5 The Incredible Quantum Mechanics
95
5.8 Quantum Entanglement
If we are still reeling from the implications of Wheeler’s Delayed Choice
Experiment, then “a cup of tea, a Bex, and a good lie down” 10 are surely
necessary before tackling the mysteries of Quantum Entanglement.
From our examples above, one may obtain the impression that everything
in QM is of a ghostly probabilistic nature, and that nothing can be known
for certain. As we have seen, at the microscopic level this is largely true, but
there are some quantities that must not change, and these are expressed by
conservation laws. These laws are the quantum analogues of corresponding
laws in classical physics. Indeed, they are more than analogues: they are really
the same laws, with the quantum form transitioning into the classical form as
the objects we are considering increase in complexity and size. Examples are
the Laws of Conservation of Momentum, Angular Momentum and Energy.
We shall discuss conservation laws in more detail in Chap. 8.
Let us consider another thought experiment where two electrons are
produced together such that their total combined angular momentum is zero.
Such a process is possible if the electrons are produced jointly in a physical
process where the total angular momentum that the pair can carry away is
limited to zero by the requirement of the Law of Conservation of Angular
Momentum. Then if one electron has a positive angular momentum, the
other electron must carry an equal negative angular momentum. In other
words, the two electrons are spinning at the same rate in opposite directions.
This is a classical picture—electrons are not simply spinning balls, as we shall
see in Chaps. 8 and 9. However, this model will suffice for our purposes here.
Two particles restrained in this manner by a conservation law are said to be
entangled .
It is worth reiterating that at this point we have not yet conducted
any measurements on the electrons, so we cannot say what the angular
momentum of each electron is, only that they spin in opposite directions,
and that the sum of their individual angular momenta must be zero. Indeed,
QM goes further and states that until a measurement is made, neither electron has a well-defined spin, but is a mixture, or superposition, of possible
spin states.
Let us now conduct our measurement. We select one electron and measure
its angular momentum, while we allow the second one to continue on its
10 A marketing slogan for Bex, a widely used but addictive analgesic containing phenacetin. Bex was
banned in 1977, when it was shown to cause renal cancer. The slogan became part of the Australian
vernacular.
95
5.8 Quantum Entanglement
If we are still reeling from the implications of Wheeler’s Delayed Choice
Experiment, then “a cup of tea, a Bex, and a good lie down” 10 are surely
necessary before tackling the mysteries of Quantum Entanglement.
From our examples above, one may obtain the impression that everything
in QM is of a ghostly probabilistic nature, and that nothing can be known
for certain. As we have seen, at the microscopic level this is largely true, but
there are some quantities that must not change, and these are expressed by
conservation laws. These laws are the quantum analogues of corresponding
laws in classical physics. Indeed, they are more than analogues: they are really
the same laws, with the quantum form transitioning into the classical form as
the objects we are considering increase in complexity and size. Examples are
the Laws of Conservation of Momentum, Angular Momentum and Energy.
We shall discuss conservation laws in more detail in Chap. 8.
Let us consider another thought experiment where two electrons are
produced together such that their total combined angular momentum is zero.
Such a process is possible if the electrons are produced jointly in a physical
process where the total angular momentum that the pair can carry away is
limited to zero by the requirement of the Law of Conservation of Angular
Momentum. Then if one electron has a positive angular momentum, the
other electron must carry an equal negative angular momentum. In other
words, the two electrons are spinning at the same rate in opposite directions.
This is a classical picture—electrons are not simply spinning balls, as we shall
see in Chaps. 8 and 9. However, this model will suffice for our purposes here.
Two particles restrained in this manner by a conservation law are said to be
entangled .
It is worth reiterating that at this point we have not yet conducted
any measurements on the electrons, so we cannot say what the angular
momentum of each electron is, only that they spin in opposite directions,
and that the sum of their individual angular momenta must be zero. Indeed,
QM goes further and states that until a measurement is made, neither electron has a well-defined spin, but is a mixture, or superposition, of possible
spin states.
Let us now conduct our measurement. We select one electron and measure
its angular momentum, while we allow the second one to continue on its
10 A marketing slogan for Bex, a widely used but addictive analgesic containing phenacetin. Bex was
banned in 1977, when it was shown to cause renal cancer. The slogan became part of the Australian
vernacular.