Poincare and Minkowski found a spacetime geometry explanation, and that has been the preferred explanation ever since.
Some philosophers have been debating the merits of these approaches. A new paper, Matter or geometry as fundamental in relativity theory: How not to teach special relativity, reviews them:
In this paper, I review a number of interpretational frameworks for relativistic phenomena like length contraction and relativity of simultaneity. Of central focus is the book Physical Relativity by Harvey Brown, where Brown advocates a view in which matter takes ontological priority over geometry. I discuss Brown’s claims and examine some of the criticisms they have received. I discuss the nature of simultaneity in particular, sketching the historical context and commenting on its relation to some of Brown’s broader arguments. Finally, I examine the consequences that Brown’s thesis has for what constitutes good pedagogy when teaching special relativity. ...Lots of phenomena have multiple explanations. Something can be learned from each one.
The lesson, then, from all this talk of kinematics vs. dynamics, principles vs. constructions, and so on, can be concisely stated: relativity, viewed as part of a broader investigation into the quantum field theoretic nature of particles, is fundamentally a theory about matter and how it interacts. While it may be formulated in terms of space-time geometry, viewing it as a theory about space-time geometry is putting the cart before the horse [5, p. 12]. Building a picture of relativistic physics from the bottom-up in this manner does, admittedly, lack some of the elegant conciseness of Minkowski's geometric formulation. Nonetheless, as John Bell said: "The longer road sometimes gives more familiarity with the country [1, p. 77]."
It is sometimes said that Lorentz had a different view from Einstein, but Einstein denied that there was any such difference:
In 1911 Vladimir Varićak asserted that length contraction is "real" according to Lorentz, while it is "apparent or subjective" according to Einstein. Einstein replied:The above paper uses the term "Larmor dilation" for the relativistic slowing of clocks, and maybe that is a good way of crediting his early worn on what we now call Lorentz transformations.
The author unjustifiably stated a difference of Lorentz's view and that of mine concerning the physical facts. The question as to whether length contraction really exists or not is misleading. It doesn't "really" exist, in so far as it doesn't exist for a comoving observer; though it "really" exists, i.e. in such a way that it could be demonstrated in principle by physical means by a non-comoving observer.
Source: Einstein, Albert (1911). "Zum Ehrenfestschen Paradoxon. Eine Bemerkung zu V. Variĉaks Aufsatz". Physikalische Zeitschrift 12: 509–510. Original: Der Verfasser hat mit Unrecht einen Unterschied der Lorentzschen Auffassung von der meinigen mit Bezug auf die physikalischen Tatsachen statuiert. Die Frage, ob die Lorentz-Verkürzung wirklich besteht oder nicht, ist irreführend. Sie besteht nämlich nicht „wirklich“, insofern sie für einen mitbewegten Beobachter nicht existiert; sie besteht aber „wirklich“, d. h. in solcher Weise, daß sie prinzipiell durch physikalische Mittel nachgewiesen werden könnte, für einen nicht mitbewegten Beobachter.
Here is a 2010 paper that wrongly alleges a difference between Lorentz and Einstein:
On the face of it, Lorentz and others make factual claims about physics: there is a luminiferous aether; the rod’s contraction is intrinsic, caused by motion through it, as described by Maxwell’s equations. The sentence “A moving rod contracts” is semantically like “A cooling rod contracts”: i.e. no reference to another relatum is implied.3But all of this is false, as Lorentz and Einstein did not disagree about any factual claims about the aether, nor did they disagree about whether the rod's contraction is intrinsic.
On the face of it, still, Einstein dissents, countering with different claims about the facts of physics: there is neither an aether nor an absolute motion to cause the contraction; it is not intrinsic, but a relation between a thing and an inertial frame of reference. If that first-face comparison is correct, then Lorentz and Einstein do differ over physical facts; the difference obliges us to choose between them for the purposes of physics.
The paper does cite Lorentz:
Earlier in his book, Lorentz puts length contraction on a par with the expansion of an object or a gas upon heating it: “We may, I think, even go so far as to say that that, on this assumption [i.e., the contraction hypothesis], Michelson’s experiment proves the changes of dimension in question, and that the conclusion is no less legitimate than the inferences concerning the dilatation by heat or the changes of the refractive index that have been drawn in many other cases from the observed positions of interference bands” (Lorentz 1916, p. 196).I doubt that Einstein would have disagreed with this statement.