How Einstein discovered (invented?) length contraction
He was guided by his strong sense of democracy.
As anybody knows, this phenomenon was first proposed by George FitzGerald (1889) and Hendrik Antoon Lorentz (1892) to explain the negative outcome of the Michelson–Morley experiment. Later, it was named after Lorentz (by Einstein). Wikipedia tells us, that
“Length contraction is the phenomenon that a moving object’s length is measured to be shorter than its proper length, which is the length as measured in the object’s own rest frame. … Length contraction is only in the direction in which the body is travelling.”
Lorentz even had a physical explanation, assuming there is an “aether” (an all-pervading, very etherical substance responsible for the movement of light-waves) and a state of absolute rest (within the aether): A very fast moving object is compressed by the aether. Since Einstein abandoned this invisible and paradoxical fluid? gas?, and since in Einstein’s theory (“Special Relativity”, SR) there is no absolute frame, this explanation is not applicable to Einstein’s length contraction. To tell the end at the beginning: Length contraction and time dilation (they always come together) are simple mathematical consequences of Einstein’s two postulates:
(1) Principle of relativity: The laws of physics take the same form in all inertial frames of reference.
An inertial frame is the state of an observer, where he is at rest (whatever that means) or moving in a straight and uniform way. In other words: no acceleration, hence no gravity.
(2) Invariance of light speed: Light in vacuum has always the same speed c, independent of the state of movement of the source or the receiver of light.
Let’s digress from pure science and look at psychology and sociology. The first principle derives from Einstein’s strong sense for democracy and the equality of all human beings. He hated the military rigor of German schools, and he never had any doubts that Hitler’s regime was evil. Lucky for him, at the time Hitler came to power, Einstein was abroad — where he stayed for the rest of his life.
To postulate the absolute independence of light’s propagation in vacuum was a bold step. The Michelson-Morley experiment suggested that our view of the aether is wrong; or that the experimenters didn’t consider all possibilities. It was certainly no “null result”, since the aether-wind measured by M&M lay in the range of 8 to 10 km/sec, which is 25 to 33% of the expected value! Furthermore, Einstein’s bold move, and the near-religious worship of his works and his personality, led to the absurd fact that “c” was defined in 1983 to have a value of such and such. No further measurement is allowed — it is not necessary.
… but is it real?
Back to length contraction. It is very hard to observe or to measure it, since after slowing down, the phenomenon vanishes. But what does it do to the bodies? How do concrete or glass survive their compression and subsequent expansion? Or is it all an illusion? In that case, SR get’s superfluous, because perspective (bodies getting smaller with distance from the observer) is apparent too, but needs no special, even revolutionary theory to explain it. Especially none that uses physical concepts — perspective or (another example) hyperbolic geometry are purely mathematical concepts without the variable “time”, so important in physics and in special relativity.
When I came to “P.M.-Magazin”, its founder and editor-in-chief Peter Moosleitner was very glad to have a real physicist among his editorial team. He was a great admirer of Einstein and his theories. And he wanted to explain them in simple words, illustrated by simple images.
Although Einstein was the master of Gedankenexperimente (thought experiments), he didn’t devise one for length contraction. So we had to do it for ourselves. After a long session with nearly smoking brains, we had it. But in the end Herr Moosleitner exclaimed in astonishment:
“Then that’s all an illusion!”
Well, is it? What did master Albert think?
- In his publication, “Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen”, p. 418, he says: not real, apparent.
- In his publication, “Zum Ehrenfestschen Paradoxon. Eine Bemerkung zu V. Variĉaks Aufsatz.” In: Physikalische Zeitschrift. 12, 1911, p. 509–510, he says: not apparent, real.
- In the same publication, he says (translation by Google):
“The question of whether Lorentz shortening really exists or not is misleading. Namely, it does not “really exist” insofar as it does not exist for a co-moving observer; But it “really” exists, i.e. in such a way that it could in principle be demonstrated by physical means for a non-moving observer.”
Hopelessly complicated
Now what? As Max Born in his famous book “Die Relativitätstheorie Einsteins und ihre physikalischen Grundlagen” (1922) stated:
“At first glance this matter seems hopelessly complicated.”
Indeed, it is, especially when you consult the literature. Here are some findings:
- Length contraction is unreal (Einstein 1907)
- Length contraction is real (Einstein 1949)
- Length contraction is real (Max von Laue 1913)
- Length contraction is unreal (Sexl & Schmidt 1978)
- There is no real change in physical reality (Max Born 1969)
- Length contraction is real (Wikipedia)
- Length contraction is unreal (James Terrell 1959)
- Length contraction is real (C. W. Sherwin 1961)
- Length contraction is unreal (Delbert Larson, interpreting the same data as Sherwin)
- Length contraction is real (Hsiao-Bai)
- Length contraction is unreal (A. Gamba 1966)
- Length contraction is real (Robert D. Klauber)
- Length contraction is invisible (Sexl/Schmidt 1978)
- So or so. Depends how you interpret words (Wikipedia)
etc.
Similar ambiguities concern the question: What happens to concrete or glass when it is Lorentz-compressed? Max von Laue (“Die Relativitätstheorie”, 1921) asserts:
The assumption of a rigid body is incompatible with the theory of relativity.
Wikipedia says the same. Well, this assertion (“There are no rigid bodies”) is incompatible with special relativity, where Einstein often states: We need a rigid rod to measure the length of a body. And then, don’t forget: Without rigid bodies the world wouldn’t exist!
But let’s not be fickle. What about the many “paradoxes”, associated with length contraction? Next time more!
This was an excerpt from my book “Einsteins einmalige Einsichten: Die Relativitätstheorien und wie es dazu kam”, Books on Demand 2022.