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Spontaneous Symmetry
Name: David
Status: student
Age: N/A
Location: N/A
Country: N/A
Date: N/A
Question:
One account I have heard many times about spontaneous symmetry breaking is
a pencil standing on its tip; it can fall in any direction, and thus has
symmetry. When it falls, the symmetry is broken because the physical system
is no longer symmetrical, though the laws describing it did not themselves
break the symmetry.
Can spontaneous symmetry breaking be predicted, or is this example an
oversimplification?
Replies:
David,
It cannot be predicted because it is based on the small random motions that
formulas and models do not include. All of science is composed of simplified
models that do not fit reality perfectly but are much easier to work with than
reality. It is much easier to call a baseball a single object than billions of
atoms vibrating randomly within a ball-shaped pattern. Heat and turbulence
are two factors that often contribute break these symmetries. Various models
of heat and turbulence can predict average effects over time and position, but
not specific details. Doing so would require tracking all of the individual
molecules in the air and all the molecules that these air molecules crash
into.
Dr. Ken Mellendorf
In general we cannot predict which way a system will go (i.e. which direction
the idealized pencil will fall), but we can often predict "when" such symmetry
breaking will occur. Indeed if we could predict the direction beforehand, that
would imply that the system is not truly symmetric.
The case of the pencil is a bit of a simplification, but an "idealized fully
symmetric pencil" serves as a useful illustration. However, a better and
physically more correct example has to do with magnets. In that case, given
some assumptions, we can predict at what temperature the magnetic will be
symmetric and at what temperature it will break that symmetry. We cannot tell
which direction the symmetry will break at, but we can tell at what temperature
it will happen. I will try to describe this below though I fear my explanation
may not be entirely transparent.
One standard example of predicting when the transition occurs has to do with
magnets. Suppose you have physically symmetric magnetized ferromagnet (yes,
you can have a demagnetized ferromagnet!) at room temperature. The
magnetization comes from a net over-all preferred direction of alignment of
the magnetic domains within the magnet. Not all the domains point in that
direction, indeed most do not. But a majority will and that is the magnetic
field we observe outside from the magnet. As you heat up the magnet, the
magnetic field will decrease as the magnetic domains within it begin to decrease
their magnetization. The increase in temperature allows more variation in the
individual magnetic moments. At high enough temperature, there is enough
thermal energy in the system to overcome the magnetic energy and the previous
magnetic alignment is destroyed. At this high temperature the ferromagnet has
in fact become a paramagnet with it's magnetic moments all pointed in random
directions and changing direction rapidly. At this point the system is symmetric
with regards to magnetization. Any direction is equal and there is no preferred
alignment!
If the magnet is now cooled sufficiently, the magnetic energetics will become
significant again and it will become favorable for the moments and domains to
align. In the absence of any outside influence or intrinsic property, there is
no preferred direction. The material "spontaneously" chooses a particular
direction and the earlier symmetry
is broken. This direction will also be random relative to the original direction
before you heated the magnet. In fact, if you heat and cool it repeatedly, each
time will produce a new direction.
Michael S. Pierce
You have a proposition that is not true. Symmetries can be, and are, to use
your words broken.
The same pencil standing on its eraser could, in principle, stay there in
indefinitely.
Consider the simple molecule CO2. When it stretches symmetrically:
O<----C----> its symmetry does not change. But if it stretches asymmetrically
O<---C------->O its symmetry is reduced. That this happens is observed
experimentally because the asymmetric stretch absorbs infrared radiation, but
the symmetric stretch does not. A similar change in geometric symmetry changes
when the molecule bends -- that motion is active in the infrared spectrum.
Vince Calder
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Update: June 2012
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