Biomedical Engineering Reference
In-Depth Information
electron in some sense know which spin state it should be in, before passage through
the apparatus? Similar questions puzzled Schrödinger and his contemporaries, and led
Schrödinger to state the famous
cat paradox
. In a version of this thought experiment, a
cat is placed in a closed box together with (for example) a radioactive atom that releases a
deadly poison when it decays. If the wavefunction of the living cat is ψ
L
and that of a dead
cat ψ
D
then the state of the cat at time
t
can be described by
ψ
Cat
(
t
)
c
D
(
t
) ψ
D
The coefficients are time dependent, as is the wavefunction. Before the box is closed, the
cat is alive. Once the box is closed, the cat is apparently neither dead nor alive; it is in a
mixed state. On opening the box at a certain time, the cat is either dead or alive, but is it
the act of measurement that has forced the cat into one state or the other?
There are whole rafts of similar questions that can be asked. Most of the difficulties can be
resolved by recognizing that we are asking a statistical question, not one about a specific cat.
If we prepare a large number of identical experiments, with identical cats and amounts of
radioactive isotopes, close the lids on the boxes and then examine a statistically significant
number of boxes, we will find that a fraction
=
c
L
(
t
) ψ
L
+
2
will have died and a fraction
2
|
c
D
(
t
)
|
|
c
L
(
t
)
|
will be alive, but no prediction can be made as to the state of a given cat in a given box.
References
Eyring, H., Walter, J. and Kimball, G.E. (1944)
Quantum Chemistry
, John Wiley & Sons, Inc.,
New York.
Goudsmit, S. and Uhlenbeck, G.E. (1925)
Naturwissenschaften
,
13
, 953.
Moore, C.E. (1949)
Atomic Energy Levels Volume I (Hydrogen through Vanadium)
, Circular of the
National Bureau of Standards, US Government Printing Office, Washington, DC.
Moore, C.E. (1952)
Atomic Energy Levels Volume II (Chromium through Niobium)
, Circular of the
National Bureau of Standards, US Government Printing Office, Washington, DC.
Moore, C.E. (1958)
Atomic Energy Levels Volume III (Molybdenum through Lanthanum and
Hafnium throughActinium)
, Circular of theNational Bureau of Standards, USGovernment Printing
Office, Washington, DC.
Stern, O. and Gerlach, W. (1921)
Z. Physik
,
8
, 110.
