Two mysterious things: Light and gravity II
1.2. Distortion of time - Special Relativity
Based on the fact that there is no medium to sustain light waves like 'Ether' as disproved in the Michelson-Molly experiment and that light travels by itself through the vacuum and the speed of light is constant regardless of the movement of the light source (the same velocity is measured), Einstein published the theory of special relativity (Special Relativity) in 1905(But Einstein claimed that the Michelson-Molly experiment had nothing to do with the theory). This theory applies only to inertial systems (non-accelerated coordinate systems) and assumes that the laws of physics in inertial systems do not change. This theory was derived to explain the difference between Newtonian mechanics and electromagnetism in the regime of particles moving at near the speed of light at that time. From this theory, so-called Einstein’s mass-energy equivalence was derived, in which mass (m) is compatible with energy (E) via the speed of light (c): E = mc2. This equivalence equation made Special Relativity very solid by fully explaining the relationship between the mass difference and energy released before and after atomic nuclear fission or fusion, and the space in which light travels has no medium such as "Ether". The confidence that nothing is in the vacuum became more and more solid.
Figure 5. Schematic of Sagnac's light interference test equipment. As the device rotates, the light beam in the rotating direction meets the beam in the opposite direction of rotation at the exit to yield interference(By Krishnavedala, wikipedia.org).
Sagnac's Experiment
The Michelson-Molly experiment denied the existence of "Ether", confirming that the speed of light in the vacuum is invariant and became the basis of Special Relativity. But Sagnac’s experiment was once known to prove the existence of Ether. In 1913, Sagnac experimentally showed the interference of light when a light beam is divided into two parts on a rotating platform as shown in Figure 5. The phase difference of the interfering light beams is proportional to the rotational angular velocity of the platform. This is the Sagnac effect. Lau theoretically predicted this phenomenon in advance: if the speed of light and the speed of rotation are constant, there is a time difference of light traveling in opposite directions and interference occurs. This phenomenon, of course, was also consistent with Special Relativity and the existence of stationary Ether, but the effect of Ether expected from the Michelson-Molly experiment was not confirmed. Since then, more sophisticated theoretical considerations have denied the existence of Ether, and light has moved through the vacuum and its speed has become more and more constant.
Theory of length contraction and time dilation
Special Relativity explains phenomena that cannot be felt in our daily life, such as length contraction, time dilation, and relativistic mass. This is fundamentally due to the constancy of the speed of light in the vacuum. To maintain this invariance, time expands and length shrinks.
Length contraction is a phenomenon that length is measured less by a stationary observer when an object is moving rather than in rest. It is also known as the Lorentz contraction. Usually it can be recognized only in the direction of travel, when the speed of an object approach the speed of light. This length contraction was originally proposed to compensate for the hypothesis of Ether, the presence of which had been denied in the Michelson-Molly experiment. However, Einstein explained that length contraction is only compatible with his theory of special relativity regardless of the existence of a fluid like Ether, and drastically changed the concept of time and space at that time. This idea of Einstein later has developed into Minkowski’s four-dimensional spacetime concept.
Figure 6. Length contraction: Assume three bars A, B, C lying in a stationary state S and in a motion state S'. When the left end of A and D is in the same position in the horizontal direction, the length of the bar is measured differently. In S, the distance between the left end of A and the right end of C is larger than the interval between D and F. The opposite is true for S'. (Arrows indicate the direction of motion. wikipedia.org).
Time dilation is a phenomenon in which time is observed to be dilated when observing in a certain inertial system another inertial system having a relative velocity. In a given inertial system, an observer in rest and a moving observer perceive each other's clocks to be late. This is because they move relative to each other no matter who moves. In common sense, if time of a moving object is slow, the object will feel that time of the outside world is faster. Relativity predicts the opposite. This seems to be a paradox. It is like a situation that a person looks another distant person smaller than him or her, and the distant person looks him or her smaller than the person far away. In this sense, time dilation is not a paradox, and this characteristics of time having reciprocity or symmetry, time dilation, is well understood from the relativistic point of view. Time dilation occurs even in environments where the strength of the gravitational field is different or when an object is accelerating. A watch in a high gravitational field is slower than a watch in a weak field. An atomic clock sent to space goes slower than a clock in Earth, or a GPS (Global Positioning System) clock goes faster. However, as the case with the twin paradox the reciprocity or symmetry of time is not established if not for inertial systems.
Figure . Left: When A and B are stationary, the time taken by the optical signal coming from A and returning from B to B is 2L/c. When A moves from left to right, the optical signal is generated from A at time t' = 0, B receives this signal at time t' = D/c, and A receives the reflected signal at time t' = 2D/c (wikipedia.org).
Length contraction and time dilation can be expressed by the following equations respectively, length contraction:
and time dilation:
where γ is called the Lorentz factor and v and c are the velocity of the object and the speed of light, respectively. The length L0 and the time change Δt at rest contracts and expands to L and Δt', respectively, due to the relative movement. Eqs. (1.1) and (1.2) are combined to
The product of length and time is constant regardless of length contraction and time dilation. Therefore, time dilation is substantially the same as length contract and both sides of a coin in Special Relativity. In Special Relativity, "mass" has two meanings. One is the same constant amount for all observers in all coordinate systems, "rest mass (m0)" or "invariant mass", which is equal to the "rest energy". The other corresponds to "relativistic mass (m)" or the "total energy" of an object, depending on the velocity of the observer. From Einstein's mass-energy equivalence, all masses are interchangeable with energy and converted to the total energy of the object. The total energy including the kinetic energy is expressed as follows via the Lorentz factor,
In Eq. (1.4), γm0 is the relativistic mass, having the same form as time dilation in Eq. (1.2). Therefore, energy and time can be perceived as the same, but different only in their form. On the other hand, light has zero rest mass but has energy and thus relativistic mass.
As mentioned above, Special Relativity comes from the constancy of the speed of light moving in the vacuum. However, light can bend or change its speed in strong gravitational fields. It is a phenomenon that cannot be interpreted only by the theory. In the vacuum where there is nothing, light can move by alternating the electric field and magnetic field as shown in Figure 1, but how does gravity occur and affect light through the vacuum of nothing? This is a more mysterious phenomenon than the propagation of light.
