Re: Law of Conservation of Baryon Number
- From: Hendrik van Hees <hees@xxxxxxxxxxxxx>
- Date: Sun, 20 Aug 2006 14:43:39 +0000 (UTC)
Reena wrote:
Hi,
I'm a high school student, and I constantly study all types of
science. Over the summer I've been focusing on atomic theory and read
about the law of conservation of baryon number, explaining why protons
are stable.
You've quite tough questions. I'll try to answer them.
We have the so-called Standard Model of elementary particle physics, one
of the greatest achievements of the last half of the 20th century in
physics. It describes all known elementary particles today, namely the
quarks, leptons, and the "force-carrier" particles.
To understand this model really, one needs to study quite a lot of
physics and mathematics, but I can tell you it's great fun. I'll try to
explain it with as least math as I can.
The most important notion of modern physics is the relation between
symmetries and conservation laws which goes back to a famous German
mathematician called Emmy Noether. She found this relation when
thinking about the (still not completely settled) question what the
energy of the gravitational field within Einstein's General Theory of
Relativity might be. She came up with the notion that to each symmetry
of the equations of motion of a system of point particles or fields (or
both coupled together) there must exist a conserved quantity.
Here, symmetry is a quite abstract notion. It means that you can find a
transformation of the quantities, describing a physical situation (for
instance, the three position coordinates and the three momentum
coordinates of a point particle) which does not change the equations of
motion. An example is Newtons law for the motion of a point particle (a
planet) around a fixed mass centre (a sun). In this case the problem is
perfectly symmetric under rotations which means that you can
arbitrarily rotate the position and momentum coordinates of the
particle (with the sun as rotation centre). According to Noether's
theorem there must be even three conserved quantities (because the
rotation has three arbitrary parameters, namely the direction of the
rotation axis and the angle of the rotation). As it turns out the
symmetry under rotations necessarily means that angular momentum must
be conserved.
Similar relations exist between the usual conservation laws of classical
mechanics and the symmetry of space and time (in Newton's mechanics or
Einstein's special theory of relativity):
Time-translation invariance (i.e., the laws of nature look the same at
all times) gives energy conservation.
Homogeneity of space (i.e., the laws of nature look the same at any
place) gives momentum conservation.
Isotropy of space (i.e., the laws of nature look the same in any
direction) gives angular-momentum conservation.
Of course all these conservation laws are also valid within quantum
theory which is nowadays thought to be the fundamental theory of all
physics.
In quantum mechanics, particularly in the standard model of elementary
particles, there are further much more abstract symmetries than those
of space and time. They are related to the mathematical structure of
quantum theory, with which I do not want to bother you now. The only
thing we need to know for answering your question is that (among other
important posibilities for symmetries arising in modern physics) there
are symmetries describing that different particles behave the same or
at least approximately the same under the influence of certain forces.
This idea came in the 1940ies to Werner Heisenberg. His idea was to
describe the experimental fact that protons and neutrons are very
similar. They have nearly the same mass and behave very similar under
the strong nuclear force which binds them together to atomic nuclei. If
one neglects electromagnetism, and this is a quite good approximation
in nuclear physics, since the electromagnetic interaction is very weak
compared to the strong force, the protons and neutrons behave almost
the same. Heisenberg described this fact by an abstract symmetry, the
socalled isospin symmetry.
The spin appeared in quantum mechanics when theoretical physicists
thought about how to represent spatial rotations in quantum mechanics,
and a very fundamental representation of rotations are related to the
spin of elementary particles, a notion which is hard to explain within
classical physics. One can think of it as an additional angular
momentum which a particle has even at rest. A classical extended body
can have such an intrinsic angular momentum by spinning around one of
its axes sitting somewhere at rest. However, the quantum mechanical
spin is much more abstract, but it's a good picture to have an idea
what spin means.
Heisenberg's Isospin is even more abstract. It makes use of the fact
that any system of two states which are symmetric to each other (here
the two states are proton and neutron) can be related by rotations. The
math is exactly the same as for the normal spin related to normal
rotations, but here it's describing the symmetry between protons and
neutrons.
The standard model of elementary particles has a lot of symmetries. One
important are the socalled gauge symmetries, another kind which I do
not need to explain in detail, but the whole model rests on this
symmetries. They are so to say the rule how to build the model in a
mathematically consistent way, and it's very successful.
Such gauge theories now tend to have other symmetries which were not
build in in the beginning. One of such "accidental" symmetries is
baryon-number conservation.
But now that's also a weak point of the standard model, and you are
perfectly right in your feeling that it is hard to understand why the
baryon number should be conserved or, even worse, it gives us big
trouble to understand why we exist!
The point is that one needs the violation of baryon-number conservation
to explain why there is left matter in the universe which forms stars
and planets where finally life including us could develop. All matter,
we can see (and we see only a very little of what really must be out
there in the universe, but that's another exciting story), is the tiny
relic of what is left over from the big bang. According to the big-bang
theory (the standard model of cosmology) an equal amount of matter and
anti-matter has been formed when the universe emerged as a hot fireball
in the big bang. By the way, the existence of anti-particles is a
necessary conclusion from the basic symmetries underlying relativistic
quantum-field theory which is the basis of the standard model of
elementary particles. It turns out that, if there was really perfect
baryon conservation, all the matter particles should have been
annihilated with the corresponding anti-matter particles, leaving
behind only a vast amount of light (i.e., electromagnetic radiation or
photons, the quanta of the electromagnetic field).
Indeed one finds this radiation nowadays. It's all around us and called
cosmic microwave background radiation! It is of course much colder than
when it was created in the big bang and from the annihilation of
particles and anti-particles because since than the universe has
expanded and cooled down, but all these photons are there. This is one
of the most important astronomical observations, justifying the
cosmological standard model (i.e., the big-bang theory).
However, as you well know, we are there (and all the planets, stars,
galaxies, galaxy cluster, etc. etc.), and this means necessarily that
baryon number cannot be strictly conserved.
In the standard model there is indeed a tiny violation of baryon-number
conservation. However, this is not enough to explain why we are there.
Modern astrophysical observations (concerning the above mentioned
cosmic microwave background radiation, CMBR) also teaches us that the
known particles (quarks, leptons and force carriers) cannot explain all
the matter which is out there. In fact only about 5% of the matter
contained in the universe can consist of known particles. The nature of
about 20% of matter is unknown! This is called "dark matter", since
this kind of matter cannot be seen, i.e., it must consist of
electrically neutral particles which do not radiate electromagnetic
waves (i.e., light).
The rest of the matter content is even more mysterious. It's
called "dark energy", but that's also another story. There is a lot
unknown about the universe, and to understand it better we need to
understand the subatomic elementary particles better.
It seems to me there is no support for this (I hesitate to say "proof"
since you can't really prove anything in science), and no reason to
easily accept it besides that it seems to work. You might as well say
"God makes the protons stable" or something like that.
Usually I don't tend to be too skeptical of things, but this one seems
ridiculous - randomly assigning numbers.
Spin, too, just seems to work. It's not something you can easily
describe or detect.
As I tried to explain above, spin is a rather necessary consequence of
quantum mechanics and rotational symmetry of space. It is also very
easily to detect, since each angular momentum of a charged particle
means it has an magnetic dipole moment, i.e., it is a little permanent
magnet. In fact, the magnetic dipole moment of, e.g., electrons is one
of the best known quantities in physics at all! The agreement between
the standard model of elementary particles (here most importantly
quantum electrodynamics (QED), the modern way to understand
electromagnetic interactions between particles) is accurate to 12
decimal digits!
--
Hendrik van Hees Texas A&M University
Phone: +1 979/845-1411 Cyclotron Institute, MS-3366
Fax: +1 979/845-1899 College Station, TX 77843-3366
http://theory.gsi.de/~vanhees/faq mailto:hees@xxxxxxxxxxxxx
.
- References:
- Law of Conservation of Baryon Number
- From: Reena
- Law of Conservation of Baryon Number
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