Figure 3 Explicit version of spacecraft question. - page 11
When I look to my own life, the first thing that I learned is what is called Classical or Newtonian mechanics. Using that theory it was rather straight forward (later in life) to simulate the movement of the planets around the Sun. It was not simple, but IMO nothing extraordinary.
The next fase in my life I studied SR. Special relativity much more something mathematical. I learned the concepts length contraction, time dilation and relativistic mass.
All these concepts woried me because they start from the idea of a frame at rest which contains objects at rest which have dimensions at rest, and a mass at rest. A clock at rest, within that frame shows rest time. When these objects are in linear motions all these dimensions change as a function of the lorentz transformations.
Later in life I studied GR at my own initiative.
Comparing my own learning experience and comparing that with the results of this article I understand that when you have a certain understanding of Classical mechanics that the concepts of SR are difficult to grasp, specific because, particular with GR, they are diffult to demonstrate by means of experiment to back up the predictions. The main reason is the large speeds involved, close to the speed of light,
If you want to explain something you should stick to certain rules.
One of the first rules is that you should explain something as clear as possible. Concepts which should be explained are: What are laws of nature, simultaneity, relativity of simultaneity.
A second rules is that all the concepts explained should be backup by means of examples or better by means of experiments.
A third rule is to minimize the use of words which almost mean the same. For example the use of the words: to see, to observe and to measure. Seeing implies also to measure.
One important tool to study science is mathematics, but its importance should not be overestimated. The laws of physics are descriptions of certain processes happening in the universe. Many of these processes are stable, small scale processes, and as such can be described in a mathematical notation. However it is not these laws that control these small scale processes. All these processes are physical processes and it is in the physical (mechanical, chemical) details that lie the explaination how something functions,works or operates.
An important tool to understand nature is to use clocks to measure the time of the events.
In the classical the world view a clock is much more a virtual device. That means clock's are used in a form of a 3D grid which all indicate the same time for the state of the universe. That means when reading the clock nearest you can instantaneous know the location and the time of an event. You can also know the position of the earth at every event.
The observed time of the 6 grid points nearest a grid point is the time on your clock minus the basic distance between each grid point divided by the speed of light. That means when the speed of light is 300.000 km/sec and the basic distance is 300km then the offset is 1 msec.
One of most important areas of investigation is the movement of objects through space. This field of study is called celestial mechanics. The law that describes the movement of free floating objects is Newton's Law. The most important parameter is the mass of an object and the simplest example to study is a binary system i.e. a universe with (in principle) only two objects.
There are two ways to study a binary (star) system (considering objects as point masses):
This same method can also be used to calculate (in principle) the mass of a bullet fired from a gun, because after firing the bullet is also a free moving object which movement can be described by Newton's Law. As mentioned in Reflection part 2 - Science Newton's Law does not control the movement of the body. In fact every time when you use that law you have to test if the predictions of an experiment is in accordance with the results of the experiment. In the case of firing a gun extra temporary forces (outside gravity) can be at stake which can influence the outcome, and which should be taken into account in the calculations.
One important concept in relativity is an observer. Every thing that an observer sees is not absolute but relative. As such the length of a rod (at a distance) he observers is smaller than his real length.
An other important concept is a reference frame. In fact each observer has his own reference frame in which the observer is at rest. When there are more observers then within the reference frame of observer A, all the other observers are either at rest, which means that the distance which such an observer is fixed, or moving, which means that the distance which such an observer varies. Fixed distances are only possible for observers part of the same object. For example: two observers on the surface of the earth.
Relativity also uses the concept of simultaneity, but in relativity this is called relativity of simultaneity.
As mentioned in Page 3 simultaneous events A and B in one frame X are not simultaneous in any other moving frame Y(inertial frame). That the events A and B are simyltaneous is established from the clock readings near the events A and B, based on clocks in frame X, which are all synchronized. That means that there should be a point P1 from which you should be able to observe both events A and B simultaneous and also (I assume) that the events A and B should not be able to physical influence each other.
However that same point P1 is also part of the moving reference Y. However in that reference frame the two events A and B are not simultaneous, based on clocks in frame Y, which are all synchronized. That means in frame Y either event A can influence event B or event B can influence event A. This depends which comes first.
This is strange because two events which are simultanous accordingly to observations made by two observers one at rest and one moving, is considered, firstly by the observer at rest, as that they can not influence each other and secondly, by the moving observer, as that they can influence each other This contraditionary opinion is based on a double set of synchronised clocks, resident in each reference frame with the physical constraint, that the moving set of clocks runs slower than the clocks at rest.
An other important issue is an inertial frame. The idea behind an inertial frame is that an object in empty space, on which no forces are enforced moves an a straight line with a constant speed. An observer, part of that object, can now define a frame, in which both the object and the observer are at rest and that frame is called an inertial frame. That is correct but this required an other frame from which that object is observed and from which the positions of that object are measured. At the same time it is important to consider that empty space does not exist and as such inertial motion. In practice all objects in the universe are constant subject of external forces and behave from our human earth based point of view in completely unpredictable ways at present.
SR leans very much on inertial frames and observers and may be that is a reason why people i.e. students have so much problems in understanding SR. If you want a broader view
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