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M2L8g.txt
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#
# File: content-mit-8-421-2x-subtitles/M2L8g.txt
#
# Captions for 8.421x module
#
# This file has 114 caption lines.
#
# Do not add or delete any lines.
#
#----------------------------------------
I've not done any experiment in my life
where higher order moments became important.
But I want to teach you about it because the discussion
whether those higher moments exist
or not is really an interesting discussion about what
is allowed by symmetry and what not.
So I'm bringing in higher order moments,
not so much because you needed to understand the level
structure of your favorite atom, but because it teaches us
a really nice piece of physics.
So let me now discuss higher order moments.
And the leading one is the electric quadrupole moment.
So I want to raise in general the question, what
further moments can a nucleus have?
What we have discussed so far is the magnetic moment mu.
So beyond mu, what further electric or magnetic moments
can a nucleus have?
Well, it's a question about symmetry.
And if you look at the parity of my multipoles,
if you have an electric multipole-- well,
you know if you have a dipole plus minus, you invert it.
The dipole becomes minus the dipole.
So for L equals 1, it is minus 1.
L is 1.
But in general, it is minus L. If you have a quadrupole,
you invert your coordinate system, it's L equals 2.
Plus, plus, minus, minus, you invert it.
Nothing changes.
So at least I've shown you for dipole and quadrupole
that this formula is correct.
So an electric multipole has this parity.
And for a magnetic case-- well, magnetic,
we have axial vectors versus polar vectors.
There's always an extra factor of minus 1.
So therefore, if we go magnetic, magnetic multipoles, with L
have a parity of minus L plus 1.
So this really restricts what multipoles are possible.
Instead of giving you a general discussion,
let me just look at the very important case
whether a nucleus can have an electric dipole moment.
And you will immediately see what it needs to,
and then I give you the general result.
So let's assume a nucleus have angular momentum I.
And there is a magnetic moment mu associated with that.
So the general result is that odd electric and even magnetic
multipole moments would violate-- not just one,
but two symmetries -- would violate parity and time reversal
symmetry.
So the argument goes as follows.
Let us assume this is the magnetic moment
mu or the angular momentum I.
It's a vector.
And now we are asking is it possible to have
a vector of the dipole moment.
And dipole moment, you should just think about it
as a plus minus charge separated.
We can now do the parity operation and the time reversal
operation.
If you do the time reversal operation,
the current, which generates a magnetic moment,
if you want to think about it in this picture,
goes the other way.
So mu flips.
But nothing moves, of course, for an electric dipole moment.
So reversing time is not changing anything.
So in other words, time reversal symmetry
transforms parallel mu and d into anti-parallel mu and d.
And similar, parity is not changing mu,
but it is changing d.
So in both cases, would parity or time reversal symmetry,
if you had a mu d, a scalar product of mu
and d, which would be non-0, then both P or T
would change the sign.
But that would mean that two kinds of particles would exist,
one where the sign is positive, one where the sign is negative.
But we have assumed that we have one nucleus and only
one nucleus of this kind.
So we cannot have one nucleus which has the property
of having simultaneously a magnetic and electric dipole
moment.
So therefore, we conclude that mu times d has to be 0.
And if you generalize this argument,
we have ruled out that there is an electric dipole
moment, an odd electric moment.
The first, the lowest possible electric moment
is the quadrupole moment.
So the leading electric moment is not L equals 2.
It's L equals 2.
It's not L equals 1, the dipole.
It's L equals 2, the quadrupole.
And of course, if you generalize the argument, L equals 4,
l equals 6 would be possible.
But those effects would be very small.
OK, so we've talked about parity and time reversal symmetry,
which restricts what kind of magnetic and electric dipole
moments particles may have.
And maybe in this context, I should just
mention that John Doyle, Jerry Gabrielse, and Dave DeMille
at Harvard and Yale, they just published the most accurate
result for the electric dipole moment of the electron.
They found a bound which was more than an order of magnitude
lower than the best upper bound before.
And this has really made headlines.
So to measure accurately that the electric dipole
moment vanishes, in this case of the electron,
but other people do it also for neutrons,
is testing fundamental symmetries.
In particular, it tests whether nature
is time reversal invariant.
And the reason why, until now, everybody
has found that the results are compatible with 0
is pretty much based on the argument I just gave you.