Larmor Relativity

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Larmor Relativity

Unread post by crawler » Wed Apr 01, 2020 10:10 pm

Larmor derived a factor for material length contraction due to aetherwind, & a factor for electron orbital period.
And if u invert the factor for period u get a factor for the frequency of orbit (ie material atomic ticking dilation).
Was Larmor aware of Voigt's postulate re the apparent constant speed of light? Anyhow Larmor was happy to derive or adopt what we now call the Lorentz factor for spatial coordinate contraction, & spatial time dilation.
Larmor -- 1900 -– Aether and Matter --
Larmor -- 1897 -- On a Dynamical Theory of the Electric and Luminiferous Medium, Part 3, Relations with material media. ... Medium_III

There is no such thing as time & time dilation, & no such thing as contraction of space. All we have is material length contraction (of atoms or solids etc), or at least some kind of change of size &/or shape, & we have material ticking dilation (of clocks & processes etc). And these material LC & TD will have different equations, ie different factors, different to each other, & different to the silly looking Lorentz factors. The Lorentz factors for spatial LC & TD & for material LC & TD are impossible (as are Larmor's spatial versions of Lorentz's spatial factors)(Larmor's spatial equations are identical to Lorentz's)(but Larmor's material equations are not identical to Lorentz's material equations).

The more i see of Larmor's material factors the more i like them. In effect Larmor said that a body cant get anywhere near the speed of light. Hencely Larmor's material LC has a limit of 0.5000, & his material TD has a limit of 0.6667. Much more sensible than Lorentz (& Bell). And it seems to me that Larmor's factor for material LC is perfectly in keeping with FitzGerald's theory that material LC is proportional to vv/cc.

……….… Lorentz factors … Larmor factor ….Larmor factor ..... gives a factor
…………. for LC & TD … for material LC … for material period … for ticking dilation
v/c ……... . (1-vv/cc)^0.5 ... (1-1/2 vv/cc) …. (1+1/2 vv/cc) …1/(1+1/2 vv/cc)
1.0 ……...… 0.0000000 ….... 0.5000 ……….….… 1.5000 …………. 0.6667
0.9 ......... 0.4359 ........... 0.5950 …………….. 1.4050 …………. 0.7117
0.75 ........ 0.6614 ........... 0.7188 …………….. 1.2813 …………. 0.7805
0.5 .......... 0.8660 ........... 0.8750 …………….. 1.1250 …………. 0.8889
0.25 ........ 0.9682 ........... 0.9688 …………….. 1.0313 …………. 0.9697
0.001 .... 0.999999500 ……. 0.9999995 ….….. 1.0000005 …..… 0.9999995
0.0001 .. 0.999999995 …... 0.999999995 ….. 1.000000005 …. 0.999999995
0.0000 .. 1.000000000 …… 1.000000000 …… 1.000000000 …. 1.000000000

We need to be wary of spatial (coordinate) transforms. Modern aether theory (Cahill)(Ranzan) says that we have one true absolute non-changing space with fixed absolute coordinates, this being the absolute frame where the aetherwind is zero km/s.

Atoms & molecules & objects can materially say contract due to a change in aetherwind, in which case the center of the object will retain its coordinates, but the length changes. For an observer moving with the object the apparent length never changes (because the retina contracts).

So, an observer in a moving Larmorian system will not notice that object's suffer a say length contraction, however she will see an apparent dilation of the gap tween objects (because (1) the objects have materially contracted & the gap is then wider, & (2) her retinas & metre-rods have contracted). The Einsteinian scenario i think requires that she will not notice any changes, & that the stationary observer will see a contraction of the xx gaps tween contracted moving objects (because (3) the moving space(time) in the moving system suffers a relative xx contraction)(& with it moving objects suffer a corresponding length contraction). In the Larmorian scenario there is no stationary observer except an observer in the absolute frame, & he will see that the moving object has contracted & that the gap tween objects has dilated on account of (1) (but not (2)).

And don’t forget that Larmor's factor (1-1/2 vv/cc) is not the same as Einstein's (1-vv/cc)^0.5.

Lorentz's factor looks identical to Einstein's, but Lorentzian observers wont agree with Einsteinian observers, Lorentz would use Larmor's absolute frame & Lorentz's equation (twice usually). Hencely we will have three different sets of answers re contractions & gaps & coordinates & tickings.

Lets have another look at that there silly Einsteinian scenario. (3) Moving space in the moving system suffers a relative contraction. In other words nothing contracts when that nothing is moving. And moving nothing, when it contracts, makes moving objects contract too. And if that object is a clock then that there moving nothing makes the moving clock tick slower, & the slower ticking slows time itself. So, a clock moving along with the moving nothing is affected, but a clock sitting in the stationary nothing aint affected. And the stationary nothing exists in the same place as the moving nothing. Silly aint it.
So, if i am standing in a very long train, & then i start to walk along the train, the length of every carriage immediately shrinks, & the length of my universe immediately shrinks (as seen by a stationary passenger).
But, the shrunken stationary passengers don’t see me as being larger, to them it is i that have shrunk. Silly aint it.

Ticking is more complicated. There is no such thing as time, hencely no such thing as time dilation (or time transforms) for moving systems.
Hencely simultaneous events are simultaneous in every frame.
That makes things much simpler. But the ticking of clocks & processes etc is complicated, every clock & process must have its own peculiar factor. The Larmor factor for ticking dilation possibly applies accurately to some kinds of atomic clock, but to no other kind of clock (or process even).

We don’t need time transforms, but we do need ticking transforms, because clocks in motion can have different ticking rates, & the indicated elapsed times can diverge (eg GPS).

Anyhow, thems are the basics. Objects have their true size & shape when in the absolute (rest) frame, & clocks & processes have their true frequency. In other frames an object's size or shape contracts by some factor, & a clock's frequency lessens (ie ticking dilates) by some other factor (different clocks will have different factors).

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Re: Larmor Relativity

Unread post by crawler » Thu Apr 02, 2020 10:25 pm

Voigt started the "the apparent speed of light is the same in all moving systems" farce in 1887.
Voigt used this silly trick to help him with some kind of Doppler or wave-front problem relating to light.
Voigt used the equation c = x'/t' = x/t. Got t' = t – vx/cc. Then got (1-vv/cc)^0.5 for the (Voigt) factor, used later by Lorentz Poincare & Einstein.
Voigt use a radiating plane wavefront, & a spherical wave front, & a moving observer, & a stationary observer, an illuminating surface, a shining surface, a prism, a small sphere, an illuminating point, .
Voigt's factor is a coordinate transform for moving systems, for both distances xyz & for time.
Voigt didn’t say that his factor applied to the length contraction of solids, nor to the ticking (or time) dilation of clocks.
Voigt never mentions electrons or orbits or atoms or molecules, or Maxwell, or Heaviside's ellipsoid.
Voigt never mentions aether, but he mentions an oscillating incompressible medium (just the once). What was Voigt trying to hide? If Voigt had said that the speed of sound in air was constant for all moving observers then that would have been obviously wrong, but this would be an unfair analogy because the size & shape of an observer or metre-rods or clocks doesn't depend on the speed of sound. In fact Voigt says……..
………… Such a limitation does not take place in the analogous problems of the acoustics of fluids……

Voigt in later years was sheepish about his 1887 paper, perhaps because he applied his factor to all three coordinates (ie x'y'z'), whereas Lorentz & Poincare & Einstein didn’t apply their factors to y' or z'. Funnily i reckon that Voigt's treatment of y' & z' was the most realistic. Wiki says……
…….. In 1887 Voigt formulated a form of the Lorentz transformation between a rest frame of reference and a frame moving with speed v in the x direction. However, as Voigt himself said, the transformation was aimed at a specific problem and did not carry with it the idea of a general coordinate transformation, as is the case in relativity theory……….

Why did Lorentz (& Poincare)(& i think Cohn) fall in love with c being a constant? It only makes sense if Lorentz meant apparent c, not actual c. Lorentz was not aware of Voigt's 1887 paper.

1887 -- On the Principle of Doppler. By W. Voigt. ... of_Doppler
1904 -- Electromagnetic phenomena in a system moving with any velocity smaller than that of light -- by Hendrik Lorentz ... _phenomena
1896 -- W B Morton -- ... ng_Charges
1897 -- Searle -- ... _Ellipsoid

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Re: Larmor Relativity

Unread post by crawler » Sat Apr 11, 2020 10:49 pm

Spencer has some good wordage re Voigt's transforms. There are drastic differences compared to Lorentz & Co. I will have a think.
H J Spencer – 2007-8 – Classical two-electron relativistic dynamics.
The Voigt Transform
A few modern authors, such as Miller [26] and Pais [27], still remember that Woldemar Voigt (1850-1919) was the first scientist to investigate the invariance of the form of the D’Alembertian (Wave) Equation in 1887 [28]. His analysis focused on the differential equations characterizing vibrations through an elastic, incompressible medium. Voigt’s final form of the transformation equations associated with the space and time parameters, invoking an invariant speed of propagation c were:
x′ = x – v t , t′ = t – v x / c2 ; y′ = V y, z′ = V z where V = √ (1 – v2 /c2).
These equations retain the Galilean transformation in the direction of motion (x) and preserve the universality of the time dimension.
They introduce a ‘shortening’ in the transverse y and z directions, which appears like a spiral transform with respect to the speed.
Although Lorentz would later claim that he was unaware of Voigt’s transform, Lorentz was in private communication with Voigt soon after the publication of this result, which preceded the actual proposal of Lorentz’s “own” transform in 1895, both preceding Einstein’s 1905 derivation of the Relativistic transform in 1905 [29]. As Voigt pointed out, his transform was purely an exercise in mathematics (as Lorentz always viewed his own efforts) and had nothing to do with moving media or observers in relative motion.

Voigt transforms the Transverse Amplitudes
The Voigt transform [30] is not a kinematical transformation of the space and time co-ordinates, like the Relativistic transform. Rather it is simply a reduction of the amplitude of the transverse components of the propagating wave-like displacements, like the electric and magnetic force intensities (E and B) on the wave front. In contrast to the Relativistic transform, the Voigt transform is not a ‘rotation’ from the spatial direction of motion into the time dimension and vice-versa.
Notice that as the ‘speed’ parameter ‘v’ approaches the medium’s invariant speed constant ‘c’, these transverse amplitudes reduce to zero, implying that the wave vanishes and would be unable to communicate energy or information: a point that is rarely made.
The (inverse) relativistic transform generates infinities when v reaches c and this is used to limit the velocity.

Heaviside rediscovers the Voigt Transform
Oliver Heaviside was the first to exactly solve Maxwell’s Equations in 1888 for the special case of two massive, charged point particles that continue to move at a fixed, relative constant velocity [31]. Heaviside discovered that the electric force is everywhere radial with magnitude: E = e2 (1 – v2 / c2) / r2 (1 – v2 sin2θ / c2)3/2 , with θ as the axial angle, while the lines of magnetic force are circles, centered on the relative line of motion with magnitude: B = E sinθ (v / c).
Almost no physicist has commented on these results, which both go to zero as the speed v goes to c, again implying that all high-speed EM effects (e.g. light signaling) vanish at light-speed, as the Voigt transform predicts.
This contrasts with Planck’s 1906/7 Relativistic Momentum Proposal that predicted that non-zero inertial mass always becoming infinite in such circumstances.

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Re: Larmor Relativity

Unread post by crawler » Sat Apr 11, 2020 10:58 pm

Spencer has some good wordage re Larmor's transforms.
H J Spencer – 2007-8 – Classical two-electron relativistic dynamics.
Most histories of the theory of relativity touch on the contributions of Lorentz and Poincaré but most fail to mention that there was an alternative research programme investigating EM phenomena in relative motion already underway in England under the leadership of Joseph Larmor. Surprisingly, the very detailed history of the emergence and early interpretation of the SRT by Einstein historian Arthur I. Miller [26] makes absolutely no mention of Larmor’s contributions. Many of the results of this programme preceded the relativistic pronouncements arising on the Continent – an ironical nationalistic reversal of the earlier Maxwell-Weber rivalry associated with the fundamentals of EM theory.
It is difficult for the modern reader to realize that in 1900 Joseph Larmor (1857-1942) was one of the leading physicists in the world, in the same league as Poincaré, Lorentz and Planck; today he is remembered only for his work on diamagnetism. As the leading mathematical physicist at Cambridge from 1885, he was widely viewed as Maxwell’s very worthy successor. He was appointed Lucasian Professor (Newton’s old chair) on the strength of his researches into EM phenomena involving relative motion. Based on the application of the Principle of Least Action he proposed a new dynamical foundation for EM. In a series of papers published by The Royal Society between 1894 and 1897, he eventually (due to the strong persuasion of FitzGerald) focused on J. J. Thomson’s concept of a microscopic body of electricity that became known as the ‘electron’.
Larmor’s Electron Theory of Matter
Larmor’s final form of his theory proposed that matter consisted only of positive and negative electrons; these interacted via a continuum (the EM æther) that propagated effects between these particles. He viewed these electrons as mechanical point centers of radial strain in the æther thus solving the problem of the interaction between matter and the EM æther while also suggesting that all inertial mass was electromagnetic as the electrons were accelerated relative to the stationary æther. The whole universe could thus be viewed as electro-magnetic – a major unification in its metaphysical foundations [33] .
In contrast to the widely-accepted view today that EM was in crisis in 1900 due to the ‘paradoxes’ incurred by relative motion (exemplified by the MMX), the Cambridge programme constructed a dynamical model of EM that fully explained the null result; furthermore, they viewed the MMX as a justification of their own theory. The introduction of the ‘electron’ concept (discussed in more detail in the third paper in this series [4]) meant that all material interactions involving EM in the ETM became a problem in the electrodynamics of moving bodies.
By 1895, Larmor had shown that moving matter formed from electrons would contract slightly in the direction of its motion. Larmor used his theory to construct a new theoretical model of the MMX interferometer that explained all of the null result when he introduced his new space and time transformations relating the EM variables defined in the stationary æther to similar variables defined in the rest-frame of the interferometer.
These transforms would subsequently be ‘rediscovered’ by Poincaré and named the ‘Lorentz’ transforms (see 2.2). When the constant speed of the interferometer is v (defining the x-direction) relative to the fixed æther then the space and time variables in the moving-frame (x', t') relative to the æther’s rest-frame (x, t) are related by [34]:
x' = L (x – v t), y' = y, z' = z, t' = L (t – v x / c2) where L = (1 – v2/c2) – ½ = 1 / V
Larmor also found that Maxwell’s electric (E) and magnetic (B) variables had also to transform according to the scheme:
E x' = Ex , Ey' = L(Ey – v Bz) , Ez' = L(Ez + v By) ; Bx' = Bx , By' = L(By + v Ez/c2) , Bz' = L(Bz – v Ey/c2)
Initially, he found that these EM field transforms preserved the form of Maxwell’s Equation up to the second order (v2/c2).
In 1904, Larmor also realized that this invariance was valid to all orders under these transforms i.e. they were covariant. He explained this similarity in form as being due to the measured fields in the moving frame (the laboratory) being generated from the original fields in the fixed æther and the effects of motion through the æther. In 1897, Larmor also derived the equation for the potential around a moving electron.
This indicated that the potential surfaces around the electron would contract in the direction of motion by exactly the amount predicted by FitzGerald. All of these results were eventually republished in Larmor’s best-selling book Æther and Matter in 1900 [35]. From a physical perspective, Larmor viewed the stationary frame of the æther as privileged (as did Maxwell and all who believed in the æther model of EM); compared to this frame,
all moving bodies actually became shorter and moving clocks actually ran slower.
Larmor’s transforms should therefore be viewed in space and time, in contrast to Einstein, who saw them as transformations of space-time.

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