Lorentz Contraction

• Type of physical science: Relativity
• Field of study: Special relativity

The Lorentz contraction hypothesis was developed independently by Hendrik Lorentz and George FitzGerald in an attempt to explain the failure of the Michelson-Morley experiment to detect the presence of the “ether wind,” a hypothetical substance. It is also sometimes called the Lorentz-FitzGerald contraction.

Overview

The nature of light has been a topic of controversy throughout the history of science. By the early 1700s, two major theories of light had emerged. Isaac Newton theorized that light is composed of infinitely tiny particles, while his contemporaries Christiaan Huygens and Robert Hooke proposed that light is a wave. A wave is defined as a disturbance that transfers energy through a medium or space.

Subsequent experiments, such as Thomas Young’s double-slit diffraction experiment of 1801, supported the wave theory. There remained, however, one significant problem. If light is a wave, what is the medium that carries it? Just as air carries sound waves, there must be some type of medium that can carry light waves throughout the vast vacuum of space. To solve this problem, some scientists proposed that a substance, which they called “ether,” occupies all of the visible universe. It was obvious to them that, if light can be seen from a star, then there must be ether to carry the light waves.

The ether theory solved some problems but created others. Experiments with polarizing lenses have shown that light has the properties of a transverse wave—unlike sound, which travels in compressional waves. Because transverse waves generally do not propagate through fluids in the same way as in solids, scientists had to assign the ether unusual properties for it to be able to conduct this type of wave.

In addition to having the ability to pass through all matter, occupy all of space, and be transparent and frictionless, the ether also had to be rigid enough to carry high-velocity transverse waves. In short, the ether was hypothesized to have extremely low density yet high rigidity.

In 1881, Albert Abraham Michelson, an American physicist studying at the University of Berlin, attempted an experiment which was designed to detect the effects of the ether drift. Although it was believed that the ether was at rest, it was also believed that the motion of the Earth through the ether would cause a wind. The effects of this ether wind would be detectable.

In his experiment, Michelson split a single light beam with a partially silvered mirror called a beam splitter. A portion of the beam traveled straight onward to a mirror; the other portion of the original beam traveled at a right angle to another mirror, which was equidistant from the beam splitter. Both beams were bounced back to the beam splitter, where they were recombined into a single beam and reflected to a lens, where the recombined beam was viewed. It was Michelson’s belief that the beam of light that was traveling against the ether wind would be retarded somewhat, allowing the beam that traveled at a right angle to arrive back at the beam splitter first. The two recombined beams would be then slightly out of phase with each other.

Michelson hoped to measure the shifting of the fringes caused by the interference and then deduce the effects of the ether. The experiment failed to indicate the presence of the ether. Michelson was not able to find evidence for the shifting of the interference fringes that he had predicted. In 1887, Michelson again attempted the experiment. This time, the experiment was conducted at the Case School of Applied Sciences in Cleveland, Ohio, where he was teaching. Michelson was assisted in this experiment by the chemist Edward Williams Morley. The test was to become known as the Michelson-Morley experiment.

With an apparatus which was identical in principle but much more sophisticated than the one that he had used in 1881, Michelson, with Morley’s assistance, made several attempts to detect the ether. Again, the experiment seemed to be a complete failure. Regardless of how the apparatus was oriented, no evidence of the ether was detected.

Shortly after the experiment was completed and its results disseminated throughout the scientific community, the Irish physicist George Francis FitzGerald suggested in his lectures that its results could be explained. It was FitzGerald’s contention that the motion of an object against the drift of the ether caused the object to contract. The equation that was derived for the amount of the contraction was the original length multiplied by √([1-v²]/c²), where v is the velocity of the object through the ether and c is the speed of light. It follows from this equation that, as an object’s speed approaches the speed of light, its length approaches zero (though objects with mass cannot reach light speed). Small velocities would make little difference in the contraction.

It was FitzGerald’s hypothesis that, if Michelson and Morley’s device was contracted slightly by the ether, then the beam of light traveling in the direction of contraction would have a slightly shorter distance to travel. The ether was hypothesized to have a drag effect on light, but this was not experimentally confirmed. The net result would be the same if there were no wind and, hence, no contraction. The contraction would be of exactly the correct amount to keep the speed of light a constant value.

In 1892 and later in 1895, the Dutch theoretical physicist Hendrik Antoon Lorentz, working independently of FitzGerald, published a paper entitled “Michelson’s Interference Experiment.” In this paper, Lorentz explained the results of the Michelson-Morley experiment by proposing, as FitzGerald had, that a contraction had taken place in the apparatus of Michelson and Morley. This theory became known as the Lorentz–FitzGerald contraction theory. Lorentz pointed out that, according to the interpretation of the Michelson–Morley experiment, the amount of time that it took the two beams to be separated at the beam splitter, travel to the corresponding mirrors, and be recombined at the beam splitter would not be identical for both beams. The beam that traveled against the ether drift was predicted to be slightly delayed. The beam traveling at 90 degrees to the direction of the ether drift would experience no such time delay.

Lorentz stated that the same effect would result if one of the arms of the device were slightly longer than the other. Consequently, the speed of light would not be slowed by the ether, and the difference in arrival times would be attributable to the fact that the path lengths traveled by the two beams were different. Each arm of the apparatus would experience the contraction as it was rotated to a direction which was parallel to the direction of the ether drift. The amount of that contraction would be the original length multiplied by √(1−v²/c²), the same equation that had been suggested by FitzGerald.

In the late nineteenth century, the forces between molecules in a rigid body were not well understood. It was believed that these forces were, in fact, transmitted by the ether.

Lorentz’s contention was that the action between the molecules or atoms was affected by motion through the ether.

Since the predicted contraction at low velocities was so minuscule, only a light interference method could be used to detect it. Lorentz concluded that it would be impossible to measure the contraction with a device such as a meter stick because the meter stick itself would experience a contraction. With his contraction hypothesis, Lorentz believed that he could successfully explain the results of the Michelson-Morley experiment.

Applications

In the early 1600s, Galileo Galilei laid the foundations for what came to be known as classical mechanics. His ideas later contributed to what are known as Galilean transformation equations relating events between reference frames. For example, consider an observer in a frame of reference that is at rest with respect to another observer in a second frame of reference that is moving at a rate of 50 kilometers per hour. Suppose that the observer in the moving frame of reference picks up a ball and throws it in the direction in which the reference frame is moving. If the velocity of the ball is 50 kilometers per hour relative to the person who threw it, then the observer at rest will observe that the moving frame of reference is traveling at 50 kilometers per hour and, within that frame, that the ball is traveling at 50 kilometers per hour. To find the velocity of the ball relative to the reference frame, the observer at rest must simply add the velocities of the moving frame of reference and the ball together to arrive at a velocity of 100 kilometers per hour. Suppose that an observer in a third frame of reference traveling at a constant velocity of 70 kilometers per hour observes the ball being thrown and attempts to measure its velocity. The third observer will observe the velocity of the ball to be 100 kilometers per hour minus the velocity of 70 kilometers per hour, or 30 kilometers per hour. These types of problems with the Galilean transformations involve the simple addition and subtraction of velocities.

After Galileo, wave theories of light developed through Huygens, Young, Fresnel, and Maxwell, along with the idea of a luminiferous ether. Aside from being the medium for conducting these waves, scientists decided that the ether should be at absolute rest. In other words, the ether became the frame of reference from which all other motion could be measured.

In 1887, Michelson and Morley attempted to detect Earth’s motion relative to the luminiferous ether by comparing the speed of light in perpendicular directions. It was the theory of Michelson and Morley that, when the Earth is moving against the drift of the ether, the light waves that are being carried by the ether will approach the Earth at the velocity of light plus the velocity of the Earth through the ether. Similarly, those light waves approaching the Earth against the flow of the ether will be traveling at the velocity of light minus the velocity of the Earth through the ether. According to classical physics, the velocity of light should vary depending on the observer’s motion, just as the velocity of the ball varied depending on the motion of the observer.

When the Michelson-Morley experiment failed to detect any changes in the velocity of light, Lorentz and FitzGerald, working independently, proposed that a contraction had taken place in the arms of the interferometer, which prevented these velocity differences from being noted. This ad hoc solution explained the results of the Michelson-Morley experiment and kept the ether hypothesis intact.

According to Lorentz, observers in different frames of reference will determine different lengths for the same object in the direction of motion. He explained this phenomenon by pointing out that an object becomes contracted along the axis of motion because of the interaction of the atoms and molecules within the object and the ether. He stated that his theory “certainly looks rather startling at first sight, but we can scarcely escape from it, so long as we persist in regarding the ether as immovable. We may, I think, go so far as to say that, on this assumption, Michelson’s experiment proves the changes of dimension in question.”

Not all scientists, however, accepted the contraction theory as the explanation for the failure of the Michelson-Morley experiment to detect the ether wind.

In 1895, the French physicist Jules-Henri Poincaré proposed that a single theory should be created to explain the results of all ether-detection experiments. He even went so far as to propose that a new science of mechanics should be created, one in which no velocity could exceed that of light.

In 1932, an experiment was conducted that ruled out the length contraction as a physical phenomenon. The American physicists Roy J. Kennedy and Edward Thorndike repeated the Michelson-Morley experiment, but with some modifications in the apparatus. The two physicists intentionally made the arms of their apparatus unequal in length. A light beam was split into two beams, and each beam then traveled to the end of an arm, where it was reflected by a mirror back to the beam splitter. The two beams were then recombined into one and reflected to an observer, where the interference fringes were noted. The device was then rotated to various positions, and the interference fringes were compared. No evidence of any contraction was noted.

Further experiments were performed in the early 1960s using the then-discovered Mössbauer effect. Again, there was no evidence of a physical contraction.

In 1905, Albert Einstein published a paper entitled “On the Electrodynamics of Moving Bodies.” In this paper, Einstein outlined what is now known as the special theory of relativity. In his theory, Einstein dismissed the idea of an absolute frame of reference and, hence, the idea of ether. He instead explained the nature of simultaneity: Events that may appear to be simultaneous to an observer in one frame of reference may not appear to be simultaneous to an observer in another frame of reference. In the measurement of length, for example, if an observer at rest wishes to know the length of a moving train, then that observer must know the position of the front of the train and the rear of the train at the same instant. Because the observer must measure the front and rear of the moving train simultaneously in the observer’s frame, the train’s measured length is contracted. Indeed, the amount of observed contraction matches the prediction of Lorentz and FitzGerald. There is, however, a significant difference between the interpretations of Lorentz and Einstein. To Lorentz and FitzGerald, the contraction was a physical change brought about by the ether. To them, each object had an absolute or rest length. By rejecting the concept of ether, Einstein also made meaningless the concept of absolute length. To Einstein, length is relative to the motion of the object and the observer.

Context

The Lorentz contraction hypothesis was developed as an explanation for the failure of the Michelson-–Morley experiment to detect the ether wind. With Lorentz’s theory, the ether wind concept could be saved, as well as the reputation of Michelson, an internationally known physicist. The ether was a substance which was absolutely necessary for the propagation of light waves according to the theories that existed in the nineteenth century. When James Clerk Maxwell developed his theory of electromagnetic waves in the early 1860s, he realized that the ether was still considered important in the transmission of these waves. Without the ether, many physicists of that time believed some pillars of classical physics would fall.

Although the contraction theory provided the explanation for the Michelson-Morley experiment in principle, there was no way that it could actually be verified at that time. Therefore, the contraction hypothesis remained a subject of thought experiments or mathematical exercises. As newer technology was developed, experiments were conducted in 1932 and in the early 1960s in an attempt to detect a physical contraction in the experimental device being used, but no evidence of a physical contraction was found.

In his special theory of relativity, Albert Einstein combined the ideas of Lorentz, FitzGerald, and others with his own ideas to develop a new foundation for physics. When he rejected the ether hypothesis, he did away with the need to explain a physical contraction. He did, however, incorporate the idea of a contraction into his theory. In this case, an observer at rest would observe a moving object to be contracted along its axis of motion. On the other hand, the observer in motion would find the surroundings to be normal, but would think that the other observer was contracted. This strange new world of relativity was not about physical contractions, but different methods of observation. Experiments have demonstrated that while Lorentz contraction is measurable, it is not directly visible due to light travel-time effects.

According to Einstein’s theory, an object cannot be accelerated to the speed of light. If one assumed, for the purpose of an example, that the speed of light could be reached by a spacecraft, then some rather bizarre effects would be observed. The contraction, which was minute at low velocities, would become very significant at relativistic velocities. As the spacecraft approached the speed of light, an observer would note that the spacecraft was becoming shorter and shorter. As velocity approaches the speed of light, length contraction increases toward zero; however, objects with mass cannot reach the speed of light.

Principal terms

COMPRESSIONAL WAVES: waves that propagate in a medium that oscillates in a direction parallel to that in which the waves are traveling

DIFFRACTION: the spreading of a wave as it passes through an opening or around an obstacle

ETHER: a hypothetical substance which was believed to fill the entire universe and serve as a medium for propagating light waves

FRAME OF REFERENCE: a point of reference from which motion is measured

INTERFEROMETER: a device that uses interference fringes to measure length or a change in length

TRANSVERSE WAVES: waves that propagate in a medium that oscillates in a direction perpendicular to the direction in which the waves are traveling

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