Sunday, December 17, 2006

The Universal constancy of c

It is impossible for the same thing at the same time to belong and not belong to the same thing at the same time and in the same respect.
Aristotle the Stagirite, Metaphysics

Physical entities are measured by quantities of specific units. The length of a certain object for example can be expressed as x meters or feet or any other unit. Now, the choice of units does matter when two measurements are compared. It is obvious that 6 feet is not the same as 6 meters, neither does a speed of 100km/hr equal a speed of 100miles/hour. An objective comparison of two measurements requires both measured numeric values to refer to the same unit of measurement.

When Einstein postulated the universal constancy of the speed of light c, he meant c is the same for all observers in a physical sense of course. Using the metric system, c turns out to be 300.000.000 m/s and this, according to Einstein, must be the case in all frames of reference.

Unfortunately Einstein missed to define the units for distance (m) and time (s) independently of the speed of light c. Special relativity defines a time interval as distance divided by c and distance as time interval multiplied by c:

c = 300.000.000 m/s
s = 300.000.000 m/c m = cs/300.000.000

If, in the equations above, we substitute s or m with their respective definitions we obtain:

c = 300.000.000m/(300.000.000m/c) <=> c = c

The statement c=c is surely always true independently of the actual value of c. This is a classical example of a circular argument. If the units of measurement are defined by nothing more then the postulate of the universal constancy of c then it shouldn’t come as a surprise that measurements utilizing those units can’t but confirm the universal constancy of c.

Einstein obtains THREE unknowns, namely c, m, s, by solving ONE equation. Such a solution is clearly under-determined and can only be derived by defining any arbitrary length as one meter. The time interval in which light traverses this arbitrary meter is then defined as 1/300.000.000 of a second. In special relativity units of measurement have no physical meaning. They are pure mathematical scaling factors which are set for each reference frame in such a way, that the universal constancy of c is maintained.

The core statement of special relativity after all, is that time and space are not absolute. Consequently, meters and seconds aren’t absolute either. So even though all observers measure the same numeric value for the speed of light c, they clearly use different units of measurement. If we consider two observers O and O’ in steady motion in respect to each other, the postulate of the universal constancy of c actually states:

c = 300.000.000 m/s c’= 300.000.000 m’/s’
for c=c’ to be true m=m’ and s=s’ must be true as well. This is not the case for special relativity’s definition of m and s!

Comparison of velocities by numeric value without universal units for distance and time is nonsense. The postulate of the universal constancy of the speed of light c is outright absurd: c can not be constant while meters and seconds are not.