A Simple ? on Electron Spin
KK
I am a new comer to this list. I had a simple question on Pauli's
exclusion principle, which states that no two electrons can have the
same state signified by quantum numbers. The corollary I remember is
that an electron can have a spin of either +1/2 or -1/2.
The question is this: Has it been said/postulated/proven/whatever
anywhere that an electron takes both these values in the same frame of
reference? i.e., a particular electron has a spin of +1/2 at time t1
and then a spin of -1/2 at time t2, *in the same frame of reference*.
Thanks,
KK
Jim Heckman
On 21-May-2002, kad...@yahoo.com (KK) wrote:
> Hi,
>
> I am a new comer to this list. I had a simple question on Pauli's
> exclusion principle, which states that no two electrons can have the
> same state signified by quantum numbers. The corollary I remember is
> that an electron can have a spin of either +1/2 or -1/2.
That's a pretty deep corollary, buried deep in quantum field theory
in the form of the spin-statistics theorem. Even then, the exclusion
principle applies to all fermions, i.e., all particles with half-integer
spins
such as 1/2, 3/2, 5/2, ... -- not just spin-1/2 particles like electrons.
Until quantum field theory was developed, the exclusion principle and
the fact that half-integer particles obey it were just unexplained
coincidences in plain ol' non-relativistic quantum mechanics.
> The question is this: Has it been said/postulated/proven/whatever
> anywhere that an electron takes both these values in the same frame of
> reference? i.e., a particular electron has a spin of +1/2 at time t1
> and then a spin of -1/2 at time t2, *in the same frame of reference*.
My gosh, yes. Particles change their spins all the time. Since spin
is an angular momentum, which is conserved, if a particle changes its
spin, it has to be compensated somewhere else -- by a change either
in another particle's spin, or in a so-called 'orbital' angular momentum.
--
Jim Heckman
KK
Thanks for the answer, Jim. I have one more question: What is the spin
value when the electron is changing its spin direction? From whatever
little I understand of your answer, +1/2 and -1/2 seems to be only
stable state values and there are other states, though unstable.
Right?
Thanks,
KK
Alejandro Rivero
news:uek93um...@news.supernews.com
> My gosh, yes. Particles change their spins all the time. Since spin
> is an angular momentum, which is conserved, if a particle changes its
> spin, it has to be compensated somewhere else -- by a change either
> in another particle's spin, or in a so-called 'orbital' angular momentum.
Well, it is not so clear that spin is an angular moment. It
has units of angular moment, it smells as angular moment, but
it lives in the covering group of rotations, while angular moment
lives in the group of rotations.
Just a warning for people launching to use angular momentums as
models for spin. Of course, if one keeps in non relativistic
theory one is authorized to forget the subtle things.
Alejandro.
--
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pubm...@charter.net
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Warren writes:
This thread is following what I have attempted to explore in our
latest research paper release. I will not go into detail here and
again this is conjecture from the research findings and should
not be taken as accepted fact. The full paper is available in
zipped PDF format upon request however let me explain in short
the answer to your question. We fine quantum Time and physical
time not the same process but one develops into the other. Again
our defination of physical time and quantum time is supplied in
the paper. Anyway, at the quantum level quantum time is broken
down from the quantized angular momentum of the partical known
as intrinsic spin. That is the +1/2 UP and the -1/2 DOWN or 720
degree of rotation for the electron. We break that intrinsic angular
moment up into units of 10 for Pi. Again you will have to read the
paper to see how and why. But keep in mind that this level is
quantized and the degrees are only presented at transit points
on our physical level. Work now being done in this area has to
do with nano-computering and is called "Spintronics". A new
field that yields great possibilities. Thank you for allowing me to
jump in. Warren
Request for review of the research paper e-mail to:
pubm...@charter.net
Jim Heckman
On 22-May-2002, kad...@yahoo.com (KK) wrote:
> Thanks for the answer, Jim. I have one more question: What is the spin
> value when the electron is changing its spin direction? From whatever
> little I understand of your answer, +1/2 and -1/2 seems to be only
> stable state values and there are other states, though unstable.
> Right?
Not exactly. Rather, the only values that can be *measured* are +/-1/2.
Whatever state an electron is in, if you measure its spin along a given
direction, you'll always get either +1/2 or -1/2. The probability of each
of these results depends on the state of the photon before the
measurement.
--
Jim Heckman
Jim Heckman
On 22-May-2002, "Alejandro Rivero" <riv...@sol.unizar.es> wrote:
> "Jim Heckman" <wnzrfe...@lnubb.pbz> wrote in message
> news:uek93um...@news.supernews.com
>
> > My gosh, yes. Particles change their spins all the time. Since spin
> > is an angular momentum, which is conserved, if a particle changes its
> > spin, it has to be compensated somewhere else -- by a change either
> > in another particle's spin, or in a so-called 'orbital' angular
> > momentum.
>
> Well, it is not so clear that spin is an angular moment. It
> has units of angular moment, it smells as angular moment, but
> it lives in the covering group of rotations, while angular moment
> lives in the group of rotations.
You are correct that spin "lives" in the group Spin(3) = SU(2), the
covering group of the rotation group SO(3). But spin certainly *is* an
angular momentum by any useful definition of the latter. Rotations
operate on spin in such a way that, as per Noether's Theorem, only
*total* angular momentum is conserved -- not spin and orbital
angular momentum separately.
> Just a warning for people launching to use angular momentums as
> models for spin. Of course, if one keeps in non relativistic
> theory one is authorized to forget the subtle things.
Hardly. Total angular momentum is conserved in non-relativistic
QM as well as relativistic, and spin must included there too to
keep it conserved.
--
Jim Heckman
Alejandro Rivero
> On 22-May-2002, "Alejandro Rivero" <riv...@sol.unizar.es> wrote:
> > Well, it is not so clear that spin is an angular moment. It
> > has units of angular moment, it smells as angular moment, but
> angular momentum by any useful definition of the latter. Rotations
> operate on spin in such a way that, as per Noether's Theorem, only
> *total* angular momentum is conserved -- not spin and orbital
> angular momentum separately.
> > theory one is authorized to forget the subtle things.
> Hardly. Total angular momentum is conserved in non-relativistic
> QM as well as relativistic, and spin must included there too to
> keep it conserved.
The point was that in low energy you can considerate spin,
orbital momentum, and total angular momentum separately, while as
you go up you need to fuse them, until you finally are restricted to
consider only joint conservation of spin plus orbital.
Alejandro