Why don`t we notice the contraction of length in everyday life? The distance to the grocery store doesn`t seem to depend on whether we move or not. If we look at the equation [latex]L=L_0sqrt{1-frac{v^2}{c^2}}[/latex], we see that at low speed (v<<c) the lengths are almost the same, the classical expectation. But the contraction of length is real if it is not experienced frequently. For example, a charged particle, such as an electron moving at a relativistic speed, has compressed electric field lines along the direction of motion seen by a stationary observer. (See Figure 4.) When the electron passes through a detector like a coil of wire, its field interacts much shorter, an effect observed in particle accelerators such as the 3 km Stanford Linear Accelerator (SLAC). In fact, for an electron moving through the beamline at SLAC, the accelerator and the Earth are contracted in length. The relativistic effect is so large that the accelerator is only 0.5 m long at the electron. It is actually easier to pass the electron beam through the tube because the beam does not need to be aligned as precisely to enter a short tube as it would be with a 3 km tube. This, in turn, is an experimental review of the theory of special relativity. (d) When an unstabilized cube moves at a significant fraction of the speed of light, but without taking into account the special theory of relativity, there is no contraction of length in any direction.
Due to the superficial application of the contraction formula, certain paradoxes may arise. Examples include the scale paradox and Bell`s spaceship paradox. However, these paradoxes can be solved by correctly applying the theory of relativity of simultaneity. Another famous paradox is the Ehrenfest paradox, which proves that the concept of rigid bodies is incompatible with the theory of relativity, which reduces the applicability of Born`s rigidity and shows that geometry is actually non-Euclidean to a co-rotating observer. From his theory, Einstein derived the contraction of length as well as time expansion, the equivalence of mass and energy, and more. In particular, he realized that an observer resting on a high-speed train measures the length of a high-speed train that passes in the direction of its movement by a factor (1–v2/c2)1/2, where v is the relative speed between the observer and the other train. (Paradoxically, an observer in this train measures the first as shortened by the same factor. Isn`t the theory of special relativity fun?) Researchers did not begin to correctly perceive the practical aspects of observing lorentz contraction until Terrell published an internal Los Alamos paper on the effect in 1957, followed by an article in the Physical Review (116 4). His work was discovered by theorist Victor Weisskopf, who, while he was president of the American Physical Society, wrote an article for Physics Today in which Terrell`s results were presented in a simpler form. The idea of length contraction was postulated in 1889 by the Irish theoretical physicist George FitzGerald and in 1892 by the Dutch theorist Hendrik Lorentz. Also known as the Lorentz-Fitzgerald contraction or simply the Lorentz contraction, it was used to explain the negative outcome of Albert Michelson and Edward Morley`s memorable experiment of 1887. As is known, the two Americans had tried – and failed – to detect “ether”,” a hypothetical stationary medium supposed to carry electromagnetic waves, similar to how the surface of water carries water waves.
Over the years, few people have paid much attention to observing the Lorentz contraction. Anton Lampa, an Austrian physicist who had already helped Einstein in his first position as a university professor, published a paper on the subject in 1924 (Zeitschrift für Physik 27,138). As for the appearance of a moving pole for a spectator, his work has unfortunately been largely neglected. In fact, Russian-born physicist George Gamow misunderstood the contraction of length in his famous 1940 children`s book Mr. Tompkins in Wonderland. He showed bikes that were simply shortened in the direction of walking instead of being deformed and lying down when an observer approached, or contracting when they retreated into the distance. About six decades after Penrose and Terrell`s publications, the Terrell effect is still little known — Terrell died in 2009 after living in Los Alamos — and many textbooks and scientific moderators still don`t understand the contraction of length. But when you realize what Penrose and Terrell had to say, you`ll surely wonder why you never thought of Lorentz`s contraction that way. As the German philosopher Arthur Schopenhauer once wrote in a remark often wrongly attributed to Erwin Schrödinger: “The task is. not so much to see what no one has ever seen; but to think what no one has ever thought, what everyone sees.
To save the stationary ether hypothesis, Lorentz and Fitzgerald`s solution to Michelson and Morley`s zero result was to suggest that objects moving at a significant fraction of the speed of light – when seen by another observer – appear shortened in the direction of their journey. Based on Oliver Heaviside`s calculation of how the magnetic vector potential in Maxwell`s equation between frames of reference changed, their idea was actually just one of the few “solutions” proposed. .