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Adventure of Mr. SR

T. Tsujioka    Chapter 1 Viewing a Light Signal on a Locomotive Train

In the times of Einstein, there was neither a rocket nor a spaceship. He thought of a light signal on a moving locomotive train. As a matter of course, an observer on a moving train, if it is moving without vibration, will not know the fact that he is actually on a moving train, and can use all the laws of physics as exactly as if he were on the ground.

As is conspicuous the case in mathematics, we cannot discuss concepts or even convey ideas unless the terms we use are defined; otherwise we are easily confused. In mathematics where the abstract spaces are built after definitions or axioms are given. Once mathematical framework is built, the rest relies on the power of mathematical logic, true or false. Therefore, we should be very careful with the way of proceeding before construction. We try to proceed by use of models and principles that are understandable through our mind.

(Def. 1) Frame, Light Source, Observer, Mass, Wave, Energy, Proper Time

• A ‘frame’ may be defined as a movable material object, like a train or a spaceship, of having mass that carries light sources and observers. Although an atom, a molecule, or an electron can emit light, EM (=electromagnetic) radiation, they are not called a‘frame’since an observer cannot ride on it. A star emits star light in its own frame. Such a frame is considered to be ‘external’ to the earth frame.

• An ‘observer’ may not necessarily be a human but an artificial robot, or observational equipment. They may be collectively referred to be observer equivalent. We usually need three observers to consider the situation: Observer A, Observer B, and Observer C as a grand observer like us. This concept applies as in the linguistic grammar; we need the first, second, and third person to describe the situation.

• A‘system’is referred to one aggregate of frames as a whole. It may be a group of material objects that move carrying an internal observer or equipment.

• ‘Mass’is usually a property that a material object possesses. I suppose that you intuitively know the concept of mass. Actually, ‘mass’ is classified to two types: gravitational mass and inertial mass. Light has? inertial mass and momentum. But it is sufficient for now that you may think of mass as having such a property that a material body possesses.

• A‘wave’concept is a mathematical representation of overall form for the variation of individual points of a material object or field. It may be represented by materials but the wave form is NOT a material object.

• Since it is shown from a certain consideration other than SR that a material object of mass m possesses energy equivalent to E = mc2, a frame of mass M is said to have the base energy E = Mc2, and is said to be on this base energy level from an observer of the external frame. If this system is observed to be moving at v, the total energy is observed to be E = Mc2 + (1/2)Mv2 from an observer on the external frame. If light is emitted from the frame, it is losing some energy like the sun gradually losing its energy. If light is absorbed from an outside system, it will gain energy by that amount.

• We don’t know what time is, nor do we know what makes time tick. But we recognize that time is ticking everyday. This rate of ticking is called the ‘proper time.’ If we accept the condition that laws of physics hold in every frame, it follows that the same applies to the ‘proper time,’ which does not change from frame to frame.             