Hijack from Spin - Particle Threshold?

[TrappedLight]

In the context of nonrelativistic quantum mechanics you won't find a beautiful explanation. You will need to consider the Poincare group to get at spin. I suggest you have a look at Ryder's Quantum Field Theory book, he devotes a few pages to this.

 

Very true. In fact, the full Poincare group associates spin, in general relativity, it arises as torsion. For instance, the torsional energy of a particle is

 

[math]- \frac{1}{2}\hbar \cdot \Omega[/math]

Edited September 15, 2013 by TrappedLight

[ajb]

Very true. In fact, the full Poincare group associates spin, in general relativity, it arises as torsion. For instance, the torsional energy of a particle is

 

[math]\hbar \Omega[/math]

The idea that spin requires curvature and/or torsion has been around for a long time. Einstein-Cartan theory is the oldest extension of GR to include torsion, this comes from 1922 so predates the discovery of spin!

 

It is quite interesting. You see that the Lorentz group is the structure group acting on the orthogonal frames of the tangent spaces of space-time. Note, not the Poincare group. Cartan, by adding torsion showed that the Poincare group acts on the affine frames of the tangent spaces of space-time. Thus locally we can restore some of our notions from Minkowski space-time about spin, but at the cost of adding torsion and affine frames.

 

Fascinating stuff.

Edited September 15, 2013 by ajb

[TrappedLight]

The idea that spin requires curvature and/or torsion has been around for a long time. Einstein-Cartan theory is the oldest extension of GR to include torsion, this comes from 1922 so predates the discovery of spin!

 

It is quite interesting. You see that the Lorentz group is the structure group acting on the orthogonal frames of the tangent spaces of space-time. Note, not the Poincare group. Cartan, by adding torsion showed that the Poincare group acts on the affine frames of the tangent spaces of space-time. Thus locally we can restore some of our notions from Minkowski space-time about spin, but at the cost of adding torsion and affine frames.

 

Fascinating stuff.

 

 

It might be argued, that because spin/torsion is part of the full Poincare group, that you probably would expect it in nature. I know some people don't believe that torsion exists. I bet it does though!

 

Extending it to particles is a little bit more difficult, because the current thought is that particles like an electron, don't actually spin. There is however another school of thought that particles only appear pointlike to a certain threshold. You can solve the problem by rescaling the energy. So if particles actually do spin, like a spinning top, in high energy physics, particles might have noticeable torsional effects. That is a bit speculative, but the rescaling energy part is no more speculative than how string theory deals with the problem. It has a scaling factor as well for the 1-dimensionally extended objects of the theory.

[ajb]

Extending it to particles is a little bit more difficult, because the current thought is that particles like an electron, don't actually spin.

 

Don't confuse intrinsic angular momentum (spin) with standard orbital angular momentum.

 

Extending quantum field theory to curved space-times is technical and difficult.

 

 

There is however another school of thought that particles only appear pointlike to a certain threshold. You can solve the problem by rescaling the energy. So if particles actually do spin, like a spinning top, in high energy physics, particles might have noticeable torsional effects.

Can I have some references here?

 

 

That is a bit speculative, but the rescaling energy part is no more speculative than how string theory deals with the problem. It has a scaling factor as well for the 1-dimensionally extended objects of the theory.

String theory includes fermionic degrees of freedom as well as bosonic ones from the start. So I don't quite follow what you are saying here.

[TrappedLight]

''String theory includes fermionic degrees of freedom as well as bosonic ones from the start. So I don't quite follow what you are saying here. ''

 

 

I am not a string theorist, but when I talked to one a few years back, they asked me why I didn't like the theory. I said there is problem because strings are dimensionally extended objects, while the standard model deals with particles as pointlike systems. They said it had something to do with rescaling the particles. I don't know the full details now.

 

 

''Don't confuse intrinsic angular momentum (spin) with standard orbital angular momentum.

Extending quantum field theory to curved space-times is technical and difficult.''

 

 

I don't intend to confuse the two; however, mathematically-speaking, the transition from classical spin to modern intrinsic spin is very little. We only talk about the electron spin being intrinsic because of how they behave in collision experiments. However, ... as I said. There is another school of thought where you can actually rescale the electrons energy. What happens when you do this, is that the electron will always appear to be pointlike under a threshold. This means we cannot actually 100% rule out that the electron is semi-classical and has a classical spin. This wouldn't change theory drastically.

 

 

''Can I have some references here?''

 

Sure.

 

The really important paper which attempts to describe this is

 

http://www.cybsoc.org/electron.pdf

 

Not only does it outline why there are problems with pointlike systems in the math, but it uses math to explain why particles like an electron are detected pointlike.

[ajb]

The really important paper which attempts to describe this is

 

http://www.cybsoc.org/electron.pdf

mmmmm, I don't know if that is a reputable journal. But thanks.

[TrappedLight]

mmmmm, I don't know if that is a reputable journal. But thanks.

 

 

Yes it is reputable - they have also published another paper, a decade later. Their work is actually well-known throughout academia. Many scientists are aware of the paper.

''The Louis de Broglie Foundation is a French foundation for basic research in physics with its seat in the Academy of Sciences and its offices in n ^o 23 Marsoulan street in the 12 ^th district of Paris . It was created at the National Conservatory of Arts and Crafts in 1973 by Louis de Broglie on the occasion of the fiftieth anniversary of his discovery of the wave-particle duality . Louis de Broglie bequeathed to the foundation gained the amount of its property Nobel Prize in Physics .

Legally, the Louis de Broglie Foundation has an open account within the Foundation of France .

The foundation is defined as "a place of meeting and discussion at the forefront of contemporary science for all physicists wishing to expose and confront the results and perspectives in mind humanist openness and tolerance Louis de Broglie " . She has published in 1975 the journal Annals of the Fondation Louis de Broglie .''

[ajb]

A quick google suggests that it is not a reputable journal.

 

Anyway, can you give other references to journals that have okay reputations?

 

EDIT: this is getting off topic. We do have an understanding of spin within standard physics so we should keep the conversation there. This thread should not be pushed off into very fringe ideas.

Edited September 15, 2013 by ajb

[TrappedLight]

A quick google suggests that it is not a reputable journal.

 

This thread should not be pushed off into very fringe ideas.

 

 

What sources says it isn't reputable?

 

And I am ok with the standard interpretation of spin, that it is an intrinsic property. The property of spin also arises intrinsically from the paper cited. I have also done some work on it myself. Most scientists I have posited the paper to, usually don't have a problem with the paper as such. Most scientists I have spoken to have pointed out however, that the paper never took off.

 

Usually this comes down to a number of things which I am sure you are aware of.

[ajb]

What sources says it isn't reputable?

A quick look at the titles of other papers they have published does not instil me with confidence.

 

Anyway, we should discuss this elsewhere.

[TrappedLight]

Agreed, you can discuss it here

 

http://www.scienceforums.net/topic/78687-the-nature-of-the-electron/

[Widdekind]

on page 2, the cybsoc article argues that internal EM stresses may exist, w/in the electron, trying to propel apart its charge distribution...

 

but, such "self-interaction" is not part of the successful Schrodinger solution, for Hydrogen atoms...

 

at the radius of the 1S orbital, Classical equations would predict an "auto-interaction" energy, of order

 

[math]\frac{e^2}{4 \pi \epsilon_0} \frac{1}{a_0} = \alpha^2 m_e c^2 \approx 30eV[/math]

 

so, if "self-interaction" from one region of the electron's wave-function, to another, were important; then such would already have been obvious, as a dominant term, in the famous Hydrogen wave-functions...

 

evidently, the electron wave-function does not interfere w/ itself EM'ly

[swansont]

on page 2, the cybsoc article

What is "the cybsoc article"? And what does this have to do with spin?

[Widdekind]

from post 333 ?

 

 

The really important paper which attempts to describe this is

 

http://www.cybsoc.org/electron.pdf

 

Not only does it outline why there are problems with pointlike systems in the math, but it uses math to explain why particles like an electron are detected pointlike.

[TrappedLight]

on page 2, the cybsoc article argues that internal EM stresses may exist, w/in the electron, trying to propel apart its charge distribution...

 

but, such "self-interaction" is not part of the successful Schrodinger solution, for Hydrogen atoms...

 

at the radius of the 1S orbital, Classical equations would predict an "auto-interaction" energy, of order

 

[math]\frac{e^2}{4 \pi \epsilon_0} \frac{1}{a_0} = \alpha^2 m_e c^2 \approx 30eV[/math]

 

so, if "self-interaction" from one region of the electron's wave-function, to another, were important; then such would already have been obvious, as a dominant term, in the famous Hydrogen wave-functions...

 

evidently, the electron wave-function does not interfere w/ itself EM'ly

 

 

 

The internal Poincare stresses are in fact non-electromagnetic in nature.

I did realize however, that the Poincare stress could be the appearance of a strong gravitational force field inside of particles, with a magnitude of [math]G \cdot 10^{40}[/math]. This would neutralize the internal Coulomb repulsive force. We already have existing theories for such a model, where we may assume the presence of what is called ''strong gravity'' and is a major research subject at the moment among scientists attempting to unify gravity with the rest of the forces.

Even if it isn't gravity which plays the role of a Poincare stress, for a non-zero radius of a particle, the Poincare stress is very much needed.

[Widdekind]

i personally perceive, at present, that one cannot construe "spin" as resulting, from "global" coherent spinning, of an electron's entire wave-function... that would have to be represented, by an azimuthal [math]e^{\imath \phi}[/math] type of term, which would have already appeared, in the Schrodinger solutions for H atoms

 

instead, the Schrodinger solutions can be construed, as "stable super-positions" of position eigenstates, [math]\Psi(x) = \Psi (x_1) \delta(x-x_1) + \Psi(x_2) \delta(x-x_2) \cdots[/math]

 

and the electron, partially present at each point, is, at each of those points, spinning

 

in analogy, if the electron wave-function is likened to a flock of birds, swarming around the proton, like crows around some type tree...

then each individual crow, hovering in place, is itself spinning around...

so that the overall spin of the entire flock is positive and pointing "up"...

but w/o any coherent rotation, of the flock as a whole, about the tree

 

if the electron wave-function collapsed, to some specific place in space, then it there would become fully present at that place, and would there be seen spinning