Modern Interpretation of Length Contraction

A confusing question is whether the length contraction of relativity is real. I got this explanation from xAI:

In contemporary physics, length contraction is understood as a consequence of the Lorentz transformation in special relativity, which describes how measurements of space and time differ between inertial reference frames moving relative to one another. The key points of the modern view are:

• Relativity of Measurements: Length contraction is a real, measurable effect, but it is frame-dependent. If an observer in frame ( S ) measures a rod at rest in frame ( S' ) (moving at velocity ( v ) relative to ( S )), the rod’s length in ( S ) appears shorter by a factor of

  \sqrt{1 - v^2/c^2}

  . This is described by the Lorentz transformation:
  L = L_0 \sqrt{1 - v^2/c^2}
  where

  L_0

  is the proper length (length in the rod’s rest frame), and ( L ) is the contracted length in the observer’s frame.
• Geometric Perspective: Length contraction is often explained as a consequence of the geometry of Minkowski spacetime, a flat, pseudo-Euclidean four-dimensional manifold with a metric signature (e.g.,

  (+,+,+,-)

  ). The contraction arises because observers in different frames slice spacetime differently, leading to different projections of a worldline’s spatial extent. This geometric view emphasizes the relativity of simultaneity: what one observer measures as a “length” depends on how they define simultaneous events.
• “Apparent” vs. “Real”: Modern texts avoid calling length contraction “apparent” in the sense of being an illusion, but they emphasize its dependence on the observer’s reference frame. It’s real in the sense that it’s consistently measurable (e.g., a moving object fits into a shorter space in the observer’s frame), but it’s not an intrinsic change to the object itself—its proper length remains invariant. The effect is a result of the geometry of spacetime and the conventions of measurement, not a physical compression. ...
• Textbook Treatments: Modern relativity texts (e.g., Taylor & Wheeler’s Spacetime Physics or Hartle’s Gravity) describe length contraction as a geometric effect, often using spacetime diagrams to show how different frames yield different lengths. This is closer to Varićak’s geometric interpretation than Lorentz’s physical contraction.

It goes on in detail, saying that Lorentz viewed the contraction as physical, while the modern geometric view was championed by Minkowski and Varicak.

The curious thing is where Einstein stood. Everyone assumes that he had the modern geometric view, but that is completely false. As xAI explains:

The Disagreement:

The core issue was Varićak’s interpretation of length contraction:

• Varićak’s View: Varićak argued that length contraction in Einstein’s theory was an “apparent” or “psychological” phenomenon, resulting from the convention of clock synchronization and time measurements in different frames. He contrasted this with Lorentz’s theory, where he considered length contraction an “objective” physical effect due to the ether. Varićak’s hyperbolic geometry approach framed relativistic effects in a way that emphasized mathematical elegance and suggested that some phenomena might be observer-dependent artifacts.
• Einstein’s Criticism: Einstein published a brief rebuttal in 1911, asserting that his interpretation of length contraction was closer to Lorentz’s in that it was a real, measurable effect, not merely apparent or psychological. He argued that length contraction was a direct consequence of the relative motion between frames, as described by the Lorentz transformation, and not contingent on subjective measurement conventions. Einstein likely saw Varićak’s interpretation as undermining the physical reality of relativistic effects, which he considered fundamental to his theory.

This is a surprisingly accurate account of the different views of length contraction. AI is not always right, but it is relying on mainstream sources here.

By 1911, the geometric view of relativity was very well established, and yet Einstein published a disavowal of it.

Einstein had 5 years to learn relativity, and he still did not get it.

There are people who argue that Einstein should be credited for relativity, because Lorentz and Poincare occasionally made reference to an aether or preferred frame, years after Einstein's 1905 paper. But these are not errors, and Einstein also referred to an aether. It is a simple mathematical fact that one can choose a preferred frame without affecting relativity. Cosmologists always do exactly that, using the cosmic microwave background.

Maybe Lorentz rejected the geometric view in 1911, I don't know. It is astounding that Einstein did. The geometric view was the key thing that made relativity better than Lorentz's 1895 theory. If Einstein did not agree with it, then he had nothing over what Lorentz had many years earlier. The geometric view of Minkowski's 1908 paper is what made relativity widely accepted.

Einstein's 1905 paper did have some better formulas than Lorentz's 1895 paper, but no better than Lorentz's 1904 paper. Lorentz already had the key ideas of length contraction and local time in 1895. FitzGerald had the length contraction in 1889, using an argument similar to Einstein's.

I have read a lot of Einstein commentary, but I have never seen the Einstein fans explain why he was still disavowing geometric relativity in 1911. He did not understand or accept what became the modern interpretation.

A new paper discusses some history:

On Bell's dynamical route to special relativity
Frederick W. Strauch

The Michelson-Morley experiment was published in 1887, and already in 1888 Oliver Heaviside showed that Maxwell's equations implied a contraction of electric fields in the direction of the motion. This inspired FitzGerald, Larmor, and maybe even Lorentz to figure that solid objects might contract, if held together by electromagnetics forces, as we now know that they are. This is the dynamical interpretation that is out of favor today, but it was important historically, and is a legitimate way to understand the contraction.

The paper cites this 2018 paper on The dynamical approach to spacetime theories by Brown and Read. It defends the dynamical view, and describes the geometric view this way:

In the last few decades, the approach has come to life within the philosophy of physics as a reaction to aspects of the ‘angle bracket school’ of spacetime theories, first prominently exposed in the philosophical literature of the 1970s and especially the 1980s.5 The central role of geometry in the treatment of pre-general relativistic theories in this approach has led some philosophers to the view that special relativistic effects such as length contraction and time dilation are ultimately explained by recourse to the geometric structure of Minkowski spacetime, and that all such explanations prior to the 1908 work of Minkowski are either misguided or incomplete.

I guess it is called ‘angle bracket school’ because it takes the metric on Minkowski space as the fundamental covariant object. That was the approach of Poincare in 1905-6 and Minkowski in 1907-8, so I think he means that the approaches of FitzGerald, Lorentz, and Einstein were deficient for not understanding the non-euclidean geometry of Poincare and Minkowski.

The dynamical interpretation is not wrong. It can explain the contraction on a molecular level, using Maxwell's equations. It is just not the modern view that Poincare and Minkowski invented.

Brown and Read start by saying:

In 1940, Einstein offered the following nutshell account of his special theory of relativity (SR):1

The content of the restricted relativity theory can ... be summarised in one sentence: all natural laws must be so conditioned that they are covariant with respect to Lorentz transformations. [17, p. 329]

This innocuous-sounding statement actually represents on Einstein’s part a significant departure from his 1905 ‘principle theory’ approach to SR, based upon the relativity principle, the light postulate, and the isotropy of space. The shift in his thinking did not come about overnight.

This description seems to avoid mentioning light or geometry, but those are implicit.

Poincare and Minkowski proved that Maxwell's equations were covariant with respect to Lorentz transformations. Einstein only showed a version of Lorentz's 1895 theorem about corresponding states.

Brown and Read see this as consistent with their eccentric dynamical views. I would rather rephrase it as saying that all natural laws are well-defined on Minkowski space, which has a Lorentz invariant geometry. It is interesting that Einstein was still not willing to make an explicitly geometrical statement in 1940.

They say:

We expect undergraduates to imbibe in their first course on relativity theory a profound insight largely obscure to all the nineteenth century giants, including Maxwell, Lorentz, Larmor and Poincaré: the physical meaning of inertial coordinate transformations. It was Einstein in 1905 who was the first to understand the physics of such transformations,17 and the fact they are neither a priori nor conventional.

I think they are trying to say that Einstein rejected the idea that the Lorentz transformations were just reflections of the underlying spacetime geometry. They believe the dynamical view is superior to the modern geometrical view, so I guess they are trying to credit Einstein with having a dynamical view. It appears to me that Einstein tried to avoid committing himself to being for or against the dynamical view. For example, he wrote:

One cannot ask whether the contraction should be understood as a consequence of the modification of molecular forces caused by motion or as a kinematic consequence arising from the foundations of the theory of relativity. Both points of view are justified. [letter to Varicak, 1911]

Note that Einstein does not even mention the geometric view. I would say that the contraction should be understood as the divergence between the non-euclidean spacetime geometry, and the more familiar euclidean geometry.

A 1909 paper had credited Einstein with rejecting Lorentz's molecular force contraction, but Einstein disavowed having adopted a view different from Lorentz's.

In the geometric view, aka angle bracket school, the physics is in the geometry. The Lorentz transformation is just a change of coordinates with no real physical significance.

One might similarly argue that Earth longitude being based on the Prime Meridian has no real significance. If you measure longitude you will get numbers that depend on that choice, but the physics of whatever you are observing does not. The superior geometric view is that the physics does not depend on the coordinates, and that a coordinate choice can be mathematically transformed into any other choice, without affecting the physics.