how does one calculate length and distance ?
In order to calculate the speed of light c over a distance l
- We need a clock
- We need a light source at point A
- We need a "mirror" at point B
- We needs a detector at point C
light source
A/C<-------------------->B
detector mirror
The speed of light is equal the distance between B and A plus the distance between C and B divided by the time it takes for the light pulse to go from A to B and from B to C.
For practical reason we assume that the light source and the detector are at the same point.
There are in general two conditions involved when this experiment is done:
- The distance l between (A,C) and B is variable. This is the case when point A and C are on Earth and the point B is on the Moon or B is in a satelite.
- The distance l between (A,C) and B is fixed. This is the case when both points A and B are physical connected. For example when all points are on Earth.
Distance l is variable
In this case the points A (the source) and C (the detector) and the mirror at point B are not pysical connected. The question is that suppose you want to calculate the speed of light (or if you want to calculate the distance): do you have to take the positions of each of the points A,B and C into account ?
IMO the the answer is yes i.e. you need a physical model of this experiment, implying the positions where the points A,B,and C are at the moments t1, t2 and t3.
Suppose the mirror the 1/4 light year away from the earth. In that case, because it takes then roughly 1/2 a year for the light to travel forward and backward, the position of the point A (point of emission) and point C (point of receiving) are almost at opposite locations relative to the Sun. IMO you have to take that into account. If you want to be more accurate you have to take the speed of the Sun into account.
In short if you want to calculate the speed of c you have to take the speed of sender/receiver and the speed of the mirror into account inorder to calculate the positions of each and the distances involved. If you want to calculate the distance of the mirror the same reasoning applies.
Distance l is fixed
If fixed distances are involved two cases can be studied: At Earth and in a spaceship.
The reason for this distinction is the following:
- A spaceship can move in a straight line through space. Each point of the space ship has the same speed.
- For our Earth the same can only be said if small time scale are involved. In real the movement of our Earth (If you stand on any place) is a very complicated one; it tumbles through space.
The speed of c:
- for a spaceship, assuming that both source and detector are on one end and the mirror is on the other end, is equal to two times the length of the spaceship divided by the time it takes for the light to travel the same distance.
- On earth the same logic applies.
Answer question 1
Accordingly to Literature 9 at page 19 "The distance is then simply defined as half the time difference between emission and reception"
As such Special Relativity takes neither the speed of the light source/detector and the speed of the mirror into account.
This is acceptable if you do that inside a space ship but seems questionable if you do that for example between Earth and planet Jupiter.
Reflection part 1
IMO the true difficulty in the problem lies in the behavior of the clock and in the position of your reference frame
Accordingly to Special Relativity the time of a moving clock and the length of a moving clock both change as a function of their speed.
In the first case we call this time dilition and in the second length contraction
Part of the proof lies in the Michelson and Morley experiment.
What this experiment shows that if you sent a lightsignal over two paths, of equal length, in different directions (perpendicular) the arrival time is identical.
In order to explain, by assuming that the speed of light is the same in the direction of the two paths (i.e. in all directions) we have to assume that the whole setup is shortened in the direction in which the setup moves.
Length contraction is easy to accept if you place the setup in a spaceship or on earth. Length contraction is more difficult to accept if you perform the same between source, reflectors and detector who are not physical connected. IMO length and space contraction are not one and the same.
Feedback