What is Spin?
David Kalfus
When I studied quantum mechanics as an undergraduate it
seems to me that the spin of the electron was considered to
be angular momentum in the same sense that spin in the macro
world is. But I also recall that some readings I've done
in popular explications of quantum theory have made the electron-spin
to be something more mysterious than that; recently I leafed
through a book (can't remember the title) that said flat out
that "spin" as applied to electrons was *not* in any way
related to spin as we understand it. In the glossary of the
same book it defined spin simply as "a quantized characteristic
that a particle can have". So... here are some questions that
neither I nor my classmates asked in school because we were
too busy studying...
1. What is "spin" on the particle level?
2. If it is the same as macro-world spin, then
why is it constrained to be h/4pi? There
are no geometric constraints such as apply to
orbital quantization (n).
Concerning orbital angular momentum:
3. What is the relationship between spin angular momentum
and orbital angular momentum on the partical level?
Wouldn't orbital angular momentum be directly related
to the primary quantum number n? If an electron is
raised to a higher angular momentum quantum number,
with n remaining the same, what has changed geometrically?
Is it the case that *nothing* changes "geometrically",
but that the electron somehow has an "attribute" of greater
orbital angular momentum>
J. J. Lodder
(David Kalfus) wrote:
> In article <DH83x...@murdoch.acc.Virginia.EDU>,
da...@fermi.clas.Virginia.EDU (Douglas A. Singleton) writes:
>
> >
> > If your familiar with Dirac's equation for the electron then
> > look up an article by H. Ohanian in the American Journal of
> > Physics Vol. 54 (or maybe 55) page 500 (1986). This shows
> > how the spin of the electron is not so completely divorced
> > from the "classical" concept of angular momentum as some
> > intro QM books would have you believe. This idea -- that
> > spin is a completely quantum mechanical property that
> > should not be thought of in classical terms at all -- goes
> > too far as IOhanian argues in the article (he also names
> > the names of the people who started this silly idea :-)).
> > If you can't track down the article I'll try to summarize it
> > in a few days if your still interested.
Spin is *really* angular momentum, measureble classically if you have many
spins. Flipping the spins in a ferromagnet causes a measurable macroscopic
torque on the sample. This is the Einstein de Haas effect.
Jan
Jaroslaw Chojnacki 23-59
> Spin is *really* angular momentum, measureble classically if you have many
> spins. Flipping the spins in a ferromagnet causes a measurable macroscopic
> torque on the sample. This is the Einstein de Haas effect.
>
> Jan
One more thing. It is OK when you regard electrons. Why a photon has
spin=1? It has no mass. Are there 3 Sz values? Will a beam of photons
split into 3 beams in magnetic field, as electrons with S=1/2 do (into 2
beams)? What about spin conservation in ligth absorption by atom? I see I
have a lot to learn. My intuition says nothing about that. If you could
refere me to experiments showing spin of a photon I would appreciate it
very much.
JCh
suz...@fnala.fnal.gov
<Pine.SOL.3.91.951103103722.7466A-100000-100000-100000-100000@altis>, Jaroslaw
>On Tue, 31 Oct 1995, J. J. Lodder wrote:
>
>> Spin is *really* angular momentum, measureble classically if you have many
>> spins. Flipping the spins in a ferromagnet causes a measurable macroscopic
>> torque on the sample. This is the Einstein de Haas effect.
>>
>> Jan
>
>One more thing. It is OK when you regard electrons. Why a photon has
>spin=1? It has no mass.
"Why" is always an awkward question to ask in physics. The photon is observed
to have spin 1. Massless particles are perfectly capable of having spin.
>Are there 3 Sz values?
Actually, no; because photons are massless, there are only two (+1 and -1).
Massive spin-1 particles will have 3.
>Will a beam of photons
>split into 3 beams in magnetic field, as electrons with S=1/2 do (into 2
>beams)?
No, because they are electrically neutral.
>What about spin conservation in ligth absorption by atom?
Well, it is conserved. I find it easier to discuss light emission - if you are
familiar with the nuclear physics terminology, you know that there
are electric and magnetic transitions, of various "poles" - E1, M2, and so
forth. These can be understood in terms of the conservation of angular
momentum - the more units of relative orbital angular momentum required
between the daughter atom and the emitted photon, the slower the
transition is. (The standard nuclear physics discussion doesn't include this,
though).
>I see I
>have a lot to learn. My intuition says nothing about that. If you could
>refere me to experiments showing spin of a photon I would appreciate it
>very much.
>
>JCh
>
Any particle physics text should be able to help you.
Sue Willis
J. J. Lodder
> In article
> <Pine.SOL.3.91.951103103722.7466A-100000-100000-100000-100000@altis>,
Jaroslaw
> Chojnacki 23-59 <jarekch@altis> writes:
> >On Tue, 31 Oct 1995, J. J. Lodder wrote:
> >
> >> Spin is *really* angular momentum, measureble classically if you have many
> >> spins. Flipping the spins in a ferromagnet causes a measurable macroscopic
> >> torque on the sample. This is the Einstein de Haas effect.
> >>
> >> Jan
> >
> >One more thing. It is OK when you regard electrons. Why a photon has
> >spin=1? It has no mass.
>
>
> >What about spin conservation in ligth absorption by atom?
Same story here, you can make a chunk of matter rotate by letting it
absorb a circularly polarized light beam.
Jan
Douglas A. Singleton
>In article
><Pine.SOL.3.91.951103103722.7466A-100000-100000-100000-100000@altis>, Jaroslaw
>Chojnacki 23-59 <jarekch@altis> writes:
>>On Tue, 31 Oct 1995, J. J. Lodder wrote:
>>
>>> Spin is *really* angular momentum, measureble classically if you have many
>>> spins. Flipping the spins in a ferromagnet causes a measurable macroscopic
>>> torque on the sample. This is the Einstein de Haas effect.
>>>
>>> Jan
>>
>>One more thing. It is OK when you regard electrons. Why a photon has
>>spin=1? It has no mass.
About a week ago I said that Ohanian had a nice article in AJP
(pg. 500 (1986) I think)) that gave a physical interpretation of
the spin of the electron. Well let me sketch the arguement which
also applies to the photon.
First if you take the electron as a charged sphere and let it's
radius be something like the classical electron radius one finds
that in order to get the observed magnetic moment this sphere
would have to be rotating such that points on its surface would
be going faster than light speed. This failure of the classical
piture of the electron as a charged ball elicites the pat
answer "Well electron spin is an entirely QM thing. Don't think
of it classically at all."
However both the electron and photon are described by wave
equations (the Dirac equation and Maxwell's equations). Now
in some sense (especially for the photon) one could regard
these as "classical" wave equations (i.e. one still needs
to quantize the fields of these equations to get to the
quantum theory). Anyway in classical field theory there is
a standard procedure for calculating the angular momentum
carried by a certain wave. First from the Lagrangian that
gives you the wave equations you calculate the momentum
density of the wave; the T^{0i} part of the energy-momentum
tensor. For E&M this is just the Poynting vector E x B.
Then once you have the momentum density, T^{0i}, of the wave
you then can get the angular momentum density,
L^i = e^{ijk} T_{0j} X_k. From this one can integrate over all
space to get the angular momentum carried by the wave. Ohanian
shows that for a photon you get +1 - 1, while for the electron,
which obeys the Dirac eqaution one get +1/2 , -1/2. He also
derives the g=2 factor from these semi-classical arguments.
The physical picure then is a wave that rotates in a plane
perpendicular to its direction of motion. It's impossible to
put the details of the math (especially for the Dirac eqn.)
in ascii so I still recommend the Ohanian article, or it's
actually not too hard a problem to do if you are comfortable
with the Dirac equation and the stuff in chapter 12 of Jackson.
Doug
.
Matthew P Wiener
>About a week ago I said that Ohanian had a nice article in AJP
>(pg. 500 (1986) I think)) that gave a physical interpretation of
>the spin of the electron. Well let me sketch the arguement which
>also applies to the photon.
>First if you take the electron as a charged sphere and let it's
>radius be something like the classical electron radius one finds
>that in order to get the observed magnetic moment this sphere
>would have to be rotating such that points on its surface would
>be going faster than light speed. This failure of the classical
>piture of the electron as a charged ball elicites the pat
>answer "Well electron spin is an entirely QM thing. Don't think
>of it classically at all."
That's the not the usual argument spin being a classical failure.
Classically, all angular momentum is orbital angular momentum: it can
be explained as L = r x p. For example, you can analyze a top or yoyo
trick with the angular momentum broken down into an orbital component
for the motion of the top or yoyo as a whole, and an intrinsic component
for the object itself, around its own axis. One can do a more refined
analysis, showing that this intrinsic angular momentum is really the
orbital angular momentum of the object's atoms about the object's axis.
In the case of electrons, this refined analysis provably does not exist.
At least not according to the standard reading: if one quantizes r x p,
one gets 1-fold, 3-fold, 5-fold, etc degeneracies in the solutions,
corresponding to 0,+/-,+/-2,... units of h-bar. But if one looks at
the relevant L_x L_y L_z operators only, ignoring where they come from,
one can also solve for 2-fold, 4-fold, etc degeneracies. And these
correspond to +/-.5,+/-1.5,... units of h-bar.
Mathematicians call this the representation theory of SO(3) [rotations
in ordinary 3-space] and SU(2) [rotations in complex 2-space]. The
latter is a double cover of the former.
>However both the electron and photon are described by wave equations
>(the Dirac equation and Maxwell's equations). Now in some sense
>(especially for the photon) one could regard these as "classical"
>wave equations (i.e. one still needs to quantize the fields of these
>equations to get to the quantum theory).
As you said, *especially* for the photon. The Dirac equation has h in
it already.
> Anyway in classical field
>theory there is a standard procedure for calculating the angular
>momentum carried by a certain wave. First from the Lagrangian that
>gives you the wave equations you calculate the momentum density of
>the wave; the T^{0i} part of the energy-momentum tensor. For E&M
>this is just the Poynting vector E x B. Then once you have the
>momentum density, T^{0i}, of the wave you then can get the angular
>momentum density, L^i = e^{ijk} T_{0j} X_k. From this one can
>integrate over all space to get the angular momentum carried by the
>wave. Ohanian shows that for a photon you get +1 - 1,
Where does h come in? I take it he is quantizing the EM field to
define photons.
> while for the
>electron, which obeys the Dirac equation one get +1/2 , -1/2.
So the "loophole" in the standard reading is gullibly assuming that
the electron's guts have to be vectorial--describable in x,y,z terms.
Assuming they might be spinorial--describable in complex 2-space--you
can indeed reduce the electron's spin to an "orbital" angular momentum
kind of calculation.
Neat.
> He also
>derives the g=2 factor from these semi-classical arguments.
Well, this isn't too surprising. He's working with the Dirac equation.
--
-Matthew P Wiener (wee...@sagi.wistar.upenn.edu)
Matthew P Wiener
>It's just that some of the people who first worked on spin were too
>impressed by its "weirdness" and simply claimed that one shouldn't
>think of spin in classical terms at all.
They were precise about this: it does not have a classical orbital
explanation.
> While there's is something
>to this point of view, it goes too far as Ohanian's explicit
>calculation shows.
Not in the least.
> The reason that this article by Ohanian really
>made an impression on me is that it makes you realize that there are
>many statements of "conventional" wisdom in physics which just aren't
>backed up by anything except assertion by the experts. (OK well maybe
>-many- is a bit of a stretch).
Then I gather you didn't understand the Ohanian article. Based on
what was posted, it was clear that Ohanian was _assuming_ the Dirac
equation, which includes "h" in it. A priori, this is non-classical.
Moreover, why should you assume the electron is a _field_ even, that
one later quantizes? That too is completely non-classical. And then,
the orbital explanation Ohanian finds is spinorial, something that no
one ever bothered to do in a classical situation.
All in all, I go with the experts on this one.
ale2
wee...@sagi.wistar.upenn.edu (Matthew P Wiener) writes:
.....
>
> All in all, I go with the experts on this one.
> --
> -Matthew P Wiener (wee...@sagi.wistar.upenn.edu)
Ohanian has (IMO) the best book to learn GR( Gravitation and
Spacetime). His article on spin is a must for those who are quantum
mechanics.
J. J. Lodder
(Matthew P Wiener) wrote:
> In article <DHL5B...@murdoch.acc.Virginia.EDU>, das3y@fermi (Douglas
A. Singleton) writes:
> >About a week ago I said that Ohanian had a nice article in AJP
> >(pg. 500 (1986) I think)) that gave a physical interpretation of
> >the spin of the electron. Well let me sketch the arguement which
> >also applies to the photon.
>
> >First if you take the electron as a charged sphere and let it's
> >radius be something like the classical electron radius one finds
> >that in order to get the observed magnetic moment this sphere
> >would have to be rotating such that points on its surface would
> >be going faster than light speed. This failure of the classical
> >piture of the electron as a charged ball elicites the pat
> >answer "Well electron spin is an entirely QM thing. Don't think
> >of it classically at all."
>
> That's the not the usual argument spin being a classical failure.
snip
But it is THE classical argument. Before their paper was submitted
Goudsmit and Uhlenbeck went to visit Lorentz, who presented them with this
argument.
Crushed they went back to Leyden and asked Ehrenfest not to submit the
paper for them.
Ehrenfest however told them he had sent it off already, cheering them up with:
Dont worry boys, you are still young, you can afford a stupidity.
So spin came to be on their name.
Jan
Dr. Herbert Gollisch
there is a difference between spin and classical angular momentum which
can directly seen by the associated quantum numbers:
if an electron wave function has angular momentum l=1 , then you see
the same function if you rotate it by 360 degr. , in the case of l=2
you have only to rotate by pi=180 , for l=3 by 120 and so on. Spin=1/2
means you would "see" the same electron after 2 full classical rotations
that is 720 degree.
bye, HG
Matthew P Wiener
>In article <47luih$2...@netnews.upenn.edu>, wee...@sagi.wistar.upenn.edu
>(Matthew P Wiener) wrote:
>>>[Lorenz's classical objection to Goudsmit-Uhlenbeck spin]
>> That's the not the usual argument for spin being a classical failure.
>But it is THE classical argument. [...]
Correct. But that only means that something was wrong with the obvious
way of putting the pieces together. For example, Rutherford went through
a variety of conjectured nuclear models before concluding that there was
a strong nuclear force. G&U did nothing comparable.
The proof that electron spin is something not explainable classically is
the fact that quantized orbital angular momentum is always integral
multiples of h-bar. I mean, did you ever wonder why the unit of angular
momentum was set at h/2pi and not h/4pi? It was because Bohr only knew
of orbital angular momentum.
J. J. Lodder
That is not quantum, anchored classical objects like telephones behave in
this way too.
Jan
Andre Ratel
>In article <47dpcg$m...@fnnews.fnal.gov>, suz...@FNALA.FNAL.GOV wrote:
>> In article
>> <Pine.SOL.3.91.951103103722.7466A-100000-100000-100000-100000@altis>,
>Jaroslaw
>> Chojnacki 23-59 <jarekch@altis> writes:
>> >On Tue, 31 Oct 1995, J. J. Lodder wrote:
>> >
>> >> Spin is *really* angular momentum, measureble classically if you have many
>> >> spins. Flipping the spins in a ferromagnet causes a measurable macroscopic
>> >> torque on the sample. This is the Einstein de Haas effect.
>> >>
>> >> Jan
>> >
>> >One more thing. It is OK when you regard electrons. Why a photon has
>> >spin=1? It has no mass.
>>
>>
>> >What about spin conservation in ligth absorption by atom?
>Same story here, you can make a chunk of matter rotate by letting it
>absorb a circularly polarized light beam.
>Jan
Hello,
On the question of spin, I would like to suggest section 12.3 of
Hans C. Ohanian
Classical Electrodynamics
(Allyn and Bacon, 1988)
526 pages
ISBN 0-205-10528-9
ISBN 0-205-11303-6 (international)
level: advanced undergraduate
and the article
Hans C. Ohanian
"What is Spin?"
Am. J. Phys. 54 (6), June 1986
pp 500-505
level: graduate
I would also like to point out that, although it is often said
that the photon is a "zero mass particle", its mass is _not_
zero.
The genuine mass of an object is the so-called *relativistic
mass*. This is the one which is always conserved in any reaction
involving many particles. It is given by
m^2 c^4 = m0^2 c^4 + p^2 c^2 (1)
with
m: the relativistic mass
c: the velocity of light in vacuum
m0: the rest mass
p: the momentum
For a photon, the _rest mass_ is zero
m0 = 0 (2)
and Eq. (1) yields
m = p/c (3)
(assuming m non-negative).
The photon has all the characteristics of a mass
- it has energy (and energy is equivalent to mass,
E = m c^2)
- it has momentum (and a stream of photons can excert
pressure on a surface)
- it can have angular momentum.
We have to keep in mind that rest mass is a quantity measured
in the special frame moving with the particle. In a reaction
involving many particles, total rest mass is rarely conserved.
Hoping to having been of some help,
Andre
-------------------------------------------------------------------
Andre Ratel, M. Sc. | Corollary to Fermat's principle:
-----------= Mad Scientist | A good set of approximations is the
since 1976 =---| shortest path between two totally
ara...@infobahnos.com | unrelated equations. [AR-92]
-------------------------------------------------------------------
J. J. Lodder
I disagree completely here. Relativistic mass is nothing but energy
measured in inconvenient units. Mass should be used for rest mass only,
energy should be used instead of relativistic mass.
The concept of relativistic mass should be forgotten, it causes nothing
but confusion.
This way the photon IS a zero mass particle, to every observer.
Jan
Clint Brome
>Jan
I heard that analogy at a lecture this summer, and was confused.
As many times as I go over it, it doesn't seem to make sense. If I revolve
clockwise with the telephone by 360 degrees, it's not in the original state,
but if I go 360 more degrees clockwise, it still isn't back in the original
state -- it's even more tangled up!
Am I missing something simple about the analogy?
Clint
Greg Trayling
> I heard that analogy at a lecture this summer, and was confused.
>As many times as I go over it, it doesn't seem to make sense. If I revolve
>clockwise with the telephone by 360 degrees, it's not in the original state,
>but if I go 360 more degrees clockwise, it still isn't back in the original
>state -- it's even more tangled up!
>
construction. It's going to be hard in words, but here goes; Take some kind
of 2-d frame like a circle made out of a clothes wire, then put a 2-d object
like a cardboard disk in the center and attach it to the frame via at least
three loose threads or rubber bands. (there are more elaborate gizmos using
cubes n' stuff, but this is the minimum you can get away with) Now the frame
and the disk are supposed to represent some reference frame and an object in
it, embedded topologically by the three strings (once you get the idea from
fiddling with it, you make the generalization to a continuum of strings.)
Now rotate the disk wrt the frame by 2Pi and you'll find that the strings
are topologically knotted and can't be returned to the original starting
position. But here's the clincher; rotate a further 2Pi in the same direction
(you may want to return to the original position and flip by 4Pi you know
you're not just reversing it) and then if you play with the strings, looping
n' tricks like that, you'll find that the 4Pi rotation *is* topologically
equivalent to the original position. Viola.
--
Greg Trayling Tra...@server.uwindsor.ca Ahh-ha-ha-ha-ha
http://www.cs.uwindsor.ca/meta-index/people/traylin (Mozart)
\\\ The views expressed here do not necessarily ///
\\\ represent my views at any time in the future. ///
Douglas A. Singleton
Matthew P Wiener <wee...@sagi.wistar.upenn.edu> wrote:
>In article <DHMuu...@murdoch.acc.Virginia.EDU>, das3y@fermi (Douglas A. Singleton) writes:
>>It's just that some of the people who first worked on spin were too
>>impressed by its "weirdness" and simply claimed that one shouldn't
>>think of spin in classical terms at all.
>
>They were precise about this: it does not have a classical orbital
>explanation.
OK maybe I over emphasized a bit, but Ohanian does spend the first
2 or 3 pages of the article talking about the history of spin, and
from my reading of the article he does appear somewhat critical
of Pauli and company for their "philosophical" formulation of spin.
Are you saying that in your reading of the article you found
that Ohanian was not in the least critical of the original physical
interpretation of spin ? What about on the second page where he says
something like "Pauli pontificated ..", and then gives the famous
statement that spin is a "quantum mechanical two-valuedness which
must not be thought of in classical terms". Again maybe I'm just
reading more into than is there, but certainly saying "Pauli
pontificated" doesn't sound too friendly.
>> While there's is something
>>to this point of view, it goes too far as Ohanian's explicit
>>calculation shows.
>
>Not in the least.
Why ?
>> The reason that this article by Ohanian really
>>made an impression on me is that it makes you realize that there are
>>many statements of "conventional" wisdom in physics which just aren't
>>backed up by anything except assertion by the experts. (OK well maybe
>>-many- is a bit of a stretch).
>
>Then I gather you didn't understand the Ohanian article. Based on
>what was posted, it was clear that Ohanian was _assuming_ the Dirac
>equation, which includes "h" in it. A priori, this is non-classical.
>Moreover, why should you assume the electron is a _field_ even, that
>one later quantizes? That too is completely non-classical. And then,
>the orbital explanation Ohanian finds is spinorial, something that no
>one ever bothered to do in a classical situation.
Well I thought I understood the article and I still do believe so, but
I'd be willing to change my mind. Seriously though, from your above
statement it seems like you maybe didn't read the article (you say
"based on what was posted"). Your first question about "h" makes
a good point and I'll think about it somemore, but one can consider
a classical spinor field. Check out page 580 of Goldstein; no h
in the classical Dirac field that he's using. The second question
"why does the electron have to be a field" is easier. The single
particle interpretation of the Dirac equation runs into trouble
in certain situations. For example there's the Klein paradox which
occurs when an electron runs into a very high barrier. Taking
the elctron as a field takes care of the Klein paradox (the
Klein paradox and why the electron must be treated as a field are
explained in section 3-7 of Sakuraii's advanced QM book). Finally,
sure the explanation Ohanain gets is spinorial, but that's the whole
point. He also does the same thing for the photon spin, which
might be a better case to talk about since here there is a classical
limit. Starting with the classical Maxwell Lagrangain he gets
the angular momentum in the E and B fields (the Poynting vector
~ E X B). The quantum nature only comes in at the very end when
he assumes that the energy of the photon field must be quantized
in units of hbar * omega. Same type of argument works for the
Dirac field equations. At some point you do have to make some
quantization postulate in order to introduce hbar, but the point
is that the angular momentum carried by the fields isn't completely
divorced from the classical notion of angular momentum.
>All in all, I go with the experts on this one.
Ohanian is careful to say that his argument is only a different
more physical look at spin, not some new theory.
>-Matthew P Wiener (wee...@sagi.wistar.upenn.edu)
Doug
Jean-Francois Berube
precise 2s2. By comparing a formula that calculate the amount of
energy of ionization that contain the element of the periodical
table, I find out that the error percentage was too much above normal
for the iron (about 1000 times bigger!!!).
By talking to one of my teacher, I realize that it was the third spin
that was the problem. But my question is why does a problem can coexist
with all the electron so that the atom stays together??
If someone can help me, have information about the problem of the
atom, please E-mail me at go...@odyssee.net.
Jean-Francois Berube
Matthew P Wiener
>In article <47og8a$b...@netnews.upenn.edu>,
>Matthew P Wiener <wee...@sagi.wistar.upenn.edu> wrote:
>>In article <DHMuu...@murdoch.acc.Virginia.EDU>, das3y@fermi (Douglas A. Singleton) writes:
>>>It's just that some of the people who first worked on spin were too
>>>impressed by its "weirdness" and simply claimed that one shouldn't
>>>think of spin in classical terms at all.
>>They were precise about this: it does not have a classical orbital
>>explanation.
>OK maybe I over emphasized a bit, but Ohanian does spend the first
>2 or 3 pages of the article talking about the history of spin, and
>from my reading of the article he does appear somewhat critical
>of Pauli and company for their "philosophical" formulation of spin.
When they were doing the actual physics, they were precise about what
the difference was.
>Are you saying that in your reading of the article you found
>that Ohanian was not in the least critical of the original physical
>interpretation of spin ? What about on the second page where he says
>something like "Pauli pontificated ..", and then gives the famous
>statement that spin is a "quantum mechanical two-valuedness which
>must not be thought of in classical terms".
When they were engaged in propaganda and philosophy, they could overdo
it. "Must" is obviously a matter of choice. I myself would simply
point out that doing so is normally "pointless", "misleading", "useless".
Remember, we're talking about the generation that invented quantum
mechanics. They had to isolate what was new and was not. Spin is
most definitely new.
> Again maybe I'm just
>reading more into than is there, but certainly saying "Pauli
>pontificated" doesn't sound too friendly.
Well no, but I'm not sure why you're telling us this.
>>> While there's is something
>>>to this point of view, it goes too far as Ohanian's explicit
>>>calculation shows.
>>Not in the least.
>Why ?
As I explained: Ohanian's explanation includes a heavy dose of quantum
mechanics in it already. What he has done is revived Belifante's
explanation of spin as _orbital_ angular momentum in a second quantized
world, and shown that it also works with photons.
>>Then I gather you didn't understand the Ohanian article. Based on
>>what was posted, it was clear that Ohanian was _assuming_ the Dirac
>>equation, which includes "h" in it. A priori, this is non-classical.
>>Moreover, why should you assume the electron is a _field_ even, that
>>one later quantizes? That too is completely non-classical. And then,
>>the orbital explanation Ohanian finds is spinorial, something that no
>>one ever bothered to do in a classical situation.
>Well I thought I understood the article and I still do believe so, but
>I'd be willing to change my mind. Seriously though, from your above
>statement it seems like you maybe didn't read the article (you say
>"based on what was posted").
I've looked at it since. Your summary of the physics itself was fine.
I don't think Ohanian made claims as strongly as you did.
> Your first question about "h" makes
>a good point and I'll think about it somemore, but one can consider
>a classical spinor field. Check out page 580 of Goldstein; no h
>in the classical Dirac field that he's using.
And what angular momentum does he get?
> The second question
>"why does the electron have to be a field" is easier. The single
>particle interpretation of the Dirac equation runs into trouble
>in certain situations. For example there's the Klein paradox which
>occurs when an electron runs into a very high barrier. Taking
>the elctron as a field takes care of the Klein paradox (the
>Klein paradox and why the electron must be treated as a field are
>explained in section 3-7 of Sakuraii's advanced QM book).
Yes, yes, I totally advocate doing this. I simply meant that doing so
is highly non-classical. The classical electron was a particle, right?
Of course, this may well be a historical accident. During the years
when cathode and beta rays were first analyzed, perhaps someone could
have done the Davisson-Germer experiment, someone else develop a Dirac
field theory for it, and then somebody else amazes everyone with the
particle interpretation.
That's not as far-fetched as you might think. Complex numbers had
their uses--why not spinors? Although the Dirac equation is usually
presented as the square root of the Klein-Gordon equation, Dirac
actually found it in trying to generalize (sig.v)^2= |v|^2.I--for sig
the Pauli spin matrices, v=(x,y,z) a 3-vector, and I the 2x2 identity
--to a 4-vector (t,x,y,z).
OK, so I'm willing to grant that "electrons are particles" is not hard
wired in the classical mode.
(One can take a different message from the Klein paradox, by the way:
it is simply not possible to trap energetic electrons.)
>Finally, sure the explanation Ohanain gets is spinorial, but that's
>the whole point. He also does the same thing for the photon spin,
>which might be a better case to talk about since here there is a
>classical limit.
That is my point: in the classical case, one gets integral spin.
> Starting with the classical Maxwell Lagrangain he
>gets the angular momentum in the E and B fields (the Poynting vector
>~ E X B). The quantum nature only comes in at the very end when he
>assumes that the energy of the photon field must be quantized in
>units of hbar * omega. Same type of argument works for the Dirac
>field equations. At some point you do have to make some quantization
>postulate in order to introduce hbar, but the point is that the
>angular momentum carried by the fields isn't completely divorced from
>the classical notion of angular momentum.
That much is true. As I said in my previous posting, I am impressed
at the feat of recovering electron spin as an orbital angular momentum,
by stretching our notion of what sort of stuff gets spun around.
>>All in all, I go with the experts on this one.
>Ohanian is careful to say that his argument is only a different more
>physical look at spin, not some new theory.
That was clear. And if someone finds a way to dynamically explain
higher SU(n) symmetries, that would be way cool. It just won't be
classical.
J. J. Lodder
> j...@knoware.nl (J. J. Lodder) writes:
>
> >In article <47qbol$3...@h20-hrze.uni-duisburg.de>,
> >h...@dagobert.uni-duisburg.de (Dr. Herbert Gollisch) wrote:
>
> >> Hallo,
> >> there is a difference between spin and classical angular momentum which
> >> can directly seen by the associated quantum numbers:
> >> if an electron wave function has angular momentum l=1 , then you see
> >> the same function if you rotate it by 360 degr. , in the case of l=2
> >> you have only to rotate by pi=180 , for l=3 by 120 and so on. Spin=1/2
> >> means you would "see" the same electron after 2 full classical rotations
> >> that is 720 degree.
> >> bye, HG
>
> >That is not quantum, anchored classical objects like telephones behave in
> >this way too.
>
> >Jan
>
>
> I heard that analogy at a lecture this summer, and was confused.
> As many times as I go over it, it doesn't seem to make sense. If I revolve
> clockwise with the telephone by 360 degrees, it's not in the original state,
> but if I go 360 more degrees clockwise, it still isn't back in the original
> state -- it's even more tangled up!
>
> Am I missing something simple about the analogy?
>
> Clint
Yes:
DIY mathematical experiment: rotation of an anchored object
Find a modern phone attached to the wall with a flat cable,
so you can easily see the twist.
Strech it and untwist, you may have to hold the phone upside down.
Use tape or find another, if too inconvenient.
Now we rotate in a deliberately awkward manner to make clear what happens.
Hold the phone in your right hand,
take hold of the cable 25 cm away from the phone.
Now rotate the phone in a full 50 cm circle around your left hand.
Find a helper if necessary. (For US citizens a foot will do also)
Phone is now back where it was, phone plus cable is not,
there is a twist that cannot be removed without rotating the phone.
Repeat the rotation, but wait, you have to pass the phone either over,
or under its cable when describing the circle.
The awkward way of moving the phone makes this obvious.
Make the other choice the second time.
And now surprise:
the cable is untwisted after a 4\pi rotation, once over, once under.
You can also rotate twice over or twice under,
and untwist by looping the cable back over the phone.
So anchored macroscopic objects behave as spin under rotations,
SU(2) instead of SO(3).
It is not clear if this is merely an
analogy, or that it will ultimately have a deep meaning.
Wait for the final theory of everything,
and enjoy yourself in the meantime,
Jan
Dr. Herbert Gollisch
: > >That is not quantum, anchored classical objects like telephones behave in
: Yes:
: Jan
Hi,
these macroscopic models are interesting enough for discussion with my
students. However, now tell me how to anchor an electron?
It is a - relatively - free particle. Otherwise you could not
read these words.
Another important point which is directly connected to spin, and
for which I know no macroscopic analogy, is Pauli's exclusion
principle. There is no classical law that would
explain this behaviour of spin-1/2 particles. On the other hand,
it is crucial for the forming of atoms, molecules and hence the
world as we know it.
so long, HG
Douglas A. Singleton
Greg Trayling <tra...@server.uwindsor.ca> wrote:
>br...@axnd02.cern.ch (Clint Brome) wrote:
>> I heard that analogy at a lecture this summer, and was confused.
>>As many times as I go over it, it doesn't seem to make sense. If I revolve
>>clockwise with the telephone by 360 degrees, it's not in the original state,
>>but if I go 360 more degrees clockwise, it still isn't back in the original
>>state -- it's even more tangled up!
>>
[good description of topological twisting toy deleted]
It's hard to describe this device in words. I only got the idea
right after seeing an explicit picture which can be found in the
beginning of Chapter 4 or 5 of Kerson Huang's quantum field theory
book.
Doug
.
J. J. Lodder
Chojnacki 23-59 <jarekch@altis> wrote:
> Hi all!
>
> In this newsgroup somebody say:
> > >> if an electron wave function has angular momentum l=1 , then you see
> > >> the same function if you rotate it by 360 degr. , in the case of l=2
> > >> you have only to rotate by pi=180 , for l=3 by 120 and so on. Spin=1/2
> > >> means you would "see" the same electron after 2 full classical rotations
> > >> that is 720 degree.
> >
> > >That is not quantum, anchored classical objects like telephones
> > >behave in this way too.
>
> As someone else pointed I cannot imagine telephon returning to its
> starting position when rotated by 720 degree. If I understand it well it
It is the phone plus cable. After 360 degrees the phone is back where it
was, the cable is not. It has a twist. After 720 phone and cable can be
brought exactly to their starting position.
> is possible only when we rotate more than 3 dimensional object, and e.g.
> the 4-th coordinate x4 flips to minus x4 after 360 degrees and returns to
> x4 after another 360 degree rotation. So electron after 360 degree
> rotation will have its spin in opposite direction.
No, only the wave function has changed sign. The spin is back in its
original direction.
All this can be verified exp: Neutron interferometry, magnetic field in
one arm, rotating the spin in one arm through 360 degrees changes
interference pattern, back after 720 degrees!.
Relative phases of vawe functions can be measured, at least in principle,
and here also in practice.
> I do not see classical objects of this property. Or we are not able to
> recognize this hidden dimension in more complex objects?
>
> It is just my understanding of the question. Please correct any
> shortcomings.
>
> Jaroslaw Chojnacki
> e-mail:jar...@altis.chem.pg.gda.pl
Johan Wevers
>I disagree completely here. Relativistic mass is nothing but energy
>measured in inconvenient units.
Yes, but it is a conserved quantity in many-particle reactions.
>Mass should be used for rest mass only,
>energy should be used instead of relativistic mass.
Why? This is only a matter of convention. And not a very clear one for
starters, read the articles in the magazine of the Dutch Physical society
(nr. 16 and a reply in 17) which try to clear this matter out. (I recommend
this because I see you have an .nl adress).
>The concept of relativistic mass should be forgotten, it causes nothing
>but confusion.
I don't agree. In fact, I find the hidden assumption that mass == rest mass
confusing. If you talk about mass in a context where this matters you'd
better specify the type of mass.
>This way the photon IS a zero mass particle, to every observer.
The photon is always a zero rest-mass particle. It changes nothing if you
call the quantity E/c^2 total or relativistic mass, it's rest mass is
still 0.
--
ir. J.C.A. Wevers || The only nature of reality is physics.
joh...@vulcan.xs4all.nl || http://www.xs4all.nl/~johanw/index.html
Finger joh...@xs4all.nl for my PGP public key. PGP-KeyID: 0xD42F80B1
J. J. Lodder
joh...@vulcan.xs4all.nl (Johan Wevers) wrote:
> J. J. Lodder <j...@knoware.nl> wrote:
>
> >I disagree completely here. Relativistic mass is nothing but energy
> >measured in inconvenient units.
>
> Yes, but it is a conserved quantity in many-particle reactions.
Of course, it is nothing but energy measured in inconvenient units!
>
> >Mass should be used for rest mass only,
> >energy should be used instead of relativistic mass.
>
> Why? This is only a matter of convention. And not a very clear one for
> starters, read the articles in the magazine of the Dutch Physical society
> (nr. 16 and a reply in 17) which try to clear this matter out. (I recommend
> this because I see you have an .nl adress).
Sure, some conventions are worse than others.
The mass of ... is ... clearly refers to an invariant property.
>
> >The concept of relativistic mass should be forgotten, it causes nothing
> >but confusion.
>
> I don't agree. In fact, I find the hidden assumption that mass == rest mass
> confusing. If you talk about mass in a context where this matters you'd
> better specify the type of mass.
There was some justification for relativistic mass, back before Minkowsky,
1910, when special relativity was poorly understood, nowadays there is
none.
Nowadays one should never confuse an invariant with the time component of
a four vector.
Jan
J. J. Lodder
h...@dagobert.uni-duisburg.de (Dr. Herbert Gollisch) wrote:
> : >
> : > >That is not quantum, anchored classical objects like telephones behave in
> : > >this way too.
> : >
> : > >Jan
> : >
> : >
> : > I heard that analogy at a lecture this summer, and was confused.
> : > As many times as I go over it, it doesn't seem to make sense. If I
revolve
> : > clockwise with the telephone by 360 degrees, it's not in the
original state,
> : > but if I go 360 more degrees clockwise, it still isn't back in the
original
> : > state -- it's even more tangled up!
The constraint does not have to be an attachement to a point.
DIY exp#2: Put a half full wineglas on a table. Stand with your back to
the table. Stretch out your right hand behind you, palm up. Take the glass
between two fingers. Now bring it to your mouth in normal drinking
position without spilling. Dont think just do it, cant be done with
rotation through \pi.
As I said before, we do not know if this is merely an analogy, or needed
for the understanding of spin.
BW,
Jan
Robert Stirniman
There is an important relationship between intrinsic and
extrinsic angular momemtum, microscopic and macroscopic
angular momentum, and quantum and classical level angular
momentum.
A body which is spinning within a larger macroscopic body
which is also spinning will tend to align the axis of its
angular momentum with the spin axis of the larger body.
For example, a gyroscope located on the earth, unless it is
in a frictionless gimbal, with always try to precess due to
the rotation of the earth into alignment with the earth's polar
axis, at which point it will no longer precess due to earth
rotation.
Another example. A cylinder of magnetic material spinning
around its longitudinal axis will develop a magnetic field
proportional to is angular velocity (Barnett Effect), because
the angular momemtum of the electrons in the material will
attempt to precess and come into alignment with the macroscopic
axis of the spinning cylinder, which also brings into alignment
the magnetic moment of the electrons, some of which have unpaired
spins (ferromagnetic), resulting in generation of a macroscopic
magnetic field. Similarly, it is know that a static magnetic field
itself contains angular momentum -- and spinning the source of the
static field, whether a magnet or DC current loop, will result
in a corresponding increase or decrease in the field strength.
Another example is the inventions of Henry Wallace, which were
discovered and patented about 25 years ago, when he worked at
General Electric. Wallace found that an unusual thing happens when
you spin elemental material which has a nucleus containing an odd
number of nucleotides, i.e. having an "un-paired" value of angular
momentum, resulting in a nucleus with a multiple integer of a one-
half value of the quantum h-bar. The spin of the nucleus will
begin to line up with the macroscopic spin axis, and will create
a force field related to gravity -- which Wallace called the
"kinemassic" field. If you haven't heard of Wallace or his unusual
discovery, it's might be because information about it has been
classified by the military.
Maybe I've missed it, but I've looked seriously, and there seems
to be no information in undergraduate or graduate level physics
reference books which mentions the relationship between
macroscopic and microscopic angular momentum -- much less
provides any analysis or explanation linking quantum angular
momentum to macroscopic angular momentum. Why not?
How does quantum angular momentum become organized from a
microscopic to a macroscopic level? Has anyone ever published
any work about this? I can't find any.
Robert Stirniman
=============================================================
Here's an interesting reply I received to the above questions.
Date: Sun, 5 Nov 1995
From: James Youlton <you...@annex.com>
To: Robert Stirniman <rob...@wwa.com>
Re: Angular Momentum and the Barnett Effect
On Wed, 1 Nov 1995, Robert Stirniman wrote:
> Maybe I've missed it, but I've looked seriously, and there seems
> to be no information in undergraduate or graduate level physics
> reference books which mentions the relationship between
> macroscopic and microscopic angular momentum -- much less
> provides any analysis or explanation linking quantum angular
> momentum to macroscopic angular momentum.
You're catching on. The subject of compound angular momentum, or
internal and external angular momentum, or intrinsic and extrinsic
angular momentum has been a repressed subject for about 2 and half
decades. Add to that list, spherical pendulums, Coriolis effect, except
as applied to balistics and meteorology as used by the US military,
and Shafer's pendulum, that neat little device used as the artifical
horizon of aircraft.
> How does quantum angular momentum become organized from a
> microscopic to a macroscopic level? Has anyone ever published
> any work about this? I can't find any.
There isn't any that I know of, though back in the late fifties, there
was a fellow named Edward Condon at the University of Colorado who was
fairly proficient on the subject. So much so that he wrote the rotational
dynamics section, called noninertial dynamics at the time, of the
reference "The Handbook of Physics" which he also co-edited (Chapter 5).
I don't recall offhand who the publisher was (Harcourt/Brace?), though
it was endorsed by the American Institute of Physics.
Later, when Mr Condon was the head of the USAF project 'Blue Book', he
labored to suppress his own work when the directive was handed down from
the Navy's Turtle Island project.
James Youlton
----------------------------------------------------------------------
Note:
Edward Condon was not involved with project Blue Book, but was
involved in a different study of UFOs for the USAF which
resulted in termination of the Blue Book project. Condon's
first known involvement with study of UFOs was in 1943, when
he was engaged by the military to assess the FooFighter phenomena.
After the nationwide wave of UFO sightings in 1966, Condon
was appointed head of a new committee to study the problem,
The Committee for Scientific Study of Unidentified Flying
Objects. Condon proceeded immediately to ridicule and debunk
the idea of UFOs, even before the committee had it's first
meeting to begin it's "scientific" investigation. There are
many files of information now circulating which document Edward
Condon's sad turn from the scientific pursuit of truth to the
dark side of politics. But, that's another story.
Here's an excerpt about the Condon committee which comes
from the research report about UFOs prepared by Major
Brummet and Captain Zuick in May 1974 for the USAF Air
Command and Staff College.
By September 1947, the United States Air Force (USAF)
had become sufficiently interested in the growing number
of UFO reports by reputable, respected citizens to estab-
lish "Project Sign", later named "Project Grudge", and
finally renamed "Project Blue Book", the Air Force program
for investigation of UFOs. Project Blue Book remained
in effect for over twenty-two years and investigated re-
ports of 12,618 sightings. Unexplained sightings ranged
between the official Project Blue Book report of 6 per
cent to UFOlogist estimates of 54 per cent. Despite the
wide variance in unexplained sightings, Secretary of the
Air Force, Dr. Robert Seamans, announced the termination
of Project Blue Book on December 17, 1969. The decision
to discontinue UFO investigations was based on an eval-
uation of a report prepared by the University of Colorado
entitled, "Scientific Study of Unidentified Flying Ob-
jects," more commonly referred to as the "Condon Report";
a review of the Condon Report by the National Academy of
Sciences; past UFO studies; and two decades of Air Force
experience investigating UFO reports. (6:141)"
....
Project Blue Book was terminated on December 17, 1969,
by Secretary of the Air Force, Robert C. Seamans, Jr.
The decision to discontinue UFO investigations was based
on a report prepared by the University of Colorado
(Condon Report), a review of that report by the National
Academy of Sciences, past UFO studies, and Air Force
experience in investigating UFO reports.(21:297) Sec-
retary Robert Seamans Jr., stated that the program "no
longer can be justified either on the ground of national
security or in the interest of science.(15:76) Many
experts disagree with the conclusion of the 1500 page,
$539,000 independent Condon Study that took over two
years to complete. The Condon Study concluded that :
Nothing has come from the study of UFOs in
the past 21 years that has added to scientific
knowledge. Careful consideration of the record
as it is available to us leads us to conclude
that further extensive study of UFOs probably
cannot be justified in the expectation that sci-
ence will be advanced thereby.(1:2)
One of the major critics of the Condon Study was
an amateur UFO organization, The National Investigators
Committee for Aerial Phenomena (NICAP). As indicated
by the Condon Report , NICAP in the past has spent much
effort in attacking Air Force UFO policies and attempting
to influence Congress. NICAP warned members of the
Colorado Project to beware less the Condon Project turn
out to have been "hired to whitewash the Air Force."
(End of excerpt from USAF research report)
=================================================================
Well there you have it. Has the military really been engaged
in suppression of fundamental new science knowledge for almost
50 years now, or is it just another one of those wild and crazy
conspiracy rumors?
Regards,
Robert Stirniman (rob...@wwa.com)
Dr. Herbert Gollisch
: >I disagree completely here. Relativistic mass is nothing but energy
: >measured in inconvenient units.
: Yes, but it is a conserved quantity in many-particle reactions.
: >Mass should be used for rest mass only,
: >energy should be used instead of relativistic mass.
: Why? This is only a matter of convention. And not a very clear one for
: starters, read the articles in the magazine of the Dutch Physical society
: (nr. 16 and a reply in 17) which try to clear this matter out. (I recommend
: this because I see you have an .nl adress).
: >The concept of relativistic mass should be forgotten, it causes nothing
: >but confusion.
: I don't agree. In fact, I find the hidden assumption that mass == rest mass
: confusing. If you talk about mass in a context where this matters you'd
: better specify the type of mass.
: >This way the photon IS a zero mass particle, to every observer.
: The photon is always a zero rest-mass particle. It changes nothing if you
: call the quantity E/c^2 total or relativistic mass, it's rest mass is
: still 0.
by the way, since a photon will never "rest", the designation "zero mass"
is of no relevant physical meaning. The only
relevant mass for light is E/c^2. "Rest mass" describes a principle
property of a particle, mass or energy is a variable connected to the
dynamic particle state. The confusion comes from the fact that in
our everyday world mass is practically identical to rest mass
HG
Johan Wevers
>There was some justification for relativistic mass, back before Minkowsky,
>1910, when special relativity was poorly understood, nowadays there is
>none.
>Nowadays one should never confuse an invariant with the time component of
>a four vector.
Well, there is still some use for it. In accelerator physics for example,
where the relativistic mass is used to determine the center of mass and
the acceleration. And in particle collisions, rest mass is not a conserved
quantity so it is of little use there, but relativistic mass (or E/c^2)
is usefull. On the other hand, in SR calculations rest mass is a usefull
quantity. And to avoid confusion, it is always better to state clearly
what kind of mass you want to use. As this whole discussion points out,
this is not always clear from the context...
J. J. Lodder
h...@dagobert.uni-duisburg.de (Dr. Herbert Gollisch) wrote:
> Johan Wevers (joh...@vulcan.xs4all.nl) wrote:
> : J. J. Lodder <j...@knoware.nl> wrote:
>
> : >I disagree completely here. Relativistic mass is nothing but energy
> : >measured in inconvenient units.
>
> : Yes, but it is a conserved quantity in many-particle reactions.
>
> : >Mass should be used for rest mass only,
> : >energy should be used instead of relativistic mass.
>
> : Why? This is only a matter of convention. And not a very clear one for
> : starters, read the articles in the magazine of the Dutch Physical society
> : (nr. 16 and a reply in 17) which try to clear this matter out. (I recommend
> : this because I see you have an .nl adress).
>
> : >The concept of relativistic mass should be forgotten, it causes nothing
> : >but confusion.
>
> : I don't agree. In fact, I find the hidden assumption that mass == rest mass
> : confusing. If you talk about mass in a context where this matters you'd
> : better specify the type of mass.
>
> : >This way the photon IS a zero mass particle, to every observer.
>
> : The photon is always a zero rest-mass particle. It changes nothing if you
> : call the quantity E/c^2 total or relativistic mass, it's rest mass is
> : still 0.
>
> by the way, since a photon will never "rest", the designation "zero mass"
> is of no relevant physical meaning. The only
Of course it has physical meaning: Zero mass means E^2 - p^2 = 0, (natural
units.)
Since E and p are independent observables this is a physical
result. The statement: The photon is a massless particle, makes
perfect sense, and it is even falsifiable.
> relevant mass for light is E/c^2. "Rest mass" describes a principle
> property of a particle, mass or energy is a variable connected to the
> dynamic particle state. The confusion comes from the fact that in
> our everyday world mass is practically identical to rest mass
> HG
You surprise me: Does not the photon belong to our everyday world? This is
the 20th century!
Again: The term Mass should not be used twice for objects with
different transformation properties. Rest mass is a Lorentz invariant, so
called relativistic mass is the time component of a 4-vector.
Using mass for both causes lots of confusion.
Rest mas is inevitably called mass (as in: The mass of the proton
is...),
so energy/c^2 should not be called mass also.
Sure, this is only a matter of convention, but some conventions are
better than others to promote clear thinking and to avoid errors.
Let relativistic mass go the way of the Kilogram Force, get rid of
it. It is perpetuated only by mediocre teachers attempting to
explain (parts of) special relativity without introducing 4-vectors and
(Lorentz) transformation properties.
Jan
Johan Wevers
>Again: The term Mass should not be used twice for objects with
>different transformation properties. Rest mass is a Lorentz invariant, so
>called relativistic mass is the time component of a 4-vector.
>Using mass for both causes lots of confusion.
>Rest mas is inevitably called mass (as in: The mass of the proton
>is...), so energy/c^2 should not be called mass also.
>Sure, this is only a matter of convention, but some conventions are
>better than others to promote clear thinking and to avoid errors.
Yes, and some conventions are better than others in some areas of research
than others. But not necessarily the same in each area. If you work in pure
kinematical SRT, I agree that rest mass is the most usefull quantity. But
in accelarator physics, particle physics and sometimes in GRT, relativistic
mass is the most practical unit.
>Let relativistic mass go the way of the Kilogram Force, get rid of it.
Why not let it go the way of the Angstrom and eV, units who are still in
use in some area's. And although nobody can claim that using eV's as a
unit of energy in, say, GRT is usefull, it is still usefull in accelarator
physics.
>It is perpetuated only by mediocre teachers attempting to
>explain (parts of) special relativity without introducing 4-vectors and
>(Lorentz) transformation properties.
Now why wouldn't they don't want to introduce that? :-) It makes perfect
sense to introduce the different mass concepts, especially because they
are also continiously used in different area's. And there's nothing wrong
when you make a clear distinction between these masses.
DECraig77
Mentioned a while back in this tread, was the telephone+cord model
of 1/2h_bar particles.
But an attachment point is implied. The whole assembly is attached
some where: so we get telephone+cord+anchor.
HG points out that the Pauli exclusion principle has not been taken-up yet
in this thread, so here's a shot at a two electron model:
(Afterall things _are_ rather dying-out here, with these energy vector
args.)
Rather than use a telephone + cord. I attached two recognizeably diferent
saucer to gather with duct tape, and called them electrons. Mark a point
on
the edge of each plate to indicate the direction of spin.
I attached the tape to the top of each saucer so that the tape formed a
question mark.
_______
/ \
| |
\___ |____/ /
/
/
/
/
\____|____/
A 2pi rotation will reveses the question mark. Another willbring back the
original topology,.
Now the point: An exchange of the plates is equivalent to a 2pi rotation
(for identical plates). A plate exchange followed by a 2pi rotation will
bring the aparatus back to its original state.
I'm still trying to understand the meaning of this. Apparently the
apparatus
has the property that *exchange is equivalent to 2pi rotation*. Does this
properly model two fermions? We also get, that the spin orientations are
relative, it doesn't matter if the apparatus as a whole is rotated. This
seems
to fit in with something I recall reading by RPenrose (that I didn't
understand).
I am beginning to wonder if this model has equivalence: After all, an
exchange
is equivalent to a 2pi rotation of one electron and not a phase change in
psi.
I'm I missing something here?
J. J. Lodder
Chojnacki 23-59 <jarekch@altis> wrote:
> On Thu, 16 Nov 1995, J. J. Lodder wrote:
>
> > > : DIY mathematical experiment: rotation of an anchored object
> > >
> > > : Find a modern phone attached to the wall with a flat cable,
> > > : so you can easily see the twist.
> > > : [the details deleted]
> > > : You can also rotate twice over or twice under,
> > > : and untwist by looping the cable back over the phone.
>
> This is more interesting for me. If we take as identical phones which
> can undergo looping, we have two stages: twisted after 2pi and untwisted
> 0 and 4pi (k*4pi) (after some loopings).
>
> [deleted]
> > > : It is not clear if this is merely an
> > > : analogy, or that it will ultimately have a deep meaning.
> > > : Wait for the final theory of everything,
> > > : and enjoy yourself in the meantime,
> > >
> > > : Jan
>
> > > And someone else (HG) add:
> > > Hi,
> > > these macroscopic models are interesting enough for discussion with my
> > > students. However, now tell me how to anchor an electron?
>
> Do It Yourself experiment #3:
> Take 2 boxes with different tops and bottoms. Connect them with a flat tape.
> Rotate them 2pi horizontally but keep boxes in the same position (do not
rotate
> them, eg black spots to the north). After that 'orbital' rotation you can
> untwist the tape and return to the initial state by
> rotating one box 4pi about the tape ('spin' or vertical rotation).
> Well, it looks more like an atom, but it is still only an analogy without
> physical and mathematical support as far as I know, but I am not a physicist.
>
> J.Ch.
>
> > [Nice experiment#2 with wine deleted]
> > Jan
Sure, you have got it right. There are many situations where you need the
full SU(2) rotation group for rotations of macroscopic objects.
Implications for elementary partcles unknown, but SU(2) is not
particularly mysterious and spin only.
Jan
J. J. Lodder
joh...@vulcan.xs4all.nl (Johan Wevers) wrote:
>J. J. Lodder <j...@knoware.nl> wrote:
>
>>Again: The term Mass should not be used twice for objects with
>>different transformation properties. Rest mass is a Lorentz invariant, so
>>called relativistic mass is the time component of a 4-vector.
>>Using mass for both causes lots of confusion.
>>Rest mas is inevitably called mass (as in: The mass of the proton
>>is...), so energy/c^2 should not be called mass also.
>
>>Sure, this is only a matter of convention, but some conventions are
>>better than others to promote clear thinking and to avoid errors.
>
>Yes, and some conventions are better than others in some areas of research
>than others. But not necessarily the same in each area. If you work in pure
That is confusion to me.
>kinematical SRT, I agree that rest mass is the most usefull quantity. But
>in accelarator physics, particle physics and sometimes in GRT, relativistic
>mass is the most practical unit.
The give-away mistake. Relativistic mass is never used in general
relativity, the concept is utterly useless there. You are merely using the
words, you do not understand the meaning.
Joke: ask any accelerator physisist how much relativistic mass his
accelerator can give an electron, and he will either give you either a
blank uncomprehending stare or roll on the floor laughing.
>
>>Let relativistic mass go the way of the Kilogram Force, get rid of it.
Snip
>>It is perpetuated only by mediocre teachers attempting to
>>explain (parts of) special relativity without introducing 4-vectors and
>>(Lorentz) transformation properties.
>
>Now why wouldn't they don't want to introduce that? :-) It makes perfect
Dont know, no idea: Conservatism, stupidity, laziness, parrotting, lack of
familiarity with any up-to-date textbook or research literature, general
backwardness, perhaps all combined?
>sense to introduce the different mass concepts, especially because they
>are also continiously used in different area's. And there's nothing wrong
>when you make a clear distinction between these masses.
>
>--
>ir. J.C.A. Wevers || The only nature of reality is physics.
>joh...@vulcan.xs4all.nl || http://www.xs4all.nl/~johanw/index.html
>Finger joh...@xs4all.nl for my PGP public key. PGP-KeyID: 0xD42F80B1
Seems to me you are out of touch with reality.
BW,
Jan
Johan Wevers
>>Yes, and some conventions are better than others in some areas of research
>>than others. But not necessarily the same in each area. If you work in pure
>That is confusion to me.
Not if you make a clear distincion between the different masses.
>The give-away mistake. Relativistic mass is never used in general
>relativity, the concept is utterly useless there. You are merely using the
>words, you do not understand the meaning.
Really? I got it explained in college that all mass curves space, so if
a particle gets heavier it curves space more.
>Joke: ask any accelerator physisist how much relativistic mass his
>accelerator can give an electron, and he will either give you either a
>blank uncomprehending stare or roll on the floor laughing.
Yes, in that area masses and energies are usually expressed in eV, and
in the higher energy region speeds are approximated with c.
>>>It is perpetuated only by mediocre teachers attempting to
>>>explain (parts of) special relativity without introducing 4-vectors and
>>>(Lorentz) transformation properties.
>>Now why wouldn't they don't want to introduce that? :-) It makes perfect
>Dont know, no idea: Conservatism, stupidity, laziness, parrotting, lack of
>familiarity with any up-to-date textbook or research literature, general
>backwardness, perhaps all combined?
>Seems to me you are out of touch with reality.
If you expect teachers on secondary schools to teach 4-vectors and Lorentz
transformations I don't know who is out of touch with reality...
But if you see it this way, go ahead and start a crusade against the term
relativistic mass. I'm affraid you'll be dissapointed.
J. J. Lodder
> >The give-away mistake. Relativistic mass is never used in general
> >relativity, the concept is utterly useless there. You are merely using the
> >words, you do not understand the meaning.
>
> Really? I got it explained in college that all mass curves space, so if
> a particle gets heavier it curves space more.
The source of space-time curvature is the stress-energy tensor, not the
relativistic mass. The overweight standard textbook "Gravitation" does not
even have an index entry for relativistic mass.
> >>>It is perpetuated only by mediocre teachers attempting to
> >>>explain (parts of) special relativity without introducing 4-vectors and
> >>>(Lorentz) transformation properties.
[snip]
>
> If you expect teachers on secondary schools to teach 4-vectors and Lorentz
> transformations I don't know who is out of touch with reality...
Well they also waste lots of time on Bohr orbits. Guess we should be glad
they have learned not to teach the world-aether.
It is actually easier to do it right. Pupils are told about Lorentz
already, have learned analytic geometry, rotation of coordinates,
hyperbola, and 2 component vectors, which is good enough. All there extra
is to special relativity is a couple of minus signs slipped in.
See for example the classic: Spacetime Physics, Taylor and Wheeler, 1963,
first chapters, for how it can also be done, and be done well.
> But if you see it this way, go ahead and start a crusade against the term
> relativistic mass. I'm affraid you'll be dissapointed.
Course not, it is a useful indicator: Whoever talks about relativistic
mass has not been taught relativity adequately and/or does not understand
it properly. It belongs in muddled mixes of Newtonian mechanics and
relativity and has been out of date for at least 50 years.
Best wishes,
Jan
Andre Ratel
I think I have a problem.
As a reply to a post made by J. J. Lodder on
Sun, 05 Nov 1995 12:47:34 +0100,
I made a post dated
Sat, 11 Nov 1995 16:14:11 GMT
My main purpose then was just to mention a paper written by
Hans Ohanian in Am. J. Phys.
Now, a few days later, I noticed the presence of an anterior posting
made by J. J. Lodder and dated
Tue, 31 Oct 1995 12:42:07 +0100
Since this text also contains a mention the Ohanian paper, it seems
that my article didn't bring anything new and therefore I apologize
for this. (However, I could sware that the earlier text wasn't part of
this thread when I sent my article on November 11.)
On quite a few other occasions I have seen replies appearing before
the original posting. Is it my arrow of time pointing in the wrong
direction or is there something wrong with my access to the
newsgroup?
I rather enjoy participating in a discussion but I wouldn't want
to contribute to the noise by just restating arguments made in earlier
postings to which I have no access.
Can someone help me on this?
Andre Ratel
>I disagree completely here. Relativistic mass is nothing but energy
>measured in inconvenient units. Mass should be used for rest mass only,
>energy should be used instead of relativistic mass.
>The concept of relativistic mass should be forgotten, it causes nothing
>but confusion.
>This way the photon IS a zero mass particle, to every observer.
>Jan
---
Hello,
I'm wondering now if I did the right thing when I included
in my posting, a digression on rest mass... especially
since I've seen that there is somewhere a thread on the
mass of light...<:-| Anyhow...
In the famous equation for energy
E = m c^2
m is the total relativistic mass, not the rest mass. And I'm not sure
that we should also forget this equation.
Anyway, I would be willing to keep the word "mass" to designate only
the rest mass as long as we agree not set c=1 in the equations. :-)
Andre
PS: posted and and emailed
J. J. Lodder
> j...@knoware.nl (J. J. Lodder) wrote:
>
> >I disagree completely here. Relativistic mass is nothing but energy
> >measured in inconvenient units. Mass should be used for rest mass only,
> >energy should be used instead of relativistic mass.
>
> >The concept of relativistic mass should be forgotten, it causes nothing
> >but confusion.
>
> >This way the photon IS a zero mass particle, to every observer.
>
> >Jan
>
> ---
>
> Hello,
>
> I'm wondering now if I did the right thing when I included
> in my posting, a digression on rest mass... especially
> since I've seen that there is somewhere a thread on the
> mass of light...<:-| Anyhow...
Dont worry, the thread was at an end, I have summarized in a new posting.
Dont bother with the mass of light thread in sci.skeptic, megabytes are
being wasted there with seemingly endless discussions caused by lack of
understanding of relativity caused by 'relativistic mass'.
>
> In the famous equation for energy
>
> E = m c^2
>
> m is the total relativistic mass, not the rest mass. And I'm not sure
> that we should also forget this equation.
The equation is quite suitable to go on posters together with the Einstein
haircut. It is also often useful as the *leading term* of the full
relation between energy, mass and momentum. Momenta in nuclear reactions
are often small.
As a definition without physical content it should indeed be forgotten.
>
> Anyway, I would be willing to keep the word "mass" to designate only
THE most common beginners error is that people see an 'm' in a
relativistic equation and think: Ah this is relativity, it has four-vector
indices, so I guess we must use the relativistic mass here. Wrong!
> the rest mass as long as we agree not set c=1 in the equations. :-)
Of course one should set \hbar=c=1=dimensionless in theoretical physics
when useful. It is often far easier to do the calculations in natural
units, and convert to SI only in the final result, if at all.
Get used to natural units, it saves lots of time.
E^2 =m^2 + p^2, !
A good physicist cannot be lazy enough. Useless extra work creates more
room for error.
>
> Andre
>
Jan
PS As to your next posting: postings may live for hours or even days in
limbo in cyberspace, so it is quite common that postings cross.
Also they can arrive at different times on different computers.
DECraig77
In article <jjl-221195...@mac-10.knoware.nl>, j...@knoware.nl (J. J.
Lodder) wrote:
>In article <30b25720.5...@vulcan.xs4all.nl>,
>joh...@vulcan.xs4all.nl (Johan Wevers) wrote:
>> J. J. Lodder <j...@knoware.nl> wrote:
>[snip]
>> >The give-away mistake. Relativistic mass is never used in general
>> >relativity, the concept is utterly useless there. You are merely using
the
>> >words, you do not understand the meaning.
Take a visit to alt.sci.physics. You will find a ragging discussion on
*the* mass of the photon. Some think it is zero. Some think it has
something to do with its frequency. One fellow who has attempted
to derrive an understanding from the discussions has come to the
conclusion that the rest mass of the photon is *valueless* ;-")
These inquiring souls haven't the 4-vector to lend visual
understanding.
--------------------------------------------------------------------------
-----------------
Concern about the usage of relativistic-mass in
discussions as meaningful, confusing or whatever
is overridden by concerns involving the physics
itself.
That is, the *meaning* of the total energy eq. is not known.
Concider a variant of the total energy equation:
K_m0 = k_E - ik_r, everything in terms of a reduced wave
number.
(You can get at this equation from either of two directions: the
characteristic of an inverse planar wave; or via the total-energy-
equ and the deBroglie postulates.)
When we measure total energy do we just think we're measuring
something with units of energy, or are we fooling ourselves and
actually measuring a frequency or wave number. The same goes
for momentum; are we just measuring a projection of K_m0?
E=mc2 can be taken as an identity, or an equivalence relationship.
As an equivalence, we recognise that we have two different things
that maintain a ratio, and that in all possible situations the
equivalence may not hold.
For instance, given Newton, does F=ma? Well, yes and no.
So only when the force is applied against the mass m, is the
equation necessarily valid.
Taking E=mc2 as an identity, means to say E and m are the *same*
thing, the difference in E and m being subjective; subject to the the
manner in which it is measured.
If it be that the equivalence holds, and it may, relativistic mass is as
meaningful as relativistic energy. We might conceiveably have all
things in terms of the same unit of measure. So we need qualifiers
for all of them.
J. J. Lodder
(DECraig77) wrote:
> In article <jjl-221195...@mac-10.knoware.nl>, j...@knoware.nl (J. J.
> Lodder) wrote:
> >In article <30b25720.5...@vulcan.xs4all.nl>,
> >joh...@vulcan.xs4all.nl (Johan Wevers) wrote:
> >> J. J. Lodder <j...@knoware.nl> wrote:
> >[snip]
> >> >The give-away mistake. Relativistic mass is never used in general
> >> >relativity, the concept is utterly useless there. You are merely using
> the
> >> >words, you do not understand the meaning.
>
>
> Take a visit to alt.sci.physics. You will find a ragging discussion on
> *the* mass of the photon. Some think it is zero. Some think it has
> something to do with its frequency. One fellow who has attempted
> to derrive an understanding from the discussions has come to the
> conclusion that the rest mass of the photon is *valueless* ;-")
>
> These inquiring souls haven't the 4-vector to lend visual
> understanding.
>
I know, I know, I sample the same on sci.skeptic, it is a hopeless waste
of Megabytes, it goes on and on, no use commenting on it. Confusion all
over.
It is even worse now, confusion about units and dimensions mixed in.
>
> E=mc2 can be taken as an identity, or an equivalence relationship.
>
See my previous post.
As an identity it is as useles as having both meters and inches in the
same paper, it is often useful as an approximation to the complete
relation
E^2 = m^2 + p^2, (natural units), for small momentum.
> If it be that the equivalence holds, and it may, relativistic mass is as
> meaningful as relativistic energy. We might conceiveably have all
> things in terms of the same unit of measure. So we need qualifiers
> for all of them.
Sure, it is, but it is just plain stupid to have both conventions at once.
Eddington in the first general relativity textbook used mass, nowadays the
convention is to use energy. The name does not matter, as long as you keep
a clear distinction between the magnitude and a component of a
four-vector, by any name. The modern convention, energy for the time
component, mass for the magnitude, is the best possible, given the
confused history.
Nowadays mass is intrinsic, energy is observer dependent, which makes sense.
The same word for both does not work in practice, no matter how qualified.
Use of relativistic mass in modified Newtonian calculations should be
avoided in all cases.
Best Wishes,
Jan
Paul Leopardi
in this thread:
1) In discussing rotations of co-ordinate systems for a system of spin
1/2, "The Feynman Lectures on Physics" (1963) Book III Section 6-3
states:
"We must have the situation that a rotation by 360 degrees and no
smaller
angle reproduces the same physical state ... It gives
C'+ = -C+ \
| 360 degrees about z axis ...
C'- = -C- /
Also, if something has been rotated by a sequence of small rotations
whose net result is to return it to the orginal orientation, it is
possible to define the idea that it has been rotated 360 degrees - as
distinct from zero net rotation - if you have kept track of the whole
history. (Interestingly enough this is not true for a net rotation of
720 degrees.)"
2) In discussing the space inversion operation, "The Feynman Lectures
on
Physics" Book III Section 17-2 states:
"Now let's suppose we have a state |psi0> which under the inversion
operation goes into exp(i.delta)|psi0> ...
Then suppose we invert again. After two inersions we are right back
where
we started from - nothing is changed at all ...
So if the inversion operator is a symmetry operation of a state, there
are
only two possibilities for delta: exp(i.delta) = +/- 1, ..."
3) In discussing the space inversion operation, Leonard I. Schiff
"Quantum Mechanics" (1968) Chapter 7 Section 29 "Space Inversion and
Time
Reversal" states:
"The unitary inversion operator UI is defined by ...
UI.psi(r) = omega.psi(-r) ...
Two inversions bring the coordinate space into itself, so that UI^2 is
expected to bring a state into itself. ... Thus omega^2 is a number of
unit magnitude, from which it follows that omega is also ... We shall
assume that omega has a definite value for each kind of particle. We
have
already noted ... that a 2.pi rotation of an integer spin paticle
leaves
its state function unchanged, and we expect that this is also true for
two space inversions. ... For half-odd-integer spin particles, we note
... that products of pairs of them can be superposed to give states of
integer angular momentum. Thus we can expect that omega^2 for a
half-odd-integer spin particle can be equal to the possible values of
omega for an integer spin particle. These are +/- 1, so that a
half-odd-integer spin particle can have omega = +/- 1, +/- i."
QUESTIONS
A) Arguments 2) and 3) seem to contradict each other. Can they both be
right? If so, why? If not, which one is right and why? [My guess is
that 2)
is wrong and 3) is right, but I can't explain why I believe this.]
B) Are two inversions equivalent to a rotation of 2.pi (360 degrees),
and
four inversions equivalent to a rotation of 4.pi (720 degrees)? Is
this
seemingly mysterious property a result of the fact that SU(2) is
isomorphic to the universal covering group of O(3) as stated in
Schiff,
"Quantum Mechanics", Section 27, p 206? Does this adequately explain
the
statements made after "Also..." in Argument 1)?
Best Regards, Paul Leopardi
J. J. Lodder
<leop...@zeta.org.au> wrote:
Both are right. There is no such thing as THE parity operator, it is a
mathematical construct. It need not be an actually realizable observable.
With Feynman's definition P^2 = P, but then a rotation of a spin half
through 180 degrees around an axis perp to its starting direction is not P
but \pm iP. And 360 = - Identity. Space inversion is hard to accomplish
:-), rotation of a spin is easy and the predicted minus sign can be
actually observed in neutron interferometry.
Nevertheless Feynman's P is useful, postulated symmetry under P yields
predictions for experiments that can, and have been falsified.
Electromagnetism yes, weak interactions no.
Best Wishes,
Jan