Physicists detect the enigmatic spin momentum of light

April 25, 2016, RIKEN
Credit: Petr Kratochvil/public domain

Ever since Kepler's observation in the 17th century that sunlight is one of the reasons that the tails of comets to always face away from the sun, it has been understood that light exerts pressure in the direction it propagates. Radiation pressure is produced by the momentum carried by light, and it plays a crucial role in a variety of systems, from atomic to astronomical scales.

In a recent theoretical paper, a group from the RIKEN Center for Emergent Matter Science in Japan showed that density in non-uniform optical fields has an unusual component, which is orthogonal to the propagation direction of and is proportional to the optical spin, which means the degree of circular polarization. They predicted that this spin momentum would produce a transverse spin-dependent optical force, a few orders of magnitude weaker than the usual .

Now, based on the theoretical work, a group from RIKEN, the University of Bristol, and other institutions have used an extremely precise technique to experimentally verify that light does in fact exert the extraordinary perpendicular force, which is determined by the polarization of the light. The research has been published in Nature Physics.

To measure the new type of optical momentum and force, they used an extremely sensitive nano-cantilever, capable of femtoNewton resolution—meaning it could measure a force even smaller than the force gravity exerts on a single bacterium—which was immersed in an evanescent optical field directly above a total-internal-reflecting glass surface.

According to Konstantin Bliokh, the corresponding author of the paper, "Our findings revisit fundamental momentum properties of light and, revealing a new type of optical , enrich optomechanics."

Looking to the future, Franco Nori, who led the research team, says, "Our group's investigations integrate relativistic field-theoretical, quantum-mechanical, and optical aspects of the dynamical properties of light. They offer a new paradigm which could provide insights into a variety of phenomena: from applied optics to high-energy physics."

Explore further: A new twist in the properties of light

More information: Direct measurements of the extraordinary optical momentum and transverse spin-dependent force using a nano-cantilever, Nature Physics, DOI: 10.1038/nphys3732

Konstantin Y. Bliokh et al. Extraordinary momentum and spin in evanescent waves, Nature Communications (2014). DOI: 10.1038/ncomms4300

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Nik_2213
3.4 / 5 (5) Apr 25, 2016
Wild !! Evanescent waves have some weird properties, but this surely takes the prize...
Da Schneib
3.7 / 5 (9) Apr 25, 2016
A plane circularly polarised wave spin angular momentum along the propagation direction, as observed by Beth in 1935. In non-plane waves with circular polarisation obviously there will be a component perpendicular top the average propagation direction.
Mmmm, I'd add that that component will vary from phase to phase of the signal, just for completeness' sake.
Hyperfuzzy
1 / 5 (7) Apr 25, 2016
Does the Poynting Vector of the field have the magnitude of the Normal of the spherical surface about the particle and the velocity vector of the charge with points updated f(K e/r^2, T), anyway be nice with a decent simulator. You could then sort over all atomic structures. But then, would we not have creation! Can I patent this idea!?
Da Schneib
3.7 / 5 (9) Apr 25, 2016
@Phys1
The reason photon or electromagnetic spin seems enigmatic is that the present theory does not have an expression for it.
I hope by "spin" you don't mean either Spin Angular Momentum (SAM) or Orbital Angular Momentum (OAM), because those are both pretty well defined.
Noumenon
1.4 / 5 (11) Apr 26, 2016
The reason photon or electromagnetic spin seems enigmatic is that the present theory does not have an expression for it.


If you speak of photons you must use quantum theory in which it is expressed by use of operators .

Do you mean by "present theory", Maxwell's equations?

Hyperfuzzy
1 / 5 (8) Apr 26, 2016
@Da Scheib
Electromagnetic spin angular momentum is not defined at all.
In the present theory there is only angular momentum given by r cross P , where P is the Poynting vector.

I show the field has the velocity vector of the particle and is continuously updated. Speed of light relative to the particle, i. e Maxwell. You might think of the field as being permanently attached to the particle with a speed of light update. Relative to other points we see frequency, motion, etc., Vector arithmetic. I can go on but the superposition is obvious. Though a media, i.e other charges, field to particle and particle to field ... update description of poynting vector as a 4D vector
Noumenon
1.3 / 5 (12) Apr 26, 2016
I am downvoted by the usual psychos. The ignore button would be more functional if it also eliminated the trolls from voting.


Please send Phys.Org a request to disable comment ratings. Their associate site has done this.

Da Schneib
4 / 5 (8) Apr 26, 2016
@Phys1, please review https://en.wikipe...of_light and tell me why it is either wrong or doesn't apply.

In the mathematical treatment, I see the E and A fields, which is Maxwell, and I see that the SAM of a single photon is +/- hbar, which is QM.

As for OAM, see https://en.wikipe...of_light which discusses helically polarized light. This article also discusses both Maxwell and QM.
Da Schneib
3.7 / 5 (6) Apr 27, 2016
Well, I can see I have my work cut out for me. I'm too overworked to get into this now, but I will be back before long once I've wrapped my head around what you've said and done some research. I have added this thread to my favorites to ensure I don't lose track of it.
Captain Stumpy
2.5 / 5 (8) Apr 27, 2016
Please send Phys.Org a request to disable comment ratings
And how would that stop the abuse?
it won't stop the sock-puppets... it won't stop the trolling... it won't stop unsubstantiated clams...

in fact, it won't *do* anything except undermine the ability to diagnose a problematic individual and increase the hardships in tracking socks (as then it would require a bot to search the site)

the problem with disabling the ratings is that it allows the trolls to flourish
(which is why i downrated your post)

best choices:
either disable the comments entirely (cheapest)

or moderate the site (still cheap, minimal changes to programming of profiles and permissions, free MOD's per then system i forwarded)

*******

it would be smarter and more effective to disable the comments entirely and allow other sites to pick up the comment business slack and only track shares, reading of articles or times visited for interest or popularity
Da Schneib
3.9 / 5 (7) Apr 27, 2016
@Phys1 OK, now I've had some time to digest this and do some research.

My first question is, why does gauge invariance apply here?

My second question is, if we can detect both circular and helical polarizations (and anybody who has any idea how a satellite antenna works knows we can- once again, a matter of engineering, never mind physics), and we have both Maxwell and QM descriptions for them in the beam and particle domains, what's the problem?

My third question is, if gauge invariance is at odds with experiment, why is it not anathema in the particle physics community? And I assume you mean theoretical particle physics, since experimental particle physicists are generally more interested in experiment.
Da Schneib
3.7 / 5 (6) Apr 27, 2016
@Phys1
Another question.

A clear indication that photon spin is problematic in gauge theory is that it is absent from text books or banned to a problem of some esoteric chapter.
This seems highly questionable since the spin of bosons is what distinguishes them from fermions in QM. Unit-spin bosons' Law of Spin and Statistics makes them able to cohere; half-unit-spin fermions' Law of Spin and Statistics makes them obey Pauli exclusion and prevents them from cohering. This is extremely basic QM. I can't imagine someone claiming a photon has no spin, or even that it cannot be measured since it obviously is.

Can you resolve this conundrum for me?
Da Schneib
3.7 / 5 (6) Apr 27, 2016
@Phys1
@DS
bschott is downvoting this conversation.
why bschott, do you have meaningful feedback ?
I wouldn't even bother noticing it. You'll get some 4s and 5s from me when all is said; so relax and let's talk. This is why I have these dipshits on ignore. You will have less stress if you do that too, and if you stop worrying about ratings.

@Cappy

I suggest more liberal use of the mute button. I stopped complaining about commercials when I started using it many years ago, and it's even better now that I have a fast forward on my DVR, and the same applies here. If no one talks to them they will eventually give up and go away. Then this will be a better place.
Captain Stumpy
3.3 / 5 (7) Apr 27, 2016
If no one talks to them they will eventually give up and go away. Then this will be a better place.
@DaSchneib
i see your point, and sometimes i agree
i just don't think it's the best way to combat the pseudoscience or fearmongering rant of stupidity like certain "pretend" engineers
also, there is this to consider
https://www.youtu...EwjBXlZE

i will take your argument under advisement
i still think moderation is the best and most effective means to create meaningful dialogue between opposing viewpoints while supporting the rule of law (equally) and allowing the ability to present conjecture about potential new ideas (considering the evidence, that is) in scientific discourse
I stopped complaining about commercials when I started using it
you don't watch commercials?
wow

i rather like commercials (when i see them)
IMHO - they're an indicator of societal beliefs and structure plus much more
Hyperfuzzy
1 / 5 (9) Apr 27, 2016
...
See https://en.wikipe...y_tensor for the symmetrisation step.

Give up idea of the photon and you will see that the field is a dynamic part of the particle. Don't confuse the wave property and the particle property. In fact the particle or any particle need not exist. It is only a point with a set of given attributes. So first design the conversation upon absolutes. The whole idea of particles is bogus in QM and the idea of discretes is Bogus when talking about the continuum. Albeit, you may find some truth but also some non-truth. why confuse oneself. Keep a physics that is reality. Don't argue over the nonsense.

If the above looks like nonsense, trust me, it is.
Hyperfuzzy
1 / 5 (9) Apr 27, 2016
I do not know where "enigmatic" came from. I have always assumed the field has the directional vector of the particle motion as well a the normal of the sphere about the particle. How else do you get polarization, motion, etc.. Hence, this entire talk about what is already a known, just not expressed, is confusing. Sorry, didn't think I had to. I just can't understand the belief in Dr. E. The belief in God actually has an object in Ancient Egypt, but this one is pure unadulterated BS. Or the belief of particle wave duality; particle motion give rise to waves; waves give rise to particle motion. But wave as particles??? Exactly what sort of mind will accept this bull s#it!? Is this the world of stupids or liars?

Name of God rev 3.14
Hyperfuzzy
1 / 5 (9) Apr 27, 2016
I do not know where "enigmatic" came from. I have always assumed the field has the directional vector of the particle motion as well a the normal of the sphere about the particle. How else do you get polarization, motion, etc.. Hence, this entire talk about what is already a known, just not expressed, is confusing. Sorry, didn't think I had to. I just can't understand the belief in Dr. E. The belief in God actually has an object in Ancient Egypt, but this one is pure unadulterated BS. Or the belief of particle wave duality; particle motion give rise to waves; waves give rise to particle motion. But wave as particles??? Exactly what sort of mind will accept this bull s#it!? Is this the world of stupids or liars?

Da Schneib
4 / 5 (8) Apr 27, 2016
And once again, @trolls, thanks for confirming I'm right. You wouldn't be downvoting me if you weren't afraid people would take me seriously and you'd stop getting the responses you crave.
Whydening Gyre
4.2 / 5 (5) Apr 27, 2016
Phys and DS;
Following your discourse in this and another article (testing of relativity with a satellite)has been (almost exasperatingly) fascinating (due to my lack of education in these topics). Though I am following you (barely..:-)) in a broader sense, would it sound stupid if I said you guys are making me feel kinda stupid?
Da Schneib
3.4 / 5 (5) Apr 27, 2016
Well, people of course keep on treating photons as particles with spin 1 even though the theory has no spin expression or conservation, and consequently no spin operators. They go by what they intuitively know to be correct.
Oh, you mean QED. The argument depends on second quantization.

Using QFT, we can show that since the photon is the exchange particle of the EM force and the EM force has a + and a - charge, the spin of the photon must be odd because even spins give only a single polarity; and due to renormalizability arguments (and we know QED is renormalizable thanks to Feynman, Tomonaga, and Schwinger) spins greater than 2 are not possible. There is only one odd number less than 2. Nice and simple.
Whydening Gyre
4.3 / 5 (6) Apr 27, 2016
Using QFT, we can show that since the photon is the exchange particle of the EM force and the EM force has a + and a - charge, the spin of the photon must be odd because even spins give only a single polarity; and due to renormalizability arguments (and we know QED is renormalizable thanks to Feynman, Tomonaga, and Schwinger) spins greater than 2 are not possible. There is only one odd number less than 2. Nice and simple.

Ahhhh... The ineluctable nature of science esoterotica...
Almost as good as porn..:-)
Da Schneib
3.4 / 5 (5) Apr 27, 2016
Take a circularly polarised plane EM wave travelling along z. r cross P is perpendicular to z so their is no angular momentum along z. However the beam should consist of photons with spin parallel to z. So there must be angular momentum along z. Indeed, Beth measured this in 1935. Paradox.
Actually r × P = L, the classical angular momentum, but this is classical mechanics and we're talking about photons. Spin angular momentum (SAM, here S) is an exclusively quantum property, which has no classical analog. I don't think you can use r × P here. I think you have to use the quantum properties S and L (the orbital angular momentum (OAM)); S is not conserved, but it is covariant with L, the orbital angular momentum, under J, the total angular momentum, which *is* conserved. J is quite straightforwardly L + S.

In other words, you can't say there isn't any SAM along z; and since L and S are not conserved you can't say there isn't any L either. Because r × P doesn't work in QM.
Da Schneib
3.7 / 5 (6) Apr 27, 2016
To put this in more intuitive terms, for any watchers (I'm looking at you, @Whyde!), here's the situation:

The equivalent to classical angular momentum is the quantum property OAM, also called L. But unlike classical mechanics, L is not conserved. Instead, it is co-conserved with an exclusively quantum property called SAM, also called S, which has no equivalent in classical mechanics and is also not conserved. The sum of these quantities, J, or TAM, is conserved, but this means quantum angular momentum can switch back and forth between L and S as long as J stays the same. Thus, the equation @Phys1 is using, L = r × P, and no I'm not going to try to explain cross products here, is not correct for S, though it is correct for L; and thus, angular momentum as we normally conceive of it (classical physics) does not appear to be conserved.

This is leading to an apparent paradox, and to indigestion for @Phys1.
Hyperfuzzy
1 / 5 (8) Apr 28, 2016
Stop the argument with the unknown! Try an argument of known. The electron and the proton are never created or destroyed. The field of each is a part of the particle and is updated at the speed of light relative to the particle. The center of the field is the particle, no boundary conditions defined other than Maxwell. This is space as we measure. Therefore there is no empty space. The field is everywhere. These are the waves in space-time, particles respond to these fields by moving appropriately, i.e. in creation of same, and response to same. The rest is bull$hit. Stay with Maxwell, stop trying to rationalize mass. By the way, a wave equation works well, QM a curiosity. Juz say'n
Da Schneib
4.2 / 5 (5) Apr 28, 2016
@Da Schneib
The equivalent to classical angular momentum is the quantum property OAM, also called L. But unlike classical mechanics, L is not conserved.
EM L is not conserved in either classical or quantum mechanics.
Only L+S is conserved.
There is no S in classical mechanics. Do you mean S in Maxwell's equations? That is not spin. It is the Poynting vector.

I think you and I have different views of Maxwell's equations. I would place them right at the dividing line between classical mechanics and quantum mechanics; they were, and remain, THE field theory of EM. The quantum theory of EM was started by Planck and confirmed by Einstein; and the quantum field theory of EM, QED, was discovered by Dirac and put in its modern form by Feynman, Tomonaga, and Schwinger.

I see Maxwell's equations as the same thing for EM that the Einstein Field Equations are for gravity. We're at the same stage with gravity as we were in the latter half of the 19th Century with EM.
Da Schneib
4 / 5 (4) Apr 28, 2016
[contd]
Also, L is conserved in classical mechanics; it is not in Maxwell's equations, either for light or ED.

I should be really clear: when I say "classical mechanics," I mean Newton and Galileo, up to Maxwell. I draw the line there. I would accept arguments that Maxwell might be classical, but they probably wouldn't change my opinion. I don't consider relativity to be classical either.

S has an equivalent in classical mechanics. It is closely related to polarisation. Remember, spin is a property of the vector representations of the Poincaré group. The classical field is such a rep.
I wasn't looking in ED, i.e. Maxwell's equations, I was looking at classical mechanics as I define it, i.e. Newton and Galileo where we're talking about L in terms of rotating extended bodies and spinning and orbiting planets and like that. I see S in Maxwell's equations and I'm scrambling to catch up. Now it's my turn for some indigestion. ;)

[contd]
Da Schneib
4.2 / 5 (5) Apr 28, 2016
[contd]
Keep in mind we have at least three and maybe four versions of L here:
True classical mechanics, i.e. Galileo and Newton et al.,
Maxwell equation optics, where L is the angular momentum density vector,
Maxwell ED, where L is the canonical angular momentum,
and QED where L is the orbital angular momentum of particles.

We also have two versions of S:
Maxwell equation optics, where S is the Poynting vector, the linear momentum density of the EM field,
and QED where S is the spin angular momentum, a quantized parameter of individual particles.

So this is going to get very difficult very fast unless we keep these straight, or unless you can relate them to one another.

[contd]
Noumenon
1.4 / 5 (10) Apr 28, 2016
All theories including SR/GR, except QM and QM based field theories, are considered as "classical physics". I never liked that SR/GR had that categorization either,.... but such is the quantum world view.
john berry_hobbes
3.4 / 5 (15) Apr 29, 2016
hyperscuzzy blurted:
Exactly what sort of mind will accept this bull s#it!? Is this the world of stupids or liars?


That's rich coming from a promoter of religion. Is that some kind of denial where you see exactly what you're wallowing in, but only when you can project it onto something else?

Stupid, liar and bullshit are the pillars of religion.
Noumenon
1.7 / 5 (11) Apr 29, 2016
Noumenon

1 /5 (7) Apr 26, 2016

I am downvoted by the usual psychos. The ignore button would be more functional if it also eliminated the trolls from voting.

Please send Phys.Org a request to disable comment ratings. Their associate site has done this.


Anyone that downvotes you is a psycho? Suffer from megalomania much?


I did not post " I am downvoted by the usual psychos.",.... that was Phys1. How embarrassing for you.

You get downvoted because you spew idiot drivel like you're the embodiment of the enlightenment. I knew Martin Heidegger, we used to discuss Kant (et al.), and I can tell you that Heidegger would cite you as an example of "das nichts nichtet". With apologies to "nicht".


As far I know, you and the pack of troll-raters, have zero understanding of any point made by me where I may have referenced Kant. Your "characterization" of what I believe is not based on your own demonstration of competency.

Da Schneib
3.7 / 5 (3) Apr 29, 2016
[contd]
Thus, the equation @Phys1 is using, L = r × P, and no I'm not going to try to explain cross products here, is not correct for S
Incorrect. This is the accepted expression for the total angular momentum in the present theory, classical and quantum. Look in the textbooks on QFT.
Which of the four Ls are we talking about here?

I'm sorry, that's all I have time to post right now; I'll definitely get back to this later.

Hyperfuzzy
1.6 / 5 (9) Apr 29, 2016
hyperscuzzy blurted:
Exactly what sort of mind will accept this bull s#it!? Is this the world of stupids or liars?


That's rich coming from a promoter of religion. Is that some kind of denial where you see exactly what you're wallowing in, but only when you can project it onto something else?

Stupid, liar and bullshit are the pillars of religion.

Dude, try decaf. There is no God. However the belief has an object, Amen, Amon, Amun, Rev. 3.14. knowing this does not make me a religious freak. you need to chill, juz say'n
Hyperfuzzy
1 / 5 (6) Apr 29, 2016
@HF
You don't understand what this is about.

I know. Nor anyone else. LOL
Whydening Gyre
5 / 5 (4) Apr 29, 2016
I write:
I am downvoted by the usual psychos. The ignore button would be more functional if it also eliminated the trolls from voting.

JimX reads:
Anyone that downvotes you is a psycho?

No comment.

I wouldn't comment on that, either.
Too many psychos out there...
Hyperfuzzy
1 / 5 (6) Apr 29, 2016
Phys and DS;
Following your discourse in this and another article (testing of relativity with a satellite)has been (almost exasperatingly) fascinating (due to my lack of education in these topics). Though I am following you (barely..:-)) in a broader sense, would it sound stupid if I said you guys are making me feel kinda stupid?

Don't confuse ignorance and stupidity. There are always skills and knowledge one person has and another does not.

Also, inspect the universe of discourse for the logic of relativity. Don't be surprised when you see an undefined logic loop. Which of course does not fit into Formal Logic. Also note the non-axiomatic axioms. Speed vs a propagation constant. Now, is it simply nonsense or genius?
Hyperfuzzy
1 / 5 (7) Apr 29, 2016
Take a circularly polarised plane EM wave travelling along z. r cross P is perpendicular to z so their is no angular momentum along z. However the beam should consist of photons with spin parallel to z. So there must be angular momentum along z. Indeed, Beth measured this in 1935. Paradox.

I'm trying to visualize the particle motion that will create the field we observe. With the field we are able to unlayer a set of possible motions if not the exact motion. A spiraling electron will have a time varying poynting vector displaying the changes in direction. Is this what we are trying to see? Considering the plane wave and wither perpendicular to the motion or directly behind or in front. Same thing?
Da Schneib
5 / 5 (1) Apr 30, 2016
@Phys1
There is only 1 L. That is what I am trying to tell you.
I can see how to collapse two of them, but the other two don't collapse this way because they are not conserved, and the other two are.
Da Schneib
5 / 5 (1) Apr 30, 2016
@HF
You don't understand what this is about.

I know. Nor anyone else. LOL

It is called physics ;-) .
One notes that Feynman said basically the same thing. I'd take Feynman over HF any day, just sayin'.
compose
Apr 30, 2016
This comment has been removed by a moderator.
viko_mx
1 / 5 (8) Apr 30, 2016
Such behavior is quite predictable after light (electromagnetic waves) are periodic oscilations in the structure of vacuum of space. This explains light presure and red shift intuitively.
Hyperfuzzy
1 / 5 (8) Apr 30, 2016
@HF
You don't understand what this is about.

I know. Nor anyone else. LOL

It is called physics ;-) .
One notes that Feynman said basically the same thing. I'd take Feynman over HF any day, just sayin'.

Yeah, neat pictures without causality. Please
Da Schneib
5 / 5 (2) Apr 30, 2016
@Da Schneib
Classical an quantum physics are based on the same lagrangian formalism. Given a lagrangian, the Euler-Lagrange equations determine the equations of motion and the Noether theorem determines the conservation laws. Given a Lagrangian there is a general expression for the angular momentum. This is why I say there is only 1 L.
This is quite abstract, but also quite powerful.
Noether's theorem doesn't apply to discrete symmetries, only continuous ones, and S does not show continuous symmetry, at least not in quantum mechanics.

The conserved quantity in quantum mechanics is J, not L.
viko_mx
1 / 5 (8) Apr 30, 2016
?Phys1

I do not know what kind of ideas this person is shared with the world, nor care how you interprete them. But I аm sure that the physical and moral laws of the Creator that support His order in the universe does not change with time. True science explores the facts obtajned by obsevation and experiments and does not deal with fashion trends. Because fashions are evanescent human fancies, but the Creator's laws are eternal.
Da Schneib
5 / 5 (1) Apr 30, 2016
All fine technical points aside, Noether's theorem can be stated informally

If a system has a continuous symmetry property, then there are corresponding quantities whose values are conserved in time.
https://en.wikipedia.org/wiki/Noether's_theorem
Spin is not continuous. It can only have the values,

... 2, -3/2, -1, -1/2, 0, 1/2, 1, 3/2, 2, ...

It is discrete.

More technically, only symmetries that are describable as a Lie group have corresponding conserved quantities under Noether's theorem. That is, symmetries that are differentiable.

Let us examine a circle and an equilateral triangle. The triangle can only be rotated to three different orientations and remain unchanged (for lurkers, symmetries mean that things remain unchanged under some operation, in this case rotation); the triangle has a discrete symmetry. However, the circle can be rotated to any angle and will still be a circle; the circle's symmetry therefore is continuous.

[contd]
Da Schneib
5 / 5 (1) Apr 30, 2016
[contd]
If you were right then Noether's theorem, Lagrangian and Hamiltonian theory would not apply in QM. In fact, quantisation applies to the _solutions_ of the EL equations and to the expressions derived from the Noether theorem. S results from the invariance of the Lagrangian under rotation of the four-potential. Note that the gauge-invariant Lagrangian does not respect this symmetry, hence the problem.
Hmmm, I don't see why having both SAM and OAM quantized- therefore discrete- prevents J from being continuous.

And L is also discrete; it is the reason for the existence of orbitals in atoms, where there are only certain permitted orbitals and other values are never seen.

The continuity of J comes in when we examine many different atoms; each has its own distinct set of permitted values of L. Thus, each different species has a different spectrum. And in each permitted value of L, there are two alternatives: the alternatives of S, one +, one -.
MRBlizzard
not rated yet Apr 30, 2016
Transverse and longitudinal angular momenta of light
Konstantin Y. Bliokh, Franco Nori
http://arxiv.org/...04.03113

Direct measurements of the extraordinary optical momentum and transverse spin-dependent force using a nano-cantilever
M. Antognozzi, C. R. Bermingham, R. L. Harniman, S. Simpson, J. Senior, R. Hayward,
H. Hoerber, M. R. Dennis, A. Y. Bekshaev, K. Y. Bliokh, & F. Nori
http://arxiv.org/...06.04248
john berry_hobbes
3.4 / 5 (10) May 01, 2016
Hyperscuzzy 1 /5 (2) Apr 29, 2016

Dude, try decaf.


Fuck you.
Da Schneib
5 / 5 (3) May 01, 2016
Energy is also discrete. Light can only have energy nhnu.
That does not mean that we cannot use the Noether theorem.
Errr, but it's not a discrete *symmetry*.

Conservation of energy is due to the symmetry of physics over time. By Noether's theorem.
Da Schneib
5 / 5 (2) May 01, 2016
The wave function and the electromagnetic potential are continuous functions of space and time.
It is their amplitudes that are quantised.
It doesn't matter whether the wave function and electromagnetic potential are continuous *functions*. Noether's theorem doesn't apply to functions. It applies to physical symmetries.

Symmetry of physical results over position is dual to conservation of momentum.
Symmetry of physical results over time is dual to conservation of energy.
Symmetry of physical results over rotation is dual to conservation of angular momentum.

You will find all three of these symmetries and their dual conservation laws in the Wikipedia article on Noether's theorem. There are others but they are more esoteric.
Da Schneib
5 / 5 (3) May 01, 2016
I know Da Schneib, I know.
Likewise, conservation of spin is due to symmetry under Lorentz transformation of the internal degrees of freedom of a field. No difference. Check _any_ textbook on field theory.
The symmetry of quantum mechanical spin (SAM) is not a continuous symmetry and has no conservation law associated with it. Only the SAM and the OAM *together* are a continuous symmetry, associated with a conserved value.

Check the definition of Noether's theorem. You don't even need a textbook; it's on Wikipedia.
Da Schneib
5 / 5 (2) May 01, 2016
Neither S nor L is individually conserved in quantum mechanics. Only J is, and J=L+S. Conservation of J, total angular momentum, is responsible for the orbitals of electrons in atoms. That conservation is responsible for the fact that electrons don't spiral into the nucleus under the influence of the EM attraction of the negative charges on the electrons to the positive charge on the nucleus.

Noether's theorem only links conservation laws to continuous symmetries, not discrete ones.

These facts are clearly stated (and well sourced) in the Wikipedia articles on angular momentum and Noether's theorem. I'm sorry, man, you've just plain got this wrong. I had it wrong long ago, and someone who had serious particle physics chops proved it to me; that's how I know.

I should perhaps have said that Noether's theorem does not apply to *all* continuous functions. Only to functions that show related continuous symmetries that form a Lie group.
Da Schneib
5 / 5 (2) May 01, 2016
Noethers theorem applies to Lagrangians, which a functionals. or functions of fields.
A field is a function of position and time and may also have internal degrees of freedom.
Examples are scalar fields, vector fields (EM) , spinor fields, higher spin fields.
All of these degrees of freedom are continuous in field theory, so Noethers theorem implies conservation laws of energy-momentum, orbital energy, spin ...
However, fields are not necessarily symmetric. Thus, Noether's theorem does not apply ipso facto to them.

What goes wrong is that gauge invariance does not respect the vector symmetry of the EM field.
That's very interesting. Tell me more about the vector symmetry of the EM field. I suspect it will turn out to be a symmetry over time, which will relate to conservation of energy, rather than to conservation of any type of angular momentum.
Da Schneib
5 / 5 (2) May 01, 2016
BTW, @Phys1, you push the envelope of my understanding of physics, so I will return the compliment!

I'd ask more about your paper but personally I wouldn't put any personally identifying information on here and I don't expect you would either. In fact I'd discourage it; trolls are.
Da Schneib
5 / 5 (1) May 01, 2016
I was looking more for a relation of it to angular momentum... I can see why you think the B field has angular momentum, but actually B is half of a deconstruction of the real EM field, where E is the fictitious electric field assumed to propagate with infinite speed and B is the fictitious field representing the relativistic time delay of the effect of the fictitious E field. Rotation only enters into it because we normally encounter a B field with no apparent E field in cases where there is net rotation of the electrons (J again) in the atoms within a magnetic domain.
Da Schneib
5 / 5 (1) May 01, 2016
A is generally defined as the magnetic vector potential. This is the divergence of the B field. Do you know of a different meaning for it?

Worth mentioning as well that because the B field is the relativistic correction, it must be a vector field in order to account for possible varying frames from which the scalar E field might be observed.
Hyperfuzzy
1 / 5 (5) May 01, 2016
?Phys1

I do not know what kind of ideas this person is shared with the world, nor care how you interprete them. But I аm sure that the physical and moral laws of the Creator that support His order in the universe does not change with time. True science explores the facts obtajned by obsevation and experiments and does not deal with fashion trends. Because fashions are evanescent human fancies, but the Creator's laws are eternal.

OK, but how do you apply this $hit?
Da Schneib
5 / 5 (2) May 01, 2016
Bah, like an idiot I forgot B is the curl of A, and had a brain fart and typed A is the div of B. That's what I get for posting without waiting for my coffee.

I'll point out that symmetry over inversion is inherently a discrete symmetry, whether of space or time. Symmetry over space means things remain unchanged over spatial position, which no field associated with EM can do since EM falls off by the inverse square law, and symmetry over time means if I measure it now and wait a minute and measure it again I'll get the same value (all other things remaining equal). Finally, we know that T (time reversal symmetry) and P (parity symmetry) are not individually symmetric; this was proven by the neutral kaon interactions decades ago. It is only CPT symmetry that results in Lorenz invariance, indicating that charge, parity, and time must all be reversed together for the symmetry to hold. You can't reverse just one.
Da Schneib
5 / 5 (2) May 01, 2016
Continuing the discussion it is apparent that although no discrete symmetry is *individually* conserved, certain combinations of them may yield a continuous symmetry that is. We have two examples just in this conversation:

1. CPT symmetry/Lorentz symmetry.
2. J conservation where J=L+S corresponds to rotational invariance/symmetry.
Da Schneib
5 / 5 (3) May 01, 2016
This is exercising brain cells long dormant. I haven't talked to anyone I needed to remember this stuff to communicate with in a long time. This is fun, though demanding. Thanks again, @Phys1!
compose
May 01, 2016
This comment has been removed by a moderator.
compose
May 01, 2016
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Da Schneib
5 / 5 (2) May 01, 2016
@Phys1 you're not talking about SAM, you're talking about a different S.

SAM is a discrete symmetry; a given particle can only have + or -, not any intermediate value, and all particles can only have values that are multiples of a half-integer, either even multiples (bosons) or odd ones (fermions).
Da Schneib
5 / 5 (2) May 01, 2016
I should have pointed out that the symmetry is a symmetry over reversal of spin, and since spin has a discrete value this can only be a symmetry over the possible values, which means it is a discrete symmetry.
Da Schneib
5 / 5 (3) May 01, 2016
@Phys1 and I reiterate that it is the definition of SAM, so if you think it's incorrect you're arguing that physics is incorrect. I will refer you to the article in Wikipedia on SAM: https://en.wikipe...ysics%29
Hyperfuzzy
1 / 5 (7) May 01, 2016
you know is nonsense
Hyperfuzzy
not rated yet May 04, 2016
It's the vocabulary, sometimes what we say does not relate to anything but a word we made up.

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