Tom Mattson said:
Einstein did not set c=1. At his time you still calculated c from Maxwell's theory: c=\frac{1}{\sqrt{\mu_0\epsilon_0}}. The c=1 definition did not take hold until much later, as I will make clear below.
Albrecht said:
For my feeling, your considerations are a bit too philosophical and too complicated. ...
Lorentz has used his calculations about the Maxwell theory to show, that fields in motion have to contract and so also the Michelson apparatus. That explains the result.
Let me say, that you both have a similar way of viewing the physical term "speed of light". Einstein brought a new way in defining - not just using - this physical term “speed of light”. This is not a philosophical difference, but it is a scientific difference.
Generally in Science -and in Physics too- there are two kinds of terms: the “variables” and the “constants”. They are both expressed in values. The difference is that a “variable” has a relative value (which is measured/calculated in relation/ratio to constants), where a “constant” has an absolute value (which is defined in a conventional way).
Einstein introduced a new constant in Physic, that is, he defined axiomatically that the "speed of light" belongs to the class of "constant terms of Physic". That means that its value may be expressed by any system of units (with the value of c, 1, or any other), because the value of the speed of light has an absolute meaning, but then all other values of variable physical terms of space-time should be expressed in relation to the defined constant absolute value of the speed of light.
In this context, when I measure the speed of light, according to Einstein's axiomatic system and I get a specific value, I am not measuring/calculating "the speed of light" but I am normalizing the values of the other variable physical terms that are being involved in the measurement according to "the speed of light".
Therefore, the physical term “space”, as a physical term that is being involved in the measurement of the speed of light as length, lost its absolute meaning as a physical constant and it is nowadays expressed by the speed of light as a variable physical term by the definition of the unit
meter . Same thing happened to the physical term "time" by the definition of the unit second.
When we "measure" the speed of light and we get a specific result of 299,792,458 m/s, according to Einstein's axioms, we are actually measuring coinstantaneously BOTH the variable physical terms of “space”, (in meters) AND of “time” (in seconds), by using the constancy of the ratio space/time that is expressed by the physical term “speed of light”.
The number 299,792,458 meters is the measured “space” that light travels in one second and the number 1/299,792,458 is the “time” in seconds that is needed for light to travel the length of a meter. In this context, the value 299,792,458 m/s is the speed of light only in the way that it normalizes the values of "time" and "space"; "space" becomes a variable physical term that can not be defined independently from another physical term, which is "time". And "time" becomes a variable physical term that can not be defined independently from another physical term, which is "space". This cyclical definition of "space" by "time" and of "time" by "space" is normalised by the constancy of the physical ratio “space/time” which Einstein defined as the constant physical term "speed of light".
In an analogy, this is like the relation of the circumference and of the diameter of circle. For any circle, the circumference is expressed by the diameter and at the same time the diameter is expressed by the circumference, and for all circles the ratio of the circumference to the diameter is \pi. The term \pi is expressed by a
value but, because \pi is a constant phycical term, its value has a conventional meaning. The physical value of \pi is not the numerical value calculated as a ratio but, the physical value of \pi is its constancy under any circumstances.
A constant physical term has no physical meaning regarding its value, other than normalizing the frame of reference, therefore it has only a conventional meaning.
For instance, I can define the value of \pi to equal 1 (or eny other number) and then I need just to normalize the values of the circumference and of the values of the diameter of circles accordingly and all geometrical equations are valid, although they produce different numerical solutions. The values of the solutions for the different value of \pi are different, but when each result is compared with the respective different value of \pi, the ratio is the same. The normalized ratio results are identical for any numerical value of \pi.
This is also the case with the speed of light, according to Einstein's axiomatic definition of the constancy of the speed of light.
Albrecht said:
For my opinion, the understanding of Lorentz is a traditional physical understanding.
Einstein’s understanding can be called a structural understanding.
Einstein produced-invented a new method of "logistics" in “Physical Economics". He did not produced a new abstract theory of Physics, but he applied new mathematical and geometrical expression of Physics in order to describe the physical terms and physical phenomena. Physical terms, that was not possible to be expressed in a normalized way before Einstein’s axiomatic propositions, found the mathematical formulation to be expressed in a normalized way, because of Einstein's axiomatic constancy of speed of light.
The acceptance of this new Physical constant and its consequences in the application of mathematics and Geometry in the “language” of Physics, by Einstain, was an arbitrary action but it was not causeless. It followed the same reasoning for the introduction of the term \pi in Geometry. In Geometry, without the introduction of \pi there is no way to express one-dimension physical terms in ratio to two-dimension physical terms.
In the same context, Einstein realized that the "speed of light" is expressing a ratio between space and time that constitutes the necessary normalizing factor of the description/expression of light in a "new" scientific language that he tried to formulize.
Albrecht said:
Back to the measurement of ‘c’: Constancy or non-constancy can be measured without any reference to a measurement unit (see the Michelson experiment). And for another solution: In the Shapiro experiment a radar pulse is send to Venus and reflected back to Earth. This needs some time. Now in the moment when the sun moves close to this beam of pulses, the time is extended. The easy way to understand this is that ‘c’ is reduced in the vicinity of the sun (again without using units). - But this explanation is not acceptable by Einstein because his axiom is, that ‘c’ is always constant. So Einstein has to explain that the delay is caused by a change of the ‘space’. According to him (and his followers) we have to assume that the space close to the sun is in some way contracted, so that the photons in the pulse train have to pass a larger piece of space in order to pass the same distance as seen from outside. - And this now is the base of General Relativity as understood by Einstein.
I understand Einstein's proposition in a different way. Einstein’s explanation regarding your example is that BOTH space AND time are changing, in order for light to retain a constant speed, just a change in space is not enough (maybe you understand this also but, you forgot to write it in your message). Einstein unified the time-space realms in the same way that geometry unified the one-dimension realm and the two-dimension realm: you can not say that a circle can have different circumferences because two diameters of a specific circle circumscribe different circumference of the circle, regarding the length of the arc, by moving each diameter with different speed for the same period of time. Somehow, this is an analogy of your point of view. But "space", both in classic geometry and in Einstein’s geometry is a continuum: you can not make jumps, that is, you can not move by different “geometrical speeds”.
"Moving faster/slower" in geometrical terms means that you introduce another dimension. When a geometrical point is "moving" over the circumference of a circle on a two-dimensional space it always moves in a continuum way, therefore all points have the same “geometrical speed" and for that, they remain in the same two-dimensional realm. If a point is going to “move” faster/slower than the others, then it should do it by entering into another dimension. The geometrical speed is defined by the space/time ratio.
For instance, two diameters of the same circle that circumscribe an arc, in a two dimensional surface, from one point of the circumference to another point of the circumference, circumscribe the same space on the circumference of the circle, because the circumference is a continuum, and the diameters have to move in the same "geometrical speed". The only way to have the two diameters circumscribe different lengths of space (spaces of arc) as they move from the common starting point to the common final point is by making them move in different two-dimensional planes in a three-dimensional space, making them move over a spherical surface, starting and arriving to the intersecting points of the two-dimensional planes with the spherical surface. Then the "moves" of the diameters can be continuum with different speeds covering different space-lengths in the same time periods. This is something that can not be done in a two dimensional plane.
Thus, change of speed in a continuum “space” requires the introduction of a new dimension. This is what Einstein did by proposing and by adopting a constant “speed of light” that offers “the constancy of speed”, which is required by “space continuum”, while at the same time by introducing the dimension of time, he offered the normalizing factor in order to make possible the change of speed when the speed is measured without the dimension of time.
In the same context, your reasoning has to provide a non continuum mathematical system of physics, in order to explain how the speed of light is "reduced in the vicinity of the sun". I wonder how you might be able to overcome this requirement.
PS: Einstein’s proposal did offered a new point of view and provided the frame of using “new” mathematics in Physics in the way it was not possible to do this before. It does however have its limitations, not because it is “wrong”, but because it can not explain/express what it does not express. For these unexplained physical terms, we need to enrich our “language”, it is the way of the evolutionary process of science.
Leandros