From the SelectedWorks of Vildyan Yanbikov 2015 Experimental check on the validity of the special theory of relativity Vildyan Yanbikov Available at: https://works.bepress.com/vildyan_yanbikov1/21/
Experimental check on the validity of the special theory of relativity. Yanbikov Vil'dyan Shavkyatovich. Russian Federation, Volgograd, 400064, Bibliotechnaya street, house 14, apartament 95. Phone: 8-909-391-34-70 e-mail: vildyanyanbikov@yandex.ru Аbstract: Calculation of quantitative characteristics of rotating interferometer Michelson-Morley experiment. The objective of the experiment. Confirmation alternate the Lorentz contraction of the interferometer arms as it rotates. Experimental check on the validity of the special theory of relativity. Keywords: The interferometer Michelson-Morley experiment, the rotation of the interferometer Michelson-Morley experiment, the reduction of the interferometer arms, the shift of interference fringes at rotation of the interferometer. Experimental check on the validity of the special theory of relativity. 0
Let interferometer Michelson-Morley experiment is balanced so that it can be rotated with high angular speed of rotation around the axis of the theta. Axis theta perpendicular to the plane where the arms of the interferometer. The interferometer consists of two pipes located under a corner of 90 degrees (fig.1). The axis of rotation theta passes through the midpoint of the segment MN and coincides with the axis OY. Figure D-mirror; MN-translucent mirror ; S - screen; E - a source of laser radiation. The interferometer, motionless relatively to the laboratory reference system X Y Z. Laboratory reference system moving with the speed v relative absolutely fixed reference system. At the beginning of the experience, before the beginning of rotation of the interferometer, the speed of its rotation ω around the axis θ theta equal to zero. After the beginning of the rotation of the interferometer around the axis θ theta, picture interference will be moving from its initial position, where ω = 0. The shift of the interference pattern is due to the inertia of metal atoms from which is made of pipes of the interferometer. In other words, shoulders interferometer will not have time to contract and to recover because of the inertia of the atoms of the material of the pipes. Negatively affects the optical light moves signals inside the interferometer. By increasing the speed of rotation ω shift of the interference pattern should increase. The shift of the interference pattern at a certain speed ω will be greatest in the case, when the axis θ of rotation theta perpendicular to the vector of velocity of the Earth relative to the cosmic ether. The velocity vector v will be in the plane rotating interferometer arms. Let the arm length stationary relative to the absolute frame of reference interferometer, with v = 0 equal to L. Then moving in the laboratory frame of reference, at ω = 0 the arm length along the axes OX and OZ will be equal Lx = L and Lz = L 3/2 ; At rotation of the interferometer with angular velocity ω therefore, when taking into account the inertia of metal atoms, the arm length along the axes OX and OZ will be equal to L x and L z. However, due to the inertia of the atoms will be performed inequality L x < Lx and L z > Lz Calculate the maximum number of interference fringes on which will move the interference pattern at a high enough speed of rotation of the interferometer. In this case, the shortening of the interferometer arms will be equal to the half of a segment Lx - Lz. Find an 1
expression for ; Will receive = ; Then for this case L x = Lx - = ; and L z = Lz + = ; At a certain maximum speed of an interferometer arm length because of the inertia of the atoms are equal and are the same length L x = L z. On the number of lanes will shift the picture interference for this case?. Time of light spreading along the axis OX laboratory reference system tx = = ; Time of light spreading along the axis OZ laboratory system of reference from records to the mirror and back will be equal to tz = + = + ; here tz = ; The difference Δt = tz - tx = ; or Δt ; Optical path difference Δ = c Δt = 2L ; The number of lanes on which will move the picture interference for this case is ΔN = = 2 ; Let the length of the shoulders for real interferometer is 1m, the wavelength of used light λ = 0.6*10 6 m. If the velocity vector of movement of the interferometer relative to the absolute reference frame perpendicular to the rotation axis θ theta, then v = 400 km/s. Get ΔN 6. So the maximum number of bands, which may shift of the interference pattern at a high enough speed of rotation of the interferometer is equal to six lanes. 2
Another case when the angular velocity of rotation ω is that run equality L x = Lx - ; and L z = Lz + ; (fig.2). Count the number of lanes on which will move the picture interference for this case. We will substitute Lx and Lz L x = Lx - = L ; L z = Lz + = L ; The passage time of the light beam along the axis OX for this case tx = ; tx = ; The passage time of the light beam along the axis OZ laboratory reference system tz = + = ; Δt = tz - tx = ; Optical path difference Δ = L ; The number of lanes on which will move the picture interference for this case is ΔN = = ; We will substitute the same values as in the previous case, get ΔN 3. Picture interference shifted into three bands. Define the angular velocity of rotation of the interferometer for this case (ΔN 3). For a quarter turn to the arm of the interferometer will be reduced in size on L x - L z (fig.2). Lag reduction in ΔL = corresponds to the shift of the interference pattern on three bands. To calculate the angular velocity of rotation ω for this case, we use the property of elastic deformation of a solid body. At the deformation of tension or compression, the resulting elongation arm of the interferometer ΔL under the force F is proportional to the magnitude of the applied force, original length L and inversely proportional to cross-sectional area S (Hooke's law) ΔL = ; where the coefficient of proportionality. The value of E is called the modulus of the first kind or the young's modulus, and describes the elastic properties of the material. We will substitute the value of ΔL in Hooke's law = ; F is the force of contraction of the arm of the interferometer when turning it one-quarter turn from the OX axis to axis OZ laboratory system of reference. We obtain the expression for the force 3
F = ; During rotation of the interferometer, the force F accelerates metal atoms from which made the interferometer, with acceleration α = ; Under the force F for a quarter turn to the arm of the interferometer will be reduced by the value = = ; where t = ; We substitute the expression for α, will receive = ; A quarter of a turn is time t = ; From the last equality, we get ω = ; Angular velocity ω is offset picture interference into three bands. Define ω for real size of the interferometer. Let shoulder length 1m, mass shoulder 2kg, the cross-sectional area of the shoulder 4sm 2, E = 2*10 4. Get ω 2 rad/s. Got acceptable speed of rotation of the shoulders interferometer. This velocity corresponds to a shift pattern interference into three bands. The shift of the interference pattern on the screen of the interferometer, when it is rotating, is a confirmation of the lorentz contraction of the interferometer arms. But this theoretical predictions. As all of this happens in practice, can only reveal the experiment. If the above formula to replace the formulas of the special theory of relativity, then the interference pattern are shifted by ΔN 1800 bands. 4
D N E D M S fig. 1 5
X L x L x ω L z L z v O fig.2 Z 6