Léon Rosenfeld was for many years the closest associate and confidante of Niels Bohr
. He was Bohr's amanuensis
, taking dictation from the scientist who famously preferred talking to writing, and lecturing to writing scientific papers loaded with mathematical equations and experimental results.
Rosenfeld was the editor of Bohr's Collected Works
and the strongest defender of the Copenhagen Interpretation
of quantum mechanics against alternative interpretations
Rosenfeld was a Marxist who thought Bohr's ideas about complementarity
could extend to "dialectical" debates about idealism versus materialism.
Einstein described nonlocality
to Rosenfeld in 1933.
Shortly before he left Germany to emigrate to America,
Einstein attended a lecture on quantum electrodynamics by
Rosenfeld. Keep in mind that Rosenfeld was perhaps the most
dogged defender of the Copenhagen Interpretation
, in which particles have no positions until they are measured.
After the talk,
Einstein asked Rosenfeld, “What do you think of this situation?”
Suppose two particles are set in motion towards each other with
the same, very large, momentum, and they interact with each
other for a very short time when they pass at known positions.
Consider now an observer who gets hold of one of the particles,
far away from the region of interaction, and measures its
momentum: then, from the conditions of the experiment, he will
obviously be able to deduce the momentum of the other particle.
If, however, he chooses to measure the position of the first
particle, he will be able tell where the other particle is.
We can diagram a simple case of Einstein’s question as follows.
Recall that it was Einstein who discovered in 1924 the identical nature, indistinguishability, and interchangeability of some quantum particles. He found that identical particles are not independent, altering their quantum statistics.
After the particles interact at t1
, quantum mechanics describes them with a single two-particle wave function Ψ12
that is not the product of independent
single-particle wave functions. In the case of electrons, which are indistinguishable interchangeable particles, it is not proper to say electron 1 goes this way and electron 2 that way. (Nevertheless, it is convenient to label the particles, as we do in the illustration.)
Einstein then asked Rosenfeld, “How can the final state of the second
particle be influenced by a measurement performed on the first
after all interaction has ceased between them?” This was the germ
of the EPR paradox
, and ultimately the problem of two-particle
Why does Einstein question Rosenfeld and describe this as an
“influence,” suggesting an “action-at-a-distance?”
It is only paradoxical in the context of Rosenfeld’s Copenhagen
, since the second particle is not itself measured and
yet we know something about its properties, which the Copenhagen Interpretation
says we cannot know without an explicit measurement..
Einstein was clearly correct to tell Rosenfeld that at a later time t2
, a measurement of one particle's position would instantly establish the position of the other particle - without measuring it
. Einstein obviously used conservation of linear momentum
implicitly to calculate (and know) the position of the second particle.
Two years later, after EPR, Schrödinger described two such particles as becoming "entangled" (verschränkt
) at their first interaction, so "nonlocal" phenomena are also known as "quantum entanglement."
Although conservation laws are rarely cited as the explanation, they are the physical reason that entangled particles always
produce correlated results for all properties. If the results were not always correlated, the implied violation of a fundamental conservation law would cause a much bigger controversy than entanglement itself, as puzzling as that is.
This idea of something measured in one place "influencing" measurements far away challenged what Einstein thought of as "local reality." It came to be known as "nonlocality." Einstein called it a "spukhaft Fernwirkung
" or "spooky action at a distance."
We prefer to describe this phenomenon as "knowledge at a distance." No action has been performed on the distant particle simply because we learn about its position. Note that this assumes the distant particle has not been disturbed by an interaction with the environment.