Electron spin
kris oddson
mathematical predictions to come true? If an electron can be a wave
and a particle, do either the wave or the particle spin in the sense
of turning about themselves?
Moataz H. Emam
You have touched on one of the big mysteries in quantum mechanics. As
far as we can tell experimentally, electrons are point particles that
have no measurable size. This means that they are not really spinning in
the conventional sense of the word. However, electrons do have a
magnetic dipole that is as if they were spinning. It is, of course,
quantized. Where does it come from? Your guess is as good as anyone's!
--
Moataz H. Emam
Graduate Student
http://continue.to/emam
1129 Lederle Graduate Research Center C, The Department of Physics,
University of Massachusetts, Amherst, MA 01003
Tel: (413) 545 0559 Fax: (413) 545 0648
Kevin A. Scaldeferri
kris oddson <odd...@odyssee.net> wrote:
Since these are both the sort of question that I don't know how to
answer (in particular, I don't know what things like "just a
concept that lets us make predictions" mean) I'll just give the
SAT-style analogy that I think you ought to ponder.
spin:angular momentum :: mass:energy
--
======================================================================
Kevin Scaldeferri Calif. Institute of Technology
The INTJ's Prayer:
Lord keep me open to others' ideas, WRONG though they may be.
Gerard Westendorp
There have been some threads on this the last couple of months/year.
(Look up "Ohanian" in the Google usenet search engine).
The answer is that the electron wave function does indeed allow one
to define a momentum density, which does indeed circulate around
a point. The total angular momentum of this circulating flow
is h_bar/2, the spin of the electron.
Gerard
Demian Cho
> Is electron spin just a concept in our minds that allows our
> mathematical predictions to come true?
No. It is physical reality. Without electron spin you will not
see periodic table, for example.
> If an electron can be a wave
> and a particle, do either the wave or the particle spin in the sense
> of turning about themselves?
Roughly spin describes a property of the system (electron) under
rotation. Spin-0 simply means your wave function doesn't look
different when you are looking it after rotating it slightly.
(Let me be little bit more precise about what it mean to rotate
wave function. Wave function is generally depends on its
position and time. Imagine you use spherical coordinate.
Then your wave function is a function of r, theta, phi.
Just for the sake of argument let's rotate your electron
with respect to z-axis. That is fix r, phi but change theta.
You measure wave function after you change theta, and
compare it with previous value to check whether it has
been changed.)
Spin 1 means wave function changes when you rotate it
but return to the original value (up to phase) if you rotate
it 360 degree.
Now, spin 2 means your wave function doesn't quite come
back to the original state when you complete one rotation
(it will be a negative of its original value), but complete
two rotations.
Cheers,
--
Demian H.J. Cho
Center for Gravitation and Cosmology
University of Wisconsin-Milwaukee
Laurence Yaffe
>In article <3b86ed0b...@news.globetrotter.net>,
>kris oddson <odd...@odyssee.net> wrote:
>>Is electron spin just a concept in our minds that allows our
>>mathematical predictions to come true? If an electron can be a wave
>>and a particle, do either the wave or the particle spin in the sense
>>of turning about themselves?
>Since these are both the sort of question that I don't know how to
>answer (in particular, I don't know what things like "just a
>concept that lets us make predictions" mean) I'll just give the
>SAT-style analogy that I think you ought to ponder.
>spin:angular momentum :: mass:energy
The more proper analogy would be:
spin:angular momentum :: frequency:energy
It is an experimental fact (which is also required for
theoretical consistency) that an electron at rest necessarily
has non-zero angular momentum, of magnitude hbar/2. Whether this
is due to the electron "turning about itself" is at best a matter
of interpretation, and not really a testable assertion. Some people
would say "yes". Others would say that so far as we know, the spin
of the electron is not "due" to anything --- it just "is".
Kevin A. Scaldeferri
Someday I really need to read that paper. In the meantime, maybe
someone can clarify something that bugs me about this. I get worried
when you start talking about the "electron wave function" since the
wave function isn't an observable but, rather, a model-dependent
entity. So, what is the model-independent observable that is really
what's being talked about here?
John Baez
>Is electron spin just a concept in our minds that allows our
>mathematical predictions to come true?
Yes - just like "momentum", "force", "electric field" and so on.
All these concepts seemed very abstract and difficult to intuit
when they were first invented. After a while they became so
familiar that it is now almost impossible to remember what it was
like to think about the world before we had them.
J. J. Lodder
> You have touched on one of the big mysteries in quantum mechanics. As
> far as we can tell experimentally, electrons are point particles that
> have no measurable size. This means that they are not really spinning in
> the conventional sense of the word. However, electrons do have a
> magnetic dipole that is as if they were spinning. It is, of course,
> quantized. Where does it come from? Your guess is as good as anyone's!
But they have a very real mechanical angular momentum as well.
For example: flipping all the spins in a magnet
will cause the magnet to rotate,
or cause a torque on it when held fixed.
Of the right amount, of course. (Einstein-De Haas effect)
Even better, idealised: stand on a perfect turntable,
with a (very strong :-) bar magnet in your hand, pointing verticaly,
rotate it through 180^o, and you will start to turn,
just as when you had been holding a gyroscope.
You can't get more 'real' than that,
Jan
Moataz H. Emam
That is true. As I said, the electron *does* have a dipole moment which
gives a magnetic field which carries angular momentum, which explains
the experiments you have described. The question is not whether spin
angular momentum is real. Rather, it is "What is spinning?" or "What is
the source of spin?". It seems to me that the best available explanation
of spin is the one given in another post by Demian Cho in relation to
the rotational symmetry of the wave function. True, this does not
satisfy the die-hard classicist because it has no mechanical visual
image associated with it, but such is the nature of quantum mechanics.
One has resigned to it a long time ago (sigh).
Kevin A. Scaldeferri
Laurence Yaffe <l...@phys.washington.edu> wrote:
>ke...@cco.caltech.edu (Kevin A. Scaldeferri) writes:
>
>>In article <3b86ed0b...@news.globetrotter.net>,
>>kris oddson <odd...@odyssee.net> wrote:
>
>>>Is electron spin just a concept in our minds that allows our
>>>mathematical predictions to come true? If an electron can be a wave
>>>and a particle, do either the wave or the particle spin in the sense
>>>of turning about themselves?
>
>>Since these are both the sort of question that I don't know how to
>>answer (in particular, I don't know what things like "just a
>>concept that lets us make predictions" mean) I'll just give the
>>SAT-style analogy that I think you ought to ponder.
>
>>spin:angular momentum :: mass:energy
>
>The more proper analogy would be:
>
> spin:angular momentum :: frequency:energy
Why do you say this? I definitely don't think of the frequency of a
particle as the intrinsic energy of the particle. Instead, I consider
the mass to be the intrinsic energy.
To clarify what I mean in my analogy, here is a lengthier version.
The spin of a particle is the intrinsic angular momentum possessed by
the particle independent of its motion. When the particle is in
motion in a particular frame of reference, the spin is added (in the
appropriate manner) to the angular momentum due to that motion to
obtain the total angular momentum.
The mass of a particle is the intrinsic energy possessed by
the particle independent of its motion. When the particle is in
motion in a particular frame of reference, the mass is added (in the
appropriate manner) to the energy due to that motion to
obtain the total energy.
>Others would say that so far as we know, the spin
>of the electron is not "due" to anything --- it just "is".
This is basically my point. It makes about as much sense to ask what
the spin of an electron is due to as it does to ask what the mass is
due to. (Of course, if you believe that electrons aren't fundamental,
then both of these questions make a lot of sense.)
Matt McIrvin
ke...@cco.caltech.edu (Kevin A. Scaldeferri) wrote:
[about Ohanian's treatment of spin]
> Someday I really need to read that paper. In the meantime, maybe
> someone can clarify something that bugs me about this. I get worried
> when you start talking about the "electron wave function" since the
> wave function isn't an observable but, rather, a model-dependent
> entity. So, what is the model-independent observable that is really
> what's being talked about here?
Well, probably a more correct treatment would use quantum fields rather
than wave functions, in which case you could construct some local
operator that would be an averaged stress-energy tensor over a small
region.
I have no idea how you'd measure that, though. In fact, I'm pretty
sure it would not be an observable unless you somehow use gravitational
means.
In the case of the Poynting vector in electromagnetism, which is the
equivalent quantity (or a piece of it) for electromagnetic fields,
certainly people constantly get into arguments over whether it is
*really* the energy-momentum density or whether we should add in some
other arbitrary piece to avoid some situation that the arguer thinks is
absurd (like the circulating Poynting vector of an electrically charged
magnetic dipole), and apart from gravity there is no way to settle the
dispute.
However, the Ohanian paper (admittedly, it's been a long time since
I read it) is more along the lines of a counterargument to the
insistence that spin cannot be visualized and nobody should try.
I've even seen people who should know better say that it isn't *really*
angular momentum, it's just this weird thing that happens to follow the
same commutation relations. That's true of, say, *isospin*, but not of
spin. Any definition of angular momentum that is useful ought to be a
conserved quantity, and angular momentum isn't conserved unless spin is
included!
--
Matt McIrvin
Laurence Yaffe
>In article <9mhdv9$18jq$1...@nntp6.u.washington.edu>,
>Laurence Yaffe <l...@phys.washington.edu> wrote:
>>ke...@cco.caltech.edu (Kevin A. Scaldeferri) writes:
>>
>>>spin:angular momentum :: mass:energy
>>
>>The more proper analogy would be:
>>
>> spin:angular momentum :: frequency:energy
>Why do you say this? I definitely don't think of the frequency of a
>particle as the intrinsic energy of the particle. Instead, I consider
>the mass to be the intrinsic energy.
I was just alluding to the fact that:
hbar * spin = (intrinsic) angular momentum
hbar * frequency = energy
Moataz H. Emam
> The mass of a particle is the intrinsic energy possessed by
> the particle independent of its motion. When the particle is in
> motion in a particular frame of reference, the mass is added (in the
> appropriate manner) to the energy due to that motion to
> obtain the total energy.
The energy due to the motion of the photon for example is E=hv where v
is the frequency of the EM field. That is the origin of the
correspondence between energy and frequency. In the case of the photon,
that is all she wrote since the photon is massless.
Bjorn Wesen
>I've even seen people who should know better say that it isn't *really*
>angular momentum, it's just this weird thing that happens to follow the
>same commutation relations. That's true of, say, *isospin*, but not of
>spin. Any definition of angular momentum that is useful ought to be a
>conserved quantity, and angular momentum isn't conserved unless spin is
>included!
I was thinking of this... and wondered: why do people ask "what is spinning"
and not "what is moving" for example ?
After all, looking at it from a QFT point of view, you can have a scalar
field and interpret it as things that "move". And you can add dimensions to
the field, call the new dimensions spinor and vector-fields and see that new
possibilities for rotational symmetry emerge and call that "spin". If spin
is difficult so should the scalar field be..
Allow me to expand this on a more general question, something I've had
trouble extracting the answers to from QFT literature (at least my books
tend to describe the math but never the big picture):
When you're talking more "seriously" about spin and particles, does it work
something like this: you have the abstract Poincare group, and you can set
up representations of it with any number of degrees of freedom. Each
representation brings with it certain "patterns" that the constitutient
degrees can perform and still qualify to be described by the poincare group.
Some of these patterns give rise to what we measure as angular momentum
(both intrinsic and extrinsic spin), some of linear momentum.. And you
associate particles with those representations because when you do real
experiments those representations on paper seem to fit the measurements ?
And where does the additional group structure come in - I mean, like the
additional degree of freedom of electromagnetisms U(1)... When you write
that the standard model has the symmetry U(1) x SU(2) x SU(3), do you really
mean that it has that symmetry _and_ poincare symmetry, and you extract all
the representations you think fit the data ? Really, isn't a representation
of solely the poincare group meaningless, as you would not be able to
measure it in any way (you need forces acting through your measuring
equipment)...
I'm trying to figure out how the current state of affairs work from as high
an abstraction level as possible... recognizing that the actual details of
the calculations can be done in different (and sometimes confusing) ways,
and why group theory is useful as an abstraction method. But I'm having
trouble pasting together the group theory of the forces with the ditto of
"space time" (not trying to get into gravity unification here though :). I
must have missed some physics on the way of learning the math :)
/Bjorn
Jim Carr
} In article <3b86ed0b...@news.globetrotter.net>,
} kris oddson <odd...@odyssee.net> wrote:
} >Is electron spin just a concept in our minds that allows our
} >mathematical predictions to come true? If an electron can be a wave
} >and a particle, do either the wave or the particle spin in the sense
} >of turning about themselves?
}
} Since these are both the sort of question that I don't know how to
} answer (in particular, I don't know what things like "just a
} concept that lets us make predictions" mean) I'll just give the
} SAT-style analogy that I think you ought to ponder.
}
} spin:angular momentum :: mass:energy
In article <9mhdv9$18jq$1...@nntp6.u.washington.edu>
l...@phys.washington.edu (Laurence Yaffe) writes:
>
>The more proper analogy would be:
>
> spin:angular momentum :: frequency:energy
Even without seeing Kevin's reply, I would second it.
Spin is the intrinsic angular momentum of a particle,
and mass is the intrinsic energy of a particle.
>It is an experimental fact (which is also required for
>theoretical consistency) that an electron at rest necessarily
>has non-zero angular momentum, of magnitude hbar/2.
Just as an electron at rest has an energy equal to mc^2.
Hence the analogy. [Aside: I have found the idea of mass
as intrinsic energy to be quite useful when explaining
that idea in special relativity and have advocated it in
these newsgroups for years. I'm not sure if anyone else
pushes the idea, but I think it is a good one.]
--
James Carr <j...@scri.fsu.edu> http://www.scri.fsu.edu/~jac/
SirCam Warning: read http://www.cert.org/advisories/CA-2001-22.html
e-mail info: new...@fbi.gov pyr...@ftc.gov enfor...@sec.gov
Toby Bartels
>Kevin A. Scaldeferri wrote:
>>The mass of a particle is the intrinsic energy possessed by
>>the particle independent of its motion. When the particle is in
>>motion in a particular frame of reference, the mass is added (in the
>>appropriate manner) to the energy due to that motion to
>>obtain the total energy.
>The energy due to the motion of the photon for example is E=hv where v
>is the frequency of the EM field. That is the origin of the
>correspondence between energy and frequency. In the case of the photon,
>that is all she wrote since the photon is massless.
This is all true, but it's irrelevant to Kevin's discussion.
There is a relationship between frequency and energy,
so you have the frequency : energy side of the analogy.
However, this relationship isn't analogous to
the relationship between spin and angular momentum,
so the complete analogy frequency : energy :: spin : angular momentum
breaks down. OTOH, Kevin's original mass : energy analogy is cool ^_^.
-- Toby
to...@math.ucr.edu
Toby Bartels
>And where does the additional group structure come in - I mean, like the
>additional degree of freedom of electromagnetisms U(1)... When you write
>that the standard model has the symmetry U(1) x SU(2) x SU(3), do you really
>mean that it has that symmetry _and_ poincare symmetry, and you extract all
>the representations you think fit the data ? Really, isn't a representation
>of solely the poincare group meaningless, as you would not be able to
>measure it in any way (you need forces acting through your measuring
>equipment)...
I'd say that a field that uses a rep of the Poincare group only
(or to say it better, that uses the *trivial* rep of the SM group),
is a field of free, noninteracting particles.
We study these in beginning QFT all the time,
but ultimately we recognise that they are unobservable
since, as you say, they participate in no interactions.
If any of these were to exist in real life,
you might think that we'd remain ignorant and never know it
(so Ockham's razor asks us to disbelieve in them).
However, they could be measured *gravitationally*;
I gather that some people supsect (or maybe just have suspected)
that dark matter is of this nature -- interacting only gravitationally.
-- Toby
to...@math.ucr.edu
Toby Bartels
>Now, spin 2 means your wave function doesn't quite come
>back to the original state when you complete one rotation
>(it will be a negative of its original value), but complete
>two rotations.
Actually, this is spin 1/2.
With spin 2, the wavefunction returns to its original value
after a rotation of merely 180 degrees.
In general, let j be the spin and let R be the rotation.
You are back at the original wavefunction iff
jR is an integral multiple of 360 degrees.
If jR is a multiple of 180 degrees but not of 360 degrees,
then the wavefunction has merely changed sign
(and thus represents the same state as before).
In order to guarantee that the state doesn't change
(which is to say that the wavefunction changes at most by a sign)
under a rotation of 360 degrees, j must be a multiple of 1/2.
-- Toby
to...@math.ucr.edu
Demian Cho
> Demian Cho wrote in part:
>
> >Now, spin 2 means your wave function doesn't quite come
> >back to the original state when you complete one rotation
> >(it will be a negative of its original value), but complete
> >two rotations.
>
> Actually, this is spin 1/2.
> With spin 2, the wavefunction returns to its original value
> after a rotation of merely 180 degrees.
Oops!
Thanks Toby.
My stupid mistake!