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Real Lorentz–FitzGerald contraction

  1. Dec 16, 2009 #1
    In this thread https://www.physicsforums.com/showthread.php?t=361915"
    I showed my viewpoint on a real length contraction https://www.physicsforums.com/showpost.php?p=2486767&postcount=21":
    and I've see no criticism on my view, neither acceptance nor denial, that a real length contraction must exist.
    Then I searched the words of Lorentz, Einstein and also what others are saying.
    Nowadays textbooks may reflect, AFAIK, the position that Lorentz viewpoint is out of order, but I find this point ‘out of consensus’.

    To ease the discussion first I post here the words of Lorentz, Einstein and others.
    In the next post is my own 'visualization' and some questions.


    Einstein words on aether:
    A. Einstein, “Zur Elektrodynamik bewegter K¨orper,” Annalen der Physik 17, 891 (1905). Reprinted as “On the electrodynamics of moving bodies”

    The reason that special relativity was considered a better explanation than the Lorentz-FitzGerald hypothesis can best be illustrated by Einstein’s own words:

    “The introduction of a ‘luminiferous ether’ will prove to be superfluous inasmuch as the view here to be developed will not require an ‘absolutely stationary space’ provided with special properties.”

    A. Einstein, “¨Ather und Relativit¨atstheorie,” address delivered on May 5th, 1920, in the University of Leyden. Reprinted as “Ether and the Theory of Relativity” in: A. Einstein, Sidelights on Relativity, Methuen and Co., London (1922).
    “The next position which it was possible to take up in face of this state of things [the acceptance of the special theory of relativity] appeared to be the following. The ether does not exist at all. (...)
    More careful reflection teaches us, however, that the special theory of relativity does not compel us to deny ether. We may assume the existence of an ether; only we must give up ascribing a definite state of motion to it.”
    “Think of waves on the surface of water. Here, we can describe two entirely different things. Either we may observe how the undulatory surface forming the boundary between water and air alters in the course of time; or else – with the help of small floats, for instance – we can observe how the position of the separate particles of water alters in the course of time. If the existence of such floats for tracking the motion of the particles of a fluid were a fundamental impossibility in physics – if, in fact, nothing else whatever were observable than the shape of the space occupied by the water as it varies in time, we should have no ground for the assumption that water consists of movable particles. But all the same we could characterise it as a medium.”
    ...“tracking the motion of the particles on a fluid [is] a fundamental impossibility in physics.” ...
    “according to the general theory of relativity space without ether is unthinkable. (...) But this ether should not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it,”

    Lorentz words on length contraction:
    H. A. Lorentz, Versuch einer Theorie der elektrischen und optischen Erscheinungen in bewegten K¨orpern, Brill, Leiden (1895). §§89-92 reprinted as “Michelson’s Interference Experiment”

    “one would have to imagine that the motion of a solid body (...) through the resting ether exerts upon the
    dimensions of that body an influence which varies according to the orientation of the body with respect
    to the direction of motion.”
    “Surprising though this hypothesis may appear at first sight, yet we shall have to admit that it is by no
    means far-fetched, as soon as we assume that molecular forces are also transmitted through the ether, like
    the electrical and magnetic forces. [Then] the translation will very probably affect the action between two
    molecules or atoms in a manner resembling the attraction or repulsion between charged particles.”


    http://digital.csic.es/bitstream/10261/3425/3/0705.4652v2.pdf" [Broken]
    Carlos Barceló1 and Gil Jannes1 (2007)

    Many condensed matter systems are such that their collective excitations at low energies can be described by fields satisfying equations of motion formally indistinguishable from those of relativistic field theory.
    The finite speed of propagation of the disturbances in the effective fields (in the simplest models, the speed of sound) plays here the role of the speed of light in fundamental physics.
    However, these apparently relativistic fields are immersed in an external Newtonian world (the condensed matter system itself and the laboratory can be considered Newtonian, since all the velocities involved are much smaller than the velocity of light)
    which provides a privileged coordinate system and therefore seems to destroy the possibility of having a perfectly defined relativistic emergent world.
    In this essay we ask ourselves the following question:
    In a homogeneous condensed matter medium, is there a way for internal observers, dealing exclusively with the low-energy collective phenomena, to detect their state of uniform motion with respect to the medium?
    By proposing a thought experiment based on the construction of a Michelson-Morley interferometer made of quasi-particles, we show that a real Lorentz-FitzGerald contraction takes place, so that internal observers are unable to find out anything about their ‘absolute’ state of motion.
    Therefore, we also show that an effective but perfectly defined relativistic world can emerge in a fishbowl world situated inside a Newtonian (laboratory) system.
    This leads us to reflect on the various levels of description in physics, in particular regarding the quest towards a theory of quantum gravity.
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Dec 16, 2009 #2
    My 'visualization' of Real Lorentz–FitzGerald contraction

    How I do visualize a real length contraction
    based solely on : there is no instant action at distance
    The sketch is rather figurative and does not make evidence of the mass growth with motion.

    consider _aaaaaaaaaaaaaaaaaaaaaaaaa the initial 'atom'/object configuration with some spatial extension in our lab,
    exert a steady force from left to right, being 'c' as the speed of transmission of the effect,
    assume atom moving from left to right
    and letters a,b,c,d,...x,y represents crescent matter densities

    we can observe a constant increase in the speed, and a constant decrease in length.
    the times t0,.tn are from a lab clock

    t0 no force _aaaaaaaaaaaaaaaaaaaaaaaa
    t1 force >______bbbbaaaaaaaaaaaaaaaaa
    t2 force >________cccccbbbbbaaaaaaaaaa
    t3 force >____________dddddcccccbbbbba
    t4 force >__________________eeeedddddcccccbbb
    t5 force >______________________fffffeeeeedddddcccc
    t6 force >____________________________gggggfffffeeeeedd
    t7 force >____________________________________hhhhhgggggfff ff
    tn force >________________________________________ ______________xxxyy
    tn+1 no force ________________________________________ ______________xxxyy

    for a shortened spatial configuration there exists a time dilation as c=length/time

    We must see it shrinking, otherwise we have to accept instant action at distance.
    This is the Lorentz view. Neighbouring atoms adjust their sizes and positions to maintain the equilibrium (already pre-existent) obeying electromagnetic laws.

    The Einstein position on this issue is 'neutral' ( because of 'c' and definition of simultaneity we have to observe this effect) and said nothing about the underlying mechanism.
    The Lorentz position on this issue is richer because he applied Maxwell laws to an moving electron and showed that the configuration change and added and we are unable to measure the changes that happen to us, as observers.
    Then MMX was negative as he said (it can be the cause of negative results of LIGO experiment)

    My questions:
    Is my 'visualization' in error ?
    how to 'visualize' mass increase ?
    How to say no to the 'real length contraction' ?
    what can we expect as the outcome of the proposed length contraction LHC experiment described in http://arxiv.org/PS_cache/arxiv/pdf/0710/0710.3489v2.pdf" [Broken]

    If not disproved the real length contraction, as I tried to show above, we must talk on relativity in the context of an absolute coordinate system (in another thread).
    In my opinion there exists no contradiction to SR. I mean: the possible existence of an absolute coordinate system does not invalidate SR, as Einstein said.
    Last edited by a moderator: May 4, 2017
  4. Dec 16, 2009 #3


    Staff: Mentor

    Hi heldervelez, that is a lot of material, so I won't even attempt to respond to all of it. However, I think there are two key points that should help.

    1) The question about the reality of length contraction depends almost entirely on your definition of "real", so it is largely a semantic argument. Length contraction is a measurable but coordinate-dependent effect. Some people think that anything that is measurable is "real" so they would say that length contraction is real, but others think that anything that is coordinate-dependent is not "real" so they would disagree. I personally don't care enough about the word "real" to fight about it either way. It is measurable and coordinate dependent, that is sufficient for me.

    2) What you describe above in your ASCII art is NOT length contraction. What you describe above is non-rigid acceleration. Length contraction is a comparison of the same object at the same event in two different reference frames. It is not a comparison of the same object at two different times in a single reference frame (e.g. before and after acceleration). A general hint is that if you are talking about acceleration you are probably not talking about length contraction, and if you are not talking about two different reference frames then you are definitely not talking about length contraction.
  5. Dec 16, 2009 #4
    Hi DaleSpam, thanks for your attention
    The reality behind our measurements, is more than semantic. We depend on light, and light speed, to acknowledge the ‘world’ and we must proceed, as much as we can, in the pursuit of what actually happens in the real world, as if we were gods with ‘instant vision’. We are somewhat limited but we have our mind to overcome our ingenuity.
    A very fine document about constraints on measurements, namely time, that I find very recently, is the Poincaré 1898 paper http://en.wikisource.org/wiki/The_Measure_of_Time" [Broken]
    You say, as many: “Length contraction is a measurable but coordinate-dependent effect”. About the measurability we can say nothing in the present time. Thus we can only wait for future measurements. If you say “ONLY coordinate-dependent effect” (you didn’t) I do not agree because Lorentz said and no one denied (AFAIK) and, not the least, I have ‘my visualization’. My mind needs ‘images’ more than equations to understand ‘physics’, i.e. first ‘a model’ then math.

    There are no rigid-bodies except in theory. All physical bodies are non rigid-bodies, and it is known that SR is based in rigid-bodies. Is it a semantic problem? I think not. But the prove that is not relevant is not possible as we can not deny whatever conclusions that we are not aware. The conclusion that it is relevant belongs to the future (or privileged information).
    In the ‘my visualization’ I know that I made the appearing of ‘acceleration’ and it is out of SR, but...
    at CERN (the lab) we are doing the same experiment:
    Start with protons at rest, accelerate them, make them collide with matter (some nuclei). After collisions we measure their mass/energy increase and time dilation and say SR predicted it! Its correct! And really it is correct, because we measure it, but less correct than the real facts.
    It is easy to adapt ‘my visualization’ to the scenario of SR. Just pick it after tn+1, when velocity is constant. The CERN is the lab referential and we are comparing protons (referential at rest) with protons with relativistic velocities (the proton referential).
    (A clearer understanding of the collision event can be portrayed on the moments represented from t0 …tn in the experiment)

    In SR we deal with relative velocities ex. (v1 – v2) in Einstein referential (ER) and the ‘world’ makes sense.
    But, in a different scenario, say ‘instant vision’ and absolute velocities, we can also have (V1 – V2), that translates to (v1 – v2) in ER, and the ‘world’ makes sense too in some absolute referential (AR).
    Last edited by a moderator: May 4, 2017
  6. Dec 16, 2009 #5


    Staff: Mentor

    I'm sorry, but I can't parse your sentences here. What are you trying to say?
    Sure, but there is Born-rigid motion acceleration, and length contraction applies even there. The point remains that what you are describing with your ASCII art is simply not length contraction (or at least it is not only length contraction). You should not include any mechanical deformation when talking about length contraction as that is a separate concept.
    Last edited: Dec 16, 2009
  7. Dec 16, 2009 #6
    you said “Length contraction is a measurable but coordinate-dependent effect” … but no measures of LC were performed until now.
    Lorentz-Fitzgerald contraction is a real effect, not only a "... coordinate-dependent effect” … Lorentz, first than Einstein, describes a radius decrease, mass and time increase to a moving body in relation to one at rest. Einstein shows the same by mere coordinate transformation, but it does not invalidate Lorentz view. IMO both views represents the same real phenomena.
    Born-rigid - it does not exist, i.e. it can not be applied to physical objects (*)
    'My visualization' is not 'mechanical deformation' but gradual deformation (EM as in Lorentz, real objects) at any scale because we can not apply the force to all extent of the object in the same instant. The visualisation of the mass increase effect will complement the understanding (to keep the ‘noise’ low I did not include it in this step).
    "..what you are describing with your ASCII art is simply not length contraction." But I did a parallel with the real experiments at CERN where it is named LC.

    These papers may help the understanding:
    The Rigid Rotating Disk in Relativity at http://math.ucr.edu/home/baez/physics/Relativity/SR/rigid_disk.html
    Relativistic contraction of an accelerated rod (2008) here http://arxiv.org/PS_cache/physics/pdf/9810/9810017v3.pdf

    I felt an Earthquake now and I must go, without time to elaborate more.
  8. Dec 16, 2009 #7


    Staff: Mentor

    The point is that length contraction has NOTHING whatsoever to do with forces or "gradual deformation". Lorentz contraction is a comparison of measurements in two different frames, not measurements in one frame at different times. If you cannot understand what the term "length contraction" refers to then there is not any point in discussing whether or not it is "real".

    I hope all is well with the earthquake.
  9. Dec 17, 2009 #8
    6.1 Ritcher, intense but long longitudinal wave of short duration. no damages.
    My visualization included a collision mechanism to boost the 'atom' and now I will describe another effect that is a 'real' length contraction, that must be present when we consider the mass increase. The acceleration can be provided by a field, instead of a collision.
    Borh radius vary with the inverse of mass. In other words : more mass, more frequency, less waveLength, or...real length contraction, by first principles and simple reasoning.
    IMO the Lorentz-Fitzgerald contraction is described everywhere as a real length contraction; the Carlos Baceló thought experiment, derived in a completely different way, and 'my visualization' point to a 'real physics' and not a mere coordinate transform.
    Einstein referential is 'the observer viewpoint' ( with his limitations on light...) it says how we must measure but omit any underlying physics process. It is correct, but Lorentz Relativity give us a more profound insight.
    Last edited: Dec 17, 2009
  10. Dec 17, 2009 #9
    Lorentz Relativity is better than Einstein SR

    IMO Lorentz Relativity is better than Einstein SR.
    It links to real physical bodies as opposed to hypothetical ‘rigid-bodies’.
    It open’s our understanding to physical processes.
    The solution of the rotating disk is natural with Lorentz relativity:
    Quoting “http://arxiv.org/PS_cache/gr-qc/pdf/0207/0207104v2.pdf" [Broken]
    by Guido Rizzi and Matteo Luca Ruggiero (2007)
    at page 6 we see the strategies used to solve The Ehrenfest’s paradox
    “ (s2) both the radius and the circumference contract, so that their ratio remains 2*pi = L/R=L’/R’
    “ (f.i. Lorentz, Eddington)”

    Quoting from here (a review) http://math.ucr.edu/home/baez/physics/Relativity/SR/rigid_disk.html" [Broken]
    “Rigid motion can occur in SR only through a conspiracy of forces.”

    I.e. rigid-bodies do not exist and rigid motion is impossible under Einstein SR, but with Lorentz Relativity there is no problem at all.

    When Lorentz presented his Relativity he knows nothing about molecular forces, neither Bohr radius, etc (they are posterior), and he stated it as an Hypothesis. Now we can state that it is far more than an hypothesis.

    --- My Visualization of mass increase (Bohr radius shortened) imply a real length contraction
    OOOOOOOOOO_ - Body at rest (lab)
    oooooooooo____ - Moving body, length contracted (real)


    Formulating a theory based on rigid-bodies is an approximation that translates into problems and paradoxes. I choose Lorentz view.
    Last edited by a moderator: May 4, 2017
  11. Dec 17, 2009 #10


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  12. Dec 17, 2009 #11


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    Re: Lorentz Relativity is better than Einstein SR

    None of that is relevant to length contraction.
    You are certainly entitled to your opinion and you are free to choose whichever interpretation you prefer for any reason or no reason at all. Since they are simply different interpretations of the Lorentz transform there is no experimental evidence either way so you can arbitrarily make any choice you prefer. I am neutral on the choice of interpretation, and in fact I switch between the two whenever convenient.
    Last edited: Dec 17, 2009
  13. Dec 17, 2009 #12
    I quoted Einstein words "“according to the general theory of relativity space without ether is unthinkable" because it is a general believe that SR Relativity superseded Lorentz Relativity and as this one was formulated on the supposition of aether, then any reference to aether is sacrilege. I mean to say ‘we can talk about Lorentz’ But Einstein Relativity is a change of perspective that blinds us from the real events. If GR needs ‘aether’ (I prefer to say 'field' or ‘medium’). The specific mention to GR does not invalidate the applicability to SR. With GR Einstein abandoned the rigid-body notion and we are here and now dealing with problems derived from the ‘rigid-body’ in SR. It seems that the relativity of bodies in motion must be reanalyzed. The Bell's book is good, thanks for the link. I can not afford it (I have access to net and fundamental papers of Lorentz, Einstein, Minkovsky, Wien. But in Minkovsky I see no new ‘physics’ only math, and these days the teaching of relativity starts in Minkovsky, more a problem than a solution, imo)
    The page 77 is very nice and reinforces my conviction that I’ve used a correct interpretation of the differences on both viewpoints.
    The moving observers are also analysed, and more, it points a central problem not stated elsewhere (afaik): ‘who observes the observer?’ (pag 76).
    But I do not share the author opinion that ‘in physical terms’ both positions are equivalent. Someday we will find much more fruitful one versus the other (imo).

    OK “The Barcelo paper is also not about the Lorentzian viewpoint. It is about Lorentz invariance being emergent”
    Not OK to “…not fundamental.” They don’t even tried, and probably they don’t know how to to prove it.
    I used the reference to show that ‘the problem of absolute viewpoint is not dead’

    In the Einstein mistakes book (again out of my reach) index I did not find any reference to a problem that I think deserves some clarification in the 1916 GR paper.

    I tried to find the origin of the sentence ‘what else could I do?’ or ‘what else could I say?’ as Einstein words and I can not find it. Could someone help me please?

    I thank you for your insightful post.
  14. Dec 17, 2009 #13


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    Interesting links, thanks, atyy!

    The relevant material in the Ohanian book seems to be on p. 283, which can be viewed through a keyhole on amazon.

    Google books lets you see the first few pages of Bell's statement of the paradox, but his treatment is very lengthy, and there are inaccessible pages scattered around in it, so it doesn't seem possible to see his treatment without paying exorbitant amounts of money for the out-of-print book. The philosophical and pedagogical motivation is given on pp. 68 and 77, which are accessible through google.

    Weiss and Baez have a good discussion of the paradox from a traditional point of view: http://math.ucr.edu/home/baez/physics/Relativity/SR/spaceship_puzzle.html
    Last edited by a moderator: May 4, 2017
  15. Dec 17, 2009 #14
    I must correct myself:
    in post 12 I said "With GR Einstein abandoned the rigid-body notion" and I think that the use of gauss coordinates by Einstein to state the solution of gravitation does not mean he abandoned the 'rigid-body' as we can see here.
    quote from above mentioned "The Rigid Rotating Disk in Relativity" review:
    "..., Einstein asserts that geometry for the rigid rotating disk is noneuclidean. ..."
    "...Turn to GR. Now all sorts of complications appear...."

    Last edited: Dec 17, 2009
  16. Dec 17, 2009 #15


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    With GR in the ray limit, we have test particles moving on geodesics of a curved metric. In the full theory, the gravitational field is just a dynamical field, like any other field. The full Einstein field equations require additional equations of state of matter (perfect fluid, Maxwell's equations, etc.) in order for physical predictions to be made, and the gravitational field does not have a metric interpretation, although it has metric symmetry, except in the ray limit.

    "The field equation (7) has physical meaning only if T is specified;
    this specification always contains the metric. Mathematical studies often consider the vacuum case, T = 0, with or without Λ. Matter models studied in some detail include perfect fluids, electromagnetic fields, collisionless particle systems idealized by kinetic theory and, to a lesser extent, elastic bodies. In these cases the system of partial differential equations consisting of (7) and the relevant matter law admits a (locally) well-posed initial value problem." Ehlers, General Relativity in http://books.google.com/books?id=2Vpa6PxOs9IC&dq=seiler+AND+fundamental&source=gbs_navlinks_s

    Also interesting is James Anderson's http://arxiv.org/abs/gr-qc/9912051. I believe it was he that formulated the no absolute structures idea http://arxiv.org/abs/gr-qc/0603087.
    Last edited by a moderator: Apr 24, 2017
  17. Jan 4, 2010 #16
    Cmb : An absolute referential

    Because it is meaningful to the Lorentz perspective I must refer that we can make experiments based on Sagnac effect to measure ABSOLUTE ROTATION relative to CMB.
    (google for 'sagnac absolute rotation' and you will find many valid references)

    So CMB can be viewed as a preferred reference frame and in relation to it we can think and analyse an ABSOLUTE MOTION.

    At Lorentz time none suspected that an absolute frame could be found.
    Last edited by a moderator: Apr 24, 2017
  18. Jan 5, 2010 #17
    Re: Cmb : An absolute referential

    Hahaha... I had a friend who would always refer to this kind of argument as the 'your mom's ***' argument. I'll use 'car' as the three letter word here.

    Basically, by that logic, one can argue that your mom's car defines a preferred reference frame, since in principle we can measure all velocities with respect to your mom's car.

    The important lesson from electrodynamics that led Einstein to SR is Poincare symmetry. And Poincare symmetry is even retained as a local symmetry in GR. The modern statement of SR is usually just given as the requirement the laws of physics have Poincare symmetry. So, does the existence of my mom's car, or some photons in space, change the symmetry of the laws of physics? No.
  19. Jan 5, 2010 #18
    Re: Cmb : An absolute referential

    Fortunately it is only a friend's argument.
    We are measuring the ABSOLUTE ROTATION of the EARTH using the SAGNAC effect with large Ring-lasers

    http://www.physics.berkeley.edu/research/packard/related/Gyros/LaserRingGyro/Steadman/StedmanReview1997.pdf" [Broken]
    (find the word 'absolute' inside the paper namely point 6.6 and 8)

    A preferred reference frame can be defined to such as the Sagnac effect has a null result.
    ( if there exist Absolute Rotation then by simple reasoning it must be rotation in relation to some coordinate system - VLBI, CMB )

    more links here
    quote from here:
    http://aa.usno.navy.mil/faq/docs/ICRS_doc.php#ICRSDATA [Broken]
    "The International Celestial Reference System (ICRS) is the fundamental celestial reference system adopted by the International Astronomical Union (IAU) for high-precision positional astronomy. The ICRS, with its origin at the solar system barycenter and "space fixed" axis directions, is meant to represent the most appropriate coordinate system for expressing reference data on the positions and motions of celestial objects."

    http://www.ringlaser.org.nz/content/about_us.php [Broken]

    I searched 'Poincare symmetry' and I found a 'math concept (group theory)' and links to 'quantum mechanics', 'Minkowski spacetime', etc...
    If you think that all physical laws are in peril, uau, ...

    The Lorentz view does not rule out Einstein view and vice-versa.
    In the Einstein formulation there is no need of any preferred reference frame as it is the 'observer viewpoint'.
    But 'no need' does not mean 'does not exist'.
    Moreover the analisys was done within the frame at rest (the lab).
    It was never concluded, I'm certain, that it is impossible an analisys from one 'preferred frame', assuming absolute velocities, that do not colide with the usual Relativity of Motion. I wouldnt be surprised if we find out that 'spacetime', interconnection between space and time - t'=f(t,v,x), is a consequence of Einstein special viewpoint and not a fundamental property of nature. Who knows.
    Last edited by a moderator: May 4, 2017
  20. Jan 5, 2010 #19


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    Re: Cmb : An absolute referential

    The Sagnac effect has a null result in every inertial frame.
    The absolute rotation is in relation to every inertial coordinate system, not a specific one.
  21. Jan 5, 2010 #20


    Staff: Mentor

    Re: Cmb : An absolute referential

    Rotation is indeed absolute, and the Sagnac effect and ring interferometers are well-understood and compatible with SR.

    Sure, in fact an infinite number of such reference frames can be defined. Those reference frames where the Sagnec effect has a null result are called "inertial frames" and form the Poincare group.

    Have you any reputable evidence to support this or is it mere speculation. If it is speculation then I would remind you of the forum rules that you agreed to.
  22. Jan 7, 2010 #21
    Mr A.T. is correct, and I appreciate the correction: "The Sagnac effect has a null result in every inertial frame." and "The absolute rotation is in relation to every inertial coordinate system, not a specific one."

    Mr Dalespam : "I wouldnt be surprised if we find out that XXX. Who knows. " Is future and conditional, hypothetical, that I translate to : there exists some probability (>0) that XXX can be true in the future.
    I can't say, for sure, that XXX will not happen.

    I know now why I have missed the point.
    When I read "ON THE ELECTRODYNAMICS OF MOVING BODIES, Einstein 1905" the word inertial is not in the text, and now, after A.T. remark, I count:
    stationay - 63 times
    I was mislead by Eistein words in the preamble : "... will not
    require an “absolutely stationary space”
    " and at "§ 1. Definition of Simultaneity
    Let us take a system of co-ordinates in which the equations of Newtonian
    mechanics hold good. 2
    foot note "2 : i.e. to the first approximation."

    --- now I realize that Einstein framework requires an inertial referential frame (irf). We don't have at our disposal any such co-ordinate system.

    Also the Einstein comment "i.e. to the first approximation." troubles me. What is the order of aproximation? and why?

    What kind of errors appear in the measures at Earth lab, that is not an irf ?

    How velocities, accelerations, rest masses, etc.. behave when we translate from one irf to the lab?
    IMO we need the proper equations otherwise we are navigating in the dark.
  23. Jan 7, 2010 #22
    A first order approximation means that the errors due to using a frame that is not perfectly inertial are of second order, or negligible, and can be discounted for a given purpose.

    It's analogous to calling earth's gravitational field near earth's surface a uniform 1G field "to a first approximation". Objects don't really fall at exactly 9.8m/s^2 everywhere, they fall at various rates depending on location. But the errors induced by falsely considering the G-field uniform are negligible for most purposes.
  24. Jan 8, 2010 #23
    Earth lab versus CMB ref (inertial ref)

    The Sun (and Earth) is moving at 370 Km/s in relation to CMB. This is a significative deviation from an inertial frame. v/c = 370/300000 = 0.001233333 ( 0.123% or 1233 ppm ) (v/c)^2 = 1.5211111E-06

    How velocities, accelerations, rest masses, etc.. do behave when we translate from an inertial reference and the lab frame?

    Measuring the world with increased accuracy requires a more accurate model .

    Can we guarantee that the Pioneer Anomaly is not a fictious force due to this change of referential?
  25. Jan 8, 2010 #24
    Re: Earth lab versus CMB ref (inertial ref)

    Looks like zero deviation on that basis, since velocity is not a deviation from an inertial frame. Proper acceleration of the frame or local gravity field non-uniformity would be deviations.

    Notice that the "equations of Newtonian mechanics hold good" regardless of reference frame velocity. But they don't "hold good" if there is significant proper acceleration of the reference frame or significant non-uniformity of a gravitational field.
    Last edited by a moderator: Jan 8, 2010
  26. Jan 8, 2010 #25


    Staff: Mentor

    Re: Earth lab versus CMB ref (inertial ref)

    I don't know what you think you are trying to calculate here, but the correct number is:
    [tex]\gamma = \frac{1}{\sqrt{1-v^2/c^2}} = 1.00000076[/tex]
    So that is 0.76 ppm, not 1233 ppm. Whether or not that is a significant deviation depends on the sensitivity of your specific experiment to anisotropy in the CMBR.

    Moving with a uniform velocity is still inertial. Non-inertial frames involve acceleration, not constant velocity.
    Last edited: Jan 8, 2010
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