For the student of physics, there comes a moment of intellectual pleasure as he or she realizes for the first time how changes of length, time and simultaneity conspire to preserve the observed speed of light. Yet Einstein's theory  provides little understanding of how Nature has contrived this apparent intermingling of space and time.He is correct that there is some merit to viewing the LT as a physical effect caused by motion. Einstein called this a "constructive" approach in 1919, as opposed to what he called a "principle theory".
The language of special relativity (SR) may leave the impression that the Lorentz transformation (the LT) describes actual physical changes of space and time. Thus we have Minkowski's confident prediction that,Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows and only a kind of union of the two will preserve an independent reality .The impression that the LT involves some physical transmutation of "spacetime" might seem consistent with the change of that nature contemplated in general relativity (GR). ...
The effects described by the LT can be explained in their entirety by changes occurring in matter as it changes inertial frame. This is not to suggest that the LT does not describe a transformation of space and time. But what the LT describes are changes in what is observed, and in the Lorentzian approach17 offered here, what is observed by an accelerated observer is essentially an illusion induced by changes in that observer.
This view relies crucially on the conclusion reached in Sect. 1 that the LT does not involve actual physical change in the properties of space. But once that conclusion is reached, it becomes apparent that there is something elusive in Einstein's theory, and that it is the Lorentzian approach that better explains the origin of the contraction, dilation and loss of simultaneity described by the LT.
Once the LT is explained from the wave characteristic of matter a good deal else becomes apparent. The de Broglie wave is seen to be a modulation rather than an independent wave, thus explaining the superluminality of this wave, its significance in the Schrodinger equation, and its roles in determining the optical properties of matter and the dephasing that underlies the relativity of simultaneity.
Einstein's bold assertion that the laws of physics must be the same for all observers revealed the elegance of SR and something indeed of the elegance of the universe itself. It is suggested nonetheless that it is a Lorentzian approach that will provide the deeper understanding of the physical meaning of SR.
The relativity principle was not "Einstein's bold assertion". It was conventional wisdom, until Maxwell and Lorentz suggested electromagnetic tests of it. Then it was Poincare who proposed how it could be a symmetry of nature, including electromagnetism and gravity. Einstein only recited what Lorentz had already said.
But to entertain these thoughts is to embark upon a process of reasoning, associated primarily with Lorentz, that became unfashionable2 following Einstein's famous paper of 1905 . Lorentz had sought to explain the transformation that bears his name on the basis of changes that occur in matter as it changes velocity. This was, it is suggested, an idea before its time.Einstein later wrote that he also sought a constructive approach, but could not get it to work.
Historically, it is not true that Einstein's famous 1905 paper caused the constructive view to become unfashionable. Minkowski's 1908 paper did that.
In the preferred (Minkowski) view, the LT is not really a transmutation of space and time. Minkowski spacetime has a geometry that is not affected by motion. The LT is just a way to get from one set of artificial coordinates to another.
The LT was already reasonably well known by 1905. There had been significant contributions to its development, not only from Lorentz and Fitzgerald, but also by (among others) Heaviside, Larmor and Poincaré. It was Heaviside's analysis of the disposition of fields accompanying a charged particle (the "Heaviside ellipsoid") that had suggested to FitzGerald the idea of length contraction. Larmor had described an early form of the LT and discussed the necessity of time dilation . Poincaré had recognized the relativity of simultaneity and had studied the group theoretic properties that form the basis for the covariance of the transformation .Here he recites this strange criticism that the LT was just a mathematical construct for Lorentz and Poincare, and therefore inferior to the 1905 Einstein view that has been accepted ever since.
But these "trailblazers" (Brown , Ch. 4) appear to have missed in varying degrees the full significance of the transformation3. It is not only particular phenomena, but all of Nature that changes for the accelerated observer. Lorentz struggled to explain how all aspects of matter could became transformed in equal measure, being discouraged by experimental reports that seemed to show that particles do not contract in the direction of travel (see Brown , p. 86). A wider view seems to have been noticed by Poincaré , who has been regarded by some as codiscoverer of SR (see, for instance, Zahar , and Reignier ). But it is not apparent that these earlier investigators saw the changes described by the LT as anything more than mathematical constructs. In his paper of 1905 , Einstein simply asserted that the velocity of light, and other properties of Nature, must appear the same for all uniformly moving observers, thereby effecting an immediate reconciliation between Maxwell's equations and classical mechanics.
In 1905, Einstein's approach may have been the only way forward. It was not until 1924, only a few years before the death of Lorentz, and well after that of Poincaré, that de Broglie proposed that matter is also wavelike , an idea that might have suggested to Lorentz why molecules become transformed in the same degree as intermolecular forces.
A lot of historians and others make this argument. They cannot deny that Lorentz and Poincare had the LT formulas ahead of Einstein, so they say that Einstein had the physics while Lorentz and Poincare just had some mathematical ideas without realizing the physical relevance. In particular, they say that Lorentz had a "local time" that was not necessarily related to the time given by local clocks.
The trouble with their argument is that Lorentz and Poincare explicitly use their theory to explain the Michelson-Morley experiment, and that explanation only makes sense if the distances and times in the LT formulas are the same as those measured by meter sticks and clocks in the lab.
There were three historical formulations of SR, using Einstein's terminology:
The Michelson-Morley experiment could be interpreted as evidence for (1) a stationary Earth; (2) an emitter (non-wave) theory of light; (3) an aether drift theory; or (4) the relativity principle combined with a constant speed of light. FitzGerald and Lorentz reject the first 3 possibilities based on other experiments, and were led to option (4). They then deduced the LT as a logical consequence of those principles.
The constructive theory has been unfashionable, but the above paper gives a good account of the merits of that view. I prefer to call this the bottom-up view. If there is a contraction, then the distance between molecules decreases, and this view explains it in terms of the molecular forces. The view is completely consistent with modern quantum field theory, but not usually mentioned in the textbooks.
Einstein preferred the principle theory formulation that he got from Lorentz. The Einstein idolizers rave about how great this was, but geometric theory has been the dominant one among theoretical physicists since 1908.
I would say that the constructive theory has the most physical LT. In it, solid objects really contract because of increases in the forces that hold the molecules together. In the geometry theory, the LT is more of a mathematical illusion. The contraction is an artifact of trying to use Euclidean coordinates on a non-Euclidean spacetime. In a sense, the LT is merely mathematical, because it has more to do with how we measure than to physical changes, but it also explains the Michelson-Morley and other experiments.
Here is a more complete version of the above Minkowski quote:
The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.The geometric view is a mathematical view "sprung from the soil of experimental physics". The story of SR is that Maxwell's equations and experiments like Michelson-Morley drove Lorentz, Poincare, and Minkowski to a series of discoveries culminating in our modern understanding that spacetime has a non-Euclidean geometry. Einstein had almost nothing to do with it, as he ignored Michelson-Morley, did not make any of the key breakthrus, and never even liked the geometric view.
I can understand Shanahan giving a defense of the constructive (bottom-up) view. It is a completely legitimate view that was historically crucial and useful for modern understanding. It deserves more respect, even tho it is not the preferred view. But he is wrong to endorse the opinion that Lorentz and Poincare, but not Einstein, missed the full significance of the LT.
Shanahan is essentially saying that the LT can be considered a transmutation of matter and fields, or a transmutation of space and time. If you emphasize the wave-like nature of matter, he argues, then the LT makes logical and physical sense as a transmutation of matter and fields. It is no stranger than transmuting space and time.
My problem with this dichotomy is that it ignores the Poincare-Minkowski geometric view where no physical things (matter, fields, space, time) get transmuted. The physics is all built into the geometry, and the contraction seems funny only because we are not used to the non-Euclidean geometry.
The full significance of the LT is that it generates the Lorentz group that preserves the non-Euclidean geometry of spacetime. Poincare explained this in his 1905 paper, and explained that it is a completely different view from Lorentz's. Lorentz deduced relativity from electromagnetic theory, while Poincare described his relativity as a theory about “something which would be due to our methods of measurement.”
Einstein's view was essentially the same as Lorentz's, except that Einstein had the velocity addition formula for collinear velocities, and lacked the constructive view.
I am beginning to think that the historians have some fundamental misunderstandings about relativity. SR only became popular after that 1908 Minkowski paper presented it as a non-Euclidean geometry on spacetime, with its metric, symmetry group, world lines, and covariant equations. Publications took off that year, and within a couple of years, textbooks started to be written. Minkowski's geometry theory was the hot theory, not Einstein's.
Today the general relativity (GR) textbooks emphasize the non-Euclidean geometry. The SR textbooks pretend that it is all Einstein's theory, and the geometry takes a back seat. The SR historians appear to not even understand the non-Euclidean geometry at the core of what made the theory popular.
(Shanahan once posted an excellent comment on this blog, and then deleted it. I do not know why. Maybe I will reinstate it as an anonymous comment. I also previously mentioned his current paper.)