The State of Experimental Evidence for Length Contraction, 2002
| Scientific Paper | |
|---|---|
| Title | The State of Experimental Evidence for Length Contraction, 2002 |
| Read in full | Link to paper |
| Author(s) | Delbert J Larsen |
| Keywords | Length Contraction |
| Published | 2002 |
| No. of pages | 15 |
Read the full paper here
Abstract
The idea that physical objects become shorter as they move is now well established in physical theory. Both the classical theories of Lorentz, Larmor, Fitzgerald and Poincare and the more radical special theory of relativity of Einstein incorporate a physical length contraction into their worldview. However, no direct measurement of length contraction has ever been done. One experiment that tried to observe the effect of a length contraction was done by Sherwin, who found no evidence of a length contraction. This paper will analyze the assumptions underlying Sherwin's experiment to show that Sherwin's experiment is in fact equivocal concerning the existence of a length contraction. This paper will also make mention of another important recent observation that has relevance to the issue of the existence of physical length contraction.
Overview
Delbert J. Larson — an accelerator physicist who worked on the longitudinal dynamics design of the cancelled Superconducting Super Collider — wrote this paper in July 2002 as a revision of his own earlier position. It is dedicated to the memory of John E. Chappell, Jr., whom Larson describes as "singly and heroically devoted to debunking the special theory of relativity."
The paper's subject is an unusual one: not whether Length Contraction is theoretically necessary, but whether anyone has ever measured it. Larson's contention is that no one has. He accepts that there is strong direct evidence for Time Dilation, citing the CERN muon lifetime measurements of Bailey et al. (Nature 268, 301, 1977), but insists that contraction has only ever been inferred. What makes the paper unusual among dissident writing is that its main argument works against the author's own previous conclusion: in an earlier Physics Essays paper (7, 476, 1994) Larson had treated C. W. Sherwin's 1987 rotating-spring experiment (Phys. Rev. A 35, 3650) as evidence that contraction does not exist, and here he retracts that reading, showing that Sherwin's null result rests on an unstated assumption and is therefore equivocal.
The departure from the mainstream lies in the framework rather than the arithmetic. Larson works inside a Lorentzian Aether picture in which contraction would be a real, orientation-dependent physical effect relative to a preferred frame — as against Einstein's relative contraction, in which no earth-based observer would see any orientation dependence at all. That distinction is what makes Sherwin's experiment a discriminating test in the first place.
The argument
Why the standard evidence does not settle the question
Larson summarizes the result of his 1994 paper: if moving observers wrongly assume the Speed of Light is isotropic and equal to c in their own frame, and if a Larmorian or Lorentzian time dilation exists in nature, then those observers will conclude that the Lorentz transformations govern electrodynamic phenomena — "even if a length contraction does not actually exist in nature." Electrodynamic evidence, including the behaviour of particle accelerators, is therefore compatible with either answer.
The Michelson-Morley Experiment gets special treatment. Larson points to what he calls node entrapment: the electromagnetic oscillation is forced to be null at the mirrors, and "it is this enforced boundary condition that also forces zero fringe shifts to result." If that is right, the classic null result is not evidence for contraction, and with it removed "you quickly find that there are no experiments that show the reality of the length contraction."
Sherwin's rotating spring
Sherwin's design was ingenious. A spring is spun rapidly. On the Lorentzian view a spring aligned with its motion through the aether is contracted, while the same spring aligned perpendicular to that motion is not. Rotating it therefore drives a periodic change in its equilibrium length. Sherwin tuned the rotation to resonance with the spring's natural harmonic frequency, expecting to pump up detectable oscillations — his reasoning being that a length disturbance can propagate through the spring no faster than the speed of sound, so on a quarter-turn the spring cannot reach its new equilibrium and Hooke's-law restoring forces F = kΔx will excite motion. No oscillations were seen. Sherwin read this as support for Einstein (whose theory predicts no orientation dependence for an earth-based observer, since the motion is symmetric about the centre of rotation and every inertial frame is equivalent) and against Lorentz; Larson in 1994 read it as evidence against contraction per se.
The retraction: rigid contact versus slippage
The new argument turns on what determines an object's length. Larson takes it to be the spacing between atomic nuclei, fixed by the balance between the energy cost of wave-function curvature — which favours larger size — and the Coulomb potential energy, which favours smaller size, the equilibrium set by minimizing the total energy via the Schrödinger equation and more accurately by Quantum Electrodynamics. In a lattice the calculation is harder but the same competition applies.
He then draws atoms as circles at rest in the aether and as ellipses when the object moves. In Sherwin's spinning spring, both he and Sherwin tacitly assumed the spring is rigid all the way down to its atomic connections — that a fixed point A on one atom stays welded to a fixed point C on its neighbour, so that the atoms rotate bodily as the spring revolves and any change in equilibrium length must propagate mechanically. Larson's alternative is that neighbouring atoms slide along their common boundary as the spring turns: the contact point migrates from A–C to B–D over a quarter turn. On that picture "rather than the speed of the length contraction be required to propagate along the spring at the speed of sound, the length contraction is already there! It is just that the contact point moves along the atomic boundaries as the spring is rotated." He sketches the extension to two rows of atoms and notes that three dimensions requires only adding atoms above and below the gaps.
The conclusion is deliberately symmetric: if atoms slide, Sherwin's null result is exactly what a Lorentzian aether predicts; if they maintain rigid contact, Sherwin's original argument stands. "Once again, an underlying assumption about nature must be made in order to interpret the results of an experiment," and so no conclusive statement can be made either way.
Earth tides at CERN
The second, briefer strand concerns storage-ring measurements. CERN researchers detected changes in the orbital period of stored particles correlated with lunar position, and inferred from them a change in the path length traversed, on the assumption that the particle speed is constant — at LEP the electron velocity is extremely close to c under either theory. Larson observes that such measurements could in principle discriminate: if there were no Lorentzian contraction, and if Lorentzian time dilation alone were responsible for the apparent contraction, and if the particle speed really is constant, then the earth's daily rotation ought to produce a diurnal variation in orbit times. He does not carry the analysis out, calling it "very worthy of future study," but says in the conclusion that it "may provide some suggestion that a length contraction does exist."
What a definitive test would look like
Larson proposes one: accelerate spheres large enough that ultrashort laser pulses can be fired across them while they move, and measure the shadows cast — before, during and after the motion, the before-and-after measurements serving to confirm that the spheres were not mechanically altered by the acceleration and deceleration. His verdict stands as the paper's last line: "As of July, 2002, it is still not proven that a length contraction exists."
Assessment
The paper's outstanding merit is intellectual honesty. Larson's central act is to dismantle his own strongest piece of evidence, and he does it carefully, identifying an assumption — atomic-scale rigidity — that Sherwin genuinely did leave unstated and that genuinely does carry the inference. The general moral he draws, that an experiment's verdict is only as strong as the auxiliary assumptions used to read it, is sound and too rarely applied to celebrated null results. His insistence on distinguishing a real Lorentzian contraction from Einstein's reciprocal one is also correct and is what makes a rotating-body test meaningful at all; and unlike much writing in this area, the paper concedes that time dilation is directly and firmly measured.
The difficulties begin with the slippage picture itself, which is offered as a cartoon and never as mechanics. Atoms in a metallic lattice are not hard shapes in contact along boundaries; the "sliding" Larson describes is a shear rearrangement of the lattice, and a shear rearrangement has its own restoring forces and its own finite propagation speed — the transverse sound speed. Nothing in the paper shows that the slippage mode is free of the very Hooke's-law response that drives Sherwin's predicted resonance, so the escape route is asserted rather than demonstrated. No magnitude is computed anywhere: the effect being sought is second order in v/c, and without an estimate of the predicted amplitude against the experiment's sensitivity, neither Sherwin's original inference nor Larson's rebuttal can be weighed.
The node-entrapment claim is likewise asserted here and referred back to the 1994 paper. As stated it does not account for the interferometer's actual behaviour: Michelson-Morley-type experiments do produce fringe shifts when the arms are physically altered, and the modern optical-resonator versions of the test constrain orientation dependence to parts in 1017 or better while resting on quite different boundary conditions. The remark that "Einstein's relativity is the most in doubt, because of the experimental tests of Bell's Theorem" is a non-sequitur as it stands: the Aspect experiments bear on locality and realism in quantum mechanics, and Larson supplies no chain of reasoning connecting them to length contraction. The LEP tide argument is left as a promise rather than a result; and since the paper offers no calculation of the expected diurnal signature, its closing hint that the tide data may favour contraction is not supported by anything in the text.
The proposed definitive experiment has a subtlety Larson does not address. Measuring a moving object by the shadow it casts is a measurement by light, and what a camera or a shadow records is not the contracted shape but the shape distorted by differential light-travel time across the object — the Terrell-Penrose effect, which for a sphere famously restores a circular outline. A shadow experiment would therefore need a careful timing analysis before its result could be read as a length. Set against this, it is worth noting what the paper does not weigh: relativistic heavy-ion physics routinely treats the colliding nuclei as contracted pancakes and gets the initial energy density and the observed particle multiplicities right, and the sharply transverse electromagnetic field of an ultrarelativistic charge — the same contraction expressed in the field rather than in matter — is designed into the accelerators Larson himself builds. That is indirect evidence, exactly as he says all the evidence is; but it is a considerable body of it, and the paper's standard of a "direct measurement" may be one that no property of a fast-moving object can meet.