Dr Faustus of Modern Physics - Department of Speech, Music and ...

21.2. DOUBLE ANALYTIC-SYNTHETIC STATEMENTS 95
21.2 Double Analytic-Synthetic Statements
In modern physics the distinction between a definition (analytic statement)
and synthetic statement is sometimes blurred into statements which are
viewed to be both analytic (true by definition) and synthetic about some
reality (true or false), or rather sometimes analytic and sometimes synthetic,
sometimes definition and sometimes fact.
Such a statement makes it possible to say something about reality which
cannot be denied, and it is directly recognized as such. When you hear a
physicist making a statement claiming that something cannot be denied, then
the statement is such a double analytic-synthetic statement.
As a preparation you may ask yourself if the statement “well educated
people are superior to not so well educated people” is analytic or synthetic?
Maybe the answer is not so clear. Is it in fact such a double analytic-synthetic
statement? See also my knol Is One Dollar = One Euro?
Einstein’s mastery can be admired in his careful choice of axioms of special
and general relativity:
• The speed of light in vacuum is constant.
• Heavy mass is equal to inertial mass.
The constancy of the speed of light is a definition since according to the
1983 standard length unit of a meter is defined as a certain fraction of a
lightsecond = the distance traveled by light in one second. The speed of
light is thus by definition equal to 1 lightsecond per second, no more no less.
On the other hand, a physicist is convinced that the speed of light is
constant as a physical fact. A physicist would say that because the speed
of light is constant in reality, it can be used to define the length standard.
So we have a definition which is a physical fact at the same time: Double
analytic-synthetic.
Einstein was a master of this form of double-play: The basic assumption
of special relativity is that the speed of light is constant, and Einstein uses
this statement sometimes as analytic and sometimes as synthetic. Very clever
and very confusing. But according to Kant it is not reasonable.
In general relativity Einstein uses the equality of heavy and inertial mass
both as definition and physical fact. In this case experimental verification of
equality could give a Nobel Prize.