So if spin isn't really spin

[unusualname]

To others: has anyone else around here studied Jabs' proof yet?
(Unusualname: I presume you've studied it?)

Hi strangerep, I have only briefly looked through the paper, I just posted a link to it after a search in order to answer lugita15's question, but was not aware of the paper previously.

I cannot say I understand the details but I will say that it does not surprise me that such an argument can be constructed. If spin can be derived from a non-relativistic wave equation (cf Greiner link above), notwithstanding that the derivation is 'ad-hoc' or 'hand-waving', then it seems reasonable that a non-relativistic argument exists for the exclusion principle, even though it might appear 'unnatural' (ie hand-wavy).

In fact the relativistic derivation is not so 'natural' either, and this would suggest that spin (and associated statistics) is not a so well understood a physical phenomenon.

Perhaps a future theory will make it clear.

 

[dextercioby]

[...]. If spin can be derived from a non-relativistic wave equation (cf Greiner link above), notwithstanding that the derivation is 'ad-hoc' or 'hand-waving', [...].

Let me point out one thing: spin 1/2 comes from a linearization of the Schrödinger equation for spin 0 (a result by Levy-Leblond in the 1960' s made popular by Greiner's book in the 1980's), but the general theory of spin comes from the very rigorous theory of symmetries for the Galilei group (promoter of whom is the same guy, Levy-Leblond).

My opinion is that Levy-Leblond's work is on equal footing with Dirac's 1928 one, it's just that the special relativity of Einstein, Poincaré & Lorentz is a better description of nature than the Galilei relativity.

 

[unusualname]

Let me point out one thing: spin 1/2 comes from a linearization of the Schrödinger equation for spin 0 (a result by Levy-Leblond in the 1960' s made popular by Greiner's book in the 1980's), but the general theory of spin comes from the very rigorous theory of symmetries for the Galilei group (promoter of whom is the same guy, Levy-Leblond).

My opinion is that Levy-Leblond's work is on equal footing with Dirac's 1928 one, it's just that the special relativity of Einstein, Poincaré & Lorentz is a better description of nature than the Galilei relativity.

I'm guessing vanhees71, Dickfore etc would also call Dirac's argument "hand-waving" - I guess it's easy to be critical with hindsight

Greiner does reference Levy-Leblond on the first page of the relevant chapter (13) and points out that his own argument is simplified in parts.

In the end, although these non-relativistic arguments predict spin behaviour qualitatively, you need relativity and even qed to get accurate agreement with nature, but I still think it's interesting that 'spin' can be predicted by non lorentz-invariant equations.

 

[Demystifier]

Dirac linearized Klein-Gordon equation with a motivation to avoid the probability non-conservation problem.

But Schrodinger equation does not have this problem. So is there another motivation for linearization of the Schrodinger equation?

 

[dextercioby]

Other than showing that spin 1/2 can be obtained from spin 0 (just like in a specially relativistic QM), I don't see any...

 

[Demystifier]

So, linearization of second-order differential equations may lead to new physics.

So shall we get something new if we linearize the Maxwell equations (for A^{mu})?
How about Newton equation?

 

[photon rush]

I think historically people used to think that the particles actually were spinning, but then they wised up and they were stuck with the name "spin." From how I'm understanding it, it helps to think of it as if it is spinning, although there's no reason to think that that's ACTUALLY happening.

the was I understand it is that spin occurs in accelleration in accelleration(actually a physical spin)

 

[chrisbaird]

I'll throw my two cents into this already long thread.

Electrons do spin, just not in a classical way. Everything that you would expect a spinning ball of charged mass to exhibit (magnetic moment, additive angular momentum, etc.), the electron also exhibits. But, if you treat the electron as a purely classical ball of spinning mass, all the effects are the same, but the numbers do not quite match experiment. This tells me, the electron is spinning, just not in a classical sense of rotating mass. Rather, it spins in a quantum way. If you want a picture to put in your mind of the electron's quantum spin, picture a point charge with a spin vector attached.

 

[billschnieder]

The following article makes an interesting contribution to this topic

The zitterbewegung interpretation of quantum mechanics
David Hestenes
Foundations of Physics (1990)
Volume: 20, Issue: 10, Publisher: Springer Netherlands, Pages: 1213-1232
http://geocalc.clas.asu.edu/pdf-preAdobe8/ZBW_I_QM.pdf

Abstract:
The zitterbewegung is a local circulatory motion of the electron
presumed to be the basis of the electron spin and magnetic moment. A
reformulation of the Dirac theory shows that the zitterbewegung need not
be attributed to interference between positive and negative energy states as
originally proposed by Schroedinger. Rather, it provides a physical interpretation
for the complex phase factor in the Dirac wave function generally.
Moreover, it extends to a coherent physical interpretation of the entire Dirac
theory, and it implies a zitterbewegung interpretation for the Schroedinger
theory as well.

 

[yoron]

Let's look at electron spin.

---Quote--

" Ralph Kronig, one of Landé's assistants, suggested in early 1925 that it (spin) was produced by the self-rotation of the electron. When Pauli heard about the idea, he criticized it severely, noting that the electron's hypothetical surface would have to be moving faster than the speed of light in order for it to rotate quickly enough to produce the necessary angular momentum. This would violate the theory of relativity."

--End of quote--

And.

---Quote----

A true electron orbit is not nearly so simple as a circle or ellipse.
According to quantum physics, there is no set motion. We can talk about an
average radius of an orbit. We can talk about the angular momentum and
energy of an orbit. We can talk about how much of the orbit is in the
horizontal plane. In reality, the electron's orbit is not any specific
motion. It bounces all over the place. Higher energy electrons have a
greater average radius. Different electrons have different angular
momentums. Exact path cannot be determined.

Dr. Ken Mellendorf
Physics Instructor
Illinois Central College

= End of quote_

So what is a electron, and what is that spin?

 

[Fra]

Dirac linearized Klein-Gordon equation with a motivation to avoid the probability non-conservation problem.

But Schrodinger equation does not have this problem. So is there another motivation for linearization of the Schrodinger equation?

I think Demystifier raises a good question here.

Ever since I was first exposed to this, I always took the emphasis to be the fact that scalar boson vs fermion, appears to simply a matter of perspective.

I see the change from KG-equation to Dirac-euqation as a way to recode the same information that in principle already exists in the KG equation. After all, they are mathematically equivalent. You can encode the same information in two pictures. It's just coded differently (by condensing some dynamic into the state space).

In my personal view this corresponds to a change in the observer. Thus the question why the fermion picture makes more sense than then scalar boson picture - not totally unrelated to the question why are ther no elementary scalar bosons in nature - is dual to the question "why would an observer that hypotetically observed a scalar boson still end up concluding that it was a spin ½ fermion?

The latter perspective is the one I take, and here I expect there to be some not yet fleshed out argument where the "perspective" where information is encoded as fermions rather than scalar bosons are a more efficient and fit code.

I'm not aware of any papers that put it this way, but I except that it would be possible to work on his and produce such a formal argument. I suspect that would be a deeper argument than the original probability conservation issue.

/Fredrik

 

[Drakkith]

but does it really matter if we don't quite have an accurate mental image of what's going on? I mean, the angular momentum is still there, just as an orbiting electron would have, so where is the problem with there being a dipole moment due to spin?

The problem is that we are people and would rather have a way to visualize what is going on. QM is so different from "normal" everyday effects that the average person can observe that it simply doesn't make sense to most people. This leads to people being unable to believe that these effects are true and can keep people from learning if they can't live with a purely mathematical model, even those that are already in college classes.

 

[photon rush]

I would like people to understand from both classical and quantum viewpoints; however people get confused by seeing the same thing just in a different form. If I ask someome how a merry-go round spins; they will percieve it differently by viewing it at a distance, rather than they would if they were actually on it spinning.

 

[photon rush]

fra I admire an open mind

 

[strangerep]

I see the change from KG-equation to Dirac-euqation as a way to recode the same information that in principle already exists in the KG equation. After all, they are mathematically equivalent.

I think it's not correct to say they're "mathematically equivalent". A spin-0 rep of
the rotation group is not equivalent to a spin-1/2 rep (nor to a spin-1 rep, etc).

 

[strangerep]

I cannot say I understand the details [of Arthur Jabs' paper] but I will say that it does not surprise me that such an argument can be constructed. If spin can be derived from a non-relativistic wave equation (cf Greiner link above), notwithstanding that the derivation is 'ad-hoc' or 'hand-waving', then it seems reasonable that a non-relativistic argument exists for the exclusion principle, even though it might appear 'unnatural' (ie hand-wavy).

I wouldn't call Jabs' argument "hand-wavy", although certainly it is written for a particular group of readers and more elaboration might be helpful to widen that group.

Maybe I'll try to write an elaborated version in a separate thread if I find the time. Until then I'll just offer a few more observations on what's needed to grasp Jabs' argument.

1) We must understand that, in QM, one models two indistinguishable particles via a tensor product space of (identical) one-particle Hilbert spaces $H$. I'll denote the tensor product (2-particle) Hilbert space as $H \otimes H$. Actually, I'll go further and give labels to the component spaces: $H_a \otimes H_b$. (But note that they're not (skew-)symmetrized, at least not yet.)

2) Then we must clarify exactly what "exchange" means in the context of a tensor product space. Let's pick two state vectors $\psi_1(x_1,...) \in H_a$ and $\psi_2(x_2,...) \in H_b$, where the x's denote a position coordinate and the "..." denote other quantum numbers, including spin, spin-orientations, and (possibly) a pose angle $\chi$.

3) What then does it mean to "exchange" the particles in a way that relates obviously to physical transformations. I think it means that we must apply a transformation in $H_a$ such that $\psi_1(x_1,...) \to \psi_2(x_2,...)$ and another transformation in $H_b$ such that $\psi_2(x_2,...) \to \psi_1(x_1,...)$

4) To perform the translation $x_1 \to x_2$, in $H_a$ we use an operator like $e^{iP\cdot (x_2 - x_1)}$ (and vice-versa in $H_b$). But what about the rotation transformations? (For simplicity, restrict here to the case where both particles are spin-1/2 at rest). There's now a difficulty because of double-valuedness of the rotation group. For spin-1/2, we confront a 2-sheeted complex function, so it's possible that the transformation might change sheets in $H_a$, but not in $H_b$, depending on where we take the branch cut. Often, one takes a branch cut along the +ve real axis, but this is arbitrary. So one thing at least is certain: the physically measurable consequences of the theory must not depend on where we choose the arbitrary branch cut. IOW, they must not depend on which part of the Hilbert space we call the "1st sheet", and which we call the "2nd sheet".

5) Arthur Jabs' solution to this is to demand that the both rotation transformations be performed in the same sense (i.e., both clockwise or both anticlockwise). The familiar spin-statistics result then follows straightforwardly from this demand by cranking the mathematical handle.

6) The thing that still leaves me a little perplexed is this: although demanding a consistent sense for the rotation transformations sounds asthetically pleasing, I have trouble seeing why it's essential (a priori) from a physical perspective. But hey, the double-valuedness of rotations is tricky at the best of times -- needing the "Dirac belt trick" or similar devices to illiustrate it.

In fact the relativistic derivation is not so 'natural' either, and this would suggest that spin (and associated statistics) is not a so well understood a physical phenomenon.

As Jabs' notes in his paper, we understand that bosonic (resp. fermionic) statistics go with
integral (resp. half-integral) spin, and that other choices are inconsistent. But the older proofs don't really give a deeply satisfying insight into why this is so. I found Jabs' approach interesting for exactly this reason.

 

[photon rush]

someone please help me out if I'm wrong; but can't we record spins from wavelengths in an angular momentum barrier through 3d scanning to determine an objects rate to absorption?

 

[photon rush]

Is this not the correct procedure for converting quantum into classical?

 

[photon rush]

how about converting half spins into hertz pendulum effect to where if f denotes the frequency the period is T=1/f

 

[Fra]

I think it's not correct to say they're "mathematically equivalent". A spin-0 rep of
the rotation group is not equivalent to a spin-1/2 rep (nor to a spin-1 rep, etc).

Yes your right in what you say, but I meant it in a different way. With mathematically equivalent I did not refer to state space information but to the entire theory as an interaction tool. Both are "formally" possible, it's just they they are not equally efficient in a deeper view.

The information encoded in the dirac state is different than the KG state, but there is more implicit information that in the traditional view is not acknowledged. I do acknowledge it though.

The traditional picture is that only information encoded in the initial state is acknowledged. Other constraints such as dynamical evolution rules are not thought of as "information", it's thought of as just timeless elements of reality - not sujbect to inferencial query in the physical sense of measurement.

In my own view, this is inconsistent because on symmetry grounds there simply is no good reason why some information is subject to inferencial constraints and some information is not. This connects very much to the foundation of QM and notion of "theory" in general as well.

To use the KG picture, there are further constraints in the initial state (corresponding to specifying the spinor components). If you specify these, we have en equivalent description of the system, that makes the same predictions and without problems of probability non-conservation. It's only if you ignore the additional constraints in the initial KG state that this is an issue.

It's just that in the dirac state space picture, the notion of spin ½ appears on it's own in the explicit sense. In the KG picture the information about the spin½ requires information both from the state space and history (derivatives), like an extended state space. And I interpret it simply as a property of the way information is encoded by the observer. No need to even bring in classical analogies. The question I am instead facing is; why is it the case that apparently all observers in nature "choose" to encode it this way? I think it's when you look at the observer as a informaiotn processing and encoding structure it may be easier to see that it's simply a more "economic" way to represent information in the diracy picture, and this I think ultimaltey can be understood not in terms of "mathematical simplicity" which was to me always a very volatile argument, but "simplicity" in hte sense that a bounded observer with limited resourses simply will always CHOOSE the code-wise "simplest" representation in a context of evolving law and interacting observers.

I also suspect this is also connects to why no one yet observed fundamental scalar bosons, we have yet to see also higgs boson. The interesting angle I propose is that instead of asking in a realist sense why are there no scalar boson, one can ask this: How would information about a scalar boson be processed and REpresented by an observer? would this observer be stable?

This is how my take on this has alwas been. But what I miss, is a formalised presentation of things as per this view. Since some years ago I deicded to try to work out this on my own... but I still have plenty of work left. Nothing published yet.

/Fredrik

 

[photon rush]

Hypothetically speaking, if we achieve quantum teleportation to transport people; wouldn't they rule the world. A good way to get rid of some 'ol school bullies I guess lol