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Einstein's box This thought experiment, dreamed up by Einstein in 1905, was designed to determine the mass equivalence of a pulse of electromagnetic radiation(m= E/c) Einstein considered a closed system(a box)of mass M, which is initially at rest in an inertial frame of reference S. The walls at either end of the box are of equal mass. A photon is emitted from a photon gun on one wall, down the central axis of the box, towards the other end wall. From the phenomenon of radiation pressure (given by E= pc)we know the photon emitted must have momentum. Therefore to with velocity V. When the photon hits the far side of the box the system will come conserve the momentum of the system the box must move in the opposite directior to rest again, with a slightly different position to its starting point. This shift in position can be made arbitrarily large by repeating the process If the assumption that the carrier remains massless is valid then the system, which was initially at rest, will have its centre of mass shifted without any external forces acting on the system. This clearly violates the law of mechanics which states that a body, which is initially at rest, cannot undergo translational motion unless there is an external force acting on the body The only way that this problem is able to be solved is if the photon has transported an amount of mass- so that even though the box has moved the centre of mass is still about the original point Einstein's derivation has some conceptual problems with it, namely that the box is treated as a rigid body a concept that is inconsistent with the principles of special relativity. The approach taken by French circumvents the rigid body problem by considering only the two end walls of the box, arriving at the same result utilizing the centre-of-mass theorem Burt Peierls [9] and Jones have carried out Einstein box calculations applying it to the theory of optical momentum. Burt& peierls obtained results in agreements with the nondispersive Abraham expression, while Jones obtained the dispersive Abraham result( the equations for these are(6)and(10) respectively in Loudons paper [10). However, neither are happy with their calculations; Burt Peierls worry over the rigid box assumed in their calculation and the impact on the validity of the results; and Jones adds an artificial forward bodily impulse in order to attain his desired result of the minkowski form of the momentum Loudon [10]notes that the Einstein box is useful for the understanding of optical momentum but the very small shifts in position would be difficult to measure These thought experiments seem likely to remain in the mind and not to be realised on the laboratory bench The proponents At first people were swayed towards Minkowski's theory. In 1950 Laue [3] demonstrated certain limiting requirements that must be satisfied by the transformation properties of the components of the momentum-energy tensor of a light wave. Laue derived these requirements from the following considerations and his criterion was based on an incorrect assumption from another frame of10 Einstein’s box This thought experiment, dreamed up by Einstein in 1905, was designed to determine the mass equivalence of a pulse of electromagnetic radiation (m = E/c2 ). Einstein considered a closed system (a box) of mass M, which is initially at rest in an inertial frame of reference S. The walls at either end of the box are of equal mass. A photon is emitted from a photon gun on one wall, down the central axis of the box, towards the other end wall. From the phenomenon of radiation pressure (given by E = pc) we know the photon emitted must have momentum. Therefore to conserve the momentum of the system the box must move in the opposite direction with velocity v. When the photon hits the far side of the box, the system will come to rest again, with a slightly different position to its starting point. This shift in position can be made arbitrarily large by repeating the process. If the assumption that the carrier remains massless is valid then the system, which was initially at rest, will have its centre of mass shifted without any external forces acting on the system. This clearly violates the law of mechanics which states that a body, which is initially at rest, cannot undergo translational motion unless there is an external force acting on the body. The only way that this problem is able to be solved is if the photon has transported an amount of mass – so that even though the box has moved, the centre of mass is still about the original point. Einstein’s derivation has some conceptual problems with it, namely that the box is treated as a rigid body, a concept that is inconsistent with the principles of special relativity. The approach taken by French circumvents the rigid body problem by considering only the two end walls of the box, arriving at the same result utilizing the centre-of-mass theorem. Burt & Peierls [9] and Jones have carried out Einstein box calculations applying it to the theory of optical momentum. Burt & Peierls obtained results in agreements with the nondispersive Abraham expression, while Jones obtained the dispersive Abraham result (the equations for these are (6) and (10) respectively in Loudon’s paper [10]). However, neither are happy with their calculations; Burt & Peierls worry over the rigid box assumed in their calculation and the impact on the validity of the results; and Jones adds an artificial ‘forward bodily impulse’ in order to attain his desired result of the Minkowski form of the momentum. Loudon [10] notes that “the Einstein box is useful for the understanding of optical momentum but the very small shifts in position would be difficult to measure. These thought experiments seem likely to remain in the mind and not to be realised on the laboratory bench”. The proponents At first people were swayed towards Minkowski’s theory. In 1950 Laue [3] demonstrated certain limiting requirements that must be satisfied by the transformation properties of the components of the momentum-energy tensor of a light wave. Laue derived these requirements from the following considerations and his criterion was based on an incorrect assumption from another frame of
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