------------------------- Aaron Bergman supplied the background in a post to a sci.physics.* newsgroup: =============================================================== Imagine two wires next to each other with a current I in each. Now, according to simple E&M, each current generates a magnetic field and this causes either a repulsion or attraction between the wires due to the interaction of the magnetic field and the current. Let's just use the case where the currents are parallel. Now, suppose you are running at the speed of the current between the wires. If you simply use a galilean transform, each wire, having an equal number of protons and electrons is neutral. So, in this frame, there is no force between the wires. But this is a contradiction. ================================================================ First of all, the invariance of the galilean transform, (x'-x.c') =(x-x.c), insures that it is an error to imagine there is any difference between the data and law in one frame and in another; the usual, convenient rest frame is the best frame and only frame required for universal analysis. [Well, (x'<>x, x,c'<>x.c, but (x'-x.c')=(x-x.c).] Second, given that you decide unnecessarily to adapt a law to a moving frame, don't confuse coordinate systems with meaningful physical objects, like the velocity relative to a coordinate system instead of relative to a physical body or field. In other words, what does current velocity with respect to a coordinate system have to do with physics? Nothing. Certainly not anything in the example Bergman gave. What is relevant is not current velocity with respect to a coordinate system, but current velocity with respect to wires and/or a medium. The velocity of an imaginary coordinate sys- tem has absolutely nothing to do with meaningful physical vel- ocity. You can - if you are insightful enough and don't violate item (e) - identify a coordinate system and a relevant physical object, but where some v term in the pre-transformed law is in use, don't confuse it with the velocity of the coordinate transform. Velocities With Respect to ... What? ----------------------------------------------- Albert Einstein opened his 1905 paper on Special Relativity with this ancient incompetency: =============================================================== The equations of the day had a velocity term that was taken as meaning that moving a magnet near a conductor would create a current in the conductor, but moving a conductor near a wire would not. This was belied by fact, of course. The important velocity quantity is the velocity of the magnet and conductor with respect to each other, not to some absolute coordinate frame (as far as we know) and not to an arbitrary coordinate system. One possible cause was the idea: "but the equation says the magnet must be moving wrt the coordinate system" or "... the absolute rest frame". There not being anything in the equation(s) to say either of those, it is amazing that folk will still insist the velocity term has nothing to do with velocity of the two bodies wrt each other.
Subject: 11. The Twins Paradox absurdity. Most of SR demonstrates a symmetry. The contractions and dilations one oberver supposedly sees for another system, are exactly what the other system sees for him. The Twins Paradox says, however, that this symmetry fails. If the travelling twin left at t=0 and returned at t=100, then t'=g(t-xv/cc) and t' > t, which would say that the travelling twin's clock is ticking away faster. The symmetry would say the traveller sees the stationary clock ticking away faster than his. However, the traveller has to change direction, and thus by magic, as it were, the supposed lack of simultaneity forces the travelling twins clock to somehow be the ruling clock. As we have seen on a number of grounds, the idea that simultaneity does not hold across inertial frames is absurd, and the correct use of generalized coordinates, which preserves ratio scale quality shows it to be true that simultaneity holds reign. There is no lack of simultaneity, and there is no differential aging of such twins.
Subject: 12. The "how does an absurd SR work" non-absurdity. If you have understood the ratio versus interval scale discussion, you know a lot of it already. (a) anytime SR uses a difference of transformed values it creates ratio scale data out of the degraded interal scale data. Most of SR does just that in practice. We have shown that such ratio scale data is 'just' rescaled galilean data. (b) as often as not it is E=mc^2 that is what is meant about SR working. Even if it is true that it is basic SR - and there are some who say that identity was known before Einstein - it has nothing directly to do with the derivation and transform absurdities. (c) sometimes it is meant that instead of galilean force, F, being F=ma, it is the relativistic force equation that is supported daily at every second of the day at accelerators like CERN. However, F=ma came from long before accelerators and Maxwell, and non-relativistic force models exist that at least come much closer than F=ma. (d) to show that Einstein's work is absurd in no way says that his Second Principle is wrong, only that his implementation is absurd. A correct implementation may be much closer to T'=T/g than to T'=T, etc. This would still require differences of the interval data to be used, unless there is some true, non-distorting ratio scale transform available.
Subject: 13. The "strange effects of nothing" absurdities. According to Special Relativity, nothing can have amazing effects. There are no coordinate systems in nature; they're 'just' imaginary. But in SR, they are supposed to have real effects. One you see being talked about fairly frequently. Let a charged particle move at velocity v through an electromagnetic field. Now, imagine a coordinate system moving at that same velocity. The velocity of the charged particle is thus zero, they say, and there is no effect of the electromagnetic field. They really do say such stupid things, folks. Einstein started his SR paper in somewhat that way. Before Maxwell, there was an equation for the effect of an electric field, and another equation for a magnetic field. The magnetic one had a velocity term in it, the electric one didn't. So, they decided back then, the equations insisted that if you moved the magnetic near conducting wires there would be an induced electric current; after all, there is a velocity term in the magnetic equation. But, they said, the electric equation equation said there was no effect if you waved the wires near a magnetic; after all, there was no velocity term in the electric equation. In other words, the v in the magnetic field was not a velocity of a magnet and a wire wrt each other, but with respect to something that doesn't exist in nature: a coordinate system. You will hear it said to this very day by trained SRians, that Galilean physics says moving the wires will give you no current. And they will say that if you transform the Maxwell equations - with the SR transforms - so that the imaginary coordinate system is moving at the velocity of the magnet, there is no induced current. In other words - that they won't use - if you draw a coordinate axes system on a piece of paper and put the wires on it and move the magnet, you'll get a current, but if you tape the coordinate system to the magnet and move the magnet, you'll get no current. That is what SR says. But if you think about it deeply enough, in terms of the ratio scale versus interval scale discussion, you'll see why they have to say such idiotic things. You see, when you take the generalized form, such as (x-x0) and transform it, the velocity terms drop out, or cancel each other arithmetically if you leave the equation in primed form instead of simplifying it back to the unprimed form. But if you don't mind using the degraded interval data and transform you have only one transform velocity term in the bag, and so the transform velocity term doesn't drop out. And if you already had a velocity term in the equation, at the same speed, it is true that the algebraic effect is that there might now be a zero result. Sure, subtract the velocity of an imaginary velocity from a real one (perhaps the velocity of a charged particle or a magnet) and you get a zero result if the two are the same. Try telling your mortgage company that you now owe them nothing because you subtracted an imaginary payment from the amount you owed them. Hey. If it works in physics - SCIENCE! - how can a mere finance company or bank deny your logic?
Subject: 14. The "lasting effects of no effect" absurdity. You know about length 'contraction': a moving object is shortened by the fact of its movement, according to SR, even though you can't tell it is really moving or not if it isn't accelerating. Inertial movement is obviously relative. I see something moving wrt me, and I see you moving wrt me, so you may or may not see the thing moving wrt you. You will unless the object and you are moving at the same speed in the same direction wrt me. And what speed you see the object moving at determines how much shorter the thing is while moving. So, SR says every object has an infinite number of different lengths all at the one time: one for every possible velocity it can be seen moving at. No mathematician would try solving a set of simultaneous equations including: v=40; v=-20; v=10000000, but SR implies a universe in which an infinite number of such equations will work fine. So, how to get around such absurdities? Why it's simple. Just claim the effects are only observations, not real effects. People do this right here on the Internet in these newsgroups. The title of this section is: The "lasting effects of no effect" absurdity. Let's list some of the supposed, lasting consequences of the non-real effects: A travelling twin comes back younger than his stay at home brother. A muon coming to earth from space lasts longer than one in the laboratory.
Subject: 15. The "brag about your absurdities" absurdity. The Special Relativity transformations terribly screw up almost every equation known to humankind, and probably those of every alien species in the universe, as well as any in heaven and hell. But Special Relativity makes a virtue of this, proudly claiming that it is the quantity dx'^2+dy'^2+dz'^2+(icdt')^2 that is invariant. Even the simplest formulas no longer work on the data after tranform, for instance the circle formula: x^2+y^2=r^2. You can find points that fit x'^2+y'^2=r^2, of course; they just don't correspond to the circle you started with. "So, the 'repairs' we made to your automobile just made things worse and destroyed most of what had been working? So what? It is our ashtray repairs that are world famous."
Subject: 16. The "contraction circus" absurdity. Just what is it that contracts? There are three basic possibilities: (I) The whole universe contracts, parallel to the line of the moving object's direction. (II) The whole universe contained in a cylinder centered on the moving object and extending forwards and rearwards contracts. (III) The moving object only contracts. The really 'cute' one is (II). ============================================================ (III) The moving object only. Let there be two markers in space at a constant distance of 10^10 kilometers from each other, as measured by an observer at rest wrt the markers. Let a spaceship exist that is measured by the observer as one kilometer long while it is a rest wrt the observer. The distance between the markers is thus 10^10 spaceship lengths. Let the spaceship depart the observer and eventually pass one marker at .7071c. The observer sees the spaceship now as being .5 kilometers in length at t=0, and the moving clock to be ticking only half as fast as his own. The spaceship does not see his length as having changed, and if the distance between the objects didn't also change, then its perceived distance to the second marker is now 2*10^10 kilometers, so it takes twice the time to get to the second marker as one might have supposed, so according to both the stationary and moving clocks, the transit time from one marker to the other will be the same. QED: if only the object contracts, there is no transit time difference between the two systems at a given velocity. ======================================================== (I) The whole universe contracts. (a) Is the contraction instantaneous throughout the universe? How could you tell? And what possible difference could it make? Those are not rhtorical questions. There would be no way SR could have a meaningful application, right? If you suggest that time would not similarly be dilated throughout the universe, you are suggesting an apparent change in v, for v is constant in SR only because d/t=d'/t', and in this case we have no possible d'<>d because all the universe's measuring sticks contract sim- ilarly. Similarly? Identically! (b) Does the contraction propagate through the universe at the speed of light from the location of the moving object? Except for questions like "speed of light from any viewpoint?" this might not be different that the instantaneous model. Hmm. Or maybe a number of widely distributed observers in one frame could tell that something had happened? Again, none of these are rhetorical questions. (c) Does the contraction propagate through the universe at less than the speed of light from the location of the moving object? One could see that parts of the universe had contracted. Your own measuring stick wouldn't contract until after it had measured the distant contraction. Whole Universe Summary: who knows what effect could be eventually discovered; what is knowable is that there would be no simple(ton) visible contraction. =========================================================== (II) The whole universe contained in a cylinder centered on the moving object, and extending forwards and rearward, contracts. This is compatible with standard SR; elsewise a transit time between two markers would show the same elapsed time as for an observer at rest wrt the markers, as we saw in the dis- cussion of the 'object only' case. Let there be a spaceship be at rest between two stars, and with its axis of incipient motion passing through both stars. When it accelerates to any appreciable velocity, is it the center cylinder of the forward star that is snatched from its guts and hurtles toward the spaceship, or the rearward star's guts? Or both? That assumes the center of contraction is at least somewhere from the rearward star almost to the forward star. If the center of contraction were somewhere very distant from the ship, it could be that both star centers and the spaceship would all be yanked instaneously through the center of one start to a point that could be light years distant. Unless the contraction wasn't instantaneous, and then we'd have some mess indeed, figuring out how much and how far the contraction had taken effect before the ship once again changed velocity. At a simpler level, of course, contraction along the line of movement implies faster than light transit of information if the contraction is instantaneous, or at least faster than light. In any case, we'd certainly see some calamitous effects were objects other than light moving at high v anywhere in the near universe, wouldn't we? If SR were correct. ============================================================ Summary. ============================================================ For our three possibilities in the contraction circus, (I) The whole universe, parallel to the line of a moving object's direction contracts, and why wouldn't time also dilate universally? (II) The whole universe contained in a cylinder centered on the moving object and extending forewards and rearwards contracts, and would yield stellar catastrophes we'd almost surely have seen by now. (III) The moving object only contracts, and SR's claim about transit time differences would be invalid. The less unlikely possibility seems to be the one where you not only couldn't tell there had been contraction, but you'd be darn silly saying there had been. Then again, that last is the standard SR position, isn't it? The contractions don't really occur, they're just observational differences (which you couln't see in the whole universe case). That's what SRians on these newsgroups say; and they also say the time differences are real and lasting, except when they aren't. <g>
Subject: 16. Einstein's anti-simultaneity argument. Einstein (a) defined a test for clocks at rest wrt each other in a stationary system (we'd now say inertial), to determine that they are synchronized. [At clock A at time ta send light to clock B which reflects it at tb to clock A at ta', with observers at each clock noting the time the clock says at the three events. If tb-ta=tb-ta' then the clocks are synchronized.] (b) had a stationary system thereby synchronize its clocks. (c) posited a second inertial - but moving - system whose clocks at all times and places would show the first system's times at the immediately adjacent first system location. (d) posited the first system running the synchroni- zation test on the second system clocks; that is, with a completely non-definition test. With r=distance between the clocks - per stationary system - he got tb-ta=r/(c-v) and tb-ta'=r/(c+v). He concluded that clocks synchronized in one inertial system cannot satisfy the definitional test for synchronization in a second inertial frame. If the second system had indeed run its synchronization test like the first system had, the times would be tb-ta=r/c and tb-ta=r/c. His proof is much like having a stationary pianist playing a stationary piano and then turning on his stationary piano stool to play a second piano that is moving past him, while he stays stationary.
Subject: 17. A straightforward pro-simultaneity argument. The SR formula for time dilation holds true if SR holds true; it says that for a fixed location, x, T'=T/(sqrt(cc-vv). Because his stationary system clocks are synchronized, the three times in the stationary system clock synchron- ization are valid times at any fixed location, x, in the stationary system, and for any such fixed location, t'=t/sqrt(cc-vv), whether t=tb-ta or t=tb-ta'. This is to say, equal intervals in one inertial system are nec- essarily equal intervals in any other. As shown earlier in this faq, non-simultaneity is an artifact of poor usage. The generalized coordinate form (x-x0), etc, of an equation should be used; if you do so, there is no time difference in t' at different locations of x, etc. Simultaneity is absolute. Eleaticus !---?---!---?---!---?---!---?---!---?---!---?---!---?---!---?---!---? ! Eleaticus Oren C. Webster ThnkTank@concentric.net ? ! "Anything and everything that requires or encourages systematic ? ! examination of premises, logic, and conclusions" ? !---?---!---?---!---?---!---?---!---?---!---?---!---?---!---?---!---?

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