Spin speed
Ralph E. Frost
the other day how the different theories handle or represent different "spin
speed"?
I was also wondering if this "spin speed" was all (or a major influence)
that separates the different levels of organization into different groups.
Say if one thing spun one-half, or twice or three-twoths faster that some
standard clump; does the spin rate enter into the symmetry-breaking,
conjugations and shape-shifting you folks talk about?
Can anyone shed light in this dark region of my ignorance?
Thank you for your patiences and any help you can provide.
--
Ralph E. Frost
Frost Low Energy Physics
http://www.dcwi.com/~refrost/index.htm Phase II
Imagine you didn't want a student body of several billion people to learn
about math and science. What one science education tool would you withhold?
[Moderator's note: The usual statement in quantum mechanics is that
particles have different, quantized values of spin angular momentum.
This can indeed be used to classify elementary particles. The most
important distinction is that between particles whose angular momentum
is an integer vs. a half-integer multiple of h/2pi. -MM]
Doug Merritt
>
> Given all the various ways that spin turns up in physics, I was wondering
> the other day how the different theories handle or represent different "spin
> Say if one thing spun one-half, or twice or three-twoths faster than [...]
>
> [Moderator's note: The usual statement in quantum mechanics is that
> particles have different, quantized values of spin angular momentum.
> This can indeed be used to classify elementary particles. The most
> important distinction is that between particles whose angular momentum
> is an integer vs. a half-integer multiple of h/2pi. -MM]
Some of the frequently asked questions about particle physics are along the
lines of: "just what *is* this thing that spins? What is its structure? Which
part is the central axis, how wide is it, how fast does its periphery spin?"
Those questions are based on common sense notions of macroscopic physics,
but unfortunately, they don't have good analogues in quantum physics.
For instance, the electron has spin 1/2, but is usually regarded as a
point particle. A point has no structure, and therefore doesn't have
components that one can point to, and say, "this part rotates at radial
speed X".
Therefore the usual answer to such questions is to say things like, "it
doesn't work like that; it's the wrong question to ask, just as much as
it would be infeasible to ask what color an electron is. Simply to ask
about the color shows a misunderstanding of the quantum nature of color."
Answers like that tend to be unsatisfying unless and until the asker gets
indoctrinated deeply into conventional quantum theory; since often that
doesn't happen, the dissatisfaction lingers.
There is, IMHO, a reasonable (but not complete!) answer to the
dissatisfaction: firstly, the electron is treated as a point particle
because no experiment has ever shown evidence of structure, unlike the
proton. In the proton, particle collisions show evidence of substructure,
which is taken as partial supporting evidence that protons are composed
of three quarks. With the electron, collisions behave as though the electron
is just a point (to within experimental error, of course).
So practicing physicists shrug and say, well, it acts like a duck, it
walks like a duck, it quacks like a duck, it must indeed *be* a duck.
(Or rather, a point particle. :-) The fact that other experiments show
very clearly that it has spin 1/2 must mean that somehow a point can
spin; we're not philosophically sure what that means, but oh well, that's
just the way things are.
On the other hand, the existence of point particles does cause serious
problems. If all the mass of the electron is contained in zero volume,
then it has infinite density at that point, and its gravity goes to
infinity at that point. Similarly with the electron's charge; its
electrostatic attraction goes to infinity at that point. These infinities
and divide-by-zero issues make it easy to raise objections, such as:
"shouldn't the electron be a black hole, if it is a singularity???"
There are several ways to resolve such difficulties. One can assume that
electrons are not point particles, but their substructure is too small
to have been resolved by experiment. Or one can propose a renormalization
scheme such that the infinities evaporate as part of the formal mathematical
treatment. Or one can propose a quantum gravity scheme that has the
side effect that apparently-point particles undergo some kind of quantization
such that there are no singularities/infinities.
None of the above approaches (nor other, more exotic approaches) are
completely satisfactory; all such that have been proposed have weaknesses
and/or are incomplete explanations.
So, to date, all anyone can say for sure is:
1) Common sense/Newtonian physics definitely doesn't entirely apply
here, and
2) No one is completely sure exactly what does apply (although there
are incomplete good ideas/partial theories on the subject)
In the above, I focused on what is not known on issues related to spin.
I haven't added to Matt McIrvin's excellent moderator comment about what
*is* known about spin. There's a *lot* that is known, in a pretty definite
sense. Issues of spin are well-understood to form the basis for the
difference between fermions and bosons (e.g. the difference in qualitative
behavior between a photon and an electron), the behavior of lasers,
the demonstration of Bose-Einstein condensates that has been in the news
in recent years, etc.
There's much that is known, and much that is unknown. Your seemingly-simple
questions highlight both.
Doug
--
Professional Wild-Eyed Visionary Member, Crusaders for a Better Tomorrow
Gordon D. Pusch
> On the other hand, the existence of point particles does cause serious
> problems. If all the mass of the electron is contained in zero volume,
> then it has infinite density at that point, and its gravity goes to
> infinity at that point. Similarly with the electron's charge; its
> electrostatic attraction goes to infinity at that point. These infinities
> and divide-by-zero issues make it easy to raise objections, such as:
> "shouldn't the electron be a black hole, if it is a singularity???"
It's a bit trickier than that, since the electron has an ``extended''
component to its stress-energy-momentum density by virtue of its
coulomb field. The appropriate solution would be Reissner-Nordstrom,
not Schwarzschild:
ds^2 = - [1 - 2M/r + Q^2/r^2] dt^2 + [1 - 2M/r + Q^2/r^2]^(-1) dr^2
+ r^2 (d\theta^2 + sin^2(\theta) d\phi),
and IIRC, for all known elementary particles, the Q^2/r^2 coulomb component
overwhelms the 2M/r component, so there is no event-horizon, but rather a
``naked'' singularity...
> There are several ways to resolve such difficulties. One can assume that
> electrons are not point particles, but their substructure is too small
> to have been resolved by experiment. Or one can propose a renormalization
> scheme such that the infinities evaporate as part of the formal mathematical
> treatment. Or one can propose a quantum gravity scheme that has the
> side effect that apparently-point particles undergo some kind of quantization
> such that there are no singularities/infinities.
There is another possible interpretation, advocated by A.O. Barut, David
Hestenes, and others: Spin is related to the Zitterbewegung motion.
The momentum and velocity operators for Dirac particles are not proportional
to each other, and in fact, not even collinear; as a result, the expected
four-velocity is not constant, but precesses about the four-momentum at
a proper angular frequency of 2mc^2/\hbar. It follows that the probability-
current for a Dirac wavepacket has a non-zero vorticity, even when its
expected momentum vanishes. Barut and others advocate interpreting ``spin''
in terms of this vorticity: Crudely speaking, one visualizes the electron
as ``zipping around in a small circle'' with an expected radius on the
order of a compton wavelength, even though its momentum is constant.
(Admittedly, this picture is as hard on one's classical intuition as
most of the other aspects of QM, but it at least provides a picture
consistent with the Dirac equation and relativity, that does not either
have the electron spinning at an undefined velocity, or hand-wavingly
dismiss spin as a ``non-classical two-valuedness with no classical analog.'')
-- Gordon D. Pusch
perl -e '$_ = "gdpusch\@NO.xnet.SPAM.com\n"; s/NO\.//; s/SPAM\.//; print;'
Doug B Sweetser
There are some macro examples of systems with 4pi rotational symmetry,
and that might give a more practical appreciation for half integral
momentum.
A symmetry is just what kind of action, when done, does nothing :-)
We are all familiar with the 2pi rotational symmetry involved in
spinning in a chair. Put a quarter in your palm, and rotate that by
2pi. This time the hand is not back where it started. That requires
a rotation of 4pi to get the quarter back in its initial position.
So what is the difference? I think it has to do with the number of
rotational degrees of freedom, being three in the case of the chair,
only two for the quarter. One could in theory, but not in practice,
rotate around three different axes in the chair example, and after
2pi rotations, return to the starting point. With the quarter in
hand, the shoulder does nothing in the rotation. It is fixed. There
are less degrees of freedom. It is being confined to an even 2
degrees of spatial freedom that leads to the 4pi symmetry.
Since my formal math training is limited, I cannot cite a theorem to
back this idea up (and that also means it could be wrong). The reason
for this insight was due to efforts made to understand infinitesimal
rotations with quaternions and conjugates. For the standard conjugate
that flips the 3-vector, rotations have a 2pi symmetry. For a
different conjugate, where two degrees of spatial freedom flip sign
along with one for time, a rotation defined exactly like 3D rotation
has a 4pi symmetry. That is were I got the idea from. In the
classical quarter example, time is very well separated from space. In
quantum, time will be involved, so the point particle can cover some
ground. This has been discussed in SPR a while back, how spin is a
property of the field, not the point. Although I still do not "get"
half-integral spin, it appears more reasonable now.
doug <swee...@TheWorld.com>
http://quaternions.com
[Moderator's note: The difference is not so much rotational
degrees of freedom as the existence of a connecting path
through the space of rotations (the arm) to an unrotated
anchor point (the shoulder). A path representing a twist
through 2pi cannot be deformed to the identity (an untwisted
arm); a path representing a twist through 4pi can. So the
difference would exist even if your arm were made of rubber.
Precisely how this relates to fermions is another story. -MM]
Urs Schreiber
> There is another possible interpretation, advocated by A.O. Barut, David
> Hestenes, and others: Spin is related to the Zitterbewegung motion.
>
> The momentum and velocity operators for Dirac particles are not proportional
> to each other, and in fact, not even collinear; as a result, the expected
> four-velocity is not constant, but precesses about the four-momentum at
> a proper angular frequency of 2mc^2/\hbar. It follows that the probability-
> current for a Dirac wavepacket has a non-zero vorticity, even when its
> expected momentum vanishes. Barut and others advocate interpreting ``spin''
> in terms of this vorticity: Crudely speaking, one visualizes the electron
> as ``zipping around in a small circle'' with an expected radius on the
> order of a compton wavelength, even though its momentum is constant.
> (Admittedly, this picture is as hard on one's classical intuition as
> most of the other aspects of QM, but it at least provides a picture
> consistent with the Dirac equation and relativity, that does not either
> have the electron spinning at an undefined velocity, or hand-wavingly
> dismiss spin as a ``non-classical two-valuedness with no classical analog.'')
Can the spin of (massless) Bosons be interpreted similarily?
--
eMail: Urs.Sc...@uni-essen.de
Doug B Sweetser
Anytime one hears the phrase "even if your ... were made of rubber",
you know they are talking about topology :-) I don't have a quarrel
with your topological explanation involving flexible connecting paths
(it is a standard story and very solid). I am more concerned whether
thinking about general degrees of rotational freedom is also correct.
I deal best with very concrete examples, so let's stick with the
quarter-in-hand example. In the way described, the hand stays face up
the entire time. One could imagine an axis going through the quarter,
so the 4pi rotation is through one and only one axis.
This is not the only way to do this transformation. Do the 2pi
rotation. Now quickly flip the wrist around so that the quarter was
free to fall for a brief moment. This rotation is also 2pi, but it is
around another axes. This combination of 2x2pi rotations brings the
coin back to its initial state.
The order that this is done does not matter. That indicates the two
rotations are in a sense independent of each other. I have spent a
bit of time with an imaginary quarter trying to find a third axis, but
I cannot seem to find one, even if my arms where made of rubber.
It is my belief that the topological explanation of the 4pi rotational
symmetry of the coin in hand is correct, as well as saying that the
system is effectively constrained to 2 rotational degrees of freedom.
Jim Carr
>
>With the electron, collisions behave as though the electron
>is just a point (to within experimental error, of course).
An uncertainty that says it is very tiny (small enough that
its rotational speed would cause a problem if "spin" was
due to what we think of from macroscopic physics) if it is
not actually a point particle.
>So practicing physicists shrug and say, well, it acts like a duck, it
>walks like a duck, it quacks like a duck, it must indeed *be* a duck.
>(Or rather, a point particle. :-) The fact that other experiments show
>very clearly that it has spin 1/2 must mean that somehow a point can
>spin; ...
I would say "somehow a point can have angular momentum", since
we know it has angular momentum but we don't know if it spins.
> ... we're not philosophically sure what that means, but oh well, that's
>just the way things are.
The more precise statement leaves open the alternative that we
don't know what it means to have angular momentum rather than
just that we don't know what it means for a point mass to spin.
<... snip discussion of renormalization ...>
--
James Carr <j...@scri.fsu.edu> http://www.scri.fsu.edu/~jac/
Dopeler Effect: The tendency of stupid ideas to seem smarter when they
come at you rapidly. (anon source via e-chain-letter)