Quantum Indeterminism
In 1916
Albert Einstein found that at the microscopic quantum level the physical world is
indeterministic and
acausal for much deeper reasons than
Werner Heisenberg's 1927
uncertainty principle<.
This quantum indeterminism, or in fact quantum "
chance," as Einstein called it (
Zufall in German), appears when light interacts with matter (photons with electrons or atoms), as
Max Planck had suspected decades earlier.
Einstein wrote an article on
The Quantum Theory of Radiation in 1916...
If the hypotheses which I introduced about the interaction between
radiation and matter are correct, they must provide more than
merely the correct statistical distribution of the inner energy
of the molecules. Because, during absorption and emission
of radiation there occurs also a transfer of momentum upon
the molecules. This transfer effects a certain distribution of
velocities of the molecules, by way of the mere interaction
between radiation and the molecules. This distribution must
be identical to the one which results from the mutual collision
of the molecules, i.e., it must be identical with the Maxwell
distribution...
When a molecule absorbs or emits the energy e in the form of
radiation during the transition between quantum theoretically
possible states, then this elementary process can be viewed
either as a completely or partially directed one in space, or also
as a symmetrical (nondirected) one. It turns out that we arrive
at a theory that is free of contradictions, only if we interpret
those elementary processes as completely directed processes.
CPAE, vol.6, Doc. 38, “On the Quantum Theory of Radiation,”, p.220-221.
If light quanta are particles with energy
E = hν traveling at the
velocity of light
c, then they should have a momentum
p = E/c =
hν/c. When light is absorbed by material particles, this momentum
will clearly be transferred to the particle. But when light is emitted
by an atom or molecule, Einstein says that a problem appears.
If a beam of radiation effects the targeted molecule to
either accept or reject the quantity of energy hv in the form
of radiation by an elementary process (induced radiation
process), then there is always a transfer of momentum hv/c
to the molecule, specifically in the direction of propagation
of the beam when energy is absorbed by the molecule, in the
opposite direction if the molecule releases the energy. If the
molecule is exposed to the action of several directed beams of
radiation, then always only one of them takes part in an induced
elementary process; only this beam alone determines the direc-
tion of the momentum that is transferred to this molecule. If the
molecule suffers a loss of energy in the amount of hv without
external stimulation, i.e., by emitting the energy in the form
of radiation (spontaneous emission), then this process too is a
directional one. There is no emission of radiation in the form of
spherical waves. The molecule suffers a recoil in the amount of
hv/c during this elementary process of emission of radiation; the
direction of the recoil is, at the present state of theory, deter-
mined by “chance.” The properties of the elementary processes
that are demanded by [Planck’s] equation let the establishment
of a quantumlike theory of radiation appear as almost unavoidable.
The weakness of the theory is, on the one hand, that it does
not bring us closer to a link-up with the undulation theory; on
the other hand, it also leaves time of occurrence and direction
of the elementary processes a matter of “chance.” Nevertheless, I
fully trust in the reliability of the road taken.
CPAE, vol.6, Doc.38, “On the Quantum Theory of Radiation,”, p.232.
Conservation of momentum requires that the momentum of
the emitted particle will cause an atom to recoil with momentum
hν/c in the opposite direction. However, the standard theory of
spontaneous emission of radiation is that it produces a spherical
wave going out in all directions. A spherically symmetric wave has
no preferred direction. In which direction does the atom recoil?
An outgoing light particle must impart momentum
hν/c to the
atom or molecule, but the direction of the momentum can not be
predicted! Neither can the theory predict the time when the light
quantum will be emitted. Einstein called this “weakness in the
theory” by its German name - Zufall (chance), and he put it in scare
quotes. It is only a weakness for Einstein, of course, because his God
does not play dice.
Such a random time was not unknown to physics. When Ernest
Rutherford derived the law for radioactive decay of unstable
atomic nuclei in 1900, he could only give the probability of decay
time. Einstein saw the connection with radiation emission:
It speaks in favor of the theory that the statistical law assumed
for [spontaneous] emission is nothing but the Rutherford law of
radioactive decay.
CPAE vol.6, Doc.34, p.216.
Einstein clearly saw that the element of chance that he discovered
threatens
causality. It introduces
indeterminism into physics.
The indeterminism involved in quantizing matter and energy
was known, if largely ignored, for another decade until Werner
Heisenberg’s quantum theory introduced his famous
uncertainty
(or
indeterminacy) principle in 1927, which he said was
acausal.
Where Einstein’s indeterminism is qualitative, Heisenberg’s
principle is quantitative, stating that the exact position and momen-
tum of an atomic particle can only be known within certain (sic)
limits. The product of the position error and the momentum error
is greater than or equal to Planck’s constant
h/2π.
ΔpΔx ≥ h/2π.
Einstein's indeterminism is central to understanding the
origin of irreversibility in statistical mechanics.
For further information, see our 2014
Origin of Irreversibility paper
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