Maximum Angular Speed(MAS)

Discussion in 'Physics & Math' started by hansda, Apr 12, 2017.

  1. hansda Valued Senior Member

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    Considering the relation, Linear Speed(v)=Radius(r) x Angular Speed(w); can we say that Maximum Angular Speed = Speed of Light(c)/Radius(r). So that spin of a particle can not exceed this maximum angular speed.
     
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  3. exchemist Valued Senior Member

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    Fundamental particles have something called "intrinsic angular momentum" which is commonly called "spin" for short but is not in all respects the same in its behaviour as classical "spin". For instance an electron has intrinsic angular momentum, even though there is no evidence that it has any dimensions such as a radius or diameter, or any periphery which could be said to be spinning at any particular rate. https://en.wikipedia.org/wiki/Classical_electron_radius

    Furthermore the evidence is that the intrinsic angular momentum or "spin" of such a particle is entirely fixed. It is what it is and is unchangeable without destroying the particle. It is as fundamental a property at its mass or electric charge. So your thought experiment has no application.

    However for macroscopic objects there are certainly some nice puzzles involving relativity, such as Ehrenfest's Paradox, Mach's Principle and so forth. As rotation involves non-inertial reference frames (a rotating object experiences constant acceleration towards its centre) one has to tread carefully. I am out of my depth here so cannot advise you.
     
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  5. The God Valued Senior Member

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    • Do not promote pseudoscience or antiscience on the main science forums
    This is a problem. So we conveniently redefined the spin at quantum level and sold it too.
     
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  7. exchemist Valued Senior Member

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    No, we observed how nature seems to behave, and developed a model that accounts for it. That's what science does.

    If you don't find the model intellectually satisfying, come up with a better one that still accounts for the observed behaviour.

    (You really got it in for "spin", haven't you?

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  8. The God Valued Senior Member

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    You don't get it. Tinkering with the definition to suit the circumstances is not done thing. The problem with tjis is that characteristics (angular momentum) is same in both cases (quantum and macro level), but we are out of pur depths to fix this quantum level spin and came up with some fix.
     
  9. Q-reeus Valued Senior Member

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    I have never got to follow it all through, but someone who knows relativity and QM - Hans Ohanian, made what seems to be a plausible case for a physical basis to QM spin:
    http://people.westminstercollege.edu/faculty/ccline/courses/phys425/AJP_54(6)_p500.pdf
    You will have to have some relevant maths under your belt to be able to judge it's worth.
     
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  10. rpenner Fully Wired Staff Member

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    Ohanian is cheating a bit since in 1939 it was shown that there are classes of solutions to quantum mechanics which had well-defined mass and were compatible with Lorentz invariance.
    http://courses.theophys.kth.se/SI2390/wigner_1939.pdf
    These included wave equations with intrinsic angular momentum in half-integral steps:
    Klein-Gordon: spin 0
    Dirac: spin 1/2
    Maxwell-Proca: spin 1
    Rarita-Schwinger: spin 3/2

    So it is not surprising that in the second and third cases that Ohanian can decompose solutions into intrinsic and orbital angular momentum densities that can be integrated over volumes, that's how quantum operators work.

    So it's not surprising that Ohanian finds operators that reveal the intrinsic angular momentum in solutions to equations which admit it. Maybe it's a bit surprising how close the 1865 Maxwell classical theory resembles the Maxwell-Proca relativistic quantum field theory equations but that's because we've had some convergence on how we present these topics over the years.

    From a previous analysis I made:
    Part II of Ohanian(1984) is about decomposing J, total angular momentum for a classical electromagnetic field (eqns. 3, 4), into parts which are associated with orbital angular momentum, L, and intrinsic angular momentum, S. The paper argues that this semi-classical approach makes sense, but admits the “the methods of quantum field theory” (i.e. Quantum Electrodynamics) is required for a formal treatment. Part III similarly works with the single-electron Dirac equation and not the full multi-particle quantum field theory. Part IV, as far as I can see derives a g-factor of 2 which is not surprising as it is a manipulation of Dirac theory. Part V argues that spin arises from wave mechanics, not quantum physics.

    Angular momentum of these particular waves can be decomposed (which is possible because the Maxwell equations support circular polarization and the Dirac equation is explicitly partitioned) but the paper ignores that the relations that quantize the resulting values are intrinsically quantum in nature. It ignores that the Dirac equation and the interpretation of Maxwell's Lagrangian as that of a massless boson is quantum mechanics. Finally, it ignores that the reason that the existence of various quantum wave equations (Klein-Gordon, Dirac, Maxwell-Proca, Rarita–Schwinger equations for spin-0, -1/2, -1, -3/2, respectively) is covered by the Wigner classification scheme of what can exist at intersection of quantum physics and the Lorentz group. Notably, neither the Schrödinger nor the Klein-Gordon equations will support such a decomposition, indicating the fundamental source of spin in current physical theory is not wave equations, per se, but relativistic quantum mechanics of point particles.

    In short, Ohanian places the cart before the horse.
     
    Last edited: Apr 13, 2017
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  11. rpenner Fully Wired Staff Member

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    You don't understand physics. Physics is not math — physics is about using the language of math to describe the behavior of observable phenomena. So when a new model comes along, it is entirely permissible to reuse old concepts with new mathematical descriptions, so long as that model is a good one. There is no problem — no violation of the mathematical rule against changing definitions — since the new definitions are used in the new model — they are, in fact, part and parcel of the new model. And if we could not make new models, physics would never advance.

    Angular momentum is only important because of conservation of angular momentum which is a feature of different physical theories. According to Noether's theorem, angular momentum is a conserved quantity in any physical theory which has rotational symmetry. Thus conservation of angular momentum arises in Newtonian theory because of Galilean relativity and because of isometries of 3-D Euclidean geometry. And conservation of angular momentum arises in special relativity because of Special relativity and because of isometries of 3+1 Minkowski geometry. And quantum mechanics adds conservation of probability, which is called unitarity. Unitarity and the the Lorentzian symmetry of Minkowski geometry allow a packet of light to have intrinsic angular momentum even when it is centered on a point and the cross product between momentum and position is zero. This matches the behavior of reality and must be favored over older models and older definitions.
     
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  12. The God Valued Senior Member

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    3,075
    You are fixated. You lack the ability to think out of box. This happens because you are too much invested in your existing knowledge. So you find others who question either ignorant or crackpot or cheats.

    Well you admitted that definition of spin is different at quantum level, but you cannot call it xyx, thats what is convenient physics of yours.
     
  13. The God Valued Senior Member

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    3,075
    Ohanian is cheat, I do not know physics, someone else is ignorant......only omniscient fellow after my namesake is rpenner!!? Wow.
     
  14. Q-reeus Valued Senior Member

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    That neutrinos possess half-integer spin is perhaps the simplest argument against a fully consistent field angular momentum explanation. Which is then frustrating for anyone craving a 'common sense' resolution to an otherwise purely formal entity.
     
  15. origin Trump is the best argument against a democracy. Valued Senior Member

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    IMO allowing this type of crap in the Science section hurts the forum. Sorry for the off topic post, and I am really sorry I hit the stop ignoring button.
     
  16. The God Valued Senior Member

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    3,075
    You have no guts to take on rpenner. No doubt he knows his maths, but he has bad attitude. Probably more arrogant and hostile than me. He is a Mod, it is a forum guideline not to hurt the poster but to take on the argument, but he starts with his usual arrogance. Violates and when confronted, his followers jerk in, Paddoboy was right in calling him just that.
     
  17. exchemist Valued Senior Member

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    5,577
    I think I "get it" OK, thanks. It seems to me to be you that doesn't. Because there is no "definition" to "tinker" with, other than the definition of angular momentum in the appropriate mechanics. Has it not occurred to you why QM is called quantum mechanics? The whole point behind that choice of name is that it works differently from classical ("Newtonian") mechanics. It is idle to object to a QM concept on the grounds that it differs from classical mechanics. Of course it does.

    As I have explained ad nauseam, the label "spin" is merely a shorthand. For people like you it might have better if this term had never been attached to intrinsic angular momentum. But that is history.
     
  18. exchemist Valued Senior Member

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    5,577
    I would stop this personal attack on a moderator that knows his science, if I were you. You will acquire points.
     
  19. The God Valued Senior Member

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    3,075
    No, the label is not shorthand. That's exactly the point. It's angular momentum, you could not have called it anything else.
     
  20. The God Valued Senior Member

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    3,075
    He is posting here as member. Mine is not unforced error. He started rudely with me, my report against him would have been a waste, he got it back.
     
  21. exchemist Valued Senior Member

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    It is short for intrinsic angular momentum. That is what I have been saying.

    But tell me, what do you think the definition of angular momentum is, in Quantum Mechanics?

    Or, if you take issue with the way QM defines it, what do you think the definition of it is?
     
  22. rpenner Fully Wired Staff Member

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    Why can't they simply be described by the same Dirac theory as the electron??
     
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  23. rpenner Fully Wired Staff Member

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    On what am I fixated? How would you know it?
    What is the the box you claim I cannot think outside of? How would you know it? Are these two claims contradictory or redundant?
    You are the one objecting to new physics, not I. That means your box is over 300 years old. My box is based on study of observable phenomena in detail and reasoned arguments about how to best describe those phenomena precisely. You present no reason to suggest why my box is not more than sufficient to hold the answers reasonable people would seek.
    How would you know this unless you brought new, better knowledge to the conversation?
    Because you are not fairly questioning. You have no intent to find the best answer, but instead you only want answers that suit your biases. You have a hostile attitude towards modern physics theory before learning its content. That's what makes you a crackpot — a physics outsider with the delusion his fantasies matter to the wider world. Ohanian(1986) is his most famous paper and he's more famous for his textbook. But even it's not nearly as famous as Wigner(1939). If you want to know why I consider Ohanian to be a cheat, you have to read both articles, understand the math of both articles and read the details of my critique above. But Ohanian himself admits to cheating a bit, which is all I was saying.

    I wish your problem was merely that you were ignorant; at least in that case you could be fairly questioning.
    It's not "different at [the] quantum level" — angular momentum is not something that can exist only at certain scales as it has to have a conserved total — angular momentum is modeled differently in relativistic quantum models than in Newtonian physics. In addition to "orbital angular momentum" \(\vec{r} \times \vec{p}\) we have a new type of angular momentum "intrinsic angular momentum" which adds with the first type and follows conservation laws.
    Intrinsic angular momentum is called "spin" in particle physics discussions held in English. (Also German "Spin", French "le spin", Russian "Спин", Japanese "スピン角運動量" ["spin" angular momentum], Chinese "自旋" [a compound of "self-" and "spin"]) It's the nature of jargon that short terms are adopted for commonly discussed nouns, verbs and adjectives. Are you are claiming to the boss of English (and other languages) and Physics?
    Ohanian is cheating a bit because by using the equations of quantum field theory, he's not really explaining spin, but instead showing that theories which already have intrinsic angular momentum can have quantum operators which could be said to "localize it" just like position of a quantum particle can be localized.
    That's what I said, based on your inability to understand that physics is progressive. Where is there evidence otherwise?
    Since someone else once tried to cite Ohanian(1984) for more than it stood for, yes.
    I'm just claiming to know more than you. People who know more than I have confirmed this in the past. It is better to light a candle than to curse the darkness, but you seem set on cursing people giving out candles for free.
    How is this demonstrated? Origin is not demonstrated to be a better people by disagreeing in general, but only when standing up against false claims and poor arguments. Accusing him of cowardice seems like a violation of forum rules to me.
    Essential if you are to understand Ohanian(1986) or Wigner(1939) so without this knowledge you have no basis to criticize my opinions based on those papers.
    That's an assertion of a factual claim without supporting evidence or argument — a conclusory claim that has no weight.
    You should work on both being less hostile and better supporting your claims and then would be in a better position to advance that claim.
    Not just an unpaid moderator, but the moderator who is principally tasked with policing this sub-forum. So I do that, even while ensconced in a distant resort.
    You mistake a diagnosis of a beam in your eye with the ad hominem fallacious argument that one can't make sense if they have a wooden post in their eye. Many people noticed your concern trolling of modern physics like Spin, GR, Dark matter, CMBR, etc over the past month or so.
    I'm not aware of having "followers".
    Being that type of "right" and $7 will let you get a cup of coffee at Starbucks. Here, on the other hand, we are concerned with math and physics. And I recall you following Paddoboy around from thread to thread trolling him on a math mistake he once made.
    It is angular momentum, but not accounted for by \(\vec{r} \times \vec{p}\). Therefore a new name is entirely appropriate. And Ohanian(1986) shows one way how angular momentum can be factored into "orbital angular momentum" and "intrinsic angular momentum" or "spin".
    Only because I was examining this thread as part of my duties as a moderator. I'm on vacation today.
    Your concern trolling of spin has been previously noticed. http://www.sciforums.com/threads/spin.159033/
    Telling you that "You don't understand physics" isn't unnecessary rudeness. Your history of posts in this particular sub-forum mandate it as instruction to you and as fair warning to your readers. You also don't seem to understand the purpose of a discussion forum:
    http://sciforums.com/posts/3329356

     
    Last edited: Apr 13, 2017
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