What Is the Michelson Interferometer?

The Michelson interferometer is a precision optical instrument designed and manufactured by American physicist Michelson and Morey in 1881 to study "Ether" drift. It uses the partial amplitude method to generate two beams to achieve interference. By adjusting this interferometer, interference fringes of equal thickness can be generated, and interference fringes of equal tilt can also be generated. It is mainly used for the measurement of length and refractive index. If an interference fringe is observed to move, the moving amount of the boom of M2 is / 2, which is equivalent to the change of the air film thickness / 2 between M1 and M2. It has important applications in modern physics and modern metrology technologies, such as the study of the fine structure of spectral lines and the calibration of standard meters with light waves. Using the principle of this instrument, a variety of special interferometers have been developed. ^[1]

The Michelson interferometer is an optical

The most famous application of Michelson interferometer is that it is used in

1. Never touch the optical surface with your hand and prevent saliva from splashing on the optical surface.

2. When adjusting the screws and turning the handwheel, be sure to be light and slow, and never force the wrench.

3. The coarse adjustment screws on the back of the mirror should not be tightened too tightly to prevent distortion of the mirror surface.

4. When adjusting the coarse adjustment screw behind the reflector, first adjust the fine adjustment screw to the middle position so that fine adjustment can be made in both directions.

5. During the measurement, turning the handwheel can only slowly advance (or retreat) in one direction, otherwise it will cause a large empty return error.

In the so-called non - linear Michelson interferometer , the plane mirror on one of the interference arms of the standard Michelson interferometer is replaced with a Gires-Tournois interferometer or a Gires-Tournois etalon, and the light field emitted from the Gires-Tournois etalon Interfering with the reflected light field on the other interference arm. Because the phase change caused by the Gires-Tournois etalon is related to the wavelength of the light and has a step response, nonlinear Michelson interferometers have many special applications, such as optical comb filters in fiber optic communications. In addition, the plane mirrors on the two interfering arms of the Michelson interferometer can be replaced with Gires-Tournois etalons. At this time, the non-linear Michelson interferometer will produce stronger nonlinear effects and can be used to make antisymmetric Optical comb filter.

It is envisaged to perform experiments separately when the Michelson interferometer is at rest and linear motion at a uniform speed to form two interference fringe patterns. Since the interference fringes are planar patterns, as long as they are viewed at a vertical angle, the observers in the stationary and dynamic systems should see the same. Comparing the two patterns, the result can only be one of the same or different. If these two possible situations are used as the basis for analysis, the compatibility between the physical effects of "clock slow scaling" and the principle of constant speed of light as claimed in the special theory of relativity can be examined.

Since it is a thought experiment, we may first assume that the interference fringes before and after the movement are the same.

In order to simplify the problem, suppose that the light paths in the two directions (x and y) of the experimental device are the same when stationary, that is, lx = ly. According to the principle of constant speed of light, the speed of light in both directions is c. If a clock with sufficient accuracy is placed on the beam splitter, the time tx and ty required to separate the light split from the beam splitter into two paths and return to the beam splitter can be recorded. From lx = ly, tx = 2lx / c, ty = 2ly / c, it can be seen that the time value of the clock recording the two rounds of light is equal, that is, tx = ty. (Relativistically speaking, the time recorded by the clock is called intrinsic time, which has physical meaning, not mathematical meaning in coordinate time.)

The Michelson interferometer is now set to perform a uniform linear motion along the direction of one of the optical paths x, and the interference fringes formed are the same as when it is stationary. This indicates that the time tx 'and ty' spent by the two lights traveling back and forth during the movement are also equal, that is, tx '= ty'. This is because the Michelson interferometer determines whether the time difference between the two paths of light changes by the interference pattern. This is also the reason why Michelson and Morey used it to verify the existence of the ether. If not, the results of the Michelson-Morey experiment cannot be used to verify that the speed of light is constant. According to the theory of relativity, the time measured by the clock in its inertial frame is valid whether it is in motion or not. Therefore, the time taken by the clock at the spectroscope to move back and forth is set as For tx 'and ty'.

Since it is assumed that the movement only occurs in the x direction and there is no speed change in the y direction perpendicular to it, according to the theory of special relativity, the length (spatial scale and value) of the optical path in the y direction will not change, that is, ly '= ly. With respect to this clock, the speed of light in all directions before and after the movement is still the same value c. From ly = ly ', ty = 2ly / c, ty' = 2ly '/ c, we can see that ty = ty', that is, the time value of the light in the y direction measured by the clock before and after the movement is equal, and the measurement of this clock Nor should the scale change. Because only in this way, the light speed value calculated by 2ly '/ ty' can be exactly the same as the calculated value 2ly / ty before exercise. If only the measurement scale of the clock is changed after the exercise, then the speed of light measured at this time cannot be the same as that measured before the exercise. This is like measuring the speed with different speed clocks. The same value does not guarantee the same speed.

With tx = ty, ty = ty ', tx' = ty ', tx = tx' can naturally be derived; then according to the principle of constant light speed and the speed formula, from 2lx / tx = 2lx '/ tx', it can also be derived lx = lx '. Similarly, since the measurement scale of the clock before and after the movement does not change, the spatial scale of the x direction will not change. Now that the conclusions of lx = lx 'and tx = tx' have been reached, where is the physical effect of the motion predicted by the special theory of relativity to produce a "clock slow down"?

Obviously, in the framework of the special theory of relativity, the analysis of the first hypothetical situation in this thought experiment cannot find the "clock slow-down" effect in the physical sense. If Len said that there is such a physical effect, there will be a situation that is incompatible with this hypothetical situation and the principle of constant speed of light, which will be reflected in the next analysis of another hypothetical situation. Not to mention that the assumption that the interference fringe pattern is different before and after the movement of the Michelson interferometer does not conform to the principle of relativity, the following will be based on this second hypothesis, and then we will examine the principle of constant speed of light and the physics of "clock slow scaling". The compatibility of effects in relativity systems.

As mentioned earlier, when the Michelson interferometer is at rest, the two light paths are of equal length (lx = ly), and the interference fringes formed indicate that the two light paths have the same round trip time (tx = ty). If according to the current hypothesis, when the experimental device moves in a straight line at a constant speed in the x direction, the interference fringes are different from those at rest. According to the principle of the Michelson interferometer, the time of back and forth between the two light paths is no longer the same (tx '< > ty ').

According to the special theory of relativity, if there is a movement change in the x direction, there will be a physical effect of "clock slow scaling" in the direction, that is, the light in the x direction is lx when it is stationary and becomes lx 'when it is in motion. The clock records light The round trip time also changes from tx at rest to tx 'at movement. According to the speed formula 2lx '/ tx', the speed of light in the x direction is still c, which is the same as the value calculated at 2lx / tx at rest, which is consistent with the principle of constant speed of light.

At this time, because the speed of movement in the y direction has not changed, there will be no "scale-down" effect, that is, ly '= ly = lx, but different from lx'. According to the principle of constant speed of light, the speed of light in the x and y directions is still the same c. From the relationship of speed, distance, and time, it can be seen that the two rounds of light will have different back and forth times, that is, ty '= 2ly' / c will not be equal to tx ' = 2lx '/ c, which is in line with the assumption that the interference fringes formed before and after the movement are different. Then, before and after the movement, is the time for the light in the y direction to go back and forth, that is, is ty recorded by the same clock equal to ty '?

If ty <> ty ', because ly = ly', then the speed of light in the y direction before and after the movement calculated by the speed formula will not be the same value, which is 2ly / ty <> 2ly '/ ty', which obviously does not conform to the speed of light. Variable principle. In order to comply with the principle of constant speed of light, the back and forth time of the light in the y direction before and after the movement recorded by the same clock must be equal, that is, ty = ty ', but can it be said that the clock is slowed down by the movement? So no matter whether ty and ty 'are equal, the interpretation of the second hypothesis by the special theory of relativity will put it in a dilemma.

Of course, the theory of relativity can deny the existence of the second hypothetical situation, and then only the first hypothetical situation is left. However, in the analysis of the first hypothetical situation, we did not find any clues about the physical effect of the "clock slow-down" predicted by the special theory of relativity, which has to be questioned: the special theory of relativity can accommodate both the principle of constant light speed and physical meaning. The "clock slow-down" effect?