Description of the Light Cone (The Matrix of Light) By Prof. Dr. H. Weyl 


The theory of relativity is based on two fundamental principles, that normally have nothing to do with each other; these are 1. the relativity of simultaneity, 2. the relativity of motion. The first forces the fusion of space and time to a unified four-dimensional continuum, that is denoted by Minkowski as the "world". A world-point is a "here-now", marked for example by a starting signal, a flashing and instantly dimming spark or some other event of minute spatial and temporal extension. My body is in any instant of my life at a certain world-(= space-time-)location; thus it traverses a one-dimensional succession of world points, a world line, as well as any other body. Who once saw a graphical driving plan, knows how to graphically illustrate such a world line (the world lines of trains that are driving on a path). According to the old understanding, the spoken word "now" intersects not only the course of my inner life into past and future, but it brings this cut by a single stroke into the entire world: it intersects the world in a similar way into two parts, that are without space between each other: the past and the future, like a horizontal plane bisects the space into a lower and upper part. According to the relativity principle, however, the bisection of past-future is of a different kind when it is seen from world point 0, and it corresponds to the one that in three-dimensional space is caused by a complete circular cone (it is sketched in the vertical projection in the figure; the curved line is the world line of my body, that is of course bisected through 0 into two parts, the past part and the future part of my life). In the front cone all those world points are located that have an influence on my actions in 0, out of it are all the events, that lie finished behind, where "nothing can be changed": the mantle of the front cone separates my active future from my active past. The border is formed by the fastest possible propagation of action at all: that of light. However, all those events are located in the back cone, for which I have either lively experiences or by which I was informed somehow; only these events maybe have influenced me until now. In the exterior of it, however, all of that lies which I will experience or would experience, if my live lasts infinitely or my view might penetrate everything; the mantle of the back-cone separates my passive past from my passive future. Between active future and passive past an empty world-area lies, with which I'm neither actively nor passively connected in the instant 0 — The stage of reality is not a stationary three-dimensional space in which things are engaged in temporal progression, but a four-dimensional world in which time and space are inseparably connected to each other. This objective world does not happen, but it exists; a four-dimensional continuum, but neither space nor time. Only in the view of the consciousness that crawls upon within the world-lines of the bodies, a section of this world "lives up" and passes by as an image that undergoes spatial and temporal changes.

The fusion of space and time that is taught by the theory of relativity, was not attacked at the Nauheim discussion. Only the second point was concerned, the relativity of motion. It lies in the essence of the expression "motion", that one can only speak about motion in relation to a solid reference body (such a role is played by the "lasting and well-founded earth" in ordinary live). By itself, none of the possible states of motion of a body is preferred over other ones, i.e. so preferred that it would deserve the name "stationary". This evident principle is seemingly contradicted in a clear way by experience. Experience shows, that centrifugal forces arise at a "rotating" flywheel which stresses the flywheel - maybe until breaking; but in the "stationary" case nothing can be experienced. In an immediately stopped train everything falls apart; why, asks Lenard, is the church steeple not falling into pieces as well, as it experiences an equally strong motion pressure relative to the train, as the train relative to the church steeple. The old solution of the dilemma as defended by Lenard in Nauheim is as follows: If we attribute to space, independent of all matter by which it is filled, a certain geometrical structure by which (in particular) straight lines can be distinguished form curved ones, then the same is true for the world. The Galilean principle of inertia says, that a body that is not influenced from outside, executes a motion with a straight line as its world line. While according to Einstein: It can not be denied of course, and it comes clearly from the Galilean principle of Inertia, that there must exist some sort of "guidance" in the world which forces a very certain "natural" motion upon the body, when one brings it into motion with a certain direction and a certain velocity. But this "guidance" is a physical force-field, exactly like the electrical field from which electrical forces do arise. Together with inertial forces, something comes into light which was until now be interpreted as the "geometrical structure": the "guidance field", as something real, as an acting power of shaking force in some cases. Therefore it impossibly can be a formal or given condition of the world independent of matter and its states; on the contrary, the guidance field must interact with matter and must change when the state of matter is changing. In the development of this thought it became clear - and in this lies the success of Einstein's theory - that what was known as gravitation until now, is only a partial phenomenon of the guidance field. The planetary motion follows the path that is given by the guidance; while in the old mechanics the motion doesn't comply with the Galilean principle, but is diverted from its path by a special force that was ad-hoc invented by Newton, the "force of gravity". However, according to Einstein, inertia and gravitation constitute a inseparable unity; therefore inertial and gravitational masses must necessarily be the same; earlier it was impossible to understand the meaning of this connection.

From: "The Discussion concerning the theory of relativity at the Meeting of Natural Scientists." By Prof. Dr. H. Weyl. The Bad Nauheim Debate  (1920)  Albert Einstein, Philipp Lenard, Hermann Weyl, Ernst Gehrcke) From Wikisource)

 

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